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EXOPLANET OBSERVING FOR AMATEURS

1. o h ei 2 0 o Ny o EXTINCTION Mag AirMass o o a m FILTER PASSBAND RESPONSE 7 0 5 o D m Ml 0 00 s 0 0 300 400 500 600 700 800 900 1000 1100 WAVELENGTH nm Figure 14 01 Atmospheric Rayleigh scattering at wavelengths where CCD chips are sensitive for three observing site altitudes Filter spectral response shapes are shown for B V R and I Custom Scientific BVRclc filters and KAF1602E CCD chip normalized to 1 The Rayleigh scattering model is based on an equation in Allen s Astrophysical Quantities 2000 75 CHAPTER 14 STAR COLORS Notice how much Rayleigh scattering varies throughout the B filter response region the greatest scattering at 350 nm is 5 times the smallest at 550 nm DUST SCATTERING SPECTRUM vs ALTITUDE Allen s Astrophysical Quantities 2000 0 16 0 15 4e 0 14 rss 0 13 e 0 12 ens Yer 0 11 uc Linc 0 10 Je m 0 09 deca As es 0 08 Diner The T 0 07 Lines es ees 0 06 c X TA 0 05 hes bi 0 04 Pinea T 0 03 a 0 02 0 01 0 00 r T T T T T r T 1000 2000 3000 4000 5000 6000 7000 8000 s000 10000 ALTITUDE fi Figure 14 02 Atmospheric aerosol dust Mie scattering versus observing site altitude for three wavelengths based on a global model by Toon and Pollack 1976 cited in Allen s Astrophysical Quantities 2000 Optical Depth RAYLEIGH AND AEROSOL SCATTERING 0 30 S Rayleigh SeaLevel R
2. NEAR EDGE MISS DISTANCE L C SHAPES DIFFERENTIAL MAGNITUDE MMAG UT hr Figure D 06 Transit depth is greatest for R band consistent with a miss distance 70 73 courtesy of Cindy Foote 2 VERIFYING THAT LIGHT CURVE SHAPE IS NOT AN E B BLENDING Wide field survey telescopes provide an efficient means for detecting stars that are undergoing periodic fades with depths small enough to be caused by an exoplanet transit e g depth 30 mmag A fundamental limitation of such a survey is that in order to achieve a wide field of view the telescope s resolution is poor and this leads to many false alarms due to the blending of light from stars within the resolution 122 APPENDIX D PLANET SIZE MODEL circle If for example the resolution circle has a radius of 1 arc and the flux from all stars within this circle corresponds to 1 1th magnitude it is common for several stars to be present within the resolution circle that are fainter than 11th magnitude but with fluxes that add up to 11th magnitude If this situation occurs and if one of those stars is an eclipsing binary EB with a large transit depth the transit depth measured by the survey telescope will be smaller and possibly small enough to resemble one produced by an exoplanet This is a common occurrence There are two blending situations that need to be considered 1 the EB is part of a triple star system so the blending star is too close to the EB t
3. from my site Columns E F and G show UT times for transits that are above 20 degree elevation and between 3 5 and 10 0 UT Other details are explained in the text SpectraShift Before leaving the topic of exoplanet projects that are within the reach of amateurs I want to describe an amateur led project called SpectraShift that is designed to detect exoplanets spectroscopically Radial velocity requirements are demanding since a hot Jupiter orbiting a solar mass star will impart radial velocity excursions of only 200 m s if it s in a 4 day orbit An amateur group led by Tom Kaye is assembling a system that is expected to achieve 100 m s resolution using a 44 inch aperture telescope for the brighter BTEs This group used a 16 inch telescope in 2000 and 2004 to observe Tau Boo and they are credited with being the first amateurs to detect an exoplanet using spectroscopic measurements of radial velocity When a wide field survey camera directs an amateur team to candidates for follow up light curve observations and when the amateur light curves indicate that the suspect star is indeed fading by small amounts with a flat bottomed shape the professionals are often faced with long lead times for obtaining observing time on a large telescope for spectroscopic radial velocity observations that would confirm the secondary as being an exoplanet When SpectraShift becomes operational probably in 2008 or 2009 there will be an opportunity for them to
4. 100 80 100 120 140 150 180 200 220 240 260 280 300 320 IMAGE NUMBER Figure 8 02 Plot of FWHM arc and aspect ratio ratio of largest PSF dimension to smallest expressed as a percentage for the images used to produce the light curve Image numbers near 260 correspond to 7 0 UT Produced using the automatic analysis program CCDInspector by Paul Kanevsky There s clearly a good correlation between focus degrading and the apparent brightening of the target star 7 0 UT But how can an unfocused image affect the ratio of star fluxes To determine this consider how MaxIm DL and probably other programs as well establish magnitude differences from a set of images I ll use two images from the above set to illustrate this An image in good focus was chosen from 7 0 UT and another from 8 5 UT They were treated as a 2 image set using the MaxIm DL photometry tool The next figure shows the sharp focus image after a few stars were chosen for differential ensemble photometry 49 CHAPTER 8 FOCUS DRIFT Psi 2 Ax eae a Opt PAKS Figure 8 03 Location of photometry apertures after using this image to select an object the target or exoplanet candidate check stars and a reference star upper left corner my artificial star These notations are slightly misleading as explained in the text The measured star fluxes are recorded to a CSV file comma separated variable in ASCII format which can be i
5. Barnes JW and Fortney JJ 2004 Transit Detectability of Ring Systems around Extrasolr Giant Planets Astrophys J 616 1193 1203 Bissiner RB 2004 Detection of Possible Anomalies in the Transit Lightcurves of Exoplanet TrES 1b Using a Distributed Observer Network Caldwell JAR Cousins AWJ Ahlers CC et al 1993 Statistical Relationships Between the Photometric Colours of Common Types of Stars in the UBVRclc JHK and uvby Systems South African Astronomical Observatory Circular 715 Charbonneau D Brown T Latham D et al 2000 Detection of Planetary Transits Across a Sun like Star Astrophys J 529 pp L45 48 Charbonneau D 2004 Hubble s View of Transiting Planets eprint arXiv astro ph 0410674 Cox A Editor 2000 Allen s Astrophysical Quantities Fourth Edition Springer Verlag New York Dravins D Lennart L Mezey E et al 1998 Atmospheric Intensity Scintillation of Stars III Effects for Different Telescope Apertures PASP 110 pp 610 633 Gillion M Pont F Demory B et al 2007 Detection of transits of the nearby hot Neptune GJ 436 b arXiv 0705 2219v2 Holman MJ and Murray NW 2005 Science 307 p 1288 Howell SB 2000 Handbook of CCD Astronomy Cambridge University Press Cambridge UK Howell S 2002 The Planetary Report XXII Nr 4 July August Kaye T Vanaverbeke S and Innis J High prescision radial velocity measurements with a small telescope Detection of the Tau
6. a m D 15 T 0 10 0 05 0 00 300 400 500 600 700 800 900 1000 1100 WAVELENGTH nm Figure 14 04 Atmospheric total extinction components Rayleigh scattering and aerosol scattering Typical measured extinction coefficients for my site at 4660 feet are shown as large filled circles seasonal average At my observing site 4660 ft the yearly average measured extinction values large colored dots in Fig 14 04 agree with the model thick black trace It should be remarked that the Rayleigh component at a given site will vary by only small amounts related to barometric pressure whereas the aerosol scattering component can vary by large amounts The seasonal variation of extinction is therefore related to aerosol changes Volcanic ash lofted to the stratosphere where it will reside for many months can produce large temporary aerosol scattering events Using this graph it should be possible to use I band extinction to infer extinction at the shorter bands The opposite is less true it s difficult to infer I band extinction from a B band extinction measurement since B band extinction is dominated by Rayleigh scattering 77 CHAPTER 14 STAR COLORS My purpose in presenting this atmospheric extinction tutorial is to sensitize you to the slopes of extinction within a filter band pass So what How can the extinction slope within a given filter band possibly affect differential photometry measurements We now need to rev
7. 110 saturation see linearity non linearity scintillation 5 32 44 47 52 87 91 92 93 94 99 110 111 138 147 sky background level 53 57 58 60 83 84 90 SNR 28 30 39 46 52 57 59 62 63 83 84 89 99 107 123 star color 18 28 31 32 39 63 75 80 86 89 100 104 108 112 113 116 117 120 121 137 150 stochastic uncertainty error noise 5 59 70 87 90 stray light 35 109 TheSky Six 16 29 32 84 112 timing 13 21 22 46 81 83 95 98 100 101 Trojan exoplanets 21 22 24 26 28 162
8. 12 pixels away The next figure s left panel shows these stars with a photometry pattern for which the signal aperture radius is 3 x FWHM This aperture choice is unacceptable because some of the nearby star s flux is within the signal aperture The right panel shows that the nearby star can be excluded from the signal aperture by reducing the aperture radius from 12 pixels to 10 pixels corresponding to 2 4 x FWHM Before choosing a signal aperture radius it is important to check all bright stars to see if a radius adjustment like this one should be made 59 CHAPTER 10 PHOTOMETRY APERTURE SIZE Figure 10 03 Left panel Candidate reference star showing photometry aperture circles with the signal aperture radius 3 x FWHM Right panel Same star with signal aperture radius 2 4 x FWHM What about stars in the sky background annulus as shown in the next figure Figure 10 04 Example of a star with a nearby star that s within the sky background annulus Actually this is not a problem because MDL s photometry tool uses a sophisticated algorithm for eliminating outlier counts in this annulus AIPAWIN does the same using a different algorithm Note The current version of MDL s on the fly photometry doesn t use the sophisticated algorithm for rejecting sky background 60 CHAPTER 10 PHOTOMETRY APERTURE SIZE counts from such stars so be careful when using the MDL Information Window s ntensity readings In conclusi
9. 65 MAXIMUM COUNTS KCT Figure E 06 FWHM for bright star divided by FWHM for faint star versus Cx for the bright star FWHM SCATTER PLOT FOR BOTH STARS 7 5 FWHM FOR BRIGHTER STAR ARC NN WOW fF BR C CO N Th Om Oh Om oO oO 2 0 2 5 3 0 3 5 40 4 5 5 0 5 5 5 0 FWHM FOR FAINTER STAR ARC Figure E 07 FWHM for bright star versus FWHM for faint star The box identifies the situation of unsaturated stars 144 APPENDIX E CCD LINEARITY Whenever a star 1s unsaturated established here by the condition Cx 59 kct the following simple relationship should exist Cx const FWHM As FWHM decreases Cx will increase in order for flux to remain the same The next figure shows agreement with this theoretical relation it also shows how Cx saturates when FWHM decreases below a specific value different for each exposure time MAXIMUM COUNT vs FWHM for BRIGHT STAR MAXIMUM COUNT KCT 405 sec 10 sec 15 sec n 20 sec 430 sec o 40 sec 15 20 25 30 35 40 45 50 55 60 65 FWHM FOR BRIGHTER STAR ARC Figure E 08 Cx versus FWHM for the bright star for a selection of exposure times color coded with exposure times given by the legend Model fits are explained in the text This plot demonstrates that the brightest pixel for a star will increase until the pixel s well is full For this CCD fullness occurs when 159 300 electrons have accumulated 59 000 x 2 7 electrons per ADU where 2
10. CV and CR magnitudes than for the observations using a filter converting B filter fluxes to B magnitudes V filter fluxes to V magnitudes etc If SNR was the only source of scatter then the opposite should occur Star color is an independent variable for this analysis so in theory the residuals could be the same for unfiltered and filtered images I believe the greater scatter for the CV and CR residuals is due to the fact that an unfiltered flat was used with unfiltered images and the redder or bluer the star the worse the flat field correction Since the all sky solution procedure is designed to minimize RMS scatter the final coefficients are a compromise for all star colors in the Landolt set Typically I achieve RMS scatter of 0 025 magnitude for the B V Rc and Ic data but only 0 035 magnitude for CV and CR From this I estimate that the level of systematic effects that can be expected for transit monitoring should be 20 mmag when using a filter and 30 mmag when observing unfiltered These levels would only be encountered if the target and reference stars were far apart and their pixel locations varied by large amounts during the observing session When the flat field pattern varies significantly from filter to filter I would expect greater 39 CHAPTER 5 FLAT FIELDS systematic errors from a drift of the star field over the pixel field during an observing session BLU_LFAt_7206c E RED_LFAt_7206c Rees Figure 5 03 Flats
11. OBJECT R MAG L 11 800 4 11 910 Pred d Ingr amp Egr Air Mass Model 60 sec images 11 920 4 11 min ava 11 pb 11 930 4 5 6 7 8 8 UT AIR MASS amp EXTRA LOSSES CLOUDS DEW WAVES FOR 2007 02 25 AIR MASS EXTRA LOSSES MAG NA AIR MASS Y ae 407 e EXTRA LOSSES We 04 r r zi 08 UT Figure 8 01 Light curve showing effect of focus drift starting at 7 2 UT The lower blue trace shows that the sum of fluxes for all reference stars decreased starting at the same time I recall upon awakening and looking at the image on the monitor that the focus was bad and I immediately suspected that this was caused by focus drift but I didn t know what effect it would have on the light curve LC After processing the images and 48 CHAPTER 8 FOCUS DRIFT seeing the LC I knew right away that focus drift had affected it Here s a plot of FWHM and aspect ratio for the images used in the above figure IMAGE QUALITY 2007 02 25 FWHM Aspect Ratio 80 74 60 a 40 6 i e j Ha o E 3 5 T 7 prs 20 2 S e pun LI 54 O T EA y z Gi a oe 12 2 eo 4 Pog e 4 40 M 2 k we t Pa a kag he 5 y r us be m M E us 3 60 3 i S tu dA r ee er odd Pa N ae t t t ito eMe N S ce 80 21 T T T T T T T T T T T
12. XO 1 s brightness is V mag 11 2 and the transit depth is 23 mmag From past experience using my 14 inch telescope I know that the star s brightness and the transit s large depth will make this an easy observation SNR won t be a problem so we aren t restricted to the use of filters that allow lots of photons to come through such as clear or a blue blocking filter BB filter All filter choices are possible As an aside what would our options be if the exoplanet had a shallow depth or its star was faint A clear filter would deliver the most light and produce the highest SNR However a BB filter might be better since it excludes blue light 7 which means it would reduce the size of one of the most troublesome light curve systematic errors baseline curvature that s symmetric about transit caused by reference stars with a different color than the exoplanet star more details in Chapter 14 Star Colors For small depths this curvature can be troublesome Observers with 10 inch or smaller telescopes should consider using the BB filter often Observers with 20 inch or larger apertures should rarely have to use the BB filter It s the 12 and 16 inch telescope observers who may have difficult choices for typical exoplanet candidates with depths in the 15 to 25 mmag region Since the XO 1 transit is an easy one we are free to review other filter choice considerations such as science needs If there are no B band observat
13. aperture photometry to correct for it If such a cosmic ray defect is within the signal aperture of the target star or any of the reference stars the affected image will produce a brightness for the exoplanet that has to be rejected as an outlier The fewer images that have to be rejected because they appear to be outliers the better This is an argument for short exposures Consider the information rate for 60 second exposures versus 120 second exposures when download time is 8 seconds the two duty cycles proportional to information rate are 88 and 94 That s a gain of only 7 for the longer exposure time but a doubling of risk related to ruined images Scintillation noise is a possible consideration when choosing exposure time Scintillation noise is a fractional fluctuation of all stars in a FOV uncorrelated with each other caused by wave front interference effects produced by small scale temperature inhomogeneities at the tropopause 11 16 km at zenith Scintillation fluctuations of a star s intensity decrease with exposure time as 1g where g is exposure time Thus 4 minute exposures will exhibit half the scintillation of 1 minute exposures However the average of four 1 minute exposures will also exhibit half the scintillation of a single 1 minute exposure The only improvement in reducing scintillation by using longer exposures comes from the fact that a 4 minute exposure can be obtained more quickly than four 1 minu
14. deg deg B 12454223611 2 013 0 4 197 2 956 2 132 3 993 2 441 2 080 422361 2678 61 4481 38 17 3843 10 035 10 035 65 06 85 06 8 22454223612 2012 0 4 238 2 943 2 124 3 966 2 423 2090 422361 267861 64481 40 174032 10 054 10054 8534 8534 10 3 24542236813 2002 0 4 192 2 941 2 114 3 983 2 418 2099 422361 26 861 6448142 174219 10073 10073 8562 85 62 1 4 2454223614 2 008 0 4 203 2934 2 110 3 967 2 426 2 109 4223 61 2678 61 64481 44 17 4406 10 091 10 091 85 90 85 90 2 5 2454223615 2007 0 4 186 2 955 2 118 3 961 2 427 2 19 422361 2678 61 64481 46 17 4592 10 110 10 110 86 18 86 18 13 6 2454223 615 2002 0 4 191 2 937 2 110 3 969 2 423 2 128 4223 62 2678 62 64481 48 17 4782 10 129 10 129 86 46 86 46 Figure 13 01 Screen capture of a spreadsheet that calculates air mass after importing the CSV file when the cursor is at cell B7 Columns B through I contain CSV file magnitude difference data Columns Z through AG calculate AirMass displayed in column Y Since this screen shot is barely readable the next figure is presented showing only the left most columns where data is imported 67 CHAPTER 13 SPREADSHEET PROCESSING Epp ered A ee el Pe el IBLE E Site SIN ETT deg Sine eae N Latitude 31 45 0 52 0 85 RA 4 2153 65 5 57 60 91 5 E Longitude 110 2 0 94 0 35 Dec 57 49 0578 2 80 85 6 7 T D Ref Chk1 Chk2 Chk3 Chk4 Chk5 2454223 611 2 013 0 4 197 2 956 2 132 3 993 2 441 9 2 2454223 612 2 012 0 4 238 2 843
15. minutes of data could be obtained before ingress That s pretty short since we want 1 to 1 5 hours but it s just enough for establishing an out of transit baseline level After egress there will be lots of data since XO 1 will still be rising and it will be dark Observations should extend to at least an hour after egress so let s plan on observing 2 hours after egress to be safe Observations of XO 1 will therefore end at 1 30 AM It is worth noting that because observations will start at a low 20 degrees elevation air mass 2 9 B band observations would be unwise as would V band since both would have high atmospheric extinction values For similar reasons use of a C filter would be unwise since C band essentially equivalent to unfiltered includes B band Our tentative choice to use I band is supported by the high air mass situation 29 CHAPTER 4 PLANNING THE NIGHT at the beginning of planned observations In my experience R band would be acceptable at 20 degrees elevation For small or moderate aperture telescopes 1 e 8 14 inches it is wise to observe the target with the same filter the entire night Large apertures usually provide sufficient SNR to observe with two or possibly three filters in alternation throughout an observing session At this point in the planning process we have chosen a target and filter but the filter choice is still only tentative Reference star options have to be considered Thi
16. studies by Barnes and Fortney 2003 who had investigated the possibility of detecting the presence of rings around giant exoplanets by searching for light curve brightening just outside transit that would be produced by forward scattering of star light Ron Bissinger performed a detailed analysis of light curve observations mostly amateur and concluded that the brightenings were statistically significant but required confirmation Bissinger 2005 The Hubble Space Telescope later failed to confirm these brightenings Nevertheless each new transiting exoplanet discovery represents another possibility for detecting exoplanet rings Another light curve anomaly to look for is an extra loss of brightness just before ingress or just after egress caused by a large moon of the exoplanet responsible for the main transit event Searches have so far failed to detect the expected feature of an exoplanet moon but the value of such a discovery means that every new exoplanet discovered should be studied with this feature in mind Rings and moons will produce brightening and fading anomalies that are much smaller than the main transit event s mid transit depth The Hubble Space Telescope is ideal for this task However HST will eventually degrade and become unusable and this may happen before the James Webb Space Telescope is launched 2013 or later Amateurs wishing to beat the big space based telescopes in detecting rings or moons should consider performi
17. 0 967 1 55 mmag This is the Poisson component of RMS scatter for each image that can be expected in a final light curve Aperture Pixel Noise Consider noise contributions from the process of reading the CCD CCD read noise plus noise produced by thermal agitation of the crystal s atoms CCD dark current noise and finally from noise produced by a sky that is not totally dark sky background noise These are three additional sources of noise in each CCD reading the last two are Poisson themselves since they are based on discrete stochastic events but we ll treat them here in the traditional manner These three noise sources are small when the star in the photometry aperture is bright and the CCD is very cold to reduce dark current noise For that situation it can be stated that the star s measured flux total counts within the aperture minus an expected background level will be uncertain by an amount given in the previous section If however the CCD is not very cold which is going to be the case for amateurs without LN2 cooling and when the sky is bright too often the case for amateur observing sites these components of noise cannot be ignored I ll use the term aperture pixel noise to refer to the sum of these three sources of noise sky background level CCD dark current noise and CCD readout noise When the photometry aperture is moved to a location where there are no stars MaxIm DL MDL displays the RMS sca
18. 000 to 65 534 counts Don t believe this I was pleasantly surprised with a measurement showing that my CCD is linear all the way to 59 000 counts The implications for knowing this are significant If it s true that you can safely use the longer exposure times corresponding to Cx as high as 59 000 counts for example then your observing will be more efficient less time spent downloading images your scintillation and Poisson noise will be lower by up to 40 for each image and the importance of readout noise will be less I ll review the cautious reasoning that continues to lead CCD users to be wary of high Cx Then Pll illustrate how to measure your CCD s linearity safety zone Cautious Conventional Wisdom Each pixel is capable of holding an approximate total number of photoelectrons The term full well capacity is used loosely to refer to that number However we must make a distinction between full well capacity and linear full well capacity A user s manual may state that your model of CCD has a full well capacity of 100 000 electrons for example That s what the SBIG manual states for my ST 8 The manual also states that my CCD s gain is set so that each count represents 2 3 electrons According to these two numbers the well is full at 43 500 counts 100 000 electrons 2 3 electrons per count Since my CCD can produce higher counts I assume that SBIG s term full well capac
19. 1 COULD I DO THAT Imagine the value of an archive of exoplanet transit observations with contributions from several hundred amateurs The day may come when every transit of every known transiting exoplanet will be observed except for those faint OGLE and very faint HST ones Changes of transit shape and timings are possible and these can be used to infer the existence of new planets smaller and more interesting ones The job is too large for the small number of professional observatories and the cost of using them for this purpose is prohibitive If you are considering a hobby that s fun and scientifically useful and if you re willing to learn new observing skills and spend time processing a night s images then welcome to the club of amateur exoplanet observers 13 Chapter 2 Observatory Tour Since I will be using real data to illustrate systematic errors I will describe my observing systems Note the use of the word systems in the plural form Even with one telescope it will matter whether you are configured Cassegrain or prime focus and whether a dew shield is used or whether a focal reducer lens is used and where it s inserted Every change of configuration will change the relative importance of the various systematic error sources During the past year I have had three different telescopes so I am aware of issues related to telescope design differences such as the problems produced by meridian flips i e Celestrons
20. 1 306 0 063 with B V uncertainty contributing the greatest component of SE Note that the stated SE doesn t include the uncertainties associated with the equations converting B V to stellar radius and mass nor does it allow for the possibility that the star is off the main sequence EVALUATING THE SOLUTION How good is this result Let s compare it with a detailed model fitting analysis by professional astronomers The mystery exoplanet is no mystery It s XO 1 whose discovery was announced May 18 2006 and published in the September issue of the Astrophysical Journal by McCullough et al 2006 http xxx lanl gov abs astro ph 0605414 abstract and http arxiv org PS cache astro ph pdf 0605 0605414 pdf complete article This article reports that Rp Rj 1 30 0 11 This compares well with the simple model result calculated here of Rp Rj 1 31 0 07 The larger SE for the professional result reflects a realistic assessment of such systematic uncertainties as converting B V to stellar radius and mass The B band light curve for XO 1 is measured to have D 24 8 0 5 and L 2 95 0 03 For these inputs the procedure described above gives Rp Rj 1 29 0 06 119 APPENDIX D PLANET SIZE MODEL GRAPHICAL REPRESENTATION OF EQUATIONS The following graphs can be used instead of the equations for deriving star radius mass and limb darkening correction derived from Allen s Astrophysical Quantities Fourt
21. 7 electrons per ADU is the gain I measured from the same images But what happens to photoelectrons that are added after the pixel s well is full In theory these additional electrons could simply migrate to nearby pixels and still be counted when the photometry measurement is made To investigate this we need to see how flux ratio varies with exposure time 145 APPENDIX E CCD LINEARITY FLUX RATIO and Cx versus EXPOSURE TIME 1 02 140 1 01 130 1 00 120 0 99 110 0 98 100 o 0 97 90 5 5 amp 0 96 80 4 x lt LE 2 0 95 70 Z LL o e 0 94 60 lt gt x lt t 0 93 50 3 0 92 40 0 91 30 0 90 20 0 89 10 0 88 0 0 5 10 15 20 25 30 35 40 45 50 55 EXPOSURE TIME SEC Figure E 09 Star flux ratio blue and bright star s Cx red versus exposure time When exposure time is 50 seconds the bright star is saturated in every image nevertheless the ratio of fluxes is affected only slightly This means that after a pixel s well fills additional electrons migrate to nearby pixels and only a small percentage are lost If linearity is defined as lt 2 departure from linear then this CCD is linear even for conditions associated with the longest exposure images of this analysis Figure E 10 is a point spread function cross section of the bright star that 1s saturated in a 50 second exposure Even this star s image produces a flux that is low by only 2 The statement that the CCD is linear whenever Cx lt 59
22. 7 times as much flux or a blue blocking BB band filter 4 times the flux Also the XO 3 star field does not have a good choice for same color stars and this affects the level of RMS scatter that can be achieved XO 1 and XO 2 for example provide better reference star candidates It 1s possible to achieve 1 mmag RMS scatter per 1 minute image using a 14 inch telescope provided a good set of reference stars is nearby a R band or BB band filter is used and scintillation conditions are low Larger telescope apertures should be able to achieve lower mmag precision in spite of the fact that exposure times would have to be shortened to avoid saturation It should be each observer s responsibility to use the concepts described here to calculate an observing strategy that produces light curves with a minimum RMS scatter as well as a minimum of systematic errors based on the observer s specific telescope and observatory situation An excellent discussion of CCD hardware can be found in the book Handbook of CCD Astronomy 2000 by Steve B Howell Some of the material in this chapter is based on this book 94 Chapter 16 Anomalies Timing and LC Shape Timing Anomalies and Other Exoplanets A transiting hot Jupiter exoplanet in a circular orbit with no other planets in the system will produce transits at uniformly spaced intervals This statement neglects the very slow third order effect related to the star s oblateness but these cha
23. All of these components can be treated as stochastic noise Poisson and scintillation noise are usually the most important components I will assume that several stars are chosen for use as reference ensemble photometry Stochastic uncertainty is produced by a category of fluctuation related to random events For example it is believed that the clicking of a Geiger counter is random because the ejection of a nuclear particle is unrelated to events in the larger world such events are instead prompted by laws that are not yet understood governing events within the nucleus To observers in the outer world the particle ejections of radioactive nuclei occur at random times Photons from the heavens arrive at a CCD and release an electron called a photoelectron at times that can also be treated as random As a practical matter the noise generated by thermal agitation within the CCD and nearby circuitry is also a random process Scintillation is generated at the tropopause and causes destructive and constructive interference of wave fronts at the CCD causing the rate of photon flux at the detector to fluctuate in what appears to be a random manner All of these processes exhibit an underlying randomness and their impact on measurements is referred to as stochastic noise The Poisson process is a mathematical treatment of the probabilities of the occurrence of discrete random events that produce stochastic noise The previous
24. Bootis exoplanet 2006 J Br Astron Assoc 116 2 Landolt AU 1992 Astronom J 104 p 340 Mandushev G Guillermo T Latham D et al 2005 The Challenge of Wide Field Transit Surveys The Case of GSC 01944 02289 Astroph J 621 pp 1061 1071 REFERENCES McCullough PR Stys JE Valenti JA et al 2006 A Transiting Planet of a Sun like Star Astrophys J 648 2 pp 1228 1238 Steffen J 2006 Detecting New Planets in Transiting Systems Doctoral Thesis University of Washington Steffen JH asnd Agol E 2005 An Analysis of the Transit Times of TrES 1b MNRAS 364 L96 Toon B and Pollack J 1976 J Appl Met 15 Warner B and Harris A 2007 Asteroid Light Curve Work at The Palmer Divide Observatory Minor Planet Bulletin 34 4 160 INDEX 2MASS 83 84 air mass 14 26 29 32 45 52 62 63 677 69 71 73 74 79 81 82 84 92 100 101 108 110 115 all sky photometry 39 107 109 aperture photometry aperture 47 51 53 57 61 62 65 66 72 74 87 88 90 94 99 100 110 111 116 artificial star 50 52 65 67 atmospheric seeing 5 10 15 32 45 49 52 56 70 87 91 94 99 142 143 binning 15 27 32 33 36 38 blue blocking filter 28 55 80 83 94 check star 50 65 66 69 71 clear filter 28 29 37 55 84 105 dark frame 11 38 42 43 64 140 differential photometry 6 63 65 78 91 dust donut 34 35 104 eclipsing binary EB 3 112 114 116 122 124 127 128
25. CV magnitude begins with observations using a clear filter but with corrections designed to produce a V band equivalent usually with star color corrections CR magnitude is like CV except the goal is an R band magnitude 152 GLOSSARY BBR magnitude uses a blue blocking filter BB filter and is adjusted to simulate R band magnitude flat frame CCD exposure made of a spatially uniform light source such as the dawn or dusk sky often with a diffuser covering the aperture Flat frames can be made of an illuminated white board or made pointed at the inside of a dome dome flat Several flat frame exposures are combined to produce a master flat A master flat is used to correct for vignetting dust donuts and small pixel specific differences in bias and sensitivity QE flux Star flux is defined to be the sum of all counts that can be attributed to a star based on differences with a sky background level that is calculated from the counts in a sky reference annulus FOV Field of view FWHM Full width at half maximum describing the angular size of the distribution of light on a CCD produced by a point source 1 e star c f aspect ratio gain For a CCD the term gain is the number of photoelectrons required to produce a change of one ADU Gain can be measured by noting RMS for a subframe of two flat fields subtracted similar levels and RMS for the same subframe of two bias frames subtracted Gain Sum of median counts
26. D S is below then it s probably an exoplanet If it is to the left of the upward sloping trace central transit then there s no solution and you may be dealing with an EB blending or triple star system 134 APPENDIX D PLANET SIZE MODEL STAR RADIUS vs B V 1 60 1 50 1 40 1 30 1 20 1 00 STAR RADIUS o 0 90 0 80 0 70 0 60 0 50 STAR MASS vs B V 1 80 1 70 1 60 1 50 1 40 1 30 1 20 1410 1 00 STAR MASS 0 90 0 80 0 70 0 60 0 50 B V Figure D 18 Star s radius and mass from B V 135 APPENDIX D PLANET SIZE MODEL LIMB DARKENING EFFECT 14 1 3 1 2 121 1 0 0 9 0 8 0 7 0 6 INTENSITY W R T DISK AVERAGE 0 5 0 4 0 3 0 2 00 01 02 03 04 05 06 07 08 09 310 MISS DISTANCE FRACTION Figure D 19 Limb darkening effect LDe versus transit miss distance and filter band This completes the summary of what is done to assess a transit LC to determine if it s due to an exoplanet or EB and if it s an exoplanet to determine its size The purpose of this appendix has been to demonstrate that a simple procedure can be used to guide the choice of survey candidates for a night s observing in order to avoid spending time on unlikely EB blend candidates 136 APPENDIX D PLANET SIZE MODEL 4 0 EXCEL SPREADSHEET Now that you understand the concepts I can save you time by offering an Excel spreadsheet that does most of what s described
27. DIFF mmag Figure 13 08 Histogram of neighbor outlier data with a Gaussian fit The two vertical lines are the user specified rejection criteria For stars with R mag 11 which is the case treated in this chapter I would typically reject data that exceeds 11 mmag shown in the above figure For this case study the extra losses criterion led to the automatic removal of 5 of the data and the outlier criterion led to the removal of an additional 3 Figure 13 09 is the final light curve In this figure the small red dots are from individual 60 second images that passed the acceptance criteria for both extra losses and outlier rejection The large red circular symbols are 9 point non overlapping median combines of the accepted data red dots At the top of the panel are two vertical lines indicating the predicted times for ingress and egress In the lower right corner is a notation of which reference stars were used The upper left note states that a 13 pixel aperture radius was used for measuring star fluxes and this led to an RMS for 1 minute data of 4 1 mmag which corresponds to RMS for 5 minute averages of 1 85 mmag 72 CHAPTER 13 SPREADSHEET PROCESSING 10 810 Ap 13 R124 1 R5 1 85 mmag Depth 16 0 mmag Length 3 45 hr 10 820 AirMass coeff 3 mmag AirMass Trend slope 40 5 mmag hr 10 830 4 xt rar n dat AE 2 LP En APP A E DU EL E 10840 E ER ore
28. HJD Julian Date and Heliocentric Julian Date JD is the time of an event as recorded at the Earth center HJD is the time of an event if it were recorded at the center of the solar system The two vary throughout the year depending on RA Dec and time of year but the difference is always 8 4 minutes length of transit Interval between contact 1 and contact 4 Survey camera lengths may resemble something intermediate between this and the time between contact 2 and 3 due to insufficient SNR light curve Plot of brightness of a star versus time during a single observing session Abbreviated LC it 1s usually representing brightness in terms of magnitude with increasing magnitude plotted in a downward direction LCs may be embellished with marks for predicted ingress and egress or model fits meant to guide the eye to what the observer believes the measurements should convey limb darkening Stellar brightness distribution for a specific wavelength filter band expressed as 1 00 at the star center and decreasing toward the edge caused by star light close to the limb being emitted from higher and cooler altitudes of the stellar atmosphere An alternative representation is to normalize to the disk average brightness Two or three constants are sufficient to represent these shapes Limb darkening functions vary with spectral type linearity The property of a CCD s readout ADU counts being proportional to the accumulated number of photoelec
29. Ni sqrt s where s is the number of pixels within the signal aperture The second number the sum of counts that would be expected for these s pixels if no star were present within the signal aperture will have an uncertainty Nbs Nb x sqrt s sqrt s x Ni sqrt b The uncertainty on calculated star flux neglecting Poisson noise will be the orthogonal sum of these two uncertainties In other words since Ns Nss Nbs we derive that Ns s x Ni x 1 I b and since 1 1 b 1 we can state that Ns sqrt s x Ni Since the 2007 04 15 images exhibit Ni 4 3 counts and since s m 15 707 pixels we calculate that Ns 114 counts For XO 3 producing 346000 counts this represents an uncertainty of 0 36 mmag Notice that this is less than Poisson noise Scintillation Noise At tropopause altitudes clear air turbulence is common and the temperature inhomogeneities produced by turbulence cause slight bending of the wave fronts of starlight which produce a component of constructive and destructive interference at ground level which we observe as scintillation The smaller the aperture the greater the scintillation The naked eye s aperture 1s so small that an additional component of scintillation is produced by temperature and humidity inhomogeneities near ground level where atmospheric seeing degradation is produced These visual changes in brightness are called twinkling and because the tropopause component is
30. a network of identical amateur observatories This first decade of the 21 Century has the potential for becoming one of the most exciting periods in the history of astronomy especially for the amateur astronomer 102 APPENDIX A Evaluating Flat Field Quality Chapter 5 described a way to create a master flat field This appendix describes ways to evaluate the quality of a flat field Recall the two sets of flat fields in Chapter 5 made with different optical configurations repeated here N INF_LFAt_7206 Figure A 01 Flats for B V Rc and Ic filters for a configuration with a focal reducer lens placed far from the CCD chip The edge responses are 63 of the center N IS_6av_7222b Figure A 02 Flats using the same filters but with a configuration with the same focal reducer close to the CCD chip The response range smallest response to maximum are 88 90 89 and 89 for the B V Rc and Ic filters APPENDIX A EVALUATING FLAT FIELDS The first set of flats is relatively featureless aside from the overall pattern of a fall off toward the edge which resembles classical vignetting The second set shows more structure including two dust donuts Before we condemn the second set of flats as a bad configuration for transit systematics recall that what matters is the change of flat field error versus pixel location There s no straight forward way of knowing flat field error versus FOV location for a given filter
31. about 7396 of the way to the edge at closest approach the opposite depth versus color relationship will be found Constraining the path s geometry and star limb darkening will lead to an improved estimate for planet size and this 1s useful for theoreticians studying planetary system formation and evolution Every amateur should consider observing nominally NTE exoplanets at times they re predicted to have possible transits in order to determine whether or not they really are an NTE instead of a BTE that is waiting to be discovered As stated above GJ 436 is one example of an exoplanet that was nominally identified as an NTE which in fact was discovered to exhibit transits by an amateur group that changed it to a BTE The nominally NTE list can be found at TransitSearch org which is maintained by Greg Laughlin Times favorable for transits if they occur are given on this web site as well as likely transit depth Finally some exoplanet observers who exhibit advanced observing skills will be invited to join a group of amateurs supporting professionals conducting wide field camera surveys that are designed to find exoplanet transits So far only the XO Project makes use of amateurs this way in a systematic way but other wide field survey groups may recruit a similar team of advanced amateurs for follow up observations The main task of these observers is to observe a star field on a list of interesting candidates at specific times to identif
32. also called impact parameter We ll adopt one secondary size and vary the miss distance TRANSIT LIGHT CURVE SHAPES FOR VARIOUS MISS DISTANCES Rp 7 0 08 Rstar INTENSITY DROP mmag 9 0 60 0 55 0 50 0 45 0 40 0 35 0 30 0 25 0 20 0 15 0 10 0 05 0 00 0 05 010 015 0 20 0 25 0 30 0 35 040 045 0 50 0 55 0 60 DISTANCE STAR DIAMETER Figure D 10 Shape of LCs for various miss distances b and a fixed secondary size of Rp Rstr 0 08 Note that l ve changed terminology for center miss distance from m to b Sorry but I used both symbols for this parameter while calculating the graphs The following figure summarizes the dependence of S on many choices for planet size and miss distance 126 APPENDIX D PLANET SIZE MODEL TRANSIT SHAPE PARAMETER VERSUS PLANET SIZE SHAPE PARAMETER S 0 00 0 05 0 10 0 15 0 20 0 25 0 30 Rp Rstar Figure D 11 Shape parameter for a selection of secondary sizes and center miss distances b Recall that for this LC we determined that S 0 29 0 01 The shape alone tells us that Rp Rstr lt 0 17 From the previous section we derived m b 0 40 the thick black trace in the above figure so this means Rp Rstr 0 13 It s not our purpose here to re derive Rp Rj but let s do it to verify consistency Rp Rj 9 73 x Rp Rstr x Rstr Rsun 9 73 x 0 13 x 0 99 1 25 This is smaller than 1 31 derived from the transit depth but notice that the 1 25 estima
33. and check stars have their fluxes compared to the reference star or the average of the reference stars when doing ensemble The flux ratios are converted to magnitude differences and a file is created that contains these magnitude differences For some users the appeal of this set of magnitude differences is that changes in extinction or changes in cirrus cloud losses are removed to first order Or to put it another way information about extinction and cirrus losses are lost when recording a standard differential photometry file There s a serious disadvantage in processing images this way it may not be important for variable star work but it s often important for exoplanet LCs if any of the stars used for reference are variable you could remain clueless about it and if you somehow suspected that the reference star was not constant you would have to repeat the image processing with a different star designated for use as the reference The value of using the artificial star for reference is that extinction and cirrus losses are retained in the recorded file while also retaining magnitude differences between stars When the magnitude differences file is imported to a spreadsheet the user will have full control over which stars to choose for use as reference The user can view all stars that were measured and evaluate their constancy and be guided by this analysis in choosing which stars to use as a final ensemble reference set This re
34. arc when a large format CCD is used 35 mm longest dimension The plate scale is acceptable since the noise penalty of having to use 4 times as many pixels in the signal aperture for a 2 5 arc FWHM star will be compensated by the larger aperture collecting area Any larger aperture however will reduce the FOV which will begin to limit the number of stars available for use as reference Thus a 40 inch aperture is an approximate upper limit for the range of apertures that are optimum for exoplanet light curve measurements XO 2 is a special case because an identical star is located 31 arc away To illustrate some considerations in selecting an exoplanet optimum telescope system consider the following specific components The 20 inch Meade RCX 400 has a tube made with low thermal expansion material which would reduce the need for focus adjustments The optical design is a modified version of Ritchey Chr tien and produces sharp images for a large FOV It has an f ratio of 8 so the EFL is 160 inches yielding a plate scale of 0 46 arc pixel The FOV with a large format CCD chip would be 20x30 arc The German equatorial mount that it normally comes with is unacceptable for exoplanet observing The Optical Tube Assembly OTA alone would cost 20k and a quality fork mount purchased separately would cost 25k Integrating the OTA to the fork mount might cost another 5k Since the RCX telescope is a closed tube OTA a dome would be n
35. are near the target star to reduce scintillation since essentially all correlation is lost beyond angular distances of 10 arc a typical planet angular diameter 91 CHAPTER 15 STOCHASTIC ERROR BUDGET A classic study of scintillation was published by Dravins et a 1998 They studied scintillation s dependence upon telescope aperture air mass site altitude and exposure time Their equation relating all these parameters is o x 0 09x D xsec Z xexp A ho 2g where o fractional intensity RMS fluctuation scintillation D telescope diameter cm sec Z air mass h observatory site altitude above sea level m ho atmospheric scale height 8000 m and g exposure time sec For me h 1420 meters and D 35 6 cm so I calculate an expected typical scintillation noise to be Scintillation noise mmag 5 35 x AirMass sqrt g where g exposure time seconds For air mass 1 9 and T 60 seconds scintillation 2 12 mmag Keep in mind that the magnitude of scintillation may vary greatly from night to night as well as on time scales of a few minutes Seeing Noise When I made about 1000 short exposures of the moon for the purpose of creating an animation showing terminator movement I encountered two unexpected things 1 seeing varied across each image and 2 position distortions were present The first item means that no single image was sharp at all parts of the image One image might be sha
36. as for setting exposure time for stars to be used photometrically Measuring linearity is described in Appendix E When I first started using a CCD I would combine several flat field images and then smooth the resultant image to reduce noise Don t do this Every pixel has a slightly different behavior QE bias gain from its neighbors and this behavior must be preserved in the master flat field image I also used to produce a master flat by median combining individual flats specifying use of the background level for normalize I ve had a few bad experiences with 38 CHAPTER 5 FLAT FIELDS improper results using the normalize setting which I attribute to the use of flats with too much variation in average level Because sky brightness 1s changing fast near sunset it s difficult to adjust exposure times to produce similar levels for counts in all images I now favor the averaging of individual flat frames The only reason to median combine is to remove cosmic ray defects I rarely see this but nevertheless it is wise to do a cursory eyeball inspection of the flats before averaging them to make a master flat The longer I try to improve flat fields the more I ve come to believe that perfect flat fields are fundamentally impossible Even the meaning of a flat field or the task it 1s to perform seems more vague and impossible the more I think about it I now believe that even the idea of a perfect flat field is theoret
37. be on the order of 2 5 mmag Star fluxes ranged from 4100 to 590 000 counts so Poisson noise is calculated to range from 10 7 to 0 9 mmag respectively Aperture pixel noise is calculated to be 0 5 mmag Each star is therefore expected to exhibit values for fundamental SE that range from 3 to 11 mmag Since these noise sources are uncorrelated from star to star when two stars are compared the magnitude difference should exhibit root two greater SE or 4 2 to 16 mmag The image sets that were processed in the previous section consisted of 10 images per set so when average magnitude differences are used the expected SE will be root 10 smaller than for single image differences Therefore we can expect to encounter fundamental SE uncertainties of 1 3 to 4 9 mmag when comparing the average magnitude of stars in sets of 10 images 110 APPENDIX A EVALUATING FLAT FIELDS The measured magnitude differences between star pairs in 10 image groups 10 images per group are SE 17 28 25 20 28 and 24 mmag These six SE values correspond to six star pairings The median and average of these six SE values are both 24 mmag Thus the measured SE is greater than expected from the assumed Poisson noise scintillation noise and aperture pixel noise It is possible that scintillation noise was greater than usual for the observing session Otherwise I would have to conclude that the flat field error map exhibited large variations such as 17 mmag 1 6 Th
38. cameras As the shutter opened it would begin exposing the CCD center first and as it closed the center would be the last to have incoming light shut off This would produce a non uniform pattern of center to edge actual exposure time The shorter the exposure time the greater the percentage disparity between the center and edge Rotating shutters are better but they too have a greater likelihood of producing different actual exposure times at different locations on the CCD for short exposures CCD camera shutters differ but exposures longer than 1 second are generally considered to be unaffected by this problem Exposures that are too long are simply inconvenient and they interfere with making flat field exposures with other filters Hence the goal is to schedule the flat field exposures so that they all are within the range of 1 to 10 seconds FLAT FIELD EXPOSURES for LAF CONFIGURATION 100 4 B SS 22 min V SS 10 min R ss 05 min I ss 09 min C SS 05 min o x 104 p B V 90 5 V gt I 1 0 o I R 90 5 aa I gt C 0 3 2 LE ul a 2 a o oa x iu 20 15 10 5 0 5 10 15 20 MINUTES PAST SUNSET Figure 5 02 Exposure time versus time after sunset for various filters for an f 8 telescope system binned 1x1 and use of a double T shirt diffuser This figure shows that for the B band filter I can start flat field exposures 20 minutes before sunset but no later than about
39. collaborate with professional amateur associations to obtain the required radial velocity observations with short lead times Closing Thoughts for the Chapter There are many ways amateurs can collaborate with professionals in discovering and studying exoplanets Once basic skills have been mastered the simplest project is to 25 CHAPTER 3 EXOPLANET CHOICES choose a BTE and observe it every clear night regardless of when it is expected to undergo transit OOT observing This will provide a wealth of data for assessing systematic errors affecting light curve behavior with air mass and hour angle It may also turn up an unexpected secondary transit produced by a second exoplanet in the far off solar system This observing strategy could also produce the discovery of a Trojan exoplanet I recommend OOT observing for anyone who has the required patience and interest in understanding their telescope system A slightly more demanding project would be measuring BTE mid transit times and adding them to a data base of similar observations by others Eventually a new exoplanet in a resonant orbit will be found this way Measurements of transit depth versus filter band can be useful for newly discovered exoplanets since this information will help professionals obtain a better solution for planet size Monitoring the NTEs at favorable times will advance the goal of identifying that dozen or so exoplanets that are providing transits that no one
40. fee ee a KA c Ba E LL e a 5 2 10 850 4 prid Se et i o o Ert 4 T e ae vt a S9 s 10 860 4 tL 60 sec 10 8704 S ptavg Pred d Ing Pred d Egr Refz2 34 5 Model 10 880 4 T T T T T T T 2 3 4 5 6 7 8 9 10 UT AIR MASS amp EXTRA LOSSES CLOUDS DEW WAVES 3 0 0 200 0 100 254 0 000 w 0 100 a z 204 0 200 e lt 0 300 154 0 400 AIR MASS 4 os00 Loss 1 0 TM T T T 0 600 2 3 4 5 6 7 8 9 10 Figure 13 09 Light curve of a 11 magnitude exoplanet candidate using an R band filter The explanation of this figure is in the text The model lines are for a general purpose transit The transit model consists of 5 parameters which are adjusted by the user ingress UT egress UT depth at mid transit fraction of time spent during ingress or egress in relation to the time from ingress to mid transit and ratio of depth at completion of ingress or start of egress to the mid transit depth Note that the parameter for the fraction of time spent during ingress is a good approximation to the ratio of the exoplanet s radius to the star s radius assuming a close to central transit chord An important additional feature of the transit model is that it provides a way to accommodate curvature due to a temporal trend and a correlation with air mass The temporal trend term is a simple coefficient times UT which in this case is 0 5 mmag times UT hinged at UT 6 The trend is most lik
41. flux values have a large scatter The scatter is produced by changes in seeing or auto guiding quality This will be described later Figure E 03 plots star flux versus exposure time for both stars The brighter star shows evidence of falling below the fitted line for exposure times 40 and 50 seconds The fainter star agrees with its fit for all exposures The reasons for this will become apparent shortly The ratio of the two star fluxes is plotted in Fig E 04 LINEARITY OF SBIG ST 8XE CCD BASED ON NGC5371 STAR IMAGES 1 03 1 02 1 01 1 00 0 99 0 98 0 97 RATIO OF BRIGHTER TO FAINTER STAR 0 96 0 95 5 10 15 20 25 30 35 40 45 50 55 60 65 COUNTS MAX KCT Figure E 04 Ratio of star fluxes bright divided by faint versus Cx The ratio is normalized so that the average unsaturated value is 1 00 The legend shows the association of plotted symbols with exposure time When Cx for the bright star exceeds 59 kct it becomes fainter than would be expected from images having lower Cx values This suggests that photoelectrons may be lost when a pixel accumulates more electrons than a saturation value corresponding to 59 kct for this CCD This result is what we re after The CCD is linear for stars having Cx lt 59 ket 142 APPENDIX E CCD LINEARITY This conclusion is based on star ratios Let s see if we can come to the same conclusion using fluxes from just one star Figure E 05 plots flux rat
42. for B V Rc and Ic filters for a configuration with a focal reducer lens placed far from the CCD chip The edge responses are 63 of the center Figure 5 04 Flats using the same filters but with a configuration with the same focal reducer close to the CCD chip The response range smallest response to maximum are 88 90 89 and 89 for the B V Rc and Ic filters These figures shows how flat fields can change with filter band Figure 5 03 was made with a focal reducer lens far from the CCD in front of an AO 7 image 40 CHAPTER 5 FLAT FIELDS stabilizer Figure 5 04 was made with the focal reducer lens between the AO 7 image stabilizer and the CFW CCD assembly What a difference location makes Also what a difference filter band makes For the second set of flats it is easy to imagine that stars of different colors will require flats that are intermediate between the measured blue sky flats and the reddest stars will have requirements that depart the most from the measured ones Appendix A contains methods for evaluating the quality of your master flat field The procedures described in that appendix are time consuming and they are meant for consideration by advanced users The entire situation of how to make good quality flat fields and how to use them properly is so confusing to me that I propose the following simple solution Keep the star field fixed with respect to the pixel field during the entire observing session If th
43. fun and if a particular project seems like work then consider a different project Astronomy is one of those hobbies with many ways to have fun and I dedicate this book to those advanced amateurs who like having fun with exoplanet transit observing Chapter 1 Could I do that Could I do that was my reaction 5 years ago to an article claiming that amateurs could observe exoplanet transits Howell 2002 The article stated that transits of HD209458 had even been measured with a 4 inch aperture telescope Could this be true or was it hype for selling magazines The article appeared in The Planetary Society s The Planetary Report which was a reputable magazine I had a Meade 10 inch LX200 telescope and a common CCD camera which I had just begun to use for variable star observing Why not I decided with nothing to lose for trying My First Transit Observation in 2002 Before the next transit on the schedule I e mailed the author of the article Dr Steve Howell and asked if he had any advice He suggested using a filter such as V band green and keep the target near the center of the image On the night of August 11 2002 I spent about 9 hours taking images of HD209458 with a V band filter The next day I processed the images and was pleasantly surprised to see a small dip in my plot of brightness versus time that occurred on schedule Fig 1 01 The depth was also about right but since my observations w
44. going to spend 6 or 8 hours observing a candidate it is reasonable to spend a few minutes evaluating the merits of various candidates on a list showing predicted transits for the night in question Exoplanet candidates derived from survey camera data will contain the following information for each candidate periodicity P length of transit L depth D and maybe star color J K Let s assume that an ephemeris of predicted transit times 1s available for each UT date and possibly restricted to what s observable from the observer s site On any given night there may be half a dozen candidates with transits that can be observed If J K is not given then the observer should obtain it from a star catalog such as TheSky Six The following graph can be used to identify candidates that have transit lengths compatible with the transit being from an exoplanet instead of an eclipsing binary that is blended with another nearby star giving the appearance of a small depth Consider the following information for a survey candidate that has never been observed in a way that defines its LC accurately P 3 9 days length of transit 2 2 hours J K 0 41 Using this figure locate the point for J K 0 41 and P 3 94 Then read the y axis value of 2 8 hours This is the longest possible length for a transit i e it s the length for a central transit The survey catalog s measured length of 2 2 hours is less than this maximum length which is consistent
45. has detected yet Each person has favored observing styles and trying out the ones described here is a way to find which one is your favorite Enjoy 26 Chapter 4 Planning the Night This chapter may seem tedious to someone new to exoplanet observing However keep in mind that the requirements for observing exoplanets with 0 002 magnitude precision is significantly more challenging than observing variable stars with precision requirements that are more relaxed by a factor of 10 or 20 Any amateur who masters exoplanet observing is working at a level somewhere between amateur and professional Naturally more planning will be involved for such a task Probably all amateurs go through a phase of wanting to observe many objects each night Eventually however the emphasis shifts to wanting to do as good a job as possible with just one object for an entire night s observing Exoplanets should be thought of this way This chapter describes ways to prepare for a night s observing session The specifics of what I present are less important than the concepts of what should be thought about ahead of time Observers who are unafraid of floundering are invited to begin with a total disregard of the suggestions in this chapter since floundering on one s own is a great learning experience I encourage floundering that s how I ve learned almost everything I know You might actually conclude that what you learn first hand agrees with my s
46. have been discovered in the summer sky because that s when there are more stars in the night sky that s when the Milky Way transits at midnight It is unfortunate that the northern hemisphere summer is also the time when nights are shortest and is therefore the least favorable 23 CHAPTER 3 EXOPLANET CHOICES time for observing a complete transit Ironically for my location in Southern Arizona the monsoon season is from July to September and most of these nights are overcast with a residual of the afternoon s thunderstorms What s the table in Fig 3 02 good for when planning an observing session for an upcoming clear night You may use this table by first noting which objects are in season The season begins approximately 3 months before opposition and ends 3 months afterwards On those dates the object transits at 6 AM and 6 PM respectively An object may be observed outside the season but observing intervals will be limited the amount will depend on site latitude and object declination You ll want to calculate when transits can be observed This can be done using a spreadsheet available at http brucegary net book EOA xls htm It has input areas for the object s HJDo period transit length RA and Dec Another input area is for the observing site s longitude and latitude A range of rows with user specified N values number of periods since HJDo is used to calculate specific JD values for transits The JD val
47. images will vary with air mass as approximately the 1 3 power of air mass When aperture photometry is employed with the same aperture size for all images the photometry aperture capture fraction will vary in a systematic way with air mass and this leads to an incorrect derivation of atmospheric extinction 62 CHAPTER 11 PHOTOMETRY PITFALLS There s a way of overcoming this use larger apertures is one but the price paid is lower SNR and more blending This will be described later Ensemble differential photometry increases the chances that one of the stars is variable which would produce drifts or sinusoidal variations in the exoplanet LC To avoid this it is necessary to evaluate the constancy of all stars used for reference The importance of this precaution will be appreciated after the capability for doing it has been accomplished I am continually surprised by how many stars are variable at the mmag level In the past year I have discovered two Delta Scuti type pulsating variable stars plus several stars with longer period variations All of them were candidates for use as reference stars and I m glad my procedures identified them for rejection Star color matters when choosing reference stars For example if the exoplanet candidate star is red and all nearby stars are blue be prepared for an air mass correlated curvature of the LC baseline level To minimize these effects extra work will be required to select suitable stars
48. is the faintest one Chk1 After noticing this the user should revise the cells in the previous page s AV column to omit the Chk1 column thus using for ensemble reference the stars Chk2 Chk3 Chk4 and Chk5 The ability of the user to choose which stars to use for reference based on a graph of their behavior is the best reason for using this analysis procedure Another important feature of this analysis procedure is that it provides an objective and automatic way for removing data associated with high extra losses The threshold for acceptable extra losses can be set by the user For example I typically accept extra losses smaller than 0 1 magnitude 71 CHAPTER 13 SPREADSHEET PROCESSING Outlier data can also be removed using the same concept of a user specified threshold The threshold should depend on SNR since faint objects will have greater internal scatter For identifying outlier data I use the difference between a value and the 4 nearest neighbors A histogram of these neighbor differences will have a Gaussian shape and it is easy to adjust two parameters to fit the main part of the Gaussian as illustrated in the next figure Outliers will show themselves in the histogram as unlikely events far out in the wings This is one way to establish an outlier rejection criterion HISTOGRAM OF NEIGHBOR DIFFERENCES NUMBER gt T T T T 20 18 16 14 12 10 8 6 4 2 O0 2 4 6 6 10 12 14 16 18 20
49. magnitude per air mass and if the observing log includes elevation notations it is easy to verify that trends are compatible with an atmospheric extinction explanation I also like to record outside air temperature dew point wind max during the past 5 minutes and wind direction Whenever focus is adjusted I note this as well Intentional Defocusing Sometimes an observing session is designed for intentionally defocused imaging This 1s done when bright stars are within the FOV and Cmax must be kept below saturation for long exposures The desire for long exposures can be motivated to reduce the fraction of time lost to image downloading or to reduce scintillation cf Chapter 15 There are situations when this can be done safely One requirement is a good alignment of the telescope optics otherwise defocused images won t have circularly symmetric point spread functions Another requirement is that the telescope tube does not contract as the night air cools which would require that adjustments be made to maintain the same defocus Defocused observing should not be attempted when there are stars near the target or reference stars that could be 52 CHAPTER 8 FOCUS DRIFT included in the signal photometry aperture This is more often a problem for objects at low galactic latitudes Finally this should only be done at sites where sky background level is not high since a defocused image will require the use of a larger photometry aperture a
50. my observatory tour chapter 2 my observing control room is comfortable This is primarily in response to the requirements of autoguiding which requires that I check in on the telescope s tracking and record things on the observing log at frequent intervals 56 Chapter 10 Photometry Aperture Size Before describing how images can be processed to produce light curves it is necessary to have an understanding of some basic concepts related to photometry aperture size The following descriptions will be based on my use of MaxIm DL or MDL as I will refer to the program I ve never used other image analysis programs that are supposed to be comparable but I ll assume that they re capable of performing similar operations It will be up to the user of another program such as AIPAWIN or CCDSoft to figure out the equivalent procedure I don t want this paragraph to seem like an advertisement for MDL but I do want to say that I ve never encountered anything related to image manipulation that I needed to do for photometry that wasn t performed easily with MDL Increase Aperture Decrease Aperture Increase Gap Width Cursor X 604 Y 797 J Rad 10 Rad2 23 ESSE pns Pizel 2054 000 Magnitude 12 064 Set Gap Width Maximum 2082 000 Intensity 71641 953 al Minimum 140 000 SNR 1052 796 Increase Annulus Median 202 000 Decrease Annulus Average 365 038 BodAvg 139 038 Aie THO Tess TP StdDev 378543 BgdDev 3 822 i Centroid X 6
51. observe at times that are 1 6 of a BTE period before and after the BTE s scheduled transit In this chapter I ll show you how to create your own schedule for Trojan transit times Another exoplanet project type could be called mid transit timings The goal is to detect anomalies in mid transit times caused by the gravitational influence of another planet in a resonant orbit as described in more detail in Chapter 16 Although this is something one person could do alone it is more appropriate to combine mid transit timings by many observers in a search for anomalies The magnitude of the anomalies can be as much as 2 or 3 minutes and the time scale for sign reversals is on the order of a year Only BTE objects are suitable for this project A somewhat more challenging observing project is to refine transit depth versus wavelength Again this can only be done with BTEs As the name implies it consists of observing a BTE at known transit times with different filters for each event If you have a large aperture 20 inches or larger you could alternate between two filters throughout an event The goal is to further refine the solution for the planet s path across the star and simultaneously refine the star s limb darkening 21 CHAPTER 3 EXOPLANET CHOICES function As explained later an exoplanet whose path passes through star center will have a deeper depth at shorter wavelengths whereas if the path is a chord that crosses farther than
52. of the times for ingress and egress For this example the red reference star produced a 2 4 minute error while the blue reference star produced a 2 1 minute error 81 CHAPTER 14 STAR COLORS 11 170 11 180 11 190 OBJECT CV MAG 11 200 Using 1 red ref star 5 5 min avg 11 pt Depth 16 0 mmag Pred d Ingr amp Egr Length 2 74 hr Air Mass Corr d Model 11 210 11 170 11 190 OBJECT CV MAG 11 200 Using 1 same color ref star Depth 14 6 mmag Length 2 58 hr 8 5 min avg 17 pt Pred d Ingr amp Egr No Air Mass Corr n Needed 11 210 UT 11 170 11 190 OBJECT CV MAG 11 200 Using 1 blue ref star 5 5 min avg 11 pt Depth 13 5 mmag Pred d Ingr amp Egr Length 2 71 hr Air Mass Corr d Model 11 210 Figure 14 09 Effect of reference star color on LC shape depth length and timing For shallow transits it is therefore preferable to use a reference star with a color similar to the target star If this can t be done then an air mass model may have to be used to interpret the LC The longer the out of transit OOT baseline the easier it is to derive a proper fitting model With experience and familiarity with the color of stars near the target it is possible to process the OOT baselines to reduce curvature 82 CHAPTER 14 STAR COLORS effects But when there is uncertainty in star colors it is prudent to plan on a long obse
53. part of the explosion of known transiting exoplanets can be attributed to the role played by amateur astronomers Three of the 15 bright transiting exoplanets were discovered by the XO Project which includes a team of amateurs During the past few decades when professional observatories have become more sophisticated and plentiful it is ironic that amateurs have kept pace thanks to improvements in technology that s withim amateur budgets and we amateurs continue to make useful contributions The discovery of exoplanet is one of the most fruitful examples Not only are amateurs capable of helping in the discovery of exoplanets through collaborations with professionals but amateurs are well positioned to contribute to the discovery of Earth like exoplanets This is explained in Chapter 16 How can this be After all the professionals have expensive observatories at mountain tops and they use very sophisticated and sensitive CCD cameras But with this sophistication comes expensive operation on a per minute basis With telescope time so expensive these highly capable facilities can t be used for lengthy searches Moreover big telescopes have such a small field of view FOV that there usually aren t any nearby bright stars within an image for use as a reference The optimum size telescope for most ground based exoplanet discovery has an aperture between 20 and 40 inches as explained in Chapter 17 Such telescopes are within the reach of many
54. predict maximum transit length from an exoplanet s star color and period same as Fig B 01 Post its are used to remind me of handy magnitude equations site coordinates local to UT time conversion and nominal zenith extinction values 18 Chapter 3 Exoplanet Choices Exoplanets can be thought of as belonging to three categories 1 bright transiting exoplanets BTEs 15 known as of July 2007 2 faint transiting exoplanets FTEs 8 known as of July 2007 3 exoplanets not known to undergo transits NTEs 225 known Those in the first category are by far the most important This is because transits of bright transiting exoplanets BTEs allow investigations to be made of the exoplanet s atmospheric composition and temperature Atmospheric composition is investigated using large professional telescopes with sensitive spectrographs Atmospheric temperature is inferred from thermal infrared brightness changes as the exoplanet is occulted by the star These investigations can only be done with bright nearby exoplanets In addition to permitting atmospheric studies the BTEs permit a determination to be made of their size Since the exoplanet s mass is known from radial velocity measurements with professional telescopes the plant s average density can be derived The size and average density allow theoreticians to construct models for the planet s density versus radius which lead to speculations about the presence of a rocky core
55. program you ll need to use Every computer with a Windows operating system comes with Excel and even though Excel seems constructed to meet the needs of an executive who wants to make a pie chart showing sales it also is a powerful spreadsheet for science I ve migrated all my spreadsheet work to Excel That s what I assume you ll be using in Chapter 13 Previous Experience Whenever an amateur astronomer considers doing something new it is natural to ask if previous experience is adequate especially if there is no local astronomy club with experienced members who can help out with difficult issues Some people prefer to learn without help and I m one of them The astronomy clubs I ve belonged to emphasized the eyepiece Wow version of amateur astronomy so help was never available locally This will probably be the case for most amateurs considering exoplanet observing Being self taught means you spend a lot of time floundering Well I like floundering I think that s the best way to learn Anyone reading these pages who also likes floundering should consider setting this book aside with the intention of referring to it only when floundering fails For those who don t like foundering then read on The best kind of amateur astronomy experience that prepares you for producing exoplanet light curves is variable star observing using a CCD Pretty pictures experience will help a little since it involves dark frame and flat frame cal
56. s much more useful than the graphs in the previous figure because it doesn t require knowledge about miss distance Instead it requires knowledge about transit depth D which is easily measured TRANSIT DEPTH vs PLANET SIZE LC SHAPE amp MISS DISTANCE 100 Rp Rst 0 25 90 80 70 60 50 DEPTH mmag 40 Rp Rst 0 15 30 Rp Rst 0 12 20 RpiRst 0 10 Rp Rst 0 08 0 0 0 1 0 2 0 3 04 0 5 0 6 0 7 0 8 0 9 1 0 LC SHAPE PARAMETER S Figure D 14 Domains for exoplanets and EBs using parameters S and D as input yielding Rp Rstr and miss distance as answers This figure requires knowledge of transit depth D instead of miss distance This is better since D is easily determined by casual inspection of a LC The shape parameter S is also easily determined by visual inspection Therefore without any attempts to solve the LC this plot can be used to estimate Rp Rstr and miss distance Then by knowing B V we can specify an Rp Rstr threshold secondary boundary in the figure that separates the exoplanet and the EB domains Consider the previous example where XO 1 was determined to have S 0 29 and D 24 mmag Given that B V 0 66 we know that a threshold secondary will have Rp Rstr 0 156 cf Fig D 06 Now using the above figure draw a trace at this Rp Rstr value as in the following figure 130 APPENDIX D PLANET SIZE MODEL TRANSIT DEPTH vs PLANET SIZE LC SHAPE
57. temporal trends then solve for transit shape using a simple model The output of this analysis would be a refined set of values for mid transit time transit depth transit length a shape parameter related to the ratio of planet radius to star radius ETA should be available to anyone both for data submission and information query The need for ETA will grow with the number of exoplanet observers The ETA staff should be familiar with common shortcomings of amateur exoplanet transit observations in order to maximize the value of extracted information and minimize the amount of misleading information from ETA submissions Since the proposed network of amateur observatories described in this chapter is in response to the growing need for amateur observations and since the proposed network of advanced amateur observers will be familiar with exoplanet observing pitfalls it is natural for the ETA to be created in coordination with the amateur observatory network The professional astronomer chosen to lead the 101 CHAPTER 17 OPTIMUM OBSERVATORY amateur network of advanced observers should therefore be charged with creating the ETA I believe this is the best time for either government or institutional funding for creating such a professional amateur partnership If 2007 is eventually viewed as the year transiting exoplanet discoveries began to explode how fitting if it were also the year that a commitment was made to creating the ETA and
58. that the bluest 25 of stars have B V lt 0 47 Using the Warner and Harris equation this corresponds to J K lt 0 26 The reddest 25 of stars with acceptable colors have B V gt 1 01 which corresponds to J K gt 0 64 If there were 12 candidate reference stars in a FOV for example it 1s likely there would be 3 with J K lt 0 26 and another 3 with J K gt 0 64 If the target star is typical with J K 0 39 there should be 6 stars with a J K color difference less than 0 2 Therefore A reasonable goal for same color stars is a J K difference 0 2 85 CHAPTER 14 STAR COLORS It s possible to associate J K with star surface temperature The typical J K of 0 4 corresponds to Tstar 5800 K The bluest 25 of stars have Tstar gt 7700 K and the reddest 25 have Tstar lt 4000 K These are close to the temperature extremes that were used to calculate zenith extinction sensitivities to star color Therefore the list of extinction slope differences for red and blue stars for various filters in the previous section of this chapter should be representative of situations faced by exoplanet transit observers In other words Star color matters 86 Chapter 15 Stochastic Error Budget This chapter will illustrate how stochastic noise contributes to the scatter of points in a light curve I will treat the following error sources Poisson noise aperture pixel noise scintillation noise and seeing noise
59. the drop down menu Mouse click tags as and select New Reference Star Navigate to the artificial star in the highlighted image and left click its approximate location the set of photometry circles appear snap centered over the artificial star with the label Refl All images automatically have their reference star identified with the same aperture circles and Refl label Next open the drop down menu Mouse click tags as and select New Check Star Navigate the highlighted image to the first star chosen earlier to be the first in the series of check stars to be considered for use as reference stars during the spreadsheet phase of analysis Left click this star and proceed to do the same for the rest of the check star list Finally click the View Plot button The Photometry graph appears It can be resized to exaggerate the magnitude scale if you want to see if any of the stars are variable or noisy This encompasses a large magnitude range so small variations won t be visible but it s worth a cursory look The real purpose for displaying this graph is that it has a Save Data button Click it and navigate the directory structure to where you want to record the magnitude differences CSV file Enter a file name such as 1 r where r is the signal aperture radius and click Save If other signal aperture sizes are of interest right click on an image and a drop down menu will appear that allow
60. there must be other ideas to be guided by and the author would appreciate feedback on any results or ideas on this matter 111 APPENDIX B Selecting Target from Candidates List This appendix is for those few amateurs who are privy to a secret list of possible exoplanet transits maintained by professionals who operate wide field camera surveys As I write this only the XO Project produces such a list for use by a small group of amateur observers However I anticipate that in the future professional teams with survey cameras will solicit amateurs to conduct follow up observations using their secret candidate lists When that happens the amateurs invited to join those extended teams will want to learn how to wisely choose candidates from the list for each night s observation The candidate list is based on wide field camera surveys with poor spatial resolution but good sensitivity Because of the poor spatial resolution most candidates are faint eclipsing binaries whose light is blended with a brighter star that is mistaken by the survey candidate analysis software for being the eclipser This common situation is called EB blending The main role for amateur observers is to determine which star is fading and by how much As a bonus the amateur light curve can reveal the shape of the event and if it is closer to flat bottomed than V shaped as well as shallow there will be heightened interest in additional observations If you re
61. wide field survey camera project uses a BB filter Ohio State University s KELT Project based at the Winer Observatory AZ When a typical CCD response function is used my ST 8XE and adopting my site altitude the BB filter s white star effective wavelength is calculated to be 700 nm This is intermediate between the R band and I band filters Using a BB filter stars that are blue and red have calculated extinctions of 0 124 and 0 116 mag airmass If a set of images that contain red and blue stars within the FOV 83 CHAPTER 14 STAR COLORS were measured and plotted versus air mass they would exhibit these two slopes i e they would separate at the rate of 8 mmag airmass The following list summarizes the calculated extinction slope differences for various filters between stars that are blue spectral type A2 8000 K and red K3 4500 K B band 16 mmag airmass V band 6 mmag airmass R band 3 mmag airmass I band 1 mmag airmass Unfiltered 59 mmag airmass BB band 8 mmag airmass The BB filter offers a dramatic 7 fold reduction of extinction effects compared with using a clear filter essentially equivalent to unfiltered Keep in mind that the red and blue stars used for these calculations are near the extremes of blueness and redness so the values in the above list are close to the maximum that will be encountered The BB filter s loss of SNR compared to using a clear filter will depend on star color For a blue s
62. 0 000 0 005 4 0 010 4 0 015 4 X 0 020 4 e R MAG BRIGHTNESS CHANGE MMAG 0 025 4 ee 0 030 4 0 035 4 T T T T T 3 2 1 0 1 2 3 TIME AFTER MID TRANSIT HR Author s amateur exoplanet light curve of XO 1 made in 2006 average of two transits with a 14 inch telescope and R band filter at his Hereford Arizona Observatory Exoplanet XO 1b moves in front of the star during contact 1 to contact 2 is obscuring 2 2 of the star s disk between contacts 2 and 3 and is moving off the star during contacts 3 to 4 The smooth variation between contact 2 and 3 is produced by stellar limb darkening vi CONTENTS Preface Introduction 1 Could I Do That 2 Observatory Tour 3 Exoplanet Choices 4 Planning the Night 5 Flat Fields 6 Dark Frames 7 Exposure Times 8 Focus Drift 9 Autoguiding 10 Photometry Aperture Size 11 Photometry Pitfalls 12 Image Processing 13 Spreadsheet Processing 14 Star Colors 15 Stochastic SE Budget 16 Anomalies Timing and LC Shape 17 Optimum Observatory Appendix A Flat Field Evaluation Appendix B Selecting Target from Candidate List Appendix C Air Mass from JD Appendix D Planet Size Model 19 27 34 42 44 48 55 57 62 64 67 75 87 95 99 103 112 115 116 Appendix E Measuring CCD Linearity Appendix F Measuring CCD Gain Glossary References Index viii 138 148 150 159 161 PREFAC
63. 015 1 2 MID 3 4 0 010 i 0 005 0000 s e 0 005 PA w 0010 a E 0 015 4 ao 0 020 X 0 025 0 030 0 035 i i H H i 3 2 1 0 1 2 3 TIME AFTER MID TRANSIT HR Figure 1 01 Knowing what to do makes a difference Upper panel my first light curve of HD209458 made 2002 August 12 Lower panel a recent light curve of XO 1 made in 2006 average of March 14 and June 1 transits During the past 5 years my capability has improved 70 fold and most of this is due to improved technique Although I now use a 14 inch telescope if I were to use the same 10 inch that I used 5 years ago for my first exoplanet transit I could achieve in one minute what took me 15 minutes to do back then Some of this improvement is due to use of a slightly improved CCD and some is from use of a tip tilt image stabilizer but most of the improvement is due to improved techniques for observing image processing and spreadsheet analysis These are things that can be shared with other amateurs in a book That s the book I wanted 5 years ago You are now holding such a book It is based on 5 years of floundering and learning It can save you from CHAPTER 1 COULD I DO THAT lots of time with trial and error observing and processing ideas and give you a 15 fold advantage that I never had for my first exoplanet transit observation Minimum Requirements for Exoplanet Transit Observing You don t have to live on a mountain top to obse
64. 03 729 Y 796 857 rosshars FWHM 3159 Flatness 0 017 Screen Stretch Zoom In Zoom Out Mode Aperture x Iv eis in Calibrate Point telescope here Figure 10 01 Three aperture circles with user set radii of 10 9 and 10 pixels The Information window gives the cursor location the radius of the signal circle 10 pixels as well as the radius of the sky background annulus outer circle 29 pixels The Information window shows many other things such as magnitude star flux labeled Intensity SNR and FWHM MDL uses a set of three circles for performing aperture photometry measurements Figure 10 01 shows photometry aperture circles centered on a star Notice that in this image the central circle which I shall refer to as the signal aperture appears to enclose the entire pixel area where the star s light was registered Note also that the outer sky background annulus the area between the outer two circles is free of other 57 CHAPTER 10 PHOTOMETRY APERTURE SIZE stars When these two conditions are met the star flux reading displayed in the Information window labeled Intensity will be valid If the signal aperture is too small the flux reading will be too small and if the signal aperture is too large the flux may be correct but it will have a larger component of noise due to the many pixels involved With a too large signal aperture the pixels near the outer edge will contain no information about star
65. 130 132 134 egress 24 28 29 33 46 72 74 81 97 100 114 ensemble photometry 49 63 65 71 75 87 90 110 extinction zenith extinction atmospheric extinction 5 14 18 28 29 32 44 45 52 62 65 69 71 75 81 83 85 89 108 140 extra losses 50 51 56 70 73 flat frame flat field 11 16 17 33 34 42 62 64 73 103 111 139 140 147 149 FOV 2 15 30 32 35 46 47 52 55 56 79 83 85 92 93 95 99 100 104 108 140 gain CCD gain 88 147 148 information rate 44 46 47 147 ingress 24 28 29 33 46 72 74 81 97 100 114 image rotation 56 62 65 71 73 110 111 image stabilizer AO 7 AO L 14 15 17 35 40 41 55 100 impact parameter 21 126 J K 18 31 32 84 85 112 113 117 133 JD and HJD 24 67 69 95 115 length transit length 18 23 24 29 46 97 101 112 114 116 119 124 133 137 limb darkening 22 116 118 120 124 133 136 137 linearity of CCD 38 44 138 140 146 147 median combine 34 38 39 42 70 72 97 MDL MaxIm DL 8 10 12 16 49 59 55 57 59 61 64 66 90 95 Mie scattering 75 77 non linearity of CCD see linearity of CCD OOT out of transit 20 22 26 74 82 plate scale 15 32 99 100 Poisson noise 44 47 87 91 93 99 110 111 138 147 Rayleigh scattering 29 75 77 84 read noise 32 44 58 90 147 149 161 REFERENCES reference star 28 32 35 39 47 48 50 52 56 59 60 63 65 66 72 74 75 80 85 88 91 94 100 106
66. 2 124 3 966 2 423 10 3 2454223 613 2 002 0 4 192 2 941 2 114 3 983 2 418 M1 4 2454223 614 2 008 0 4 203 2 834 2 110 3 967 2 426 12 5 2454223 615 2 007 0 4 186 2 955 2 118 3 961 2 427 13 6 2454223 615 2 002 0 4 191 2 937 2 110 3 969 2 423 Figure 13 02 Screen capture of the part of the spreadsheet where the CSV file has been imported The user must enter site coordinates in cells C4 C5 and object RA Dec in cells H4 J5 Air mass AirMass is calculated using JD site coordinates and the target s RA and declination The next figure shows the right most section where air mass is calculated z A AB Ac AD AE AF AG Aperture 2450000 Sin Dec JD2000 GMSTO GMST1 DegRad Sin Lat 7 079 1545 18 589737 24 06571 57 2858 0 4416 JD D GMST GMST LST LST LHA LHA D4 day hr m hr hr deg deg 4223 61 2578 51 54481 38 17 5843 10 035 10 035 65 06 85 06 4223 61 2678 61 54481 40 17 4032 10 054 10 054 65 34 85 34 4223 61 2676 61 54481 42 17 4219 10 073 10 073 65 62 85 62 4223 61 2676 61 64481 44 17 4406 10 091 10 091 65 90 85 90 4223 61 2678 61 64481 46 17 4592 10 110 10 110 66 16 85 18 4223 62 2676 62 64461 46 17 4782 10 129 10 129 66 46 85 46 Figure 13 03 Screen capture of the part of the spreadsheet where air mass is calculated from the JD in column B and site coordinates and object RA Dec Appendix C contains a description of the algorithm that is used to calculate air mass An ea
67. 3 03 11 80 10 96 12 80 11 27 6 2 769 1 099 10 84 13 03 11 78 10 95 12 81 11 26 72 788 1 097 10 83 13 03 11 78 10 96 12 83 11 27 Figure 13 06 Left side of third spreadsheet page explained in the text 70 CHAPTER 13 SPREADSHEET PROCESSING In Fig 13 06 the D column is the object s magnitude corrected for extinction using the model for extinction and air mass and also corrected for extra losses column AV on the previous page Columns E through I are the corresponding versions for the check stars In a perfect world the values in each row of a column would the same Here s a plot of the corrected magnitudes CORRECTED FOR EXTINCTION amp EXTRA LOSSES 10 6 10 8 11 0 11 2 11 4 11 6 11 8 12 0 12 2 12 4 12 6 12 8 13 0 13 2 13 4 MAGNITUDE 2 3 4 5 6 7 8 9 10 11 UT Figure 13 07 Plot of magnitudes corrected for extinction and extra losses In viewing this plot stretched vertically it is often possible to identify check stars that are poorly behaved Poor behavior could be variability on a time scale shorter than the observing session length yes you do encounter such stars Poor behavior could also be noisiness due to poor SNR or occasional spikes due to cosmic rays Another form of bad behavior would be trends related to image rotation more common for stars located near a corner where rotation effects are larger From this figure we learn that the only star to be avoided
68. 3355 1458 1 5 7 802 50 23 2007 11 TrES 3 12 4 26 1 34 1 30619 4185 9101 6 7 17 669 37 55 2007 10 HAT P 2 871 55 3 46 5 53341 4213 444 5 0 16 343 41 05 2007 9 XO 1 11 18 23 2 96 39841510 3808 9170 5 8 16 037 28 17 2006 8 WASP 2 1188 20 1 78 2 15221 3991 5146 8 0 20 515 6 43 2006 7 WASP 1 1179 11 14 2 51897 3151 486 10 1 0 344 31 99 2006 6 TrES 2 11 41 17 1 70 2 47063 3857 5358 7 3 19 121 49 52 2006 5 HAT P 1 10 4 16 2 7 4 455289 3984 397 9 3 22 963 38 58 2006 4 HD189733 7 57 25 174 22185733 3988 80335 remi 20 012 22 71 2005 3 HD149026 8 15 3 0 3 2 2 6766 3530 751 5 1 16 508 38 35 2005 2 TrES 1 11 79 25 5 2 45 30300737 3898 87342 7 3 19 069 36 97 2004 1 HD 209458 7 65 16 5 2 88 3 52474859 2826 528521 8 8 22 053 18 88 1999 Figure 3 02 List of bright transiting exoplanets V mag 13 The Opposition date is the time of year when the object transits at local midnight One thing to notice about this table 1s that all 15 BTEs are in the northern celestial hemisphere This is due to a selection effect since all wide field search cameras are in the northern hemisphere If there had always been as many cameras in the southern hemisphere it is fair to expect that we would now have a list of 30 BTEs Based on the explosive growth rate shown in Fig 3 01 the list of BTEs could be in the hundreds in a few years Another thing to notice about this table is that 9 of the 15 BTEs are best observed in the summer June through September Maybe more BTEs
69. 5 minutes afterwards assuming my binning is 1x1 At 10 minutes before sunset I can start the V band flat frames Next are the I band R band and finally the clear filter flat fields Since the clear filter flats 37 CHAPTER 5 FLAT FIELDS can be made as late as 20 minutes after sunset the entire flat frame series can take 40 minutes assuming all filters are to be used on that night s observing session Figure 5 02 assumes that no binning will be used i e 1x1 binning or full resolution If 2x2 binning is planned then flat fields will have to be made later than the times in this graph Since the CCD s analog to digital converter will be dealing with 4 times the voltage for a specific sky brightness produced by 4 times as many electrons we can estimate a time to observe from Fig 5 02 by choosing the 4 second to 40 second exposure time region at these times the actual exposures required for the desired counts will be within the range 1 second to 10 seconds My sliding roof observatory is usually opened about a half hour before sunset I immediately start cooling the CCD to something close to 0 C The flats can be taken at any temperature according to SBIG they don t have to be taken at the same temperature as the light frames later in the night The reason for achieving some amount of cooling is to reduce dark current thermal noise In making flats it is sometimes stated that dark frame subtractions are optional This i
70. 557 2 013 0 000 4 197 2 956 2 132 3 993 2 441 2454223 6122800927 2 012 0 000 4 238 2 943 2 124 3 966 2 423 2454223 6130555556 2 002 0 000 4 192 2 941 2 114 3 983 2 418 2454223 6138310186 2 008 0 000 4 203 2 934 2 110 3 967 2 426 2454223 6146064815 2 007 0 000 4 186 2 955 2 118 3 961 2 427 2454223 6153935185 2 002 0 000 4 191 2 937 2 110 3 969 2 423 Each row corresponds to an image The first image has a JD time tag corresponding to mid exposure time The next value 2 013 for the first image is the magnitude difference between the object the exoplanet and the artificial star The next value is zero because this is the magnitude of the artificial star referred to itself Then there are 5 magnitude differences for the so called check stars used in this example The next step is to import the CSV file to a spreadsheet EJA B c p EIFTIGe HT T4IkTvt EwTworPgRisSTIUvVWX y z a8 ac AD Ae AF AG 1 Artificial Star All Sky Photometry of XO 3 obsn date 7503 v7508 2 Import CSV file to B7 Update RA Dec amp AS mag Y5 Cosine Aperture 2450000 Sin Dec Site SIN COS Object deg Sine 0 415 JD2000 GMSTO GMST DegRad Sin Lat 4 N Latitude 31 45 0 52 085 RA 4 21 53 655 578 0 91 0 533 7 079 1545 18 69737 2406571 57 2958 0 4416 5 E Longitude 1102 0 94 035 Dec 57 49 0 578 280 85 3 AirMass JD D GMST GMST LST LST LHA LHA T TWD Obji RefChk Chk2 Chk3 Chk4 Chk5 4 day h hr hr hr
71. 8 seconds to download full resolution or unbinned or 1x1 If I used an exposure time of 8 seconds half of an observing session would be spent downloading images Another way of saying this is that such an observing schedule has a 50 duty cycle Consider the absurd example of exposing for 2 seconds when downloading requires 8 seconds This corresponds to a duty cycle of 2096 which means 8096 of an observing session would be spent simply downloading images The higher the duty cycle the greater the information rate The longest possible exposures will produce the greatest possible information rate So why not increase the exposure time from our starting value of 60 seconds and make it 120 seconds assuming saturation issues are not a problem at this longer exposure time To answer this we must consider risk Suppose a satellite or airplane passes though the FOV and ruins an exposure The more exposures you have in an observing session the smaller is the percentage loss when one image is ruined There are a myriad of things that can ruin an image For me winds vibrate my telescope and when they exceed about 5 mph the stars begin to take on oval shapes This not only lowers the signal to noise ratio SNR but it introduces the possibility of systematic errors Cosmic ray defects are present in most exposures especially the 46 CHAPTER 7 EXPOSURE TIMES long ones and if they appear on top of a star s image there s no way for simple
72. AAAAAAAAAAAA 0 010 4 aAA A Sih A AA AAA AAA AL a aa ao a amp a 0 020 A 0 030 4 0 040 5 4 3 2 1 0 1 2 3 4 5 LOCAL HOUR ANGLE HR Figure 14 08 Light curve shapes of normal color star when blue and red reference stars are used and observations are made with a B band filter Is there any evidence for this effect in real data Yes Consider the following figure Fig 14 09 showing the effect of reference star color on measured LCs The middle panel uses a reference star having the same color as the target star The top panel shows what happens when a red reference star is used It is bowed upward in the middle Air mass was minimum at 5 5 UT which accounts for a greater downward distortion of the LC at the end when airmass 1 3 compared when airmass 1 2 at the beginning The bottom panel using slightly bluer stars for reference has an opposite curvature The curvature is less pronounced in this panel compared to the middle one due to a smaller color difference Notice also in this figure that reference star color not only affects transit shape it also affects transit depth Assuming the middle panel is correct we can say that the red star top panel produced an 10 increase in apparent depth whereas the blue star bottom panel produced a 8 decrease One additional effect to note when using a different color reference star is timing by which I mean the time of mid transit as defined by the average
73. All of these measurements and models can be used to speculate on the formation and evolution of other solar systems This in turn can influence speculation on the question of life in the universe The rate of discovery of BTEs shown on the next page is growing exponentially Therefore projects for BTEs that are described in this chapter can be done on a fast growing list of objects The faint transiting exoplanets FTEs can t be studied for atmospheric composition and temperature but they do allow for the determination of exoplanet size and density since transit depth can be measured Most FTEs are near the galactic plane near the center and this makes them especially difficult to observe with amateur telescopes Although hardware capability improves with time for both amateurs and professionals I have adopted the somewhat arbitrary definition of V mag 13 for the FTE BTE boundary At the present time most amateurs are incapable of measuring transit properties when V mag gt 13 The many non transiting exoplanets NTEs should really be described as not being known to exhibit transits Of the 225 on the list a statistical argument can be made that probably 10 to 15 of them actually are transiting but observations of them are too sparse to have seen the transits As more amateurs observe NTEs the BTEs among them will hopefully be identified This is what happened to GJ 436 which languished on the TransitSearch org web site l
74. All of these telescopes have had 14 inch apertures with catadioptic optics Celestron CGE 1400 Meade RCX400 and Meade LX200GPS Most of my illustrations will be with the last one These are typical telescopes now in use by advanced amateurs for exoplanet transit observations I use a sliding roof observatory located in Southern Arizona at an altitude of 4660 feet Atmospheric extinction values for B V R and I bands are typically 0 25 0 16 0 13 and 0 08 magnitude per air mass Figure 2 01 Hereford Arizona Observatory with a canvas covered sliding roof The Minor Planet Center has assigned it a site code of G95 All control functions are performed by a computer in my house using 100 foot cables in buried conduit the control room is shown as Fig s 2 03 and 2 04 For all Cassegrain configurations I use an SBIG AO 7 tip tilt image stabilizer It can usually 14 CHAPTER 2 OBSERVATORY TOUR be run at 5 Hz My favorite configuration is Cassegrain next figure that has back end optics consisting of the AO 7 a focal reducer and a CFW attached to a SBIG ST 8XE CCD This configuration provides a plate scale of 0 67 arc per pixel without binning Since my atmospheric seeing FWHM is usually 2 5 to 3 5 arc for typical exposure times 30 to 60 seconds there are 4 to 5 pixels per FWHM which is above the 3 pixel per FWHM requirement for precision photometry The FOV for this configuration is 17 x 11 arc The Meade LX200GPS c
75. E The search for planets orbiting other stars is interesting to even my daughters and neighbors Why the public fascination with this subject I think it s related to the desire to find out if we humans are alone in the universe This would explain the heightened interest in exoplanet searchers to find Earth like planets NASA and the NSF are keenly aware of this and they are currently formulating a vision for future funding that is aimed at Earth like exoplanet discoveries The author s favorite telescope a Meade RCX400 14 inch on an equatorial wedge The public s interest in planets beyond our solar system may also account for Sky and Telescope magazine s interest in publishing an article about the XO Project a professional amateur collaboration that found a transiting exoplanet XO 1 since then two more discoveries have been announced by this project The above picture from the Sky and Telescope article September 2006 helps make the point that amateur telescopes are capable of providing follow up observations of candidates provided by professionals using wide field survey cameras The XO Project is a model for future professional amateur collaborations Astronomers ironically have traditionally tried to remain aloof from things that excited the general public I recall JPL cafeteria conversations in the 1970s where I PREFACE defended Carl Sagan s right to communicate his enthusiastic love for astronomy to the publ
76. EXOPLANET OBSERVING FOR AMATEURS Books by Bruce L Gary ESSAYS FROM ANOTHER PARADIGM 1992 1993 Abridged GENETIC ENSLAVEMENT A CALL TO ARMS FOR INDIVIDUAL LIBERATION 2004 2006 THE MAKING OF A MISANTHROPE BOOK 1 2005 A MISANTHROPE S HOLIDAY VIGNETTES AND STORIES 2007 QUOTES FOR MISANTHROPES MOCKING HOMO HYPOCRITUS 2007 EXOPLANET OBSERVING FOR AMATEURS Bruce L Gary Reductionist Publications d b a 5320 E Calle Manzana Hereford AZ 85615 Reductionist Publications d b a 5320 E Calle Manzana Hereford AZ 85615 USA Copyright 2007 by Bruce L Gary All rights reserved except for brief passages quoted in a review No part of this book may be reproduced stored in a retrieval system or transmitted in any form and by any means electronic mechanical photocopying recording or otherwise without express prior permission from the publisher Requests for usage permission or additional information should be addressed to Bruce L Gary lt bgary cis broadband com gt or Reductionist Publications 5320 E Calle Manzana Hereford AZ 85615 First edition 2007 August Printed by Mira Digital Publishing St Louis MO ISBN 978 0 9798446 3 8 iv Dedicated to the memory of Carl Sagan A giant among men who would have loved the excitement of exoplanet discoveries that would have further inspired him to speculate about life in the universe 0 015 1 2 MID 3 4 0 010 4 0 005 4
77. FWHM be at least 3 pixels For CCD cameras using chips having 9 micron pixels and for sites with FHWM 2 5 arc this means the plate scale should be 0 7 arc pixel If the plate scale is smaller too many pixels are within the photometry aperture circle leading to SNR degradation 2 An aperture should be large enough that Poisson noise and scintillation noise are small 3 The focal length should be short enough that the FOV is likely to contain same color stars for use as reference this requirement translates to FOV larger than 12 x 18 arc 4 The telescope should be in a mount that does not require meridian flips 5 Image quality must be the same for the entire FOV in other words focal reducers cannot be used 6 There should be minimal degradation of image sharpness due to winds vibrating the telescope this translates to either the use of an open tube or a closed tube inside a dome The optimum effective focal length EFL is 100 inches when 9 micron pixel dimensions are used and FWHM seeing of 2 5 arc is to be accommodated A 30 inch telescope would have to have an f ratio of 3 3 to achieve this EFL without using a focal reducer lens When f ratio becomes small maintaining optical collimation becomes more difficult This is one reason larger apertures are undesirable A 40 inch 99 CHAPTER 17 OPTIMUM OBSERVATORY aperture with f ratio 5 will have EFL 200 inches a plate scale of 0 35 arc pixel and a FOV 17 x 11
78. Now imagine that the air is moving and carrying the temperature structure across the telescope s line of sight At one instant the line of sight to one part of the FOV 92 CHAPTER 15 STOCHASTIC ERROR BUDGET may be relatively free of temperature structure and exhibit sharpness while the opposite is true for another line of sight But as the air moves past the telescope the regions of sharpness in the FOV will vary If a typical time for variation is 1 second for example then after 16 seconds the contrast in sharpness will be of order 1 4 as large compared with the contrast for individual short exposures In theory there will always be some variation of FWHM sharpness across an image regardless of exposure time Consider using an aperture that captures a fraction of the complete PSF for a star Refer to Fig 10 02 for a plot of photometry signal aperture capture fraction versus size of the aperture in relation to FWHM For a typical choice of aperture radius 2 5 times FWHM 99 of a star s total flux is captured by the photometry aperture If FHWM varies across the image within the range 3 0 to 3 3 arc for example the capture fraction could vary between 0 987 and 0 980 or 7 6 mmag Smaller apertures would produce even larger differences Since patterns of seeing across an image will be uncorrelated from one image to the next if they have exposure times longer than 10 seconds the errors in relating an exoplanet s flux to the flu
79. T are not privy to one of those secret lists of possible exoplanet candidates maintained by professional astronomers using wide field survey cameras If you are such a member then Appendix C was written for you We want to observe a known transiting exoplanet system which means we ll be checking the bright transiting exoplanet BTE list If none are transiting tonight then we ll have to settle for an exoplanet system where transits might be occurring This might category includes exoplanets currently on the NTE list TransitSearch org BTE Trojan searches and undiscovered second exoplanets in resonant orbits that produce shallow transits at unknown times These categories are described in the previous chapter Since you ve asked to observe a transit we ll be consulting a spreadsheet that I maintain for my site that includes a spreadsheet page for each of the 15 known BTE objects Each page has a list of transit times with about a month s worth of transits as I flip through them we look for transit times for May 2007 If there aren t any transits by the BTEs then a might category observation will have been considered We re fortunate though since we note that XO 1 is scheduled to transit tonight Ingress is at 8 37 PM and egress is at 11 34 PM At mid transit XO 1 will be at an elevation of 48 degrees The sky is clear the wind is calm and one of the easiest exoplanets is transiting tonight Life is good Choosing a Filter
80. T members for 2 5 years and I am familiar with the issues that amateurs face when changing from variable star observing to exoplanet transit observing The XO Project is the only professional amateur collaboration for exoplanet discovery It is my belief that it will soon become generally recognized that the XO Project model for involving amateurs is a cost effective and very productive way to achieve results in the discovery and study of exoplanets I want to thank Dr Steve Howell National Optical Astronomy Observatory Tucson AZ for writing an article for The Planetary Society Howell 2002 after the discovery of HD209458b the first transiting exoplanet to be discovered Charbonneau 1999 In this article he explained how accessible exoplanet transit observing is for amateurs and this led to my first successful observation of an exoplanet transit I also want to thank Dr Peter McCullough for inviting me to join the XO ET in December 2004 In mid 2006 Chris Burke joined the XO Project and 5 amateurs were added to the original 4 member ET Today the ET consists of the following amateurs names of the original ET are in bold Ron Bissinger Mike Fleenor Cindy Foote Enrique Garcia Bruce Gary Paul Howell Franco Mallia Gianluca Masi and Tonny Vanmunster Thank you all for this wonderful learning experience and the fun of being part of a high achieving team I am grateful to the Society for Astronomical Sciences for permission to use fi
81. The average of two stars will have root 2 smaller fluctuations than any single star regardless of its brightness Using 4 stars for reference is even better as their average flux will exhibit 4 the scintillation noise of a single star We are fortunate that suitable reference stars are close to XO 1 If only stars with greatly different colors were within the FOV what options would we have for minimizing star color extinction effects V band and R band become attractive alternatives to B band I band and BB band because of their narrower bandpasses The narrower the bandpass the smaller star color extinction effects are Since XO 1 is in a friendly star field we don t have to change to R band or V band Our filter choice for the night is now final At this stage in formulating a plan for the night we have decided on a target exoplanet we ve decided on an exact placement of the CCD FOV on the star field and we have settled on I band We need to save the exact FOV placement so that it is easily found when observing begins This is done in TheSky Six by creating a new object in the User Defined Data list and entering RA Dec coordinates Planning is almost finished Binning At this point in planning we know an air mass range so an inference can be made about the sharpest atmospheric seeing during the observing session We consult ClearSkyClock at http www cleardarksky com to learn that average seeing is expected for
82. The primary star s B V color closely associated with spectral type is used to derive the star s mass and radius on the assumption that it s a main sequence star like 90 of stars Orbital period is used to calculate orbital velocity assuming a circular orbit The planet s radius and central miss distance related to inclination are adjusted to match the LC depth and duration A proper solution for planet radius will involve a fit to the entire LC not a solution based on agreement with the LC s depth length and shape parameter that is employed by the simple solution in this appendix A crude method is presented for determining if the shape is similar to what an exoplanet can produce versus what a blend of an eclipsing binary EB with another nearby star would produce My shortcuts reduce accuracy of course but 1f an approximate answer is acceptable then the procedure described here may be useful Section 1 is a case study that is used to illustrate the concepts employed Far more steps are shown than would be used in practice The goal for this section is to determine the size of the secondary exoplanet or EB binary star Section 2 shows how to use information about the LC s shape to assess whether the LC is compatible with an exoplanet or an EB whose light is blended with a nearby star to produce what merely appears to be a small transit depth Section 3 is a summary of only those things that need to be done after the underlying
83. actually encompasses all wavelength to circumference ratios but in common parlance Mie scattering refers to the situation where the wavelength is slightly longer than the circumference Much longer wavelengths are trivial to treat as mere blocking of light Rayleigh scattering is a subset of Mie scattering theory reserved for the case of wavelength much smaller than aerosol or molecule circumference non linearity The property of a CCD s readouts ADU counts failing to be proportional to the accumulated number of photoelectrons within a pixel when the number of photoelectrons exceeds a linear full well capacity See also linearity occultation Orbital motion of a larger object in front of a smaller one possibly obscuring some of the light from the smaller object c f transit OOT Out of transit portions of a light curve OOT data can used to assess the presence and magnitude of systematic errors produced by image rotation and color differences between the target star and reference stars photoelectron Electron released from a CCD s silicon crystal by absorption of a photon One photon releases exactly one electron photometric sky Weather conditions that are cloudless and calm no more than a very light breeze and no discernible haze due to dust photometry Art of measuring the brightness of one star in relation to either another one or a standard set of stars photometric standards such as the Landolt stars Brightn
84. ade event could be shorter than the main transit length 1f the new planet is in an inner orbit or longer if in an outer orbit Other subtle anomalies of exoplanet light curves may become important as theoreticians and observationalists continue the study of this new field Every 97 CHAPTER 16 ANOMALIES observer should therefore be prepared to accept as real an observational anomaly that 1s not readily explained Part of the excitement of exoplanet observing is that this is a young field that may produce future surprises not yet imagined Since amateurs have a unique opportunity to contribute to timing studies of known exoplanets and thereby contribute to the discovery of Earth mass exoplanets there is a growing need for more advanced exoplanet observers as more exoplanets are discovered It will be important for these amateurs to coordinate their observations and to contribute them to a standard format archive A case will be presented in the next chapter for establishing such an archive I claim that attention should be paid to what constitutes an optimum observatory for exoplanet observing This 1s also a topic for the next chapter 98 Chapter 17 Optimum Observatory Dreaming Every amateur dreams about upgrades to the backyard observatory Whenever someone asks for a recommendation of what telescope to buy I have to first ask What do you want to do with it For pretty pictures of a specific category of o
85. aging causes a square root of N reduction in noise median combining is about 15 less effective Thus when 10 images are median combined the master dark produced this way will have a noise level that is 0 36 times the thermal noise level of the individual images When this master dark is subtracted from a single light frame during calibration the calibrated image will have a slightly greater thermal noise level than the uncalibrated image The increase will be only 6 SQR 1 00 0 36 1 06 42 CHAPTER 6 DARK FRAMES Bias frames aren t needed if the dark frames are taken with the same exposure time as the light images Some observers claim that they can use the same master dark frame for several observing sessions This is not a good practice because every CCD camera ages and if a pixel changes between observing sessions you ll want to use dark frames taken with the current pixel s performance 43 Chapter 7 Exposure Times The factors influencing the choice of exposure time can be thought of as belonging to one of two categories saturation and information rate Avoiding Non Linearity and Saturation Images are not useful for photometry if any of the stars to be used in the analysis are saturated i e when the maximum count is at the greatest value that can be registered such as 65 535 called A D converter saturation Images are also not useful when a star to be used has a maximum count value that exceeds a linea
86. altitude sites and the telescope apertures are situated well above ground level Professionals also don t have to deal with large atmospheric extinction effects again because their observatories are at high altitude sites If a professional astronomer had to use amateur hardware at an amateur site they would have to learn new ways to overcome the limitations that amateurs deal with every night There are so many handicaps unique to the amateur observatory that we should not look to the professional astronomer for help on these matters Therefore amateurs should look for help from each other for solutions to these problems In other words don t expect a book on amateur observing tips to be written by a professional astronomer only another amateur can write such a book I ve written this book with experience as both a professional astronomer and a post retirement amateur Only the first decade of my professional life was in astronomy as a radio astronomer The following three decades were in the atmospheric sciences consisting of remote sensing using microwave radiometers Although there are differences between radio astronomy and optical astronomy and bigger differences between atmospheric remote sensing with microwave radiometers and optical astronomy they share two very important requirements 1 the need to optimize observing strategy based on an understanding of hardware strengths and weaknesses and 2 the need to deal with stochast
87. amateurs So far most exoplanet discovery contributions by amateurs have been with telescope apertures in the 10 to 14 inches size range Thousands of these telescopes are in use by amateurs today PREFACE This book is meant for amateurs who want to observe exoplanet transits and who may eventually want to participate in exoplanet discoveries There are many ways for amateurs to have fun with exoplanets some are educational some could contribute to a better understanding of exoplanets and others are aimed at new discoveries The various options for exoplanet observing are explained in Chapter 3 The advanced amateur may eventually be recruited to become a member of a professional amateur team that endeavors to discover exoplanets This might be the ultimate goal for some readers of this book Let s review how this works A professional astronomer s wide field survey camera consisting of a regular telephoto camera lens attached to an astronomer s CDD monitors a set of star fields for several months before moving on to another set of star fields When a star appears to fade by a small amount for a short time e g 0 030 magnitude for 3 hours and when these fading events occur at regular intervals 3 days typically a larger aperture telescope with good spatial resolution must be used to determine if the brightest star in the survey camera s image faded a small amount or a nearby fainter star faded by a large amount e g an ecli
88. ame FOV allowing for use of the same reference stars and the same image quality use of the same photometry apertures From there in the white paper I went on to argue that a network of these optimum observatories should be constructed at sites spanning a wide longitude range to assure that each transit would be observed in its entirety It is clear that such an amateur project would be cheaper than any space based telescope mission or any network of professional ground based observatories 100 CHAPTER 17 OPTIMUM OBSERVATORY I envision a network of 6 identical telescopes deployed in the backyards of amateur exoplanet observers who have a demonstrated history of quality observing and dedication to the task A range of longitudes would be needed to provide coverage of entire transits The observatories should consist of pairs with a pair at each of three longitudes Pair members should be at sufficient distance from each other to reduce the chances that bad weather at one location is correlated with bad weather at the other location A more important reason for situating identical observatories in same longitude pairs is to provide redundant observations that could support each other when a real LC anomalous feature occurs This is similar to the principle aspired to by SETI projects in which two telescopes observe the same candidate stars in coordination if an unusual signal is detected by one telescope the other one located sufficiently fa
89. amp MISS DISTANCE 100 m 0 0 ds Rp Rst 0 25 90 m 0 3 dod de E Peete wile m 0 4 80 4 m 0 5 m 08 70 4 5 m07 m 08 Rp Rst 0 20jj 5 60 nmeos E LE e ass E EBs I 991 th Q 404 Rp Rst 0 15 30 4 Rp Rst 0 12 20 4 MN AT 10 4 ees Rp Rst 0 08 0 0 0 1 0 2 0 3 04 0 5 0 6 0 7 0 8 0 9 10 LC SHAPE PARAMETER S Figure D 15 Domains for exoplanets and EBs for independent variables S and D with a threshold secondary Rp Rstr domain separator thick red trace at Rp Rstr 0 16 corresponding to B V 0 66 The blue circle corresponds to the S and D location for XO 1 From this graph it is immediately apparent that subject to the assumptions of the model XO 1 is an exoplanet instead of an EB This conclusion does not require solving th e LC for Rp Rstr as described in Section 1 Indeed this graph gives an approximate solution for miss distance m 0 5 not as accurate as the solution in Section 1 but somewhat useful Here s a handy plot showing threshold secondary boundaries for other B V values 131 APPENDIX D PLANET SIZE MODEL TRANSIT DEPTH vs PLANET SIZE LC SHAPE amp MISS DISTANCE Rp Rst 0 25 DEPTH mmag J D ue s Rp Rst 0 08 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 LC SHAPE PARAMETER S Figure D 16 The thick red traces are secondary threshold boundaries labeled with the B V color of the star abo
90. ample I once noticed that my AO 7 image stabilizer was allowing light to leak through the joint formed by the two outer mounting cases This leak was blocked by simply applying black electrician s tape around the joint Light leaks from all back end components can be reduced by wrapping a dark cloth around them while exposing flat frames Stray light that occurs during an observing session is unimportant for exoplanet monitoring For example if there s a bright star near the exoplanet it may reflect off internal structures and produce rings of light at the same location on all images where the FOV is offset the same amount from the bright star The nearby moon can produce large brightness gradients in images Don t worry about these stray light artifacts They would ruin pretty picture taking but photometry is usually unfazed by stray light in the photometry images It s worth noting that flat field corrections wouldn t be necessary for exoplanet observing if the star field could be positioned at the exact same pixel location for an entire observing session If that could be accomplished the only errors for neglecting to correct for flat field effects would be limited to star brightness biases and since these biases would be the same for all images they would not alter the shape or depth of an exoplanet transit light curve Keeping the star field fixed with respect to pixels requires not only that the autoguider work perfectly it also require
91. and a specified star color In fact each star must have an appropriate flat field for its color For observations with a V band filter what will a red star s optimum flat field look like It probably will be a blend of the V band and R band flat fields Notice how different the V band and R band flat fields are in Fig A 02 A blue star on the other hand may need to be corrected using a blend of the B band and V band flat fields 9 9 0 99 10v o 0 15 8 0 53 i 7 0 30 5 0 55 6 0 51 LI XO 2 e 0 82 E 0 79 2 0 81 0 66 Figure A 03 Star field with B V color labels This is a 14 7x12 6 arc crop of the full FOV 24x16 arc North up east left I will describe three ways to evaluate the presence of defects in a master flat field One technique checks for patterns in magnitude magnitude plots for two stars in a large set of images Another method involves observing Landolt star fields and processing them using an all sky analysis procedure The third method involves taking a long series of images of a pair of equally bright stars within the FOV without autoguiding and comparing their ratio versus time as they traverse various parts of 104 APPENDIX A EVALUATING FLAT FIELDS the CCD pixel field It resembles the first method except that it makes use of intentional movements of the star field with respect to the CCD pixel field Mag Mag Scatter Plots There s a clever reality c
92. and shadowing by dust particles on optical surfaces close to the CCD i e dust donuts For amateur telescopes the shape of the vignette function will differ with filter band The amount of these differences will depend on f ratio and the presence of a focal reducer and its placement Flat field corrections are supposed to correct for all these things Alas in practice flat fields correct for only most of them Sometimes I think the art of making quality flat fields could be a hobby all by itself It could take so much time that there would be no time left over for using the knowledge gained There must be a dozen procedures in use for making a master flat and it s possible that none of them are as good as the user imagines them to be Some observers use light boxes placed over the front aperture Provided the light source is white this can produce good flats for all filters However it is difficult to attain uniform illumination of the surface facing the telescope aperture which is where my attempts have always failed Another method is to use a white light source to illuminate a white board which in turn illuminates a second white board that is viewed by the telescope The use of two white boards reduces specular reflections which can be troublesome for shiny white boards The trick with this method is to provide a uniform illumination of the white board viewed by the telescope and within the confines of a smal
93. ands are about the same 1 30 This provides a good reality check on data quality as well as the limb darkening model Rows 13 15 show the SE on Rp Rj due to the SE on B V D and L separately The largest component of uncertainty comes from B V Even if B V were known exactly there s an uncertainty in converting it to star radius and mass given that the main sequence of the HR diagram consists of a spread of star locations and there s a corresponding spread in the relationship between radius versus B V and mass versus B V A future version of this spreadsheet will include a section for the user to enter a transit shape parameter value S and an answer cell will show the likelihood of S D being associated with an exoplanet versus an EB I also plan on expanding the limb darkening model to take into account limb darkening dependence on star color 137 APPENDIX E Measuring CCD Linearity The maximum ADU counts that can be read out of a 16 bit CCD is 65 535 It is commonly understood that you shouldn t trust readings greater than about half this value 35 000 counts due to something called non linearity Whereas you can trust ratios of star fluxes when none of them have maximum counts Cx greater than 35 000 when one of them has a Cx gt 35 000 it s measured flux is probably smaller than it should be Only for a hypothetical CCD that is linear all the way to 65 535 counts can you trust star fluxes with Cx values in the range 35
94. anet Size Model INTRODUCTION This appendix is long It has nothing to do with exoplanet transit observing tips and that s why it s in an appendix I present it for those readers who think it might be fun to play modeler and who want to interpret a well established LC in terms of planet size I must admit that the simple procedures leading to the final one described here has misled me a few times However after each failure I reviewed my assumptions and learned from them One lesson is that if an internally consistent solution is impossible then consider the star to be off the main sequence where star color to size and mass conversions are questionable Consider also the possibility that the transits are produced by a triple star system in which the depth only appears shallow when in fact it is a deep eclipsing binary that is blended with a third star that s within the photometry aperture and possibly a close binary with the eclipsing binary pair The goal of this appendix is to describe a simple model that I developed for converting a transit light curve LC to an estimate of the size of the secondary which is then used to discriminate between the secondary being an exoplanet versus a small and faint star i e an eclipsing binary system A concept description section uses actual R band measurements of an exoplanet to illustrate how a LC can be interpreted The model employs limb darkening relationships for each filter band
95. ar columns for creating column AV This column is a refinement of the extra losses column and will be used on the next spreadsheet page to adjust the object exoplanet column of magnitudes IBENEEH ETT nx AC AD AE AF AG ARAIAJAVALANABACARACAFASATAU AV Adopted FudgeL 0 136 SuggestedFudge 0 138 Desired 10 840 MC of col F 10 702 12 88 11 64 10 81 12 67 11 12 JO0o0000000000 Obj1 tHe R RRR ERR EE tHe R eR RRR REE 0 013 0 06 001 0 01 AIR MASS amp EXTRA LOSSES P a E g lt Wimmie Te Te e T 7e e Me e 0e Me e Te 00 00 EXTRA LOSSES Chk1 Chk2 Chk3 Chk4 Chkh 00000000000000 0 014 0 02 0 00 002 002 Q022 8 2 898289289299789 000 000 ee RR EE Hee RE Hee RE Hee RE HRB EF jeesgs HRB EF Hee RE jy4sgq jRysgg jeg jeg jRygsggy Regg 8 Regg gResgg Hee RE H Adopt d Chk Median Corrn 0 022 0 010 0 008 0 001 0 008 0 005 0 012 0 006 0 011 0 004 0 002 0 000 0 000 0 001 0 003 0 000 0 001 0 001 0 004 0 003 0 005 NN Figure 13 05 Right side of second page The column explanations are in the text B c DJ EJF G I H B Cy amp UT m Obji Chk1 Chk2 Chk3 Chk4 Chk5 1 2 5 6 1 109 10 83 13 04 11 79 10 97 12 83 11 28 2 2 695 1 107 10 84 13 08 11 78 10 96 12 80 11 26 32 713 1 105 10 83 13 03 11 76 10 95 12 82 11 26 4 2 732 1 103 10 85 13 04 11 77 10 95 12 81 11 27 52 751 1 101 10 84 1
96. ave Cmax 35 000 You might think that when observations are started it s OK to just set an exposure that keeps the brightest star from producing a count greater than 35 000 That s OK when the star field is already setting when you can count on images becoming less sharp for the remainder of the observing session But for rising star fields images are likely to become sharper as they approach transit and since the same number of total counts from each star will be concentrated on a smaller number of pixels Cmax will increase Furthermore atmospheric extinction is lower at transit so each star s flux and hence Cmax should increase as transit is approached I recommend taking test exposures for determining exposure time as soon as the target star field has been acquired and focus has been established Based on previous 44 CHAPTER 7 EXPOSURE TIMES observing sessions you ll know whether the sharpness of these images is typical for your site In making this assessment air mass has to be taken into account That s worth an aside Image sharpness is described by the full width at half maximum FWHM of the point spread function PSF of an unsaturated star near the middle of the image For example at my site I can expect FWHM 2 5 arc for short exposures 5 seconds near zenith and 3 0 arc for exposure times of 30 to 60 seconds I have determined that at my site short exposure FWHM varies with air mass AirMass in accordan
97. ay be more cases of triple star EBs that resemble exoplanet transits than there are actual exoplanet transits Therefore it is important to be able to interpret a transit light curve to distinguish between a triple star EB and an exoplanet This section demonstrates how amateurs can distinguish between exoplanet light curves and EB triple star blended light curves of similar depth so that additional amateur observing time is not wasted on non exoplanet candidates As an additional check the shape of the measured transit light curve can be compared with a model calculation First let s consider LC shapes for various sized secondaries either an exoplanet or EB star transiting across the center of the star they orbit The following figure was derived from a model that used sun like R band limb darkening 123 APPENDIX D PLANET SIZE MODEL LIGHT CURVE SHAPES FOR CENTRAL TRANSITS INTENSITY DROP mmag Rp 0 08 Rstar Rp 0 10 Rstar Rp 0 12 Rstar Rpz0 14 Rstar Rp 0 16 Rstar Rp 0 18 Rstar 0 60 0 55 0 50 0 45 0 40 0 35 0 30 0 25 0 20 015 0 10 0 05 0 00 0 05 010 0 15 0 20 0 25 0 30 0 35 040 045 050 055 060 DISTANCE STAR DIAMETER Figure D 07 Model light curves for central transits by different sized secondaries An R band sun like limb darkening function was used First contact occurs when the intensity begins to drop and second contact can be identif
98. ayleigh 4600 ft 0 25 Rayleigh 7500 ft T i Aerosols SeaLevel o 0 Aerosols 4600 f Z Sa Aerosols 7500 ft n 0204 ul E ra a t I 0 15 4 15 3 E o QD pom SER e ERE eL LS ut x z 0104 U410 F I tr 2 E s i 0 05 4 V 2 TETTE ee haar onr 05 Ww 0 00 4 rt 0 0 300 900 1000 1100 WAVELENGTH nm Figure 14 03 Atmospheric Rayleigh and aerosol Mie scattering versus wavelength 76 CHAPTER 14 STAR COLORS Figure 14 02 shows aerosol Mie scattering it is customary for Mie scattering to refer to the situation of the particle circumference being much greater than wavelength It s a plot of aerosol scattering versus altitude for 3 wavelengths A model fit to this data allows for the conversion to scattering versus wavelength for specific altitudes This is shown in Fig 14 03 This figure also includes the Rayleigh scattering component and it should be noted that for B band both scattering components are about the same For I band the only scattering component that s important is aerosol Mie scattering EXTINCTION COMPONENTS Rayleigh SeaLevel Rayleigh 4600 ft 0 45 Rayleigh 7500 ft Total SeaLevel Total 4600 ft 0 50 m Total 7500 ft v B Meas d 4600 ft us a 0 35 L Y Meas d 4600 ft p R Meas d 4600 ft 9 D a 030 Meas d 4600 ft n Oo y Dust SeaLevel a f Dust 4600 ft 0 25 Dust 7500 ft g E d Db 020 a
99. bjects the answer would be one kind of telescope and camera about which I would be clueless since I m no good at that But for exoplanet transit light curves I could give a pretty specific answer That s what this chapter is about Some of the following paragraphs presented in smaller font are taken from a white paper I submitted to the NASA NSF Exoplanet Task Force ExoPTF in March 2007 My white paper argued for government sponsorship of a network of amateur observatories for coordinated monitoring of known transiting exoplanets for the purpose of discovering Earth sized exoplanets Part of the case I presented was that the optimum observatory for this task is only slightly more expensive than existing amateur budgets yet sufficiently more expensive for those few amateurs who are capable of participating in such a search that financial help is needed If you interpret this to be a shameless self serving attempt to upgrade my observatory by responding to a future request for proposal by NASA you would be correct Here is the argument I presented to the ExoPTF in which I derived that the optimum observatory would consist of a 20 to 30 inch aperture telescope as part of an observatory costing 75 000 I now realize that the aperture range should be 20 to 40 inches Precision photometry 1 e 1 minute precision of 2 mmag has many requirements 1 the plate scale should assure that a star s full width at half maximum
100. by Caldwell et a 1993 Warner and Harris 2007 and others The strong correlation breaks down outside the J K range of 0 1 to 1 0 but within this wavelength region it is possible to predict V R star colors with an accuracy of 0 021 magnitude Warner and Harris 2007 This is adequate for selecting same color reference stars 84 CHAPTER 14 STAR COLORS Occasionally J and K magnitudes are missing from the star map programs in common use by amateurs these programs are also referred to by the unfortunate name planetarium programs When you need J K for only a few such stars the following web site is useful http irsa ipac caltech edu Converting between J K and B V can be done using the following equivalence based on a scatter plot published by Warner and Harris 2007 B V 0 07 1 489 J K or J K 0 15 0 672 B V In choosing same color reference stars be careful to not use any with J K gt 1 0 where J K to B V and V R correlations can be double valued Staying within this color range corresponds to 0 1 B V lt 1 5 For stars meeting this criterion the median B V is 0 65 based on a histogram of 1259 Landolt star B V values ABUNDANCE OF STARS vs V R COLOR 140 MEDIAN B V 0 64 120 100 80 60 40 20 0 7 ce 7 e656 wm OO nog m oO OG 0 tH o coo o o o o o e e e e KF B V Figure 14 11 Histogram of B V for 1259 Landolt stars on T S 9 3 This histogram shows
101. by treating the bright flat as a light frame that must be calibrated using the master flat field I m assuming all flats were made using a dark frame at the time of exposure After calibrating all bright flat fields using the 30 kct master flat you are ready to evaluate linearity for each Measure the average counts for the regions that were faintest and brightest and express their ratio as a percentage For example after calibrating my I band flat that had Cx 62 kct I measured the same areas that were faintest and brightest in the master flat also the same areas that were faintest and brightest in the Cx 62 kct before calibration and got a vignette range of 0 21 96 In other words the vignette range went from 21 to 0 21 simply by calibrating using the master flat field That s a 100 fold improvement and any flat with residual errors of 0 2 is good Flat field errors may be present in both flat fields so it cannot be concluded that both flats are good to 0 296 The result we re after however is that a flat field with counts as high as 62 000 has the same brightness distribution as the ones having a maximum count of 35 000 counts This can be interpreted to mean that my CCD is linear all the way up to 62 000 counts I performed the same analyses using 4 other filters and they all gave the same result The only problem encountered with flats having Cx gt 55 kct was the appearance of hot pixels at three locations with cold
102. ce with the following empirical equation FWHM arc 2 5 x AirMass This is a useful equation for estimating how sharp an image will be later in an observing session Suppose the test images at the start of a session show FWHM 4 0 arc when the air mass is 3 elevation 20 degrees If atmospheric seeing conditions don t change for the duration of the observing session and if the region of interest will pass overhead we should expect that near zenith FWHM 2 8 arc We can make use of the fact that a star s Cmax increase as 1 FWHM for as long as its flux is constant When FWHM changes from 4 0 to 2 8 arc we can expect Cmax to increase by the factor 2 1 Another way of calculating Cmax is to note that Cmax is proportional to l AirMass In our example AirMass goes from 3 to 1 so Cmax will increase by a factor 3 ie 2 1 This means that we want our test images to show the brightest star s Cmax 16 700 35 000 2 1 A more useful version of the previous equation is therefore Cmax at AirMass Cmax at AirMassg AirMass AirMasso oe This equation assumes star flux doesn t change with air mass Therefore we must account for changing flux with air mass caused by atmospheric extinction The biggest effect will be for the B band filter Using our example of the test images being made at AirMass 3 what can we expect for Cmax when AirMass 1 For my observing site at 4660 feet above sea level the B band zeni
103. chapters dealt with systematic uncertainties and tried to identify which ones were most important This chapter deals with sources of stochastic uncertainty in an effort to identify which ones are most important Both sources of uncertainty are important aspects of any measurement and I m a proponent of the following A measurement is not a measurement until it has been assigned stochastic and systematic uncertainties This may be an extreme position but it highlights the importance of understanding both categories of uncertainty that are associated with EVERY measurement in every field of science This chapter therefore strives to give balance to the book by describing the other half of uncertainties in photometry The components of stochastic noise will be treated using the XO 3 star field as an example with specific reference to my 2007 04 15 observations of it 87 CHAPTER 15 STOCHASTIC ERROR BUDGET Poisson Noise A Poisson distribution describes what can be expected when a finite number of random events produce a measured count an integer during a pre set time interval This is the situation for readings of each CCD pixel at the end of an exposure Consider the process of a photon dislodging an electron from a silicon crystal in the CCD related to the photoelectric effect This one event yields one electron for detection after the exposure is complete When a pixel is read by electronic circuitry this one electr
104. common to both there is a correlation between the amount of twinkling and scintillation Incidentally since atmospheric seeing is degraded mostly by turbulence near the ground visually perceived twinkling and seeing are partially correlated whereas scintillation and seeing are less correlated Everyone knows that stars twinkle different amounts on different nights Twinkling also 1s greater near the horizon Faint stars twinkle as much as bright stars Planets don t twinkle What s going on These common facts are helpful in understanding what to expect for attempts to monitor the brightness of a star that is undergoing an exoplanet transit For example the fact that planets don t twinkle means that a reference star s scintillation another word for twinkling will be uncorrelated with the target star s scintillation since the angular separation of reference and target stars is greater than the angular size of a planet and planets don t twinkle This is unfortunate for it means that a differential photometry analysis that uses one reference star will increase the target star s brightness variations due to scintillation by 41 i e the fluctuations are root 2 times the value without using a reference star Using many reference stars reduces the effect of uncorrelated reference star scintillation back to where it is dominated by just the target star s scintillation It also can be stated that there s no need to choose reference stars that
105. concepts are understood to convert the basic properties of a LC and star color to a 116 APPENDIX D PLANET SIZE MODEL solution for secondary size and likelihood of the transit belonging to an exoplanet versus an EB Section 4 describes an Excel spreadsheet that can be downloaded and run to do just about everything described on this appendix The user enters transit depth transit length period and star color B V in cells corresponding to the LC s filter band and a cell displays a 3 iteration solution for Rp Rj if a solution exists It also can be used to assess the likelihood of the LC shape belonging to the exoplanet domain based on the user s input of a shape parameter S 1 CONCEPTS OF LC INTERPRETATION A CASE STUDY I like explaining things through the use of a specific example The reader s job is to generalize from the specific I m going to treat real observations of a mystery star s transit light curve this way we can grade the results of my crude analysis procedure using a rigorous treatment by professionals Let s assume the following GIVEN B V 0 66 0 05 which can be derived from J K orbital period P 3 9415 days R band observations transit depth D 23 7 0 4 mmag transit length L 2 97 0 03 hours contact 1 to 4 The D and L values were derived from the transit light curve in Fig D 01 measured with an amateur 14 inch telescope pretend you don t know which star this 1s A
106. d ensemble photometry When the reference star is an artificial star it is a special case of differential photometry without a name as far as I know The term comparison star s is sometimes confused with reference star s this is a term left over from the days when visual observers of variable stars used stars of similar magnitude to compare with the target star residual image When photoelectrons remain in the silicon CCD elements after a read out they may be included in the next exposure s read out and can produce a faint residual ghost image from the earlier image This is more likely to occur after a long exposure when bright stars are present that saturate some CCD elements causing photoelectrons to become more firmly attached to silicon impurities than other electrons The problem is most noticeable when the following image is a dark frame the problem is worse when the CCD is very cold saturation Saturation can refer to a pixel s output exceeding it s linear full well capacity with an associated loss of proportionality between incident flux and CCD counts The ADU counts where this proportionality is lost is the linearity limit typically 40 000 to 60 000 counts Saturation can also refer to the accumulation of so many photoelectrons that the analog to digital converter A D converter exceeds its capacity for representing an output value For a 16 bit A D converter this version of saturation produces an ADU coun
107. de for an entire observing session One is to use the autoguider chip to nudge the telescope drive motors This can be done whether the autoguider chip is in the same CCD camera as the main chip or on a separate CCD camera attached to a piggy back guide telescope The main drawback for this method is that the telescope drive motors have hysteresis especially the declination drive and this produces uneven autoguiding This method at least keeps the star field approximately fixed with respect to the pixel field assuming a good polar alignment but it won t sharpen images Image Stabilizer The second method for autoguiding is to use a tip tilt mirror image stabilizer I have an SBIG AO 7 tip tilt image stabilizer For large CCD format cameras SBIG sells an AO L image stabilizer As far as I know SBIG is the only company selling an image stabilizer that s priced for amateurs The AO 7 allows me to use the autoguider image to adjust a tip tilt mirror at the rate of up to 10 Hz depending on how bright a star I have in the autoguider s FOV When the required mirror movement exceeds a user specified threshold such as 4096 of the range of mirror motion the telescope is nudged in the appropriate direction for a user specified preset time such as 0 1 second I use MaxIm DL for both telescope control and CCD control and I assume other control programs have the same capability In the planning chapter I described choosing a sky coordinate location for
108. e precision The internal consistency among measurements in an observing session All such measurements may share systematic errors which are unimportant for the task of detecting transit features Precision is affected almost entirely by stochastic processes Accuracy is different from precision accuracy is the orthogonal sum of precision and estimated systematic errors Rayleigh scattering Atmospheric molecular interactions with light waves that bend the path of the wave front and therefore change the direction of travel of the associated photon This is what makes the sky blue c f Mie scattering read noise The RMS noise produced by the process of reading a pixel s accumulation of photoelectrons at completion of an exposure Read noise counts RMS sqrt 2 where RMS is the counts standard deviation for an image produced by subtracting two bias frames Read noise for modern CCDs is so small that it can usually be neglected when assessing error budgets c f Appendix F reference star A star in the same image as the target star and check stars whose flux is used to form ratios with the target and check stars for determining magnitude differences The purpose can be detection of image to image changes or simply an average difference between a calibrated star and an uncalibrated or variable star This is called differential photometry when the reference star is another star When several reference stars are used it 1s calle
109. e T shirts diffuse sky light and by using it I never see star trails in my flats Since the T shirts let only a fraction of the incident light enter the telescope the sky flat exposures have to begin sooner than if the T shirt diffuser were not used Use of the double T shirt diffuser affords the unexpected bonus of allowing for a more relaxed flat frame observing session This is due to the fact that the diffuser s reduction of light entering the telescope requires that flat field exposures begin sooner when sky brightness changes more slowly Figure 5 01 Double T shirt diffuser is being placed on top of the telescope aperture for obtaining flat fields The Davis Weather Station is in the background As mentioned in the previous chapter the time to start exposing flat fields depends on the filter and binning choice A photometric B band filter passes much less light than any of the other filters so it requires longer exposures for the same sky brightness A common practice is to keep exposure times within the 1 to 10 second range explained below If flat fields are needed for all filters the sequence for exposing flats should start with B band and be followed by V band I band R band BB band and finally clear 36 CHAPTER 5 FLAT FIELDS Exposure times shorter than 1 second can produce slightly unequal actual exposure times at different locations on the CCD For example consider a shutter that opens and closes like the old style
110. e are a better approximation than air mass tables since the scale height for dust and water vapor is much smaller in relation to the Earth s radius than the scale height for dry air all sky photometry Use of a telescope system for transferring standard star magnitudes such as Landolt stars to stars in another region of the sky with allowance for differences in atmospheric extinction c f photometry ADU Analog to digital unit also called a data number and count is a number read from each pixel of a CCD camera using an analog to digital converter that is proportional to the number of electrons freed by photons photoelectrons at that pixel location The ADU count is the number of photoelectrons divided by a constant of the CCD called gain which is inversely proportional to an amplifier s gain artificial star Replacement of a pixel box upper left corner with values that appear to be a star that has a specific peak count 65 535 and Gaussian FWHM such as 4 77 pixels The artificial star can be used with a set of images to monitor changes in cloud losses dew accumulation losses as well as unwanted photometry losses produced by image quality degradation aspect ratio Ratio of a PSF s widest dimension to its narrowest usually expressed as a percentage Anything below 10 is good i e close to circular atmospheric seeing Apparent width FWHM of a star recorded on a CCD exposure using a telescope with good op
111. e changing elevation angle also requires inward focus adjustments Thus after transit I can count on all adjustments to be in the same 53 CHAPTER 8 FOCUS DRIFT direction inward unless I ve over corrected and have to back up Observations before transit may require focus adjustments in either direction depending on the relative importance of elevation changes versus temperature changes Usually elevation changes dominate and this requires outward focus adjustments Because I can anticipate the direction of focus adjustments during an observing session based on whether the object will be rising or setting I begin an observing session with a focus setting that was achieved going in the same direction as I anticipate will be required by subsequent adjustments This precaution assures that I am unlikely to encounter a large hysteresis adjustment until transit The problems associated with having to adjust focus using the mirror instead of a microfocuser that moves the CCD assembly are so troublesome that I question the wisdom of removing the microfocuser The principal reason that prompted me to do this was the need for providing sufficient clearance of the optical backend in relation to the mounting base that I could point to the north celestial pole in order to calibrate pointing The LX200GPS loses pointing calibration so often that this became an over riding consideration Perhaps Meade will some day improve the
112. e of a background of faint stars or radio sources that alter the measured brightness of an object The only way to reduce confusion is to improve spatial resolution Wide field exoplanet survey cameras have a high level of confusion leading to the need for amateurs to detect EB blending situations CSV file Comma separated variable file in ASCII text format 151 GLOSSARY dark frame CCD exposure taken with the shutter closed A master dark frame is a median combine of several dark frames made with the same exposure and same temperature Master darks taken at different temperatures and exposure times can be used for pretty picture and variable star work differential photometry Comparison of flux of a target star to the flux of another star called reference star expressed as a magnitude Ensemble differential photometry is when more than one reference star is used either averaged or median combined or flux summed dust donut Shadow pattern of a speck of dust on either the CCD chip s cover plate small dust donuts or a filter surface larger annular shadows Flat frames correct for the loss of sensitivity at dust donut locations at fixed locations on the CCD pixel field eclipsing binary EB EB blend EB means eclipsing binary EB blend is when an EB is close to a brighter star that is mistaken by a wide field survey camera for undergoing a possible exoplanet transit because the fade amount is a much smaller fractio
113. e suggestion that the flat field error map has a 17 mmag RMS variation can be used to infer the magnitude of systematic light curve variations 1f the image rotation and movement across the pixel field was comparable to the spacing of stars used to derive the 17 mmag value The average spacing between stars is 5 arc Typical image movements during a light curve observing session are much less than this We do not have information about the spatial auto correlation distances for these flat field errors so it is not possible to predict the magnitude of systematic light curve errors for typical movements A proper analysis would correlate magnitude differences with star separation distance and I have not done this It could be argued that the spatial structure of the flat field response distribution can be used as a guide in estimating the spatial structure of the flat field error map If this is justified then visual inspection of Fig A 06 suggests that the error map is dominated by spatial structures having wavelengths 5 arc Since typical movements of the star field for my present polar alignment are 1 arc they re on the order of 0 1 arc a bold prediction could be made that I should encounter systematic light curve errors 4 mmag and possible 0 4 mmag The reader is invited to pursue an investigation of their own system s flat field errors using their own observations and guided by the ideas presented in this appendix No doubt
114. e versus Cs flux rate is defined as flux divided by exposure time FLUX RATE vs MMAXIMUM COUNTS 1 03 1 02 1 01 1 00 0 99 0 98 0 97 NORMALIZED FLUX RATE ADU SEC 5 10 15 20 25 30 35 40 45 350 55 60 65 MAXIMUM COUNTS KCT Figure E 05 Flux rate normalized to 1 00 for unsaturated values versus Cx using the brighter star As before flux rate versus Cx suggests that the CCD is linear for Cx lt 59 kct The RMS scatter for most of the unsaturated data is 1 3 Figure E 03 suggests that the faint star is never saturated for the images under consideration Therefore the FWHM ratio for all images should reveal anomalous behavior for just the bright star Figure E 06 is a plot of FWHM for the bright star divided by FWHM for the faint star When the bright star saturates its FWHM increases This is what would be expected if the Gaussian shaped point spread function becomes flat topped when saturation occurs Another way of showing this is to plot FWHM for the bright star versus FWHM for the faint star which is shown as Fig E 07 When both stars are unsaturated the two FWHM values are within the box area Within this box both FWHM variations are correlated suggesting that either seeing or autoguiding varied and affected both stars in a similar way 143 APPENDIX E CCD LINEARITY FWHM RATIO vs MMAXIMUM COUNTS FWHM RATIO 5 10 15 20 25 30 35 40 45 50 55 60
115. ePro at 3 hour intervals Above Monitor 1 is a flat bed scanner with a small blanket This is where the cat sleeps and occasionally wakes stretches and reminds me about observing strategies 16 CHAPTER 2 OBSERVATORY TOUR On the desk behind my chair is another monitor for display of a wireless video sensor in the observatory It shows a view of the telescope when a light is turned on by a switch right side of desk It also has an audio signal that allows me to hear the telescope drive motors the sound of the wind as well as barking coyotes My two dogs observe with me on the floor and they get excited whenever coyote sounds come over the speaker Below the wireless video display monitor is something found in practically every observatory a hi fi for observing music Since my area is remote with no FM radio signals I have a satellite radio Sirius receiver with an antenna on the roof and channel selector next to the wireless monitor MONITOR Wi SATELLITE IR LOOP WIRELESS FOCUSER MONITOR 2 MONITOR WEATHER GRAPHS WEATHER MP REAL TIME Figure 2 04 Another view of control room Sometimes I have to take flat frames while a favorite program is on TV e g 60 Minutes seems to be the usual one so I have a second TV on a desk to my left Fig 2 04 The remote control for it sits on a headphone switch box next to the phone It displays a satellite TV signal that comes from a receiver in t
116. eeded to protect it from wind vibrations This will add another 15k for an automated dome A large format CCD would cost 10k SBIG s AO L tip tilt image stabilizer costs 2k Buried cables for controlling the telescope CCD and dome plus a computer system with control software would cost 3k The total cost for this system is 80k Other options are possible A ScopeCraft 24 inch f 3 1 open tube telescope with a roller driven horseshoe mount would cost 45k A dome would not be needed for such a telescope but a sliding roof observatory would be costing 10k The same CCD camera and other items would be needed so the total cost would be about the same or 70k Most hot Jupiter exoplanet transits last 3 hours Because of the need for verifying that reference star color is not affecting the transit shape depth and mid transit timing in a manner that is correlated with air mass it is important to start observations at least 1 5 hours before ingress and continue until at least 1 5 hours after egress Thus 6 hour observing sessions are common and 8 hour sessions are even better Observations for more than one observing site are sometimes needed provided the sites span a sufficient longitude When observations from two or more observatories are to be combined to produce one light curve it is helpful that they be identical systems Systematic effects can be minimized when using the same image scale same blending of interfering stars s
117. een a wavelength band and a longer one such as B V V R or J K They are correlated with each other for most stars stochastic error Uncertainty due to the measurement of something that is the result of physical events that are too numerous and impractical to calculate thermal noise or beyond present knowledge too understand because the physics of it hasn t been discovered radioactive emissions which nevertheless obey mathematical laws describing the distribution of events per unit time These mathematical laws allow for the calculation of noise levels or uncertainty for a specific measurement c f Poisson noise Stochastic errors are different from systematic errors in that stochastic SE can be reduced by taking more measurements with the expectation that after N measurements SE SEi sqrt N where SEi is the SE of an individual measurement Systematic errors are unaffected by more measurements stray light Light that does not follow the designed desired optical path as happens with reflection of light from nearby bright stars or moonlight off internal structures which is registered by the CCD Light that leaks through a housing joint CCD or CFW or AO 7 etc and is reflected onto the CCD is stray light sub frame Rectangular area of CCD specified by the user that is downloaded when fast downloads of a smaller FOV are desired 157 GLOSSARY TheSky Six A good sky map program also referred to as a planetarium prog
118. ely produced by image rotation imperfect polar alignment that causes stars to move across pixel space during the entire observing session If the master flat frame was perfect there shouldn t be such a term but no flat field is perfect 73 CHAPTER 13 SPREADSHEET PROCESSING The air mass term is a coefficient times air mass minus one For this case I chose an air mass coefficient of 3 mmag airmass This term is required when stars are used for reference that are not exactly the same color as the object as explained in the next chapter The trend and air mass terms are adjusted using the out of transit OOT portions of the light curve For this light curve the time spent by the secondary body to complete an ingress contact 1 to contact 2 also the same as the time to complete an egress contact 3 to contact 4 is 1796 of the time spent for the center of the secondary body to traverse the chord for its path across the primary star Thus the secondary has a radius that is 17 the radius of the star That s interesting If the secondary is an exoplanet and has a radius 0 17 times the star s radius it should block 2 9 of the star s light producing a 29 mmag deep transit Yet we see only 16 mmag This must mean that another star is within the signal aperture adding almost as much R band light as the star undergoing transit Appendix D has a more extensive discussion of ways to interpret light curves The next chapter treats
119. ematics is the equivalent zenith extinction coefficient for the two stars For the cool one it s 0 228 mag airmass whereas for the hot star it s 0 244 mag airmass I use the term airmass AirMass and air mass interchangeably In other words a cool star s brightness will vary less with airmass than a hot star the difference being 0 016 mag airmass Effect on Light Curves of Reference Star Color Consider an observing session with a B band filter that undergoes a range of airmass values from 1 0 to 3 0 Consider further that within the FOV are two stars that are bright but not saturated one is a cool star and the other is hot The magnitude difference between the two stars will change during the course of the observing session by an impressive 32 mmag This is shown in the next figure 79 CHAPTER 14 STAR COLORS EXTINCTION vs STAR COLOR 12 5 T i TARGET STAR s BLUE REF e RED REF 12 7 12 9 BLUE FILTER MAGNITUDE 13 1 ALL STARS HAVE SAME FLUX OUTSIDE ATMOSPHERE 13 2 um T T T T T T T T 1 1 0 1 2 1 4 7 6 1 8 2 0 2 2 2 4 2 6 2 8 3 0 AIR MASS Figure 14 07 Extinction plot for red and blue stars based on model If the target star is cool then the cool reference star should be used If instead the hot star is used for reference there will be a 32 mmag distortion of the LC that is correlated with airmass The shape of the LC will be a downward bulge in the middle at the lowest airmas
120. emory so if you want to use MDL and the following processing procedure you will simply have to determine how to replace my use of 150 images with whatever applies to your computer s capabilities The first step 1s to calibrate the 150 images using the master dark and master flat frames For the rest of this chapter I ll present a detailed version of how to do something using MDL in smaller font So the next paragraph describes in more detail how I prefer to calibrate the images in working memory using MDL Specify the master flat and master dark files in MDL s Set Calibration window Select None for Dark Frame Scaling since the dark frame is at the same temperature and has the same exposure as the light frames to be calibrated Check the Calibrate Dark and Calibrate Flat boxes Don t check bias Exit the calibration set up and calibrate all 150 raw images 10 seconds 64 CHAPTER 12 IMAGE PROCESSING The second step is to star align all 150 images This will consist of x and y offset adjustments as well as image rotations if necessary Invoke MDL s Align command and select Add All images The Align Images window appears select Auto star matching and click OK to align all images The result after 1 5 minutes will be a set of images in working memory that have been shifted in x and y and rotated if necessary to achieve alignment of the star field using the first image in the list as a te
121. ere noisy they were really a detection instead of a measurement Nevertheless it felt good to join a club of about a half dozen amateurs who had detected an exoplanet transit By today s standards my CCD was unimpressive slow downloads not a large format and my telescope was average The only thing advanced was my use of MaxIm DL version 3 0 for image processing Even my spreadsheet was primitive Quattro Pro 4 0 Today there must be 1000 amateurs with better hardware than I had 5 years ago based on membership numbers of the AAVSO American Association for Variable Star Observers I recall thinking If only there was a book on how to observe exoplanet transits There couldn t be such a book of course since the first amateur observation of HD209458 had been made less than 2 years earlier by a group in Finland led by Arto Oksanen http www ursa fi sirius HD209458 HD209458 eng html Besides this was the only known transiting exoplanet at that time Moreover not many amateurs had a 16 inch telescope like the one used by Oksanen s team The idea of amateurs observing an exoplanet transit was a novelty But that was then and this is now I now know what to do to see what a difference that makes look at the next figure 8 CHAPTER 1 COULD I DO THAT NEGATIVE OF Mv 7 73 t 1 1 i T t t t 498 48 498 56 498 64 498 72 498 80 498 88 498 96 498 52 498 60 498 68 498 76 498 84 498 92 JD 2452000 0
122. ess is often loosely defined but in this case it can be thought of as meaning the rate of energy flow through a unit surface normal to the direction to the star caused by a flow of photons incident upon a telescope aperture c f all sky photometry photometry aperture and circles A circular signal aperture within which a star to be measured is placed specified by a radius pixels surrounded by a gap with a specified pixel width surrounded by a sky background annulus An aperture configuration is specified by 3 numbers the 3 radii Some photometry programs do not have a gap capability plate scale Also referred to as image scale is the conversion constant for pixels to arc on the sky PS arc pixel 206 265 x pixel width nm EFL mm point spread function PSF Shape of light intensity versus projected location on sky or location on the CCD chip by a point source star with widths described by FWHM and aspect ratio Poisson noise Subset of stochastic noise pertaining to the case in which a discrete number of random events occur during a specified time originating from a source 155 GLOSSARY that is assumed to be at a constant level of activity during the measurement interval The Poisson process is a mathematical treatment whose most relevant statement for photometry is that when a large number of events are measured n the SE uncertainty on the measured number is sqrt n cf stochastic nois
123. fading of reference stars should be viewed as a red flag for focus drift problems Observing Log Entries I like to record in the observing log FWHM measurements of a chosen star at regular intervals such as every half hour This helps in identifying the need for a focus adjustment it also will show the presence of atmospheric seeing trends Since my focus setting depends on elevation as well as temperature I also record these values Whenever I record a FWHM in the observing log I also record the magnitude that MaxlIm DL displays when the photometry circles are over the star that I ve chosen for that purpose It doesn t matter that the magnitude scale is uncalibrated i e having an offset error because the only thing I m monitoring is constancy of the chosen star s brightness This is a good way to detect the presence of cirrus clouds It also can alert for the presence of dew accumulation on the corrector plate You can t do anything about cirrus clouds but dew accumulation will require use of a hair dryer By choosing a bright unsaturated star for this purpose the magnitudes should be constant at a level of 0 01 mag assuming SNR gt 100 Changes from one image to the next that exceed this usually indicate the presence of clouds Slow changes will of course occur due to changing air mass but these changes are small and easily identified as air mass related For example R band observing will increase the star s magnitude by 0 13
124. flux but they will contribute noise to the flux reading This can be easily seen by changing the signal aperture size and noting the way SNR changes as shown in the next figure FLUX RATIO AND SNR VERSUS APERTURE SIZE 2400 2200 2000 1800 1600 1400 1200 1000 800 600 400 SNR FLUX RATIO SNR 1 RADIUS 200 a FLUX RATIO 1 2 3 4 9 SIGNAL APERTURE RADIUS DIVIDED BY FWHM Figure 10 02 SNR and flux ratio aperture capture fraction versus signal aperture radius normalized to FWHM for the star in the previous figure The purple dotted trace is 1 radius This figure shows a maximum SNR when the aperture radius is about 3 4 of the FWHM This agrees with theoretical calculations for a Gaussian shaped PSF There are good reasons for not choosing a signal aperture radius where SNR is maximum at least for exoplanet light curve work Notice that when the maximum SNR size is chosen the photometry aperture circle captures only 65 of the total flux from the star This is easily understood by considering that as the radius is increased more pixels are used to establish the star s flux but these new pixels are adding parts of the star s PSF that are less bright than the central portion Although the new pixels are adding to the total flux they are also adding to the noise level of the total flux This happens because each pixel s count value is compared with the average count value within the sky backgrou
125. for the flats sum of median counts for the bias frames RMS for flats 2 RMS for bias 2 c f Appendix F information rate Reciprocal of the time it takes to achieve a specified SNR for a specified target star Alternative observing strategies as well as alternative telescope configurations or different telescopes can be judged using information rate as a figure of merit ingress Transit interval when the smaller object appears to move onto the star and only part of the smaller object s projected solid angle is obscuring star light Contact 1 to 2 image rotation Rotation of the star field with respect to the pixel field during a single observing session caused by an error in the mount s polar alignment The center for image rotation will be the star used for autoguiding image stabilizer Mirror assembly that tips and tilts under motor control at a fast rate typically 5 to 10 Hz using an autoguide star It is used to minimize atmospheric seeing movements of a star field When the star field drifts close to the mirror motion limit a command is issued to the telescope mount motors to nudge the star field back to within the mirror s range SBIG makes a good image stabilizer the AO 7 for regular size CCD chips and the AO L for large format CCD chips impact parameter Distance from star center to the transit chord divided by the star s radius An impact parameter of zero is a central transit 153 GLOSSARY JD and
126. fter a transiting candidate has been observed and before radial velocity measurements have been made to assess the mass of the secondary this is all the information we have to work with Using this limited information there are many steps for interpreting the LC to estimate secondary size Rp Rj exoplanet s circular radius divided by Jupiter s equatorial radius 117 APPENDIX D PLANET SIZE MODEL 0 015 0 010 0 005 0 000 0 005 0 010 0 015 0 020 R MAG BRIGHTNESS CHANGE MMAG 0 025 0 030 0 035 1 1 TIME AFTER MID TRANSIT HR Figure D 01 7ransit light curve for a mystery star whose LC we shall try to solve using the procedures described on this web page SOLUTION Star s radius Rstr 0 99 x sun s radius based on equation below Rstr 2 23 2 84 x B V 1 644 x B V 0 285 B V Planet radius Rp Rj 1 41 1st iteration Rp Rj 9 73 x Rs x SQRT 1 10 1 D 2500 which assumes central transit and no limb darkening At this point we have an approximate planet size It s a first iteration since limb darkening has been neglected The next group of operations is a 2nd iteration Star s mass Mstr 0 97 times sun s mass Mstr 2 57 3 782 x B V 2 356 x B V 0 461 x B V Planet orbital radius a 7 22e6 km a 1 496e8 Mstr 1 3 x P 365 25 where dimensions are P days Mstr solar mass amp a km Transit length maximum Lx 3 28 hr corresponds to ce
127. gures in this book that were presented on my behalf at their 2007 annual meeting and published in the meeting proceedings Thanks are also due Cindy Foote for allowing me to reproduce her amazing light curves of an exoplanet candidate made with 3 filters on the same night Almost all figures are repeated in the color center insert INTRODUCTION This book is intended for use by amateur astronomers not professional astronomers The distinction is not related to the fact that professional astronomers understand everything in this book it s related to the fact that the professionals don t need to know most of what s in this book Professionals don t need to know how to deal with telescopes with an imperfect polar alignment because their telescopes are essentially perfectly aligned They don t have to deal with telescopes that don t track perfectly because their tracking gears are close to perfect They don t have to worry about focus changing during an observing session because their tubes are made of low thermal expansion materials They don t have to worry about CCDs with significant dark current thermal noise because their CCDs are cooled with liquid nitrogen Professionals don t have to worry about scintillation noise because it s much smaller with large apertures Professionals can usually count on sharp images the entire night with insignificant changes in atmospheric seeing because their observatories are at high
128. h Edition 2000 STAR RADIUS vs B V STAR RADIUS Figure D 02 Converting star color B V to stellar radius assuming main sequence STAR MASS vs B V 1 80 1 70 1 60 1 50 1 40 1 30 1 20 1 10 1 00 0 90 0 80 0 70 0 60 STAR MASS 0 50 Figure D 03 Converting star color B V to stellar mass assuming main sequence 120 APPENDIX D PLANET SIZE MODEL LIMB DARKENING EFFECT 14 1 3 1 2 1 1 1 0 0 9 0 8 0 7 0 6 INTENSITY W R T DISK AVERAGE 0 5 0 4 0 3 0 2 T T T T T T Ep T T 00 01 02 03 04 05 06 07 08 09 1 0 MISS DISTANCE FRACTION Figure D 04 Converting miss distance and filter band to intensity at that location normalized by disk average intensity assuming a sun like star The following two figures show how transit shape and depths could behave when the miss distance changes from near center to near edge These are real measurements graciously provided by Cindy Foote that were categorized as EB based on the depth values The concept is the same whether it s an exoplanet or small EB because in both cases a central transit should produce a greater loss of light in B band than R band and for a near edge transit the reverse is true 121 APPENDIX D PLANET SIZE MODEL mag 0 7 0 8 i 2454163 0 JD 0 6182 0 2578 Figure D 05 Transit depth is greatest for B band consistent with miss distance lt 0 73 courtesy of Cindy Foote
129. h as those exceeding 3 but the approach cannot be used to identify errors of much lower amounts In this section we will pursue the less ambitious goal of answering the question What are typical error differences in the flat field for randomly chosen pairs of pixel location areas This question is relevant to the task of producing exoplanet light curves with a minimum of systematic shape errors After all if it can be shown that a pair of stars maintain the same flux ratio for many pixel offset settings then it is fair to assume that image rotation movements of a target star and its ensemble of reference stars will maintain a similar stability of flux ratios To perform this test we don t need Landolt star fields we only need stars that do not vary on hourly time scales The previous section dealt with a set of observations of a star field with a variety of position offsets and since these images have already been processed I will use them in this section to evaluate the new less ambitious question We must keep in mind that every star s flux measurement is noisy due to Poisson noise scintillation noise and aperture pixel noise These sources of noisiness could mask real changes in flux ratios produced by flat field errors Let s calculate noise levels from these sources before proceeding with a calculation of observed flux ratio changes The images were made with 10 second exposures at air mass 1 25 so scintillation is estimated to
130. h image because that would be very inefficient Let s approach this by adopting 60 seconds as a default exposure time and then ask what are the merits of either increasing or decreasing exposure time A typical transit will last 3 hours and the ingress and egress portions of this will be 20 minutes Referring to the figure on the cover ingress is from contact 1 to contact 2 and egress is from 3 to 4 For such a transit it is desirable to obtain information about the shape of ingress and egress in order to constrain model fitting the size of the exoplanet in relation to the star and also the star center miss distance Therefore exposure times should be less than about 4 minutes on account of this consideration Another reason to have ingress and egress shapes well established is to be able to assign an accurate mid transit time A transit timing archive can be used to establish the presence of timing anomalies and these can be used to infer the existence of another exoplanet in the same star system I think 4 minutes is the longest exposure time that should be considered for any exoplanet transit observing situation What about shorter exposure times We now must consider a concept called information rate Information rate can be described as inversely proportional to the observing time required to achieve a specified SNR for a specific star using a specified filter Long image download times reduce information rate My CCD requires
131. he columns and graph are explained in the text Column B is UT based on the first page s JD Column C is total flux based on the first page s check star magnitudes converted to flux and added together Column D is a magnitude corresponding to total flux Column E is air mass copied from the previous page The graph plots columns D versus E The fitted slope is based on user entered values for zenith extinction 0 168 in this example and zero air mass intercept 8 889 Column F is unaccounted for extra opacity based on the difference between total magnitude and the extinction model the next figure shows the right side of this page which includes a plot of opacity versus time Columns G through L are extinction corrected magnitudes for the exoplanet and check stars Figure 13 05 next page shows the right side of this spreadsheet page The graph is for extra opacity unaccounted for by the simple extinction model versus UT and air mass versus UT Columns AC through AG are image magnitude corrections based 69 CHAPTER 13 SPREADSHEET PROCESSING on each star s measured magnitude versus its extinction corrected magnitude If there were no clouds or dew losses or bad seeing losses either atmospheric or related to the wind shaking the telescope these columns would be zero plus stochastic noise Column AV is a median combine of columns AC through AG the check stars The user is free to choose from any of the check st
132. he living room At the left end of the table in Fig 2 04 is a secondary computer used to display IR satellite image loops that show when clouds are present It also offloads computing tasks from the main computer such as e mail notices of GRB detections to minimize the main computer s competition for resources This assures that the AO 7 tip tilt image stabilizer is running as fast as possible The secondary computer has a LAN connection with the primary computer which allows downloading images from the 17 CHAPTER 2 OBSERVATORY TOUR main computer for off line image analysis without interfering with the main computer s resources On top of the main computer below table to left is an AB switch for sending the main monitor s video signal to another monitor in my living room This allows me to keep track of tracking from my living room chair while reading or watching TV The remote monitor in the living room is on a swivel that allows me to keep track of it from my outdoor patio chair Comfort is important when a lot of hours are spent with this all consuming hobby Charts are taped to every useful area On one printer is a graph for converting J K to B V star colors On the side of the main monitor is a list of currently interesting exoplanet candidates with current information from other XO Project observers Charts are readily visible for estimating limiting magnitude simplified magnitude equation constants and a quick way to
133. heck to see if a drifting star field is producing systematic brightness changes due to flat field errors thanks Peter McCullough for showing me this PI illustrate it with an unfiltered 6 hour observation session of the previous figure s star field The stars in this image were observed to rotate clockwise about the autoguider location in the sky which was 16 5 arc to the south of the main chip s FOV center Stars in the center moved 6 pixels during the 6 hour observing session and those near the upper edge moved 9 pixels If the flat field did a perfect job of correcting all star fluxes to what they would be if they were near the center of the image then this motion would be unimportant A star near the edge requires a larger flat field correction than a star near the center and any imperfections in the flat field are likely to affect edge stars more To see if stars have been correctly flat field corrected we can take advantage of the fact that when a star field drifts any incorrect flat field corrections are likely to differ for stars at different locations Consider Stars 5 and 6 in Fig A 03 Their measured magnitudes during the entire observing session are plotted in the next figure Notice how well behaved they are in the sense that they did not change brightness with respect to each other This result is unsurprising since the two stars are close together and have similar colors It shows what can be expected if flat field e
134. his may be too risky Consider the implications of one part of an image having a PSF for which this aperture captures 9596 of the total flux versus 96 at the center This 1 difference corresponds to 10 mmag and if our goal is to eliminate systematic errors above the 2 mmag level for example then we cannot tolerate 196 changes in the aperture capture fraction for the target star or any of the reference stars during the entirety of the observing session By choosing a radius that is 3 times FWHM 99 of the total flux is captured I feel comfortable with this choice but there s no clear way of arguing for a best aperture size since each observing session is different and one might be absolutely OK using a small aperture while another would be riddled with intolerable systematic errors My subjective solution to this problem of not knowing how small a signal aperture is acceptable is to process the images using 2 or 3 aperture sizes As Chapter 12 describes MDL can easily produce ASCII files of flux measurements with different aperture sizes so this is one option to consider especially in those cases where image sharpness varies greatly from image to image or from image center to the edges There s more to choosing photometry apertures than the concern about aperture capture fraction The same image in Fig 10 01 has a bright star not shown in this figure that would be useful to use as a reference star but a fainter star is located 9 arc
135. ht variations can differ by similar amounts depending on the location of jet stream winds It s possible to evaluate the presence of seeing noise by reprocessing images using a large photometry aperture For example when the 2007 04 15 images are processed using an aperture radius of 20 pixels instead of 15 the measured RMS scatter increases to 2 76 mmag Some increase can be expected from a larger aperture pixel noise the predicted total noise changes from 2 65 to 2 67 mmag but the fact that the measured noise increased more than the predicted amount instead of decreasing suggests that seeing noise was not important for this observing session I use a special spreadsheet to help guide the choice of reference stars It allows me to see the predicted effect of adopting various sets of reference stars and aperture sizes For example notice in Fig 15 01 that Star 4 is much brighter than the other stars that I adopted for use as reference If it replaced Star 1 the RMS scatter is predicted to be reduced to 2 50 mmag This is a small payoff considering the extreme redness of Star 4 which can be verified in the photometry analysis spreadsheet by actually trying out the use of Star 4 instead of Star 1 for reference It should be noted here that the case of 2007 04 15 based on use of an I band filter is not meant to show a representative RMS scatter for light curves Lower scatter can be achieved by observing with an R band filter 1
136. htward to be EBs Similarly for any other B V a vertical line can be placed upon this figure to show the domains where exoplanets and EBs are to be found as Fig s D 13a b illustrate Since XO 1 has B V 0 66 0 05 we can use the left panel to determine that it must be an exoplanet This determination is based on the shape parameter S and the miss distance that was determined from Section 1 plus the B V color for XO 1 Even if we hadn t performed a solution for miss distance we could say that s it was likely that the B V and S information was in the exoplanet domain If S were slightly smaller say 0 27 then there would be no dispute about the light curve belonging to an exoplanet Well all this is subject to my model assumptions such as the main sequence one 128 APPENDIX D PLANET SIZE MODEL TRANSIT SHAPE PARAMETER VERSUS PLANET SIZE SHAPE PARAMETER S 0 00 0 05 0 10 0 15 0 20 0 25 0 30 Rp Rstar TRANSIT SHAPE PARAMETER VERSUS PLANET SIZE SHAPE PARAMETER S B V 1 20 0 00 0 05 0 10 0 15 0 20 0 25 0 30 Rp Rstar Figure D 13a b Domains for distinguishing exoplanets from EBs based on B V shape parameter S and miss distance b for two examples of B V The blue circle in the left panel is located at the measured shape and center miss distance for XO 1 129 APPENDIX D PLANET SIZE MODEL There s another graph that can be used for the same purpose as the previous ones and I think it
137. ibration But variable star observing requires familiarity with photometry and that s where previous experience is most helpful One kind of photometry of variable stars consists of taking an image of stars that are known to vary on month or longer time scales and submitting measurements of their magnitude to an archive such as the one maintained by the AAVSO Another kind of variable star observing which requires more skill is monitoring variations of a star that changes brightness on time scales of a few minutes For example cataclysmic variables are binaries in which one member has an accretion disk formed by infalling gas from its companion The stellar gas does not flow continuously from one star to the other but episodes of activity may occur once a decade approximately An active period for gas exchange may last a week or two during which time the star is 100 times brighter than normal The cataclysmic variable rotates with a period of about 90 minutes so during a week or more of heightened activity the bright spot on the accretion disk receiving gas from its companion will rotate in and out of view causing brightness to undergo large superhump variations every rotation 90 minutes The amplitude of these 90 minute variations is of order 0 2 magnitude Structure is present that requires a temporal resolution of a couple minutes 11 CHAPTER 1 COULD I DO THAT Any amateur who has observed cataclysmic variable su
138. ic There was a pecking order in astronomy at that time which may still exist to some extent in which the farther out your field of study the higher your status Thus cosmologists garnered the highest regard and those who studied objects in our solar system were viewed with the least regard My studies were of the moon but I didn t care where I was in this hierarchy At that time there was only one level lower than mine those who speculated about other worlds and the possibilities for intelligent life on them How things change We now know that planets are everywhere in the galaxy Billions upon billions of planets must exist This is the message from the tally of 248 extra solar planetary systems as of mid 2007 Among them are 22 exoplanets that transit in front of their star 15 that are brighter than 13 magnitude and the number is growing so fast that by the time this book appears the number could be two or three dozen It is important to realize that bright transiting exoplanets are far more valuable than faint or non transiting ones The bright transits allow for an accurate measure of the planet s size and therefore density and spectroscopic investigations of atmospheric composition are also possible successful in two cases Even studies of the exoplanet s atmospheric temperature are open for investigation When 2007 began only 9 bright transiting exoplanets were known Six months later there were 14 Few people realize that
139. ic noise and systematic errors during data analysis This book was written for the amateur who may not have the background and observing experience that I brought to the hobby 8 years ago How can a reader know if they re ready for this book Here s a short litmus test question do you know the INTRODUCTION meaning of differential photometry If so and if you ve done it then you re ready for this book Lessons Learned One of the benefits of experience is that there will be many mistakes and lessons learned and these can lead to a philosophy for the way of doing things One of my favorite philosophies iss KNOW THY HARDWARE It takes time to learn the idiosyncrasies of an observing system and no observing system works like it might be described in a text book There usually are a myriad of little things that can ruin the best planned observing session Only through experience with one particular observing system can these pitfalls be avoided I therefore encourage the serious observer to plan on a long period of floundering before serious observing is begun For example during the floundering phase try different configurations prime focus Cassegrain use of a focal reducer placement of focal reducer use of an image stabilizer etc During this learning phase try different ways of dealing with finding focus tracking focus drift auto guiding pointing calibration etc Keep a good observing log for checking back to see what wo
140. ically impossible unless it is for an extremely narrow filter Instead of trying to achieve the perfect flat field it might be better to spend more effort learning to live with imperfect ones Consider flats taken near zenith after the sun has set Since the sky is blue the flats we re getting this way are meant for use with blue stars Moreover since the sky becomes slightly bluer as the sun sinks below the horizon flats taken shortly after sunset will differ from flats taken late after sunset In essence the early and late flats are meant for stars of different blueness Red stars deserve flats taken with a red sky but this is not easily achieved Using a red filter with a blue sky just means the effective wavelength is weighted to the blue side of the filter s bandpass In theory we should use a different flat for each star depending on its color This of course is not practical even if we knew the color of all the stars in the image The narrower the filter the less these troublesome effects will be Unfiltered flats correcting unfiltered images of a star field can therefore be expected to exhibit the worst systematic errors An upper limit for the size of these subtle effects can be estimated from all sky measurements of Landolt star fields using all sky photometry procedures When I evaluate telescope constants for all sky equations for a specific telescope configuration I always have larger residuals for converting unfiltered star fluxes to
141. ied by the inflection where the slope changes from steep to shallow A shape parameter is defined as the ratio of time the secondary is partially covering the star to the entire length of the transit e g contact 1 to contact 2 divided by contact 1 to mid transit For example in the above figure consider the trace for Rp Rstr 0 12 contact 1 and 2 occur at 0 55 and 0 44 and contact 1 to mid transit is 0 55 For this transit the shape parameter is S 0 55 0 44 0 55 0 20 Let s estimate the shape parameter for a real transit In Fig D 08 my readings of contact 1 and 2 are 1 48 and 1 05 hour The shape parameter 1s therefore 0 29 0 43 1 48 Assigning SE uncertainties and propagating them yields S 0 29 0 01 Figure D 09 shows how the shape parameter varies with secondary size for central transits 124 APPENDIX D PLANET SIZE MODEL 0 015 0 010 0 005 0 005 0 010 0 015 0 020 R MAG BRIGHTNESS CHANGE MMAG e 0 025 0 030 0 035 3 2 1 0 1 2 3 TIME AFTER MID TRANSIT HR Figure D 08 Measured light curve with the contact times indicated TRANSIT SHAPE PARAMETER VERSUS PLANET SIZE aa 0 4 0 3 0 2 SHAPE PARAMETER S 0 1 0 00 0 05 0 10 0 15 0 20 0 25 0 30 Rp Rstar Figure D 09 Shape parameter S versus planet size for central transits 125 APPENDIX D PLANET SIZE MODEL We next consider how the LC shapes vary with miss distance
142. iew some stellar blackbody spectrum theory Blackbody Spectrae and Filter Band Passes Hot stars shine mostly in the blue whereas cools stars shine mostly in the red as the following graph shows BLACKBODY SHAPES 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 FLUX proportional to watts per m 2 per nm 200 300 400 500 600 700 800 900 1000 1100 WAVELENGTH nm Figure 14 05 Blackbody spectral shape versus temperature 4500 K to 8000 K T 4500 K corresponds to spectral class K3 and 8000 K corresponds to A2 Notice that not only do hot stars radiate more photons at every wavelength region but the difference is greatest at short wavelengths 78 CHAPTER 14 STAR COLORS HOT amp COLD STAR SPECTRAE AND B FILTER RESPONSE 50 T 4500 K 48 46 T 8000 K 44 B FILTER 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 FLUX proportional to watts per m 2 per nm on A O 200 300 400 500 600 700 800 900 1000 1100 WAVELENGTH nm Figure 14 06 B filter response and spectral shapes of hot and cold stars Notice in Fig 14 06 that within the B band response a cool star radiates less and less going to shorter wavelengths whereas it is the reverse for the hot star The effective wavelength for a cool star is 467 nm whereas for a hot star it is 445 nm The more interesting parameter for light curve syst
143. imply too imprecise for evaluating typical flat fields There is little prospect that better quality all sky photometry can be counted on for improving the value of its use for evaluating flat fields After all an RMS scatter in the range 0 017 to 0 024 magnitude is pretty good for all sky photometry 2007 06 04 V Mag Residuals V Mag Residuals wrt Fit ce 5 e e c 111539 36 4211539 37 311539 38 x 411539 40 511539 41 6L1539 42 711539 43 8L1539 44 9 L1539 45 10 L15359 46 0 10 7 8 g 10 11 12 13 14 V mag Figure A 08 V magnitude residuals with respect to model fit using the two parameter values 19 670 and 0 055 plotted versus star magnitude This method for evaluating a flat field will only be useful for ruling out the presence of large errors These large errors are more likely to be present when the flat field has a large amount of vignetting or when there is reason to suspect the presence of a large stray light component in the flat field Only when flat field errors of 3 or larger are thought to be present or need to be ruled out will this method for evaluating a flat field be useful 109 APPENDIX A EVALUATING FLAT FIELDS Star Ratio Changes with Star Field Offsets The previous section shows I hope that attempting to establish a flat field shape using accurate magnitude information of Landolt stars is a too ambitious goal It may be useful for identifying gross errors suc
144. in this appendix The user simply enters light curve depth D length L and star color B V in the appropriate cells and the spreadsheet calculates a 3 iteration solution for Rp Rj provided a solution exists Here s the link for the Excel spreadsheet that does everything described in Section 1 http brucegary net book EOA xls htm SS hee Elewe E Eee 1 Planet Size Iteration Model Bruce L Gary v7203 _2 Enter values in the light blue cells B5 B8 etc amp read the result in B10 D10 etc 3 Object XO 1 4 Enter filter band B V Ror B SE V SE R SE SE Depth of transit mmag 248 0 5 240 10 237 04 231 10 237 O04 ken Length of transit hr 2 95 0 03 2 96 007 297 003 297 0 05 297 0 10 _7 Period days interval between transits 3 9415 3 9415 3 9415 3 942 3 9415 8 Enter B V 0 66 0 04 0 66 0 04 O66 O04 O86 O04 O88 004 g 10 Rp Rj solution 1 29 1 29 1 31 1 31 1 31 A 0 06 0 07 0 06 0 06 0 06 12 13 SE due to SE of BY 0 06 0 06 0 06 0 06 0 06 14 SE due to SE of D 0 01 0 03 0 01 0 03 0 01 5 SE due to SE ofL 0 00 0 01 0 00 0 00 0 01 Figure D 20 Example of the Excel spreadsheet with XO 1 entries for several filter bands B5 C6 for B band etc and the Rp Rj solution B10 B11 for B etc The line for SE of Rp Rj solution is based on changes in D L and B V using their respective SE In this example note that the Rp Rj solutions for all b
145. inch Meade LX200 GPS You ll need a super wedge for equatorial mounting CCD cameras are so cost effective these days that almost any astronomical CCD camera now in use should be adequate for exoplanet observing If you have an old 8 bit CCD that s not good enough you ll have to buy a 16 bit camera For a bigger field of view consider spending a little more for a medium sized chip CCD camera My CCD is a Santa Barbara Instrument Group SBIG ST 8 You ll need a color filter wheel for the CCD camera and this is usually standard equipment that comes with the camera Although I recommend use of a tip tilt image stabilizer it s definitely not a requirement Few people use such a device for removing small fast movements of the star field Software Yes software is a requirement and your choice can be important I ve been using MaxIm DL CCD for 6 years and it s an impressive program that does everything MDL as I ll refer to it controls the telescope the telescope s focuser the CCD the color filter wheel and the image stabilizer if you have one It also does an excellent job of image processing and after it performs a photometry analysis you may use it to create a text file for import to a spreadsheet Other exoplanet observers 10 CHAPTER 1 COULD I DO THAT use AIPAWIN and it also does a good job CCDSoft might do the job but I find it lacking in user friendliness and capability Spreadsheets are an important
146. ine how high Cx can be while still being within the linear region is to expose a series of twilight sky flats using exposure times that produce maximum counts Cx that span the entire region of interest 30 to 65 kct kct kilo counts 1000 counts Any filter will work but you ll have a stronger result by using the filter that has the worst vignetting For me the I band filter is slightly worse than the others with a faintest area to brightest area ratio 0 79 It s not necessary to do this for other filters since one photoelectron is the same as another from the standpoint of silicon crystals in the CCD Figure E 01 band flat field with Cx 62 kct before and after calibration using a 34 kct Cx flat frame The faintest area upper right to brightest have a vignette range of 21 and 0 2 implying that the flat field response was reduced 100 fold to acceptable levels The CCD appears to be linear even for ADU values as high as 62 kct 139 APPENDIX E CCD LINEARITY Average the images with Cx between 25 and 35 kct which everyone will accept as being free of linearity problems Call this a master flat for use with the brighter flat fields Let s define vignette range to be a percentage version of the faintest to brightest area of the linear master flat For example my I band vignette range is 21 1 e faintest to brightest counts 0 79 Next divide a bright flat by the master flat This can be done
147. ions for a known exoplanet then a B band observation could be valuable There are occasions when C filter clear filter observing is acceptable XO 2 is a good example since it has a binary companion 31 arc away that has the same color and brightness as XO 2 Because the two stars have the same color there is almost no penalty for observing unfiltered I m referring to the star color extinction effect that causes baselines to 28 CHAPTER 4 PLANNING THE NIGHT be curved symmetrically about transit This is explained in Chapter 14 so for now just accept my assertion that the presence of reference stars having the same color as the target star exoplanet star is a consideration in choosing a filter When high air mass observing is required I band is a good choice all other things being equal The presence of moonlight should influence filter choice Even though you can t see it when there s moonlight the night sky is blue A moonlit night sky will be just as blue as a sunlit day sky and for the same reason Rayleigh scattering If the moon will be up during a transit avoid using a B band filter or a clear filter I band observations are affected the least by moonlight R band is almost as good and it passes more light so 1f SNR is going to be important consider using an R band filter on moonlit nights If SNR is likely to be very important then consider using a BB band filter which at least filters out the bright sky B band photo
148. ir firmware quality control so that pointing calibration will not be lost between observing sessions When this happens I would recommend the use of Meade s microfocuser and forsake the ability to observe north of 75 degrees declination I ve belabored this focusing problem partly to serve as a warning to any observer who is considering focus adjustments using the primary mirror I also hope I have illustrated the merits of buying a telescope having a tube made with low thermal expansion material The focusing problems just described in excessive detail would not be tolerated in a professional telescope We amateurs with limited budgets must spend extra effort on such matters When using amateur hardware in an attempt to perform professional quality observations whatever is saved in hardware investment cost is paid for with an extra workload 54 Chapter 9 Autoguiding Some CCD cameras have two chips a large main one for imaging and a small one beside it for autoguiding CCDs with just one chip can be autoguided if a separate CCD camera is attached to a piggy backed guide telescope If you have neither of these ways to autoguide may I suggest that you consider a hardware upgrade My CCD camera is a Santa Barbara Instruments Group SBIG ST 8XE The X and E at the end just signify that l ve upgraded a ST 8 to have a larger autoguider chip SBIG s TC237 and USB communication There are a couple ways to automatically autogui
149. is could be accomplished then the expected small movements of the star field can be counted on to produce only small changes in flat field error for each star regardless of its color The solution I propose to minimize the effects of imperfect flat fields is to achieve an accurate polar axis alignment 2 arc and use some form of autoguiding to keep the star field fixed with respect to the main chip s pixels With this solution all the fundamental flaws in flat field correcting will be reduced to second order effects 41 Chapter 6 Dark Frames Creating a master dark frame is straightforward compared with creating a master flat frame Whereas a master flat frame can be used with light frames taken when the CCD is at a different temperature and flat frames for one filter cannot be used with light frames made with a different filter the opposite is true for dark frames The same master dark can be used with light images using any filter but the best result is obtained when the light frames are taken with the same exposure time and CCD temperature as the master dark You may object to this last requirement by noting that astronomy CCD image processing programs have the option of specifying Auto Scale and Auto Optimize which are supposed to compensate for differences in exposure times and CCD temperatures These options may work for pretty pictures but I don t trust them for precision exoplanet transit observing It is commo
150. ission telescope will stare at the same star field Lyra Cyngus for 4 to 6 years It will therefore not be used to search for Earth sized planets in the known transiting exoplanet systems Within a few years there could be several dozen transiting exoplanets and probably all of them will be outside the Kepler Telescope s FOV Thus ground based and other space based telescopes will be needed for transit timing variability studies Any transit observation meant to contribute to an archive of mid transit timings should be made with careful attention to accurate image time tags This means the computer that records images should use a program that automatically synchronizes the computer s clock with a time standard I use AtomTimePro which I ve set for updates every 3 hours The user should also pay attention to the meaning of image time tags For example MaxIm DL records start times in the FITS header but when it performs photometry the CSV file has a JD value corresponding to the mid exposure time 95 CHAPTER 16 ANOMALIES Amateur timings are likely to exhibit uncertainties of 1 or 2 minutes for each transit s mid transit time This is based on my analysis of XO 1 amateur timing measurements Averaging of many timing measurements will reduce this uncertainty The next graph is a plot of 28 XO 1 transit timings by mostly amateurs during the period 2004 to 2007 There is nothing unusual about the pattern of timings in relation to a s
151. ist for years before it was observed at the right time and found to undergo 6 milli magnitude deep transits by a team of amateur observers Gillon et al 2007 This underscores the potential value of NTEs for the amateur observer 27 CHAPTER 3 EXOPLANET CHOICES For those NTEs that are truly NTE which is probably 9596 of them since we do not know the inclination of the exoplanet s orbit we have only lower limit constraints on its mass Since transits have not been observed the exoplanet s size is unknown which means nothing is known about the planet s density Atmospheric composition and temperature can t be determined since transits don t occur Some NTEs may eventually be discovered to undergo transit and will switch categories RATE OF DISCOVERY OF BRIGHT TRANSITING EXOPLANETS DISCOVERY RATE YR 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 DISCOVERY YEAR Figure 3 01 Rate of discovery of BTEs The curve is an exponential fit with a doubling time of 1 2 years The open blue square symbol for 2007 is 8 because 4 BTEs were announced during the first 6 months of the year Observing Project Types All categories of exoplanets are worth considering for a night s observing session It s understandable that the beginning observer will want to start by observing a few easy transits of BTEs Once the excitement of this has worn off however there may be an interest in other observing projects re
152. ity was a conservative way of saying that a pixel fills at a linear rate up to 100 000 electrons then becomes non linear as it continues to fill further In other words I assumed the manual meant to say that my CCD s linear full well capacity was 100 000 electrons This would imply that my CCD might be linear up to 43 500 counts but I remained cautious for a long time by keeping exposures short enough that stars to be used photometrically had Cx less than 35 000 counts The fact that stars would produce Cx all the way up to digital saturation 65 535 counts means that my CCD s silicon crystal pixels must be capable of holding at least 150 000 electrons at readout time 65 535 x 2 3 For a long time I neglected to measure my CCD s linearity thinking that all the specifications in the manual were compatible with the common wisdom of keeping Cx below about half scale in order to avoid non linearity problems I also postponed 138 APPENDIX E CCD LINEARITY measuring linearity in the belief that it would be difficult It isn t and it can be fun especially if you learn good things about your CCD The following methods are presented in a way that hopefully illustrates properties of CCDs and ways to explore these properties from special observations and analysis Once this understanding has been accomplished subsequent measurements of linearity will be almost effortless Twilight Sky Flats Method The simplest way to determ
153. kct is conservative since saturation above this value may depart from linear by only a small amount 146 APPENDIX E CCD LINEARITY 70000 56000 W A ceo N o a o o Pixel Value mS o T Rp p 2 2 2 2 4 i i D 4 E D 0 10 20 30 40 Pixel Location Along X Figure E 10 PSF of a saturated star the bright star with Cx 60 3 in a 50 second exposure The flux of this star is only 2 low compared with an extrapolation of what it should be based on measurements with the CCD in the linear region Conclusion I conclude that flux measurements with this CCD are linear to 1 3 for all Cx up to 59 000 counts For a CCD gain of 2 7 electrons ADU the 59 000 counts corresponds to 159 000 electrons The measurements reported here therefore show that my CCD has a linear full well capacity of 159 000 electrons This is more than the full well capacity of 100 000 electrons listed in the manual which shows that SBIG was being conservative in describing this CCD model The various methods for assessing non linearity can be summarized 1 Flat field method safe to 62 kct 2 Two Star flux ratio vs Cx safe to 59 kct 3 Star flux rate vs Cx safe to 59 kct In no instance is there evidence to support the common wisdom that to avoid non linearity effects it is necessary to keep Cx 35 kct Each observer will want to measure
154. l sliding roof observatory this can be difficult Wind can also blow over the white boards unless they re secured I ve always obtained good results from this method but it s too cumbersome for me to use routinely Sometimes master flats are produced by median combining a large number of images of different star fields For pretty picture work at least a dozen images are needed For exoplanet observing you would need hundreds of images for median combining in order to reduce residual star effects to the required smoothness needed for mmag precision 34 CHAPTER 5 FLAT FIELDS The twilight sky overhead is a convenient way to produce flat fields For most telescopes these images can be taken when the sky is bright and exposure times are short enough that stars do not appear in any of the images The telescope can either be stationary or tracking Master flats produced this way are acceptable for most uses but for precision exoplanet monitoring the presence of even faint stars in the master flat are unacceptable A diffuser placed over the aperture can eliminate stars in the flat field images That s the method I ve adopted which I ll describe after a detour discussion of stray light All flat field procedures can be degraded by stray light For example an open tube telescope that does not have sufficient baffling in front of the CCD camera may register light from the ground or other locations not within the CCD s FOV For another ex
155. lat to assure that all pixel values are above zero Check the minimum value to be sure it s not zero if it is then repeat the image subtraction with the specification that a fixed level be added to all pixels Read the standard deviation of the difference images and call them SEb and SEf With this nomenclature each pair can be used to calculate CCD gain according to the following formula G Fs Bs SEt SEb Where repeating Fs is the average level of the sum of two flat fields Bs is the average level of the sum of two bias frames SEf is the SE of the difference between the same two flat fields and SEb is the SE of the difference between two bias frames As a bonus read noise can be calculated from Read Noise G x SEb sqrt 2 Maybe yov d like some values to compare with When I did this for my 5 year old SBIG ST 8XE using cropped versions of the middle 50 area I get the following Fs avg 85328 89173 95628 Bs avg 213 209 213 Fd SE 177 43 181 35 185 49 Bd SE 9 80 9 79 9 77 The first group gives G 85328 213 177 43 9 80 2 71 electrons ADU Groups 2 and 3 give G 2 71 and 2 78 electrons ADU The average of these 3 determinations is 2 73 0 03 electron ADU which is the best estimate of gain with 148 APPENDIX F CCD GAIN this simple pairing For greater accuracy other pair combinations can be used and other flat field and bias field images can be added t
156. lated to exoplanet transits One of my favorite projects is to monitor known BTEs out of transit OOT If no other exoplanets are present in the BTE s solar system then the observed light curve will be a very uninteresting plot with constant brightness for the entire observing session However if another exoplanet exists in the BTE s solar system its orbit 1s likely to be in the same plane as the known BTE and it may produce its own transits on a different schedule from the BTE Since the known BTE was based on a data base of wide field survey camera observations the transits produced by the BTE will 20 CHAPTER 3 EXOPLANET CHOICES be the easiest to detect Therefore an observer searching for a second exoplanet in a BTE solar system should be prepared for a more difficult to detect transit The second exoplanet s transit depth will probably be much shallower and it could either last longer or be shorter and it will come at times that differ from the BTE transit Before selecting an exoplanet to observe extensively in the OOT mode check its impact parameter This 1s the ratio transit chord s closeness to star center divided by star radius If the impact parameter is close to one then it s a close to grazing transit this means that any outer planets in that system would not transit An impact parameter of zero corresponds to a transit that goes through the star s center this means that all other planets in the system are likely t
157. mplate This set of images might be worth saving to a directory but that s optional to do this with MDL select File BatchSave amp Convert etc The third step is to add an artificial star in the upper left corner of all images This is done using a free plug in written by Ajai Sehgal You can get a 32x32 pixel version from the MDL web site the 64x64 version was written at my request and you may either ask Ajai or me for it to be sent by return e mail as an attachment or download it from the web site http brucegary net book EOA xls htm I prefer to use the 64x64 version since it allows the use of large photometry apertures The artificial star will be Gaussian shaped with the brightest pixel equal to 65 535 and a FWHM 3 77 pixels With MDL the artificial star 1s added to all images by opening the Plug In menu and clicking Add 64x64 reference star As an aside consider what we have in working memory now 150 images all stars are at the same pixel locations including an artificial star with a fixed star flux in all images If we compare the flux of a star with that of the artificial star and convert that to a magnitude difference we have a way of keeping track of the star s brightness in all images that has the added feature of retaining more information than simple differential photometry With differential photometry the user specifies a reference star or stars for ensemble differential photometry and all object stars
158. mported to a spreadsheet where the user can select from among the check stars to serve as reference The artificial star is not used for reference instead it serves to determine extra losses that might be produced by clouds dew on the corrector plate or image quality degradations due to poor tracking wind shaking the telescope or poor focus causing the PSFs to spill outside the photometry aperture These details are not relevant to this chapter s message and they ll be treated at length in Chapters 12 and 13 Note that in this image essentially all of each star s flux is contained within the signal aperture The next figure is a screen capture of the photometry circle locations on the defocused image 50 CHAPTER 8 FOCUS DRIFT Figure 8 04 Same photometry apertures at the same x y locations as in the previous image for the defocused image In this defocused image some stars have PSFs that are spread out in the famous comet shape coma pattern with the comet tails directed away from the optical center indicated by the cross hair The length of the coma tail is greater the farther the star is from the center Thus stars near the edges have a smaller fraction of their total flux within the aperture than stars near the center The ratio of fluxes and hence magnitude differences will therefore be affected The object s measured brightness can have either sign depending on whether the target sta
159. n of the light from the blend of stars in the survey camera s aperture egress Transit interval when the smaller object is moving off the star and only part of the smaller object s projected solid angle is obscuring star light Contact 3 to 4 ensemble photometry Use of 2 or more reference stars in an image for determining a target star s magnitude exoplanet Planet orbiting another star Also referred to as an extra solar planet extinction zenith extinction atmospheric extinction Loss of light due to the sum of Rayleigh and Mie scattering plus narrow line absorption usually expressed in terms of magnitude per air mass An extinction curve is a plot of the logarithm of measured star fluxes versus air mass usually magnitude a base 10 logarithm times 2 5 versus air mass A straight line fit to these data has a slope corresponding to zenith extinction extra losses Reductions of a star s flux level that are not accounted for by atmospheric extinction The most common origins for extra losses are clouds dew accumulation on the corrector lens wind driven telescope vibrations smearing the PSF for the affected images and loss of focus causing the signal aperture to capture a smaller percentage of the entire star s flux in the poorly focused images filter bands Wavelength interval with associated response function for the following commonly used standards B band V band Rc band Ic band BB band J band H band and K band
160. n practice to set the CCD cooling to as cold as can be stabilized with a duty cycle of 90 just prior to the time target observations are to begin When I finish taking flat frames there s usually a half hour before target observations can begin so during that time my thermoelectric cooler is working at full duty cycle to get the CCD as cold as possible After acquiring the target and synchronizing the mount s pointing I back off on the cooler setting to about a degree C warmer than what had been achieved at that time Before starting observations of the target I ll perform a set of focus images at about the same area in the sky as the target The FWHM at the best focus setting will be used for determining exposure time explained in the next chapter During the time it takes to determine focus the CCD cooling has stabilized If there s time I ll take dark frames before starting to observe the target The best quality dark frames however will be made at the end of the target observations A total of at least 10 dark frames should be taken with the same exposure time and CCD temperature These images will be median combined not averaged Median combining will remove the effect of cosmic ray defects that are usually present in most of the dark frames especially if their exposure times are as long as 60 seconds Dark current thermal noise averages down approximately as the square root of the number of images that are median combined Whereas aver
161. nd annulus and a difference is added to the total flux But each pixel is noisy due to thermal jostling of electrons in the CCD elements and electronics read noise and sky brightness contributions to the counts from each 58 CHAPTER 10 PHOTOMETRY APERTURE SIZE pixel For example in this image the RMS noise for each pixel is 3 5 counts The noise level of the total flux increases with the square root of the number of pixels added and since the number of pixels increases as the square of the radius the noise on total flux readings should be proportional to the signal aperture radius Beyond a radius of 1 4 x FWHM where total flux has essentially reached an asymptote the SNR decrease as l radius For some observing projects small signal apertures are appropriate such as detecting and tracking faint asteroids For the asteroid situation SNR could be 2 to 3 and brightness precision isn t important But consider some of the problems that might occur with bright stars where brightness precision is paramount In Chapter 8 describing focus drift it was shown that when PSF changes during an observing session aperture capture fraction may differ across the image This is a situation in which the user faces competing goals the desire for small stochastic noise levels versus small systematic errors If we adopt an aperture radius of twice FWHM the aperture capture fraction rises to 96 but SNR is reduced to 60 of its peak value Even t
162. nd large photometry apertures increase the component of sky background noise to the final measurement precision This translates to not using an intentionally defocused observing strategy during full moon unless an I band filter is used Some of the reasons for these precautions will be better understood after reading the following chapters Precaution when Focusing the Mirror Focusing is accomplished in one of two ways moving the primary mirror or moving the CCD camera assembly The latter is preferable However because I removed the microfocuser from my Meade LX200GPS telescope in order to clear the base for reaching the north celestial pole as part of the pointing calibration my focusing is accomplished by moving the primary mirror This is a crude way to focus and it causes problems for exoplanet observing The remainder of this section should serve as a warning about focusing with the primary mirror The primary mirror is moved in or out using a rod attached to reducing gears attached to the focusing knob When making an adjustment in a direction opposite to the previous one the mirror will not move until a hysteresis range of movement is overcome For my telescope this is approximately a half turn of the focus knob or 5 turns when using a 10 1 gear reducer Since my focusing is accomplished using a wireless MicroTouch focusing unit sold by Starizona the hysteresis for reversing direction amounts to 650 steps of a stepper motor at
163. never an exoplanet s light curve is to be produced from a set of images there will usually be several stars suitable for use as reference stars Consider the example of XO 3 whose star field is presented in the figure on the next page Note that XO 3 has a B V color of 0 45 whereas all other stars are redder larger values of B V Only two stars have close to the same color stars 1 and 6 In the following example these two stars will be used for ensemble photometry reference On the date 2007 04 15 this star field was observed with an I band filter with exposure times of 60 seconds binned 1x1 and CCD cooler set to 24 C with my 14 inch telescope FWHM was typically 6 pixels so I chose a signal aperture photometry radius of 15 pixels 2 5 x FWHM a safe choice With this aperture the measured fluxes for XO 3 Star 1 and Star 6 were 346000 161000 and 963000 counts The maximum counts for these stars varied with FWHM of course but 88 CHAPTER 15 STOCHASTIC ERROR BUDGET typically they were 9200 4300 and 22000 counts SNR 3000 1100 and 8000 Using the above equation we calculate Np values for the three stars to be 388 265 and 647 counts Measurements of each star will have Poisson uncertainties of 1 22 1 78 and 0 73 mmag 1 e 1086 sqrt 2 3 x Flux For each image the three flux readings will be converted to magnitudes and the XO 3 magnitude will be adjusted by whatever amount is needed to bring the average magnitude of
164. ng a median combine of many ingress and egress observations Rings are likely to be present for both ingress and egress so folding of egress to match the shape of ingress is permissible Moons are likely to be in an orbit that resonates with the exoplanet s orbit about the star which means that if one ingress shows a fade feature other ingress events are also likely to show the same fade feature This means that there probably is reason to stack ingresses and also stack egresses But don t fold egress data with ingress because a moon is not likely to affect both Data averaging is advisable I recommend 5 minute bins However running averages are unsafe at any size and should be avoided because they easily produce the impression of self consistent patterns that don t exist Small amplitude oscillations within a transit are sometimes thought to exist in measurements but it is prudent to assume that at this time none of them are real Still small features within a transit are worth searching for After all the star undergoing transit may have sunspots A credible detection of such a feature would require confirmation from simultaneous observations by another observer Observer teams may some day coordinate observations of the same transit for this purpose Don t forget that it is always worth observing a transiting exoplanet between transits in a search for anomalous fades caused by another exoplanet in the same star system The length of such a f
165. ng an expensive observing facility but the concept also can apply to observations with amateur hardware One last Philosophy I ll mention is WHEN YOU SEE SOMETHING YOU DON T UNDERSTAND WHILE OBSERVING OR DURING DATA ANALYSIS STOP DON T PROCEED UNTIL YOU UNDERSTAND IT This one is probably difficult to making a convincing case for unless you ve ignored the advice and wasted time with fundamentally flawed data or analysis procedure This advice is especially true if you re writing a computer program to process data because program bugs are a part of every programming experience A corollary to this advice might be Never believe anything you come up with even if it makes sense because when there s a serious flaw in your data or analysis it may show itself as a subtle anomaly that could easily be ignored These are some of the themes that will be a recurring admonition throughout this book Some readers will find that I m asking them to put too much work into the process My advice may seem more appropriate for someone with a professional dedication to doing things the right way If this is your response to what I ve written then maybe you re not ready yet for exoplanet transit observing Remember if it s not fun you probably won t do a good job If you don t enjoy floundering with a telescope trying to figure out its idiosyncrasies then you probably won t do a good job of learning how to use your telescope properly This hobby should be
166. ng session he has removed his mechanical engineer hat his programmer s hat and all the other hats he wore while preparing the telescope system for observing and he becomes the telescope operator carrying out the observing request of the astronomer whose hat he wore before the observing session began The admonition to know thy hardware can be met in different ways as illustrated by the professional astronomer many man team and the amateur astronomer one man team INTRODUCTION I once observed with the Palomar 200 inch telescope and believe me when I say that it s more fun observing with my backyard 14 inch telescope At Palomar I handed the telescope operator a list of target coordinates motion rates and start times and watched him do the observing I had to take it on faith that the telescope was operating properly With my backyard telescope I feel in control of all aspects of the observing session I know exactly how the telescope will perform and I feel comfortable that my observing strategy is a good match to the telescope system s strengths and weaknesses Based on this experience I will allege that amateur observing is more fun Another of my philosophies i GOOD DATA ANALYSIS IS JUST AS IMPORTANT AS GETTING GOOD DATA It is customary in astronomy as well as many observing fields to spend far more time processing data than taking it A single observing session may warrant weeks of analysis This is especially true when usi
167. nges are very slow If the hot Jupiter is in an elliptical orbit the transits will shift steadily in time due to precession of the orbit s periastron location of closest approach to the star In that case the transits may also change shape or entirely disappear though unlikely in a lifetime A more interesting possibility is for the hot Jupiter to exhibit anomalies that change over the course of a few months due to another planet in an orbit close to that of the hot Jupiter Algol et al 2005 Holman and Murray 2005 Steffen 2006 The greatest effects will be produced when the orbit periods are resonant For example if an Earth like planet is in a 2 1 period resonance with the hot Jupiter it can cause the hot Jupiter to shift its orbital position in ways that cause transits to alternate between coming early or late with a periodicity on the order of a year The amplitude of these timing anomalies can be as high as 3 minutes Steffen 2006 This is perhaps the most exciting aspect of amateur participation in exoplanet transit observing Ground based professional telescopes are too expensive on a per minute basis for such long term projects Space based telescopes devoted to such a project could do a good job with this but so far the ones in orbit or scheduled to launch are designed for specific tasks that render them unsuited or unable to conduct the required follow up observations of all transiting exoplanets For example the Kepler M
168. ns The moonless night sky is not blue but extinction is still greatest at B band and smallest at I band so for dark skies air mass is more important than sky color when choosing a filter On May 5 at my site the moon rises at 10 35 PM I recommend using an I band filter for the XO 1 observations This is tentative however since other considerations are important Next we run TheSky Six a planetarium program from Software Bisque to find out the elevation of XO 1 during the night and specifically during the predicted transit Acceptable elevations depend on filter B band observing will require high elevations e g EL gt 30 degrees whereas I band observing can be done at much lower elevations e g EL gt 15 degrees We need to allow for acceptable elevations for the entire transit from 1 5 hours before first contact to 1 5 hours after last contact Transits of hot Jupiters large exoplanets orbiting close to their star have transit lengths similar to XO 1 3 hours The best observing situation is for mid transit to occur at midnight but this rarely happens We need to study XO 1 s elevation versus time for the 7 hours centered on mid transit in order to be sure of our filter choice Sunset occurs at 7 03 PM so quality observing could start at 7 58 PM lower quality observations could start at 7 45 PM When quality observing can begin XO 1 will be at 20 degrees elevation and rising If observing began at 7 58 PM 40
169. ntral transit Lx 2 Rstr x Rsun Rp Rj x Rj 2 ma 24 x P where Rsun 6 955e5 km Rj 7 1492e4 km Miss distance m 0 42 ratio of closest approach to center to star s radius m SQRT 1 L Lx 7 Limb darkening effect LDe 1 16 divide D by this I m I av 1 0 98 0 15 0 98 m 0 15 m 0 746 for B band 118 APPENDIX D PLANET SIZE MODEL 1 0 92 0 19 0 92 x m 0 19 x m 0 787 for V band 1 0 885 0 23 0 85 xm 0 23 x m 0 828 for R band 1 0 78 0 27 0 78 xm 0 27 x m 0 869 for I band Corrected transit depth D 20 4 mmag 1st iteration for D D D LDe this is the D that would have been measured if the star were uniformly bright Planet radius Rp Rj 1 31 2nd iteration for Rp Rj Same eqn as above but now assumes m 0 42 and appropriate limb darkening Transit length maximum Lx 3 25 hr 2nd iteration for central transit length Same eqn as above Miss distance m 0 405 Same eqn as above Limb darkening correction LDe 1 165 divide D by this Same eqn as above No more iterations are needed since the two miss distance results amp limb darkening corrections are the same We have a stable solution Rp Rj 1 306 To assign a SE to this solution it is necessary to repeat the above procedure using a range of values for the measured transit depth and length When this is done using an Excel spreadsheet we get Rp Rj
170. o be mastered by those making the transition Image analysis skills will also differ from the variable star experience This book explains the new and more rigorous observing and image analysis skills needed to be a partner with professionals in exoplanet studies The reader is entitled to know who I am and my credentials for writing such a book I retired from 34 years employment by Caltech and assigned to work at the Jet Propulsion Laboratory JPL for studies in planetary radio astronomy microwave remote sensing of the terrestrial atmosphere and airborne sensing of the atmosphere PREFACE for studies of stratospheric ozone depletion I have about 55 peer reviewed publications in various fields and four patents on aviation safety using microwave remote sensing concepts and an instrument that I developed I retired in 1998 and a year later resumed a childhood hobby of optical astronomy I was one of the first amateurs to observe an exoplanet transit HD209458 in 2002 I have been a member of the XO Project s extended team ET of amateur observers from its inception in 2004 The XO Project was created by Dr Peter McCullough a former amateur but now a professional astronomer at the Space Telescope Science Institute STScI The XO project has announced the discovery of three exoplanets XO 1b XO 2b and XO 3b All members of the XO team are co authors of the announcement publications in the Astrophysical Journal have worked with fellow E
171. o be resolved by ground based telescopes and 2 the EB and the blending star are far enough apart usually gravitationally unrelated but close together in our line of sight that their angular separation is within the resolution limits of ground based telescopes The second of these blending situations is probably more common than the first When a survey telescope produces many candidates per month it is not feasible to rule out an EB explanation for each one by measuring radial velocities during the course of a few nights with a telescope large enough to produce spectrograms that have the required accuracy Although radial velocity measurements would allow the determination of the secondary s mass and thus distinguish between EB and planet transits large telescope observing time is too costly for such an approach A better alternative is to perform follow up observations of the survey candidates using telescopes with apertures sufficient to identify the most common blending situation Amateurs with telescope apertures 8 to 14 inches for example have more than sufficient resolution to determine which star within the survey s resolution circle is undergoing transit thus easily identifying most cases of EB blending These amateur telescopes also have sufficient SNR for an 11th magnitude star for example to allow the transit light curve to be determined with good enough quality to sometimes identify the presence of a triple star system EB There m
172. o the analysis Calculating read noise Read Noise 2 73 x 9 80 sqrt 2 18 9 electrons for the first group The other two groups give 18 8 and 19 2 for a best estimate Read Noise 18 9 0 2 electrons The SBIG manual states that read noise 1s approximately 15 electrons It s possible my CCD has aged But read noise is usually not an important contributor to total error so the 19 electrons versus 15 electrons read noise won t matter This accuracy is more than adequate for error budget calculations 149 GLOSSARY 2MASS Two Micron All Sky Survey a catalog of point sources stars and extended sources galaxies covering the entire sky using filters J H and K Of the 2 1 billion sources more than 500 million are stars J and K magnitudes can be converted to B V Rc and Ic magnitudes for most sources Therefore J K star colors can be converted to B V and V R star colors which is useful since all stars that amateurs will want to use for reference are in the 2MASS catalog air mass Ratio of number of molecules of air intercepted by a unit column traversing the atmosphere at a specified elevation angle compared with a zenith traverse An approximate formula for air mass is secant zenith angle or 1 sine elevation angle Because of the Earth s curvature the maximum air mass for dry air is 29 tabulations are available To the extent that dust and water vapor contribute to line of sight extinction the above formula
173. o transit As you may have guessed BTEs have impact parameter values 0 4 typically This means that exoplanets in orbits twice the size of the known exoplaent are likely to produce transits Given that a planetary system exhibits orbital periods that are proportional to orbital radius raised to the 1 5 power a second exoplanet in an orbit that 1s twice the size of a hot Jupiter will have a period of 2 8 times that of the hot Jupiter There s a variant of the OOT observing project type which could be called looking for Trojans This project is based on the presence of Trojan asteroids in our solar system Jupiter is accompanied by swarms of asteroids in approximately the same orbit as Jupiter but preceding and following by 60 degrees of orbital position These locations are gravitationally stable and are called Lagrangian points L4 and L5 There are about 1100 Trojans and none of them are large exceeding 370 km If they were lumped together in one object it would have a diameter 1 that of Jupiter In solar systems with a Jupiter sized planet orbiting close to its star the so called hot Jupiter that most BTEs resemble the BTE would have to be accompanied by a much larger Trojan companion to produce observable transits These larger Trojan companions cannot be ruled out by present theories for solar system formation and evolution so they are worth an amateur s attention as a special project The search strategy 1s straight forward simply
174. omes with a micro focuser but I removed it in order to have sufficient clearance of the optical backend with the mounting base to be able to observe high declination targets This configuration also allows me to reach the north celestial pole which is needed for pointing alignment calibration Without the micro focuser I need a way to make fine focus adjustments during an observing session even while continuing to observe a target This has been achieved by a wireless focuser sold by Starizona with the remote unit physically attached to the mirror adjustment focusing knob and the local unit connected to my computer Figure 2 02 My favorite configuration AO 7 focal reducer CFW CCD SBIG ST 8XE The telescope is a Meade LX200GPS 14 inch aperture f 10 without a focal reduce I also have a wireless weather station with the sensors at the top of a 10 foot pole located near the sliding roof observatory shown in Fig 5 01 The pole is wood and the communications are wireless because lightning is common during our summer monsoon season July August The weather station is a Davis Vantage Pro 2 supplemented by their Weather Link program for computer downloads from a data logger This program produces graphical displays of all measured parameters outside air temperature dew point barometric pressure rain accumulation and wind 15 CHAPTER 2 OBSERVATORY TOUR maximum and average for user specified intervals which I ve ch
175. on the most important aperture size to choose carefully is the signal aperture radius Whenever there s concern about what aperture size to choose it is very easy in MDL to process the images with several choices The files produced with different aperture sizes can be imported to different spreadsheets as described in Chapter 13 and systematic behaviors of each star can be performed to determine which aperture size to accept This chapter s message is to start with a default signal aperture radius 3 x FWHM and adjust in response to the presence of interfering stars Consider using 2 5 x FWHM and 3 5 x FWHM Only the brave or foolhardy will use 2 x FWHM for precision photometry 61 Chapter 11 Photometry Pitfalls This chapter is meant to prepare you for the next two chapters which are a daunting description of my way of overcoming pitfalls of the standard ways of producing light curves that may be acceptable for variable stars but inadequate for exoplanet transits Most variable star light curves LCs require precisions of 0 05 to 0 01 magnitude whereas exoplanet LCs should be about 10 times better i e 2 to 5 mmag precision per minute Perfection can indeed be the enemy of good enough because achieving perfection takes so much more effort It should not be surprising that producing exoplanet LCs should require more than twice the effort of a typical variable star LC Sometimes I ll spend more than half a day with jus
176. on will contribute to that pixel s ADU count by an amount that depends on the CCD gain For my SBIG ST 8E CCD the gain is 2 3 electrons per count where each count is also called an ADU or analog data unit Therefore the number of photoelectrons needed to produce a count of C is n 2 3xC for my CCD This is true whether I define C to be the count from just one pixel or the sum of counts produced by a star that may be registered by several pixels called flux You can measure your CCD s gain and it may differ significantly from the value given in the User s Manual For example my CCD has a gain of 2 7 instead of 2 3 electrons per ADU Stochastic events have the property that the SE uncertainty of the total number of events is the square root of the number of such events provided the number of events is large Thus when we measure n stochastic events occurring within a specified integration interval we must state that we have really just measured a value n sqrt n events Since the measurement C is based on 2 3xC events for this particular CCD we must state that we have measured 2 3xC sqrt 2 3xC events Stated in terms of counts we measure C sqrt C 2 3 This fundamental uncertainty is referred to as Poisson noise To summarize Poisson noise from a bright star 1s Np 7 sqrt C gain Np sqrt C 2 3 for the SBIG ST 8E CCD This result can be expressed in terms of mmag Poisson SE mmag 1086 sqrt 2 3xC Whe
177. ooler temperatures they absorb and re emit at their cooler temperatures in accordance with a blackbody spectrum determined by their cooler temperature c f Fig 14 05 blue blocking filter A filter that passes photons with wavelengths longer than 490 nm A BB filter passes 90 of a typical star s light and during moonlight it blocks most of the sky background light coming from Rayleigh scattered moon light CFW Color filter wheel check star Another star in the same set of images as the target star which is processed using the same reference stars reference stars are sometimes called comparison stars for out of date reasons Precision exoplanet photometry usually does not make use of check stars because at the mmag level of precision every star will have a unique dependence on air mass due to its color difference with the reference stars A check star can provide a false sense of security that systematic errors are not present or a false sense of alarm that systematics are present The use of check stars is left over from variable star work where mmag systematics are unimportant clear filter A filter that passes most of the light within the wavelength region where CCD chips are sensitive A clear filter is used instead of no filter unfiltered in order to achieve parfocality with the other filters two filters are parfocal when they require the same focus setting confusion A technical term referring to the presenc
178. osen to be 5 minutes I find the graphs of wind and temperature to be very useful during an observing session WEATHER M MONITOR 2 WIRELESS THESKY 6 VIDEO amp AUDIO e RADIO UT CLOCK INSIDE SRO FOR MONITOR m 1 c Figure 2 03 The author is shown manning the control room at the beginning of an observing session making flat fields Equipment is described in the text What used to be a master bedroom is just the right size for everything needed in an observatory control room The main computer is connected to the telescope via 100 foot underground cables in buried conduit This computer has a video card supporting two monitors one for MaxIm DL and the other for TheSky Six and other supporting programs labeled Monitor 2 in the above figure Another computer is dedicated to running the Davis Weather System program that downloads readings from the data logger and displays then as graphs on its own monitor The Davis Weather System also has a real time display panel I find this useful for quick readings of wind speed wind direction temperature and dew point temperature when recording outside conditions in the observing log A radio controlled UT clock is synchronized with WWVB radio time signals every night When accurate time tagging of images is important I visually compare the radio controlled clock with the main computer s clock which is synchronized using internet queries by a program AtomTim
179. perhumps will have sufficient experience for making an easy transition to exoplanet observing Amateurs who have experience with the other kind of observing measuring the brightness of a few stars a few times a month for example will be able to make the transition to exoplanet observing but it will require learning new skills Someone who has never performed photometry of any stars may want to consider deferring exoplanet observing until they have some of the more traditional photometry experience I ll make one exception to the above required experience level description Anyone with work experience making measurements and performing data analysis regardless of the field is likely to have already acquired the skills needed for exoplanet monitoring even if they have never used a telescope For example before retiring I spent three decades making measurements and processing data as part of investigations within the atmospheric sciences I think that experience alone would have been sufficient background for the astronomy hobby that I started 8 years ago I ll agree that my amateur astronomy experience when I was in high school using film was helpful And I ll also agree that my decade of radio astronomy experience 4 decades ago was also helpful but the differences between radio astronomy and optical astronomy are considerable For anyone who has never used a telescope yet has experience with measurements and data analysis I am willing to sugge
180. pixels nearby Star Flux Ratio versus Maximum Counts Method This method will involve more analysis but it will provide more information about how your CCD responds to too much light The method involves taking images of two stars in the same FOV with several exposure times The two stars should have a flux ratio of about 2 1 magnitude difference 0 75 Be sure the stars are near zenith otherwise you ll have to correct for extinction The shortest exposure time should be whatever produces Cx 10 to 20 kct for the brightest star I ll illustrate this method using a pair of stars near NGC 5371 with V magnitudes 9 0 and 9 7 My exposure sequence ranged from 5 to 40 seconds Figure E 02 is a plot of Cx versus exposure time for the bright star 140 APPENDIX E CCD LINEARITY MAX COUNTS vs EXPOSURE TIME MAX COUNTS OF BRIGHT STAR 5 10 15 20 25 30 35 40 45 50 55 60 EXPOSURE TIME SEC Figure E 02 Maximum counts versus exposure time for the brighter of two stars FLUX vs EXPOSURE TIME 6000 5000 4000 3000 FLUX KCT 2000 1000 D 5 10 15 20 25 30 35 40 45 50 55 60 EXPOSURE TIME SEC Figure E 03 Flux versus exposure time for two stars 141 APPENDIX E CCD LINEARITY There are two things to notice about Fig E 02 First typical Cx flux values increase with exposure time until a saturation value of 60 kct is reached Second for each exposure time below saturation Cx
181. psing binary Amateur telescopes are capable of making this distinction since they can quickly determine which star fades at the predicted times and how much it fades As a bonus the amateur observations can usually characterize the shape of the fading event whether it is flat bottomed or V shaped If the star that fades has a depth of less than 30 milli magnitudes mmag and if the shape of the fade is flat bottomed there is a good chance that a transiting exoplanet has been identified Armed with this information the professionals are justified in requesting observing time on a large telescope to measure radial velocity on several dates and thereby solve for the mass of the secondary If the mass is small it must be an exoplanet As more wide field survey cameras are deployed by the professionals in a search for transiting candidates there will be a growing need for amateur participation to weed out the troublesome blended eclipsing binaries This will allow the professionals to focus on only the good exoplanet candidates for big telescope spectroscopic radial velocity measurements The role amateurs can play in this exploding field is exciting but this role will require that the amateur learn how to produce high quality transit light curves A background in variable star observing would be helpful but the exoplanet requirements are more stringent because the variations are so much smaller that a new set of observing skills will have t
182. quires extra work for the user but with the extra effort comes a significant increase in analysis power as the next chapter will illustrate 65 CHAPTER 12 IMAGE PROCESSING The next step is to invoke the image analysis program s photometry tool in order to create a file containing star magnitudes relative to the artificial star for the 150 images Before proceeding with this you will need to carefully choose photometry circle sizes as described in Chapter 10 If you are unsure about the best signal aperture radius create files for each of several plausible signal aperture sizes Using MDL invoke the photometry tool Analyze Photometry All images in working memory are selected by default in the Image List and the highlighted image in this list is displayed in the work area Check the boxes labeled Act on all images and Snap to centroid Open the drop down menu Mouse click tags as and select New Object Navigate around the highlighted image and find the exoplanet star left click it The aperture circles appear and are snap centered on the star the Obj1 label is displayed it can be dragged to an out of the way location nearby if the label overwrites stars to be measured You may not notice it but all images have the same photometry circles centered on the same star you can check this by highlighting an image in the Image List to see that image highlighted in the work area Next open
183. r the exoplanet candidate labeled Obj1 in the figure is closer to the center or farther from it compared with the reference stars labeled Chk in the figure For this image we can expect the reference stars to suffer greater losses than the target leading to an apparent brightening of the target The magnitude of this effect will be greater for smaller photometry apertures Larger apertures would reduce this effect However the best solution is to never have to use poorly focused images Referring back to Fig 8 01 and noting the blue trace labeled Extra Losses mag an increase in losses is usually produced by cirrus clouds However in this case it was produced by a spreading out of the PSF beyond the signal aperture circle as focus degraded 51 CHAPTER 8 FOCUS DRIFT The lesson of this chapter is keep all images in good focus an exception is treated at the end of this chapter If that doesn t work for whatever reason then when processing the images use a large photometry aperture to assure that most of the flux is measured for all stars most means 99 If you re not sure that the aperture size was sufficiently large then if you use an artificial star for setting the differential magnitudes check to see if the magnitude for any of the stars or the magnitude corresponding to total flux for all the non target stars drops when the target appears to change values Any correlation between target brightness and
184. r away to not be affected by the same local interferences can provide corroboration not yet implemented A network of advanced amateur observatories optimized for exoplanet transit observing should have the guidance of a professional astronomer He will know other professionals to contact when unexpected observed behaviors are encountered Once the initial construction costs have been borne the part time professional will probably constitute the major cost for continued operation of the exoplanet observing network At the present time there is no universal archive for exoplanet timings or light curve measurements Each group of observers maintains their own archive but these groups do not share because of an understandable desire to announce discoveries and continue to be funded by their sponsoring agency However a greater good will eventually be served by creating a global archive fashioned along the lines of the AAVSO American Association of Variable Star Observers Even non members of the AAVSO can submit observations to their immense archive of star brightness observations and submit queries for what s in the archive for a specific star for a specific date interval I am suggesting the creation of an Exoplanet Transit Archive ETA that would maintain light curve observations as well as mid transit timing submissions It would be possible for the ETA to perform automated analyses of submitted LC data to solve for air mass curvature and
185. ram showing star locations for any site location any date and time and any orientation zenith up north up etc J H and K magnitudes are shown for virtually every star shown plus V magnitude estimates Limiting magnitude is 16 V mag User objects and telescope FOVs can be added to the catalog transit Orbital motion of a smaller object in front of a star that is larger obscuring some of the light from the star c f occultation transit depth Magnitude difference between the measured value at mid transit and a model predicted value at the same time In the absence of systematic errors affecting the shape of the light curve which often have a component of curvature correlated with air mass and a trend correlated with time the transit depth is simply the difference between the average of the out of transit magnitudes and the mid transit value which is what most observers do even when systematic effects are present unfortunately transit timing analysis Search for patterns in a plot of mid transit time minus predicted transit time versus date using a fixed period interval between transits Anomalies that persist for months before changing sign with sign reversal periods of many months are predicted to occur if an Earth mass exoplanet is present in an orbit whose period is in a simple resonance with the transiting exoplanet s period such as 2 1 158 REFERENCES Algol E Steffen J Sari R et al 2005 MNRAS 359 p 567
186. re is no way to probe the flat field s quality at short spatial wavelengths In theory a flat field could be constructed by repeatedly dithering RA and Dec until all regions of the CCD have been sampled by Landolt stars I don t recommend doing this for several reasons that are described below Nevertheless it is feasible to check the quality of a flat field by observing a Landolt star field with a few carefully selected RA and Dec offsets Figure A 07 includes 8 Landolt stars brighter than 13 magnitude It was observed with 10 different RA Dec offsets producing 70 locations on the CCD pixel field where a measured magnitude could be compared with a Landolt magnitude the number is less than 80 because some RA Dec offsets placed Landolt stars outside the FOV All observations were made with a V band filter Star color effects are removed by solving for a star color coefficient in an expression for V magnitude V mag 19 670 2 5 LOG o S g Kv x AirMass 0 055 x C where S is star flux counts g is exposure time seconds Kv is zenith extinction for the V band filter magnitude air mass and C is a linearized version of star color C defined as C 0 57 x B V 0 30 The linearized version is C C 1 3 x G The constants 19 670 and 0 055 were derived from a least squares fitting procedure using the 70 star flux measurements All images for this session were made near transit so air mass was constant and it didn t matter
187. rity limit linearity saturation Not many amateurs measure where their CCD begins to become non linear but conventional wisdom holds that anything greater than mid range is unsafe In other words whenever the maximum counts Cmax exceeds 35 000 a perfect CCD would produce a slightly higher count If you measure your CCD s linearity limit you may be pleasantly surprised When I measured mine I discovered that it was linear over a much greater range than represented by conventional wisdom It was linear all the way to 59 000 counts This measurement can be done using several methods described in Appendix E Knowing this has allowed me to use longer exposure times and longer exposures are desirable for a couple reasons 1 scintillation and Poisson noise cf Chapter 15 are reduced slightly because a greater fraction of an observing session 1s spent collecting photons instead of downloading images 2 read noise is reduced since exposure times can be longer and there are fewer readings per observing session and 3 a smaller fraction of an observing session is wasted with image downloads which means more time is spent collecting photons I highly recommend that each exoplanet observer measure their CCD s linearity in order to have the same benefits For the remainder of this chapter I ll assume that this measurement has not been made and you will want to be cautious by using exposure times assuring that all stars to be used h
188. rked One of my neighbors has a 32 inch telescope in an automated dome and it s a really neat facility But as he knows I prefer to use my little 14 inch telescope whenever its aperture is adequate for the job for the simple reason that I understand most of the idiosyncrasies of my system whereas I assume there are many idiosyncrasies of his system that I don t understand At a professional observatory the responsibility for know thy hardware is distributed among many people Their staff will include a mechanical engineer an electrical engineer a software control programmer an optician to perform periodic optical alignment someone to perform pointing calibrations and update coefficients in the control software a telescope operator a handy man for maintaining utilities and ground keeping and a director to oversee the work of all these specialists Therefore when an astronomer arrives for an observing session or when he submits the specifics of an observing request for which he will not be present all facets of know thy hardware have already been satisfied In contrast the amateur observer fills all of the above job responsibilities He is the observatory director he does mechanical and electrical calibration and maintenance he s in charge of programming pointing calibration scheduling and he s the telescope operator and the amateur is also his own funding agency Thus when the amateur starts an observi
189. rp in the upper left hand area FWHM 1 5 arc and fuzzy elsewhere 3 5 arc while the next image might be sharp in the middle only My impression is that the sharpness auto correlation function usually went to zero 5 arc away and the areas where one image was sharp were poorly correlated with the next image s sharp areas The second item means that position distortions within an image were present which made it impossible to combine two images with just one offset for bringing all regions of the FOV into alignment A time lapse movie of these images resembles looking into a swimming pool and seeing different parts of the pool bottom move in ways that were uncorrelated These two phenomena were seen for about two hours so it wasn t just an early evening atmospheric effect I used a V band filter an exposure time of 0 1 second and images were spaced 8 seconds apart Some of these moon images can be seen at http brucegary net Moon Moon7524 htm and an animation of seeing can be found at http brucegary net ASD x htm Fig 4 Since these were short exposures the spatial seeing differences were entirely atmospheric unlike long exposures that can be influenced by imperfect tracking Even with perfect tracking we can predict that the longer the exposure the smaller the spatial differences in sharpness To understand this imagine a 3 dimensional field of atmospheric temperature with inhomogeneities that are frozen with respect to the air
190. rrors at the two star FOV locations are not present MAG MAG SCATTER PLOT FOR TWO STARS SAME COLOR AND CLOSE TOGETHER 2007 02 16 UNFILTERED 2 88 4 2 84 4 2 83 4 2 82 4 2 81 4 CV of STAR 6 B V 0 51 2 80 4 2 79 4 2 78 T T T T T T T 1 12 31 12 32 12 33 12 34 12 35 12 36 12 37 12 38 12 38 CV of STAR 5 B V 0 55 Figure A 04 Mag mag scatter plot for two stars with same color and close together for the 6 hour clear filter observing session of 2007 02 16 105 APPENDIX A EVALUATING FLAT FIELDS Figure A 05 shows what happens in a mag mag scatter plot when one of the stars is near the edge Star 8 and the other is near the center Star 5 Keep in mind that for these observations the telescope was configured so that the flat fields had a pattern very similar to those pictured in Fig A 01 where there s a smooth fall off of response from 100 near the center to 63 near the corners In other words the flat field response function is steep near the edges where Star 8 is located In this scatter plot Star 8 near the FOV edge exhibits excessive scatter whereas Star 5 near the FOV center is well behaved Star 8 moved 8 pixels during the observing session and the flat field correction during this movement ranged from 9 4 to 10 0 This suggests that the flat field correction was imperfect and produced an extra component of magnitude variation that was not present for stars near the center or
191. rve exoplanet transits My 2002 transit observation was made from my backyard in Santa Barbara CA located only 200 feet above sea level Dark skies are also not even a requirement my Santa Barbara residence was within the city and my skies didn t even resemble dark until after midnight For pretty picture imaging where dark skies matter more I disassembled my telescope and put it in my trunk for a drive to the nearby mountains I now live in Arizona but my darker skies are only a bonus not a requirement What about seeing Good atmospheric seeing is nice but again it s not a requirement I actually had more moments of good seeing in Santa Barbara than here in Arizona at a 4660 foot altitude site In fact some of the sharpest images of planets come from Florida and Singapore both sea level sites Seeing is mostly influenced by winds at ground level and the height of the telescope above ground My median seeing in Arizona is 3 0 arc for typical exposure times 30 to 60 seconds Telescope aperture matters yes but an 8 inch aperture is adequate for the brighter transiting exoplanets 10 magnitude For most transiting exoplanets a 12 inch aperture is adequate Since the cost performance ratio increases dramatically for apertures above 14 inches there are a lot of 14 inch telescopes in amateur hands I ve never owned anything larger and everything in this book can be done with this size telescope My present telescope is a 14
192. rving session Even when a reasonable fit is achieved using different color reference stars be prepared for errors in transit depth and timing Blue Blocking Filter Some observing situations are best approached using a blue blocking filter As the next graph shows it blocks everything blueward of V band PASSBANDS FOR BVRI BB amp JHK FILTERS 1 0 0 94 Rc ne J H K Vue A w ead B Sn nn TRANSPARENCY AT ZENITH e Cn L f o44 iT 034 Li 0 2 4 0 14 oo fbi ti di Swi DEC E i ZELLE Li i i i 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 WAVELENGTH nm Figure 14 10 Filter response functions times atmospheric transparency for standard B V Rc Ic filters as well as the 2MASS J H and K filters Also shown is the blue blocking BB filter response Actual response functions will depend on the CCD response The BB filter is attractive for two reasons 1 it reduces a significant amount of sky background light whenever the moon is above the horizon and 2 it reduces extinction effects by a large amount without a significant SNR penalty Concerning the first point the night sky brightness spectrum will be similar to the site s extinction spectrum during moon lit nights On moonless nights there s no reduction of sky background level from use of a BB filter For these reasons at least one
193. s Wide field camera candidate follow up 22 CHAPTER 3 EXOPLANET CHOICES Calculating Ephemerides for BTEs Many of the exoplanet observing projects listed above involve the BTEs This section describes how to calculate when their transits occur The following list of known transiting exoplanet systems brighter than 13 magnitude is complete as of mid 2007 It is presented as an example of the kind of list that each transit observer will want to maintain until such time as it is maintained by an organization dedicated to serving the amateur exoplanet observer cf Chapter 17 s description of my idea for an Exoplanet Transit Archive At the present time http exoplanet eu catalog transit php is an excellent web site listing transiting exoplanets maintained by Jean Schneider Since it does not list transit depth transit length object coordinates or other information useful for planning an observing session I maintain a spreadsheet of transiting exoplanets brighter than 13 magnitude BTE _list xls Go to http brucegary net book EOA xls htm for a free download of it Here s a screen capture of part of it Object V Depth Length Period HJDo Opposition RA Dec Discovery Name Mag mmag hr day add 2450000 mo fr Date 15 HAT P 3 1186 14 2 1 2 889703 4218 7594 4 5 13 740 48 03 2007 14 XO 3 98 85 27 3 19142 3351 9663 12 0 4 xxx 57 xx 2007 13 GJ485 10 68 8 0 6 254385 4222 616 3 5 11 703 26 71 2007 12 X0 2 11 18 14 5 2 7 2 615838
194. s as shown in the next figure We ve just shown that when using a B band filter hot and cool stars can distort LC shapes by the amount 16 mmag per airmass in opposite directions producing opposite LC curvatures What about the other filters For R band the two zenith extinctions are 0 120 and 0 123 mag airmass for cool and hot stars The difference is only 3 mmag airmass which is much less than for B band Nevertheless a LC bulge of 3 mmag airmass is important for depths as shallow as 10 to 20 mmag Unfiltered observations are more dangerous than filtered ones when choosing reference stars on the basis of color A cool star has an effective zenith extinction coefficient of 0 132 mag airmass unfiltered versus 0 191 mag airmass for a hot star That s a whopping 59 mmag airmass Clearly attention to star color is more important when observing unfiltered A much less serious warning applies to observations with a blue blocking filter described in greater detail later 80 CHAPTER 14 STAR COLORS All of the above cited zenith extinction coefficient dependencies on star color are for a site at 4660 feet Lower altitude sites will experience greater effects LIGHT CURVE OF TARGET NO TRANSIT USING REFERENCE STARS OF DIFFERENT COLOR 0 040 o TARGET MINUS BLUE REF TARGET MINUS RED REF 0 030 4 0 020 4 B Q o o o o o n HUS nnns 0 010 4 DOUnunuuuuaguagnaganunoeo BLUE MAGNITUDE DIFFERENCE 0 000 4
195. s you to change the radius The photometry for all images is immediately recalculated click the graph s Save button and save the CSV file with another descriptive name such as 1 1 where the value for r is different When finished creating CSV files for all the signal apertures of interest click Close and you re back to MDL s main work area All files in working memory may be deleted alt F E Perform the above analysis with the other two groups of 150 raw images Use different CSV filenames of course such as 2 r and 3 r where the r stands for the signal aperture radius If more than one signal aperture is used the CSV file names could look like the following 1 10 2 10 3 10 for the 10 pixel radius photometry and 1 12 2 12 3 12 for the 12 pixel radius photometry etc This completes the image processing phase of analysis 66 Chapter 13 Spreadsheet Processing I hope you re somewhat familiar with spreadsheets I use Excel which I think can be found on every computer using a Microsoft operating system If you use a different spreadsheet then you ll have to translate my instructions to whatever is needed by your spreadsheet Let s assume that after doing the image processing described in the last chapter we have 3 CSV files They re in ASCII i e text format and the data lines will look something like the following p JD Ts Obj L Refl CREL Chk2 n ORKI Chk4 a Chke5 2454223 6114930
196. s can be wrong by an hour or two When planning an observing session for a candidate it 1s wise to allow extra observing time before ingress or after egress to be sure of capturing it Otherwise you may issue a no show report that can be misleading Exoplanet candidate observing can be useful if only a partial transit event is observed This at least will show which star is undergoing transit and it is usually possible to categorize the candidate as being an EB blend versus a shallow transit from measured depth of only a part of the transit event Therefore when planning a night s observations it s OK to selecting a candidate when only part of the predicted transit can be observed Many of the considerations presented in Chapter 3 for selecting an exoplanet for a night s observations also apply to selecting an exoplanet candidate 114 APPENDIX C Algorithm for Calculating Air Mass from JD Site Coordinates and RA Dec 1 Subtract 2451545 from JD 2 Multiply this by 24 065709824419 and add 18 697374558 3 Subtract 24 x INT above value 24 4 Add EastLongitude 15 this is GMST 5 If 0 add 24 this is LST 6 Multiply by 15 and subtract RA deg this is LHA 7 If LHA gt 180 subtract 360 8 Calculate cosine LHA i e Cosine LHA 57 2858 9 Multiply by Cosine Latitude 10 Multiply by Cosine Dec 11 Add Sine Dec x Sine Latitude 12 Air mass is reciprocal of above LTS APPENDIX D Pl
197. s is the subject of the next section Deciding on FOV Placement Even if the observations were to be near zenith there s a situation that can influence filter choice It has to do with what stars are near the target star To be more specific it has to do with the feasibility of positioning the CCD s main chip FOV so that a bright star 1s present in the autoguider chip s FOV it also has to do with the desire to have same color bright reference stars present in the main chip s FOV This is where TheSky Six is very helpful as the next figure illustrates Figure 4 01 XO at center of main chip FOV Autoguider chip s FOV is on left 30 CHAPTER 4 PLANNING THE NIGHT This figure is a screen capture inverted of TheSky Six with my main chip s FOV centered on XO 1 There are no bright stars in the autoguider s FOV so this positioning is unacceptable By moving slightly to the right a sufficiently bright star can be used for autoguiding V mag 11 3 according to TheSky This improved positioning is shown in Fig 4 02 The next consideration is what stars can serve as reference for XO 1 There s a bright star in the upper left corner but is it the same color as XO 1 Using TheSky a click of the mouse on XO 1 then a click on the star in the upper left leads to the answer XO 1 s J K 0 412 and the bright star s J K 0 218 The bright star is bluer than XO 1 by delta J K 0 194 The bright star is also 1 38 magni
198. s not true for precision photometry I strongly recommend the use of dark frame subtraction for all flats When exposing flats of the sky near zenith after sunset exposure times have to be increased every few minutes to assure that the maximum count is within a range of values that is slightly below values where non linearity and other versions of saturation occur For 16 bit CCDs A D converter saturation occurs at 65 535 counts counts and ADU are the same thing The conventional wisdom is to keep the maximum flat field counts within the range 30 000 to 35 000 the latter value being where many observers believe non linear effects can be expected Images with maximum counts lower than 30 000 can be used but the noise component for these 1mages is a greater percentage of the signal component and they may reduce the quality of the combined flat images the master flat Every time the exposure time is changed a new dark frame has to be taken for use with that flat and those following with the same exposure This can slow things down but that s a fair price to pay for the assurance of minimizing the effects of bad pixels later My CCD is linear up to 59 000 counts and I suspect that the common wisdom of avoiding exposures that produce counts above 35 000 is out of date for modern CCDs Each observer will want to measure their CCD s linearity range in order to know how to be guided on setting flat field exposure times as well
199. s observing scheduling of flat frames will have to be made later than shown in Fig 5 02 as explained in the next chapter Finalized Plan In the observing log we note that the goal for the night is an XO 1 transit and we include the ingress and egress times We note that an I band filter will be used and 2x2 binning will be employed We don t know when to start flat fields yet but we know it will be close to sunset No configuration changes were made since the previous observing session and none are planned for the new observing session so that s noted Since we ll complete observing at 1 30 AM there s no need for a nap We have time before observing begins so how about joining me for dinner at Delio s Pizza a few miles from my place Besides every observing session can benefit from pizza snacks a dark beer and observing music There s only one more thing to do before we can go to dinner however scheduling flat field observations That s the subject of the next chapter 33 Chapter 5 Flat Fields It would be nice if CCDs responded to a uniformly bright source such as the daylight sky by producing the same output counts for all pixels This does not happen for two reasons pixels differ slightly in their efficiency at converting photons to electrons and converting electrons to counts during readout and a uniformly bright sky does not deliver the same flux of photons to all CCD pixels due to such optical effects as vignetting
200. s that the polar axis be aligned perfectly Consider observing a source at 60 degrees declination with a polar axis alignment error of only 0 1 degree During a 6 hour observing session the image would rotate as much as 0 2 degree The effect is greater for higher declinations If the autoguider is located 20 arc from the center of the main chip for example then stars in the middle of the FOV will move 7 arc during the observing session and stars near the corners farthest from the autoguider will move more If a good quality flat field correction were not made this amount of movement could be ruinous if a target or reference star moved across a dust donut The vignette response function is usually steep near the edges so this is where small inaccuracies in the flat field can produce errors with systematic trends If a 2 arc polar alignment error is present then these effects would probably be too small to correct for but perfect autoguiding would still be required Although it s a worthy goal for amateurs to achieve a perfect polar alignment and to 35 CHAPTER 5 FLAT FIELDS achieve perfect autoguiding flat field corrections are a prudent safeguard and must be performed I ll use my telescope system to illustrate how the scheduling of flat frames can be done at about sunset I point the telescope at zenith well before sunset and place a double T shirt diffuser over the aperture illustrated in the next figure The two whit
201. sier way to have this capability is to download a sample spreadsheet from http brucegary net book EOA xls htm The user then imports the other two CSV files to the spreadsheet below the previous one and deletes title lines A better procedure is to concatenate the three CSV files to one CSV file using Windows Notepad then import this one CSV file to the spreadsheet 68 CHAPTER 13 SPREADSHEET PROCESSING The next spreadsheet page is devoted to plotting an extinction curve It copies contents from the first page converts JD to UT and does other things Here s a screen shot of the left half of this page ele D a ee ee eR Intercept 8 889 1 0 9 06 Extr 0 168 l 2 0 9 23 3 0 9 39 R band ZeroShit 19 923 m 0 m 0 m 0 m 0 m 0 m 0 Cy UT TotFlux Mag m Opacity Obj Chkl Chk2 Chk3 Chk4 Chk5 00 2 676 3579 9 099 1 109 0 023 10 716 12 900 11 659 10 835 12 696 11 144 2 585 3613 9 086 1 107 0 013 10 715 12 941 11 646 10 827 12 669 11 126 2 713 2 732 2 751 2 769 2 788 2 807 2 825 2 844 2 853 2 881 2 900 2 918 2 937 2 956 2 975 2 994 3 012 3 031 E 4 15 18 21 3 050 22 3 068 amp E a E a amp lt ul a gt E i ee m m ee l Ma iMa O D OO C O1 A CO h2 OW CO C C1 A CO N AIR MASS NOTROT ROT ROT ROT ROT ROT ROT ROT RO gt gt d a d d a f a mss S S E s e eem moe Figure 13 04 Left side of the second spreadsheet page T
202. sists of two parts 1 processing images to acquire star fluxes for several stars from many images and 2 converting these star fluxes to a light curve using a spreadsheet This chapter deals with the first part processing images and creating files of star fluxes that can be imported to a spreadsheet for performing the second analysis part Please view the specific instructions as merely one way to deal with issues that you will want to deal with using whatever tools you feel comfortable using My examples will be for the MaxIm DL MDL user so if you use another image processing program you ll want to just glean concepts from my explanations Imagine that we have 450 raw images from a night s observations This could be from a 6 5 hour observing session consisting of 60 second exposures Given that my RAM is limited to 1 GB there are limits to how many images I can load without having to use virtual RAM which really slows things down By setting MDL to disable the undo feature it is possible to work with twice as many images in working memory My CCD has pixel dimensions of 1530 x 1020 and a 1x1 unbinned image uses 1 1 Mb of memory compressed I can easily load 150 raw images into working memory without involving virtual RAM This is 1 3 of the 450 images to be processed so what I ll describe in the next few paragraphs will be done three times Each user will have a different limit for the maximum number that can be loaded into working m
203. ss distance OR do it manually by following the steps below 4 Determine the star s radius Rstr and mass Mstr from B V cf Fig D 18 5 Calculate 1st iteration of Rp Rj using following equation Secondary size Rp Rj 9 73 x Rstr x SORT 1 10 D 2500 6 Calculate secondary s orbital velocity central transit length and miss distance using these equations Planet orbital radius a 1 496e8 x Mstr x P 36525 where P days Mstr sun s mass amp a km Transit length maximum Lx Rstr x Rsun Rp Rj x Rj 2 a 24 x P where Rsun 6 955e5 km Rj 7 1492e4 km Miss distance m SQRT 1 L Lx 7 Using the miss distance and filter band determine limb darkening effect LDe cf Fig D 19 8 Convert the measured transit depth D to a value that would have been measured if there were no limb darkening using the following eq D D LDe 9 Repeat steps 5 6 and 7 using D instead of D 10 If step 7 LDe is the same as the 1st time then there s no need for additional iterations The last calculated Rp Rj is the answer Otherwise repeat steps 5 8 until a stable solution emerges 133 APPENDIX D PLANET SIZE MODEL TRANSIT DEPTH vs PLANET SIZE LC SHAPE amp MISS DISTANCE DEPTH mmag Rp Rstz0 08 00 01 02 03 04 05 06 OF 08 09 10 LC SHAPE PARAMETER S Figure D 17 If the D S location for the LC is above the red line corresponding to the star s B V then it s probably an EB If
204. st that this is adequate for jumping in and starting exoplanet observing without paying your dues to the AAVSO conducting variable star observations The concepts are straightforward for anyone with a background in the physical sciences What are the entry costs for someone who doesn t own a telescope but who has experience with measurements and data analysis in other fields Here s an example of what I would recommend as a starter telescope system for such a person Meade 10 inch telescope monochrome 16 bit CCD with color filters equatorial wedge for polar mounting Maxim DL CCD Total cost about 5000 Celestron telescopes are another option but their large aperture telescopes gt 8 inch are mounted in a way that requires meridian flips and these can ruin the light curve from a long observing session It has been estimated that tens of thousands of astronomical CCD cameras have been sold during the past two decades and most of these were sold to amateur astronomers The number of telescopes bought by amateurs is even higher Many of these amateur systems are capable of observing exoplanet transits Amateur astronomy may not be the cheapest hobby but there are many more expensive ones With the growing affordability of CCD cameras and telescopes and a consequent lowering of the 5000 entry level the number of amateurs who may be tempted by exoplanet observing in the near future may be in the thousands 12 CHAPTER
205. t are correlated with their colors Since J K colors are available for almost all stars that an amateur will encounter for this purpose I have chosen to use this color instead of B V Knowing a star s J K means that we can infer the star s radius and mass assuming it s a main sequence star Knowing the secondary s orbital period allows us to calculate its orbital radius using the simple relationship that orbital radius is proportional to P times total system mass From orbital radius and period we can calculate the secondary s orbital velocity and combining this with the star s radius we can derive the time it takes for a central crossing If we define transit length to be the full width at 1 3 maximum for the transit feature then we have a parameter that closely corresponds to the time it takes for the center of the secondary to traverse the transit chord across the star Exoplanet transits from survey cameras will fold many transit events to produce a less noisy transit shape It will have a noise level 5 to 15 mmag that is not much smaller than transit depth In practice the transit length listed in the survey candidate catalog will be shorter than contact 1 to contact 4 and is often an approximation of full width at 1 3 113 APPENDIX B SELECTING TARGET maximum To the extent that this is true the above figure will give reliable guidance on maximum possible transit length Exoplanet candidate ingress and egress time
206. t of 65 535 156 GLOSSARY SBIG Santa Barbara Instruments Group located in Goleta CA west of Santa Barbara formerly located in up scale Montecito east of Santa Barbara and never located in Santa Barbara scintillation Intensity fluctuations of stars observed from the ground caused by atmospheric temperature inhomogeneities at the tropopause Scintillation can vary by large amounts on minute time scales doubling but time average fluctuation levels are fairly predictable using dependencies on air mass site altitude telescope aperture wavelength and exposure time sky background level Average counts within the sky background annulus Dark current is one contributor to background level and it increases with CCD temperature doubling every 4 degrees Centigrade Sky brightness is another contributor A full moon will raise sky brightness from 21 magnitude per square arc to 17 or 18 magnitude square arc The increase is more than 3 or 4 magnitudes in B band which is the motivation for using a BB filter when moon light is present SNR signal to noise ratio the ratio of measured flux to SE uncertainty of that flux For bright stars SNR is affected by Poisson noise and scintillation whereas for faint ones the dominant components are thermal noise generated by the CCD silicon crystals dark current electronic readout noise and sky background brightness SNR mmag 1086 SNR star color Difference in magnitude betw
207. t one LC The amount of effort needed for producing good exoplanet LCs will depend on the shortcomings of your telescope system The closer to professional your system the less effort required If your telescope tube is made with materials that don t expand and contract with changing ambient temperature then one category of concern is removed If your observing site is high and remote from city lights other categories of concern are reduced If your aperture is large and collimation is good SNR and blending issues are less important The next two chapters are presented for observers with moderate apertures 8 to 14 inches at poor to moderate sites sea level to 5000 feet with telescope tubes that require focusing adjustments as temperature changes and with equatorial mounts that may have polar alignment errors of 0 1 degree or greater These shortcomings probably apply to most exoplanet observers Let s review some of the LC shortcomings that may be acceptable for variable star observing but which are not acceptable for exoplanet observing Some of these have been mentioned in the preceding chapters but others have not An imperfect polar alignment will cause image rotation which causes the star field to drift with respect to the pixel field during a long observing session This causes temporal drifts and possibly variations whenever the flat field 1s imperfect and no flat field is perfect The size and shape of star
208. tached to the focus knob s 10 1 reducer shaft I try to avoid reversing direction for two reasons 1 the mirror changes tilt enough to cause image shift and 2 the hysteresis amount is not exactly the same for each reversal of direction so I can never achieve an accurate adjustment with one command when a reversal of direction is involved Before explaining the strategy I ve adopted for this problem I should describe results of my measurements of desired focus setting in absolute position readout counts versus temperature and elevation angle It is believed that the most important cause for needing to make a focus change is the telescope s change in temperature As a telescope cools the tube shrinks and this requires that either the CCD assembly must be moved out or the mirror must be moved in For my telescope there is an additional factor contributing to the need for focus adjustment elevation angle I ve produced a plot of desired focus setting versus elevation angle for a selection of temperatures For a typical observing session the elevation angle effect is more important than temperature effects Moreover due to hysteresis there is a different set of desired focus setting traces for inward versus outward adjustments and they are offset by the hysteresis amount the 650 steps mentioned above Inward focus adjustments are required when temperature cools with time during an observing session After transit th
209. tar Each star will move though an arc whose length will be greater for stars farthest from the autoguider s guide star The main chip s FOV will change during the observing session and any reference stars near the FOV edge are at risk of being lost An important goal of exoplanet transit observing is to keep the star field viewed by the main chip fixed with respect to the main chip s pixels Therefore autoguiding will be most successful if the mount s polar axis is aligned accurately Observer Involvement with Monitoring Amateurs have different philosophies about how much attention must be given to observing during an observing session Some prefer to start the entire process with a script that controls the various control programs I prefer a greater presence in the control room throughout the observing session After the flats have been made and an observing sequence has been started it may be theoretically possible to go to bed with an alarm set for the end of the session I like to spot check such things as auto guiding focus setting seeing extra losses CCD cooler setting and record items in an observing log at regular intervals After all if a passing cirrus cloud causes the autoguider to lose track the following observations will be useless until the observer reacquires the autoguider star Autoguiding needs are the main reason I stay involved with observing for the entirety of an observing session As you may have gathered from
210. tar the BB filter delivers 89 of the counts delivered by a clear filter at zenith For a red star it is 94 The corresponding increases in observing time to achieve the same SNR are 41 and 13 However SNR also depends on sky background level and the BB and clear filters respond differently to changes in sky background During full moon the sky background is highest being 3 magnitudes brighter than on a moonless dark night away from city lights Also during full moon Rayleigh scattering of moonlight produces a blue colored sky background I haven t studied this yet but I suspect that whenever the moon is in the sky the BB filter s lower sky background level is more important than the few percent loss of signal leading to an improved SNR instead of a degraded one In any case a slight loss of SNR is worth extra observing time in order to achieve dramatic reductions of systematic errors in light curve baseline curvature that would have to be dealt with for unfiltered observations Getting Star Colors The 2MASS 2 Micron All Sky Survey star catalog contains billion entries It is about 99 complete to magnitudes corresponding to V mag 17 5 TheSky Six includes J H and K magnitudes for almost every star in their maps The latest version of MPO Canopus with PhotoRed built in makes use of J and K magnitudes to calculate B V Rc and Ic magnitudes J K star colors are correlated with the more traditional star colors B V and V R as shown
211. te came from the light curve shape S and extra information about miss distance The consistency check 1s successful Our goal in this section is merely to distinguish between exoplanet light curve shapes and EB shapes It will be instructive to consider secondaries at the threshold of being a star versus a planet This is generally taken to be Rp Rj 1 5 For such threshold secondaries the Rp Rstr will depend on the size of the star which in turn depends on its B V spectral type Let s list some examples going from blue to red stars Blue star B V 0 30 spectral type F1V Rstr Rsun 1 5 Rp Rstr 0 10 Sun like B V 0 65 spectral type G2V Rstr Rsun 1 0 Rp Rstr 0 15 Red star B V 1 20 spectral type K6V Rstr Rsun 0 7 Rp Rstr 0 22 127 APPENDIX D PLANET SIZE MODEL The following figure shows the dependence of threshold secondary Rp Rstr versus B V THRESHOLD SECONDARY Rp Rstr vs B V 0 24 0 23 0 22 0 21 0 20 0 19 0 18 0 17 0 16 0 15 0 14 0 13 Rp Rstr for Threshold Secondary 0 12 0 11 0 10 0 09 0 08 B V Figure D 12 Relationship of threshold secondary Rp Rstr versus B V In order to use the above figure to distinguish between exoplanet versus EB shapes we need to take into account the primary star s color For example if B V is sun like we can draw a vertical line at Rp Rstr 0 15 and consider everything leftward to be exoplanets and everything rig
212. te exposures due to the difference in number of image downloads Using the previous example in which a 4 minute exposure has a 7 advantage in duty cycle compared to 1 minute exposures we can calculate that a sequence of 4 minute exposures will have a 3 496 lower scintillation per unit of observing time than the sequence consisting of 1 minute exposures sqrt 1 07 1 034 The same argument can be applied to Poisson noise described in Chapter 15 The fractional uncertainty of a flux measurement due to Poisson noise is proportional to l flux and since flux is proportional to exposure time the same ig relationship exists between Poisson noise and exposure time I don t know of an objective way to assess all these factors but they will be different for each observatory It is my subjective opinion that 60 second default exposure time is a good compromise when saturation considerations permit it 47 Chapter 8 Focus Drift I once neglected to lock the mirror after establishing a good focus and went to sleep while observing a transit candidate I m glad this happened the focus drifted and caused an effect that was too obvious to ignore and this led me to investigate causes The problem showed itself as an apparent brightening of the target relative to several reference stars near the end of the observing session 11 830 11 840 4 11 850 4 11 860 4 11 870 4 11 880 4 se Doe eles ze denen 11 890 392775
213. th extinction is typically 0 25 magnitude AirMass Changing AirMass from 3 to 1 can therefore be expected to change a star s measured brightness by 0 50 magnitude This corresponds to a flux ratio of 1 6 i e 2 512 We therefore must reduce our desired Cmax for test images to 10 400 counts 16 700 1 6 At lower altitude observing sites the correction would be greater See Fig 14 04 for a graph that can be used to estimate zenith extinction for other observing site altitudes for each filter band Imagine the frustration of choosing an exposure time that produces Cmax 35 000 counts at the beginning of a long observing session and discovering the next day when the images are being reduced that the brightest stars and maybe the target star were saturated in most images This is a case where a small effort at the beginning of observations can lead to big payoffs for the entire observing session 45 CHAPTER 7 EXPOSURE TIMES Information Rate When all stars of interest in the FOV are faint the previous considerations may not be important In this case different criteria should be used to choose exposure time Starting with a trivial example if transit length 1s expected to be 3 hours it would be foolish to take exposures as long as an hour even though at least one of them would be completely within the transit phase At the other extreme we don t want exposures to be significantly shorter than the time required for downloading eac
214. the image MAG MAG SCATTER PLOT FOR TWO STARS SAME COLOR amp DIFFERENT LOCATION 2007 02 16 UNFILTERED 12 38 12 38 4 12 37 4 12 36 4 12 35 4 CV of STAR 5 B V 0 55 N 2 4 12 33 4 12 32 4 12 31 T T T T T T T T 1 11 25 11 26 11 27 11 28 11 28 11 30 11 31 11 32 11 33 CV of STAR 48 B V 0 53 Figure A 05 Mag mag scatter plot for two stars with same color but far apart 5 arc for the same 6 hour unfiltered observing session of 2007 02 16 The purpose of the mag mag scatter diagrams is to detect whether flat field error effects are present For the case illustrated by the previous two figures there appears to be a problem with stars close to the FOV edge When this happens stars near the edge should not serve as reference stars since the mag mag scatter plot does not tell us how to adjust the flat field This is one reason the target and candidate reference stars should be placed near the FOV center 106 APPENDIX A EVALUATING FLAT FIELDS All sky Photometry Method for Flat Field Evaluation There are 1259 Landolt stars that have been calibrated with extreme accuracy Landolt 1992 Most of them are in groups of 20 to 50 stars located along the celestial equator at RA intervals of 1 hour Most Landolt stars have been observed on several occasions and have been accepted for inclusion when they are found to be constant but long term variables are occasionally encountered I ve found two Each gro
215. the important matter of light curve baseline curvature produced by the use of reference stars having a different color than the transited star 74 Chapter 14 Star Colors For LC analyses of variable stars where the goal is to measure changes with precisions of 10 to 50 mmag it is common practice to use as many reference stars as possible in an ensemble mode For eclipsing binaries which have deep transits this is also an acceptable practice But when the transit depth is less than 25 mmag as any exoplanet transit will be it matters which stars are used for reference The problem arises when the target and reference stars have different colors This is because a red star exhibits a smaller atmospheric extinction compared to a blue star regardless of the filter used Atmospheric Extinction Tutorial We need to review some basic atmospheric extinction theory in order to better understand why star color matters The atmosphere has three principal extinction components in the visible region 1 Rayleigh scattering by molecules 2 Mie scattering by aerosols dust and 3 resonant molecular absorption by oxygen ozone and water vapor The first two components are more important than the third The Rayleigh scattering component is shown in the next figure RAYLEIGH SCATTERING Rayleigh SeaLevel Rayleigh 4600 ft Rayleigh 7500 ft S B Passband 25 en V Passband R Passband Passband 0 30 3 0
216. the main chip that assures the autoguider s FOV includes a star bright enough for autoguiding Using a 14 inch telescope a star with V mag 11 is acceptable for 5 Hz autoguiding when using an R band filter If the brightest star that can be placed in the autoguider s FOV is fainter it may be wise to consider observing with either a clear filter or a blue blocking filter described in Chapter 14 My CCD with a photometric B band filter produces star fluxes that are only 16 of flux values produced by an R band filter by a typical star so a star would have to be 2 magnitudes brighter to be useable for B band autoguiding 55 CHAPTER 9 AUTOGUIDING With an SBIG tip tilt image stabilizer it is usually possible to produce long exposure images that are as sharp as those in the average short exposure unstabilized images Tracking is possible for the entire night provided cirrus clouds don t cause the autoguide star to fade significantly Image Rotation and Autoguiding As pointed out earlier whereas a successful autoguide observing session that lasts many hours will keep the autoguider star fixed to a pixel location on the autoguider chip if the telescope mount s polar axis is imperfectly aligned the main chip s projected location on the sky will rotate about the autoguide star during an autoguided observing session This will be seen in the main chip images as a star field rotation about an imaginary location corresponding to the autoguider s
217. the night In order to know if it is safe to observe with 2x2 binning instead of 1x1 we need to calculate the sharpest seeing expected during the observing session At my site FWHM is typically 3 0 arc at zenith Our smallest air mass for the night will be 1 5 Since FWHM is proportional to AirMass cf Chapter 7 we can plan on FWHM gt 3 4 arc A plate scale of 1 7 arc or smaller could be used without serious degradation to photometry precision Since my 1x1 plate scale is 0 67 arc we could bin 2x2 and the plate scale of 1 34 arc would be acceptable Based on this we note in the observing log that we plan on 2x2 binning Why observe 2x2 instead of 1x1 There are two reasons Modern CCD chips perform on chip binning and they have less read noise for 2x2 versus 1x1 binning The component of readout noise is reduced by a factor two for 2x2 binning since there is only one readout for a 2x2 reading versus 4 readouts for reading the same 4 individual pixels and noise grows as the square root of the number of readouts The second benefit for 2x2 binning is that download times are 4 times faster e g 2 seconds instead of 8 seconds and this improves the percentage of time spent collecting photons during an observing session cf Chapter 7 Knowing whether 32 CHAPTER 4 PLANNING THE NIGHT binning is going to be used affects when flat frame exposures of the twilight sky can begin If 2x2 binning is chosen for the night
218. the two reference stars into agreement with what is expected for them from an atmospheric model for extinction 12 38 11 62 FU 1 11 37 0 76 10 76 10 82 10 50 R 0 55 10 18 3 14 81 _ 13 07 4 10 25 12 17 XO 3 8 980 11 30 0 45 9 54 1 74 9 28 4 10 13 9 03 15 34 i 1 90 1384 7 15 52 1 10 538 g 01259 gt 13 46 11 51 206 1241 AL 12 67 gt 926 11 87 gt e 9 87g 11 43 0 49 8 50 10 92 8 21 Figure 15 01 XO 3 star field showing BVRclc colors of several stars The B V star colors are shown in large blue numbers Using the above example the ensemble photometry adjustment will have an uncertainty given by x 1 78 0 7320 0 96 mmag The general equation for this homework for the reader is V Ensemble Photometry Poisson SE 1 n x SE SE SE SE where n is the number of reference stars and SE are the Poisson uncertainties for each reference star expressed in mmag units Clearly as n increases the effect of uncertainties due to Poisson noise diminishes approaching the limit zero for an 89 CHAPTER 15 STOCHASTIC ERROR BUDGET infinite number of reference stars XO 3 s Poisson noise uncertainty of 1 22 mmag must be orthogonally added to the Poisson uncertainty produced by the reference stars Hence after performing an ensemble photometry adjustment using these two Ys reference stars XO 3 will exhibit a total Poisson noise uncertainty of 1 227
219. their CCD linearity in ways that reveal safe Cx limits The payoffs are significant By adopting higher Cx limits longer exposures are permissible and this reduces scintillation per image it reduces Poisson noise per image it reduces the importance of read noise and it improves information rate due to smaller losses to image download time 147 APPENDIX F Measuring CCD Gain Steve Howell s book Handbook of CCD Astronomy 2000 presents a way to measure CCD gain using only bias frames and flat frames I ll embellish his description in ways that could be helpful for typical amateur hardware I suggest making 3 pairs of bias frames and 3 pairs of flat frames in quick succession Only one pair of each is needed to get one gain measurement but 3 pairs allows for a way to estimate the accuracy of the result Crop all of them the same way to preserve the flattest part of the flat field Cropping may also be influenced by the desire to avoid known bad pixels Sum and difference each pair calling the sums Bs and Fs and calling the differences Bd and Fd where B denotes bias frames and F denotes flat field frames In performing a difference be sure to specify that the image processing program adds a fixed amount of counts to all pixels such as 100 counts if you don t do this about half the pixels will be zero and this will ruin the SE calculation In performing a difference between flats subtract the lower value flat from the higher value f
220. tics and collimation and short exposures 0 1 to 1 second Seeing as it is often referred to will depend on exposure time and elevation angle Seeing FWHM increases approximately as a constant plus sqrt g where g is exposure time Seeing FWHM also increases with air mass as approximately airmass Amateurs using CCDs usually say the seeing is good when FWHM 3 0 arc Professionals would say the seeing is good when FWHM 1 0 arc Seeing degradation is due mostly to ground level temperature inhomogeneities caused by wind driven turbulence The scale height for this component of seeing 150 GLOSSARY degradation is 7 meters Other components of seeing are at the top of the planetary boundary layer 5000 feet and tropopause 25 000 to 55 000 feet binning Combining of groups of pixels either 2x2 or 3x3 during the readout phase of collecting electrons from pixels to an output register for the purpose of achieving faster image downloads that have less readout noise used when the loss of spatial resolution is acceptable blackbody spectrum Plot of power energy per unit time radiated by a 100 emissive material such as an opaque gas per unit wavelength versus wavelength A version also exists using power per unit frequency A star s atmosphere is 100 emissive no reflections and radiates with an approximate blackbody spectrum Narrow absorption lines are produced by atoms and molecules at higher altitudes and c
221. traight line fit This corresponds to a constant period So far however all observations are clustered near opposition at yearly intervals so a one year periodicity cannot be ruled out Other periodicities appear to be constrained to amplitudes less than 0 001 day or 1 4 minutes XO 1B TRANSIT TIMINGS P 3 941510 DAY 0 020 0 010 4 X 4 a 4 im 1 l w ooo 4 M t4 uoc o ub 6 z E 0 010 4 HJDo z 3808 9170 D 020 T T T T T T T T T T T T 3100 3200 3300 3400 3500 3600 3700 3800 3900 4000 4100 4200 4300 HJD Figure 16 01 Transit timings for XO 1 This is just one example of what amateurs are capable of doing in a search for timing anomalies As more amateurs join the ranks of exoplanet transit observers there will be a more data dense archive of timings to work with for this and the other exoplanets Light Curve Shape Anomalies Jupiter and Saturn both have rings and moons so it is reasonable to wonder if hot Jupiter exoplanets also have them Specifically can amateurs detect their presence from high quality light curves Shortly after TrES 1 was announced in 2004 a group of amateurs observed transits of this exoplanet and shared their light curves I saw evidence of a brightening right 96 CHAPTER 16 ANOMALIES before ingress and possibly right after egress in several of these light curves Joe Garlitz in Oregon also noticed this unusual feature Someone called my attention to
222. trons in a pixel A CCD may be linear for readings from zero to 90 of the maximum reading possible 1 e 0 90 x 65 535 59 000 counts Linearity and saturation have different meanings but are commonly used interchangeably magnitude Ratio of star fluxes converted to a logarithm Magnitude differences are calculated using the formula dM 2 5 x LOG Si So where Si is the flux of star i and So is the flux of star o Flux ratio can be calculated from magnitude differences using the following Si So 2 512 A mmag milli magnitude magnitude 1000 median combine Finding the middle value in a set of values arranged by value The median combine process is relatively unaffected by an occasional outlier value whereas averaging is vulnerable to outlier corruption The standard error uncertainty of a median combine is 15 greater than the SE of an average provided all data are belong to a Gaussian distribution i e outliers are not present A median combine can be performed on a group of images as well as single set of values since a group of images is just a set of values for each pixel location MDL MaxIm DL Diffraction Limited s program for control of telescope CCD image stabilizer focuser and also image processing with photometry analysis 154 GLOSSARY Mie scattering Aerosols airborne dust with a circumference greater than the wavelength of light produces Mie scattering Mie scattering theory
223. tter for both the signal aperture and sky background annulus For the 2007 04 15 observations this RMS was 4 3 counts The fact that each pixel s reading has a finite uncertainty has two effects 1 the average level for the sky annulus background is not perfectly established and 2 the flux within the aperture the sum of differences between the signal aperture pixel readings and the average background level is also uncertain Among the b pixels within the sky background annulus the average count is Cb and the standard deviation of these counts is Ni which we will identify as the source for aperture pixel noise We will assume that every pixel in the image has a stochastic uncertainty of Ni The average value for the sky background level has an uncertainty given by Nb Ni sqrt b 1 Star flux is defined to be the sum of counts above a background level One way to view this calculation is to subtract the background level from each signal aperture pixel count and then perform a summation An equivalent view is to sum the signal aperture counts then subtract the sum of an equal number of background levels The second way of viewing the calculation lends itself to a simple way of calculating SE on the calculated flux since we re simply subtracting one value from another and each value has its own uncertainty The first value the sum of signal aperture counts 90 CHAPTER 15 STOCHASTIC ERROR BUDGET will be uncertain by the amount Nss
224. tude brighter than XO 1 Since the brighter star has 3 6 times the flux of XO 1 we would not be able to use an exposure time that kept XO 1 slightly below saturation That s a down side to using the bright star for reference What about the two stars that appear to be about the same brightness as XO 1 and are closer Figure 4 02 has been annotated with star color for the FOV position that includes the two same brightness stars in the main chip s FOV oim gt 0220 RN 0 56 XO XO 75 arc radius 0 65 e DO00GPS STBE Figure 4 02 Colors J K of XO 1 and possible reference stars Note that the two stars similar in brightness to XO 1 are both redder than XO 1 the average difference is 0 12 using J K colors This is half the color difference compared to using the bright blue star in the upper left and since longer exposures can be used to place all three stars just below saturation this positioning of the FOVs is a better choice An alternative would be to position the main chip s FOV so that 31 CHAPTER 4 PLANNING THE NIGHT the bright blue star J K 0 22 and the star with J K 0 56 are both within the FOV since the average of their J K colors differ from XO I s J K by only 0 01 magnitude When there s a choice between using two reference stars versus using one it is better to use two Why Because of something called scintillation that is described in Chapter 15
225. ues are converted to date format for convenience add 34981 5 and specify your favorite date format The spreadsheet includes an approximate conversion of HJD to JD accurate to 1 2 minute Columns show UT times for ingress mid transit and egress when the object is at an elevation higher than a user specified value such as 20 degrees One page is devoted to each of the 15 known BTEs The following figure shows part of the display for the XO 1 page In this figure cells C2 C6 contain BTE specific information such as HJDo period length of transit and RA Dec coordinates Site coordinates are at F2 F3 The user enters the year at G2 and the UT range that you re willing to observe in cells G3 G4 Cell H6 is a minimum elevation angle used as a criterion for display of columns E G A 4 digit version current JD is entered in cell C7 this is used to suggest to the user a number of periods elapsed since HJDo to enter in cell B10 Cells below B10 are integer periods since HJDo that lead to column C s HJD transit times Column D converts these values to UT date Columns H through AB not shown are used to calculate elevation angle at the observer s site column H Pages similar in format to this one are present for the other BTEs so by simply flipping through the spreadsheet pages it is possible to determine whether any of the BTEs are observable on a given night The user may screen capture each page and print them for later transfer to a monthly obser
226. uggestions If you don t like floundering then for the rest of this chapter imagine that you re visiting me in Southern Arizona for an instructive observing session Together we ll plan observations that illustrate decisions that have to be made for a typical exoplanet transit Let s assume that it s 2007 May 5 and you ve asked me to show you how to observe an exoplanet transit not yet chosen In the afternoon we begin an observing log This is an essential part of any observing session and starting it is the first step for planning a night s observations We begin the log by noting the time for sunset A table of sunset and sunrise times for any observing site is maintained by the the U S Naval Observatory it can be found at http aa usno navy mil data docs RS OneYear html Moonrise and set times are also available at this site CCD observing can begin about 55 minutes after sunset Sky flats are to be started at about sunset the exact time for taking flats depends on the filters that are to be used the telescope s f ratio binning choice and whether a diffuser is placed over the aperture treated in the next chapter Filter and binning choices can t be made until the target is chosen That s what we ll do next Choosing a Target Since we re going to spend 6 or 8 hours observing it is reasonable to spend a few minutes evaluating the merits of various exoplanet candidates I will assume that you 27 CHAPTER 4 PLANNING THE NIGH
227. up of Landolt stars is spread over an area that is usually larger than a typical FOV Using my FOV of 11 x 17 arc for example it is possible to include 6 to 10 Landolt stars in one image that are bright enough for an amateur to achieve a high SNR e g 7500 o a 6 0 52 e o e Figure A 06 left Flat field with V band filter to be evaluated using Landolt stars Figure A 07 right Landolt star field at RA Dec 15 38 51 00 19 33 FOV 11 x 17 arc used in evaluating flat field quality by comparing measured with Landolt magnitudes Figure A 06 is a flat field using a V band filter It is darkest in the upper right corner where a 1 095 flat field correction factor 1s required Figure A 07 is a calibrated image showing 8 Landolt stars If this image had been calibrated using a good flat field then it should reveal this fact by showing agreement with the Landolt star magnitudes at each of the 8 FOV locations sampled This is just 107 APPENDIX A EVALUATING FLAT FIELDS one of ten sets of images where each set has been positioned with RA Dec offsets so as to uniformly sample as much of the CCD area as possible If there is agreement between all 8 stars and their Landolt V magnitudes for all 10 image sets then it would be fair to surmise that the flat field is accurate A more accurate surmise would be that the large spatial wavelength components representing the flat field are accurate Using this technique the
228. using their J and K magnitudes for deriving star color Other subtle systematic effects are present at the mmag level but this review should suffice to convince the reader to be prepared for extra work if you want to produce good quality LCs Most of the extra work will involve spreadsheets I hope you like using spreadsheets because anyone who hates them won t do a good job using them The next two chapters should be viewed as a guide to the concepts that matter My specific implementation of the precautions that should be taken is just one implementation out of many that must exist Every month I improve my spreadsheets I also change some image analysis procedures though less often A year from now I would probably be embarrassed by the shortcomings of what is presented in the next two chapters I therefore recommend that you read these chapters for concepts instead of specific implementations As patent attorneys like to write into every first paragraph The following description is merely one embodiment of the invention and it is meant to include all other embodiments 63 Chapter 12 Image Processing The morning after a long observing session may require as little as an hour to perform a good quality analysis resulting in a light curve or it may take much longer Many factors dictate how much effort is required to perform the tasks described in this and the next chapter The task of converting images to a light curve con
229. ve which is the EB realm and below which is the exoplanet realm This figure allows a quick assessment of a LC s association with an exoplanet versus an EB If the LC is an EB blend such as the triplet case described by Mandushev et al 2005 there may not be a solution using either the above figure or the analysis of Section 1 To assist in evaluating this it is helpful to have transit light curves for more than one filter band Again this procedure is only as good a guide as the underlying assumptions the principal one bring that the star undergoing transit is on the main sequence 3 0 SUMMARY OF TRANSIT LIGHT CURVE ANALYSIS Much of the preceding was meant to show the underlying concepts for quickly evaluating a transit LC It may have given an unfair impression of the complications involved This section will skip the explanations for why and just present a sequence of what to do like a cookbook The figures needed by these steps are repeated after the instructions 132 APPENDIX D PLANET SIZE MODEL 1 Determine the candidate star s B V OK to derive it from J K 2 Use the measured LC to determine transit depth D and shape parameter S 2 Using D and P to determine if the LC is likely to be an exoplanet or EB or neither cf Fig D 17 3 If the LC is for an EB no more analysis is needed If it s an exoplanet then proceed 4 Use the Excel spreadsheet link below to convert B V D L and filter band to Rp Rj and mi
230. ving calendar As a convenience I mark my calendar a month ahead for all observable BTE transits Trojan searches can be scheduled by creating two additional spreadsheets One of them will require subtracting 1 6 of a BTE s period from HJDo and the other will have 1 6 period added to HJDo A fuller description of the use of this and other spreadsheets that support this book is available at the web site http brucegary net book EOA xls htm 24 CHAPTER 3 EXOPLANET CHOICES A B C D E 2 i CHUNK E M 1 XOlTransit Times 34981 5 57 30 6 75 3 3 UT times are JD if RA amp Een Tc HJD 3808 9170 2007 7 332 sl P 3 94151 day 3 5 UT window open end of twilight 4 L 2 6 hr 10 0 UT window close latest bed time ES RA 16 00 hr 508 142 5 7 Season Mo HJD JD LB Dec 28 2 deg DOY 20 ELmin min EUN 4288 desired JD UT UT UT EL Mid 4102 tal Try 121 JD mid DATE ing mid egr miday T FUT hr DOY amp 10 XO1 119 4277 957 6 26 2007 15 10 9 176 6 1 11 xO1 120 4281 888 5 30 2007 7 98 946 10 94 30 95 180 56 12 X01 121 4285840 7 4 2007 6 58 8 06 954 44 01 184 55 13 XO1 122 4289781 7 8 2007 5 18 666 8 14 568 67 188 52 14 2XO1 123 4293723 7 12 2007 3 79 5 27 675 73 5 3 192 48 15 XO1 124 4297 664 7 15 2007 2 389 3 87 5 35 86 39 196 44 16 XO1 125 4301 606 7 20 2007 7b 25 200 40 7 XO1 126 4305 547 7 24 2007 62 1 1 204 36 Figure 3 03 Sample Excel spreadsheet showing XO 1b transit events and their visibility
231. what value was used for Kv If the flat field used in calibrating these images was good then it should be possible to achieve a good quality fit for all 70 Landolt star magnitude measurements For this set of images the residuals had an RMS deviation of 0 023 magnitude A plot of these residuals versus star magnitude is shown in Fig A 08 In this figure it is apparent that some stars are persistently brighter or fainter than the model fit and this could be due to the star changing brightness during the two decades between the time the Landolt measurements were made 1980s and the present It is not unreasonable to hypothesize that a star changed brightness by 0 024 magnitude during that time this is the largest average difference found from the above fitting procedure If star brightnesses are adjusted to produce zero averages the RMS scatter becomes 0 017 magnitude Whichever choice is made the resulting conclusion is approximately the same the flat field was successful at about the 0 02 magnitude level The RMS residuals range 0 017 to 0 024 magnitude correspond to ratios within the range 1 6 to 2 2 108 APPENDIX A EVALUATING FLAT FIELDS Does this constitute a validation of the flat field Not really After all the maximum flat field correction for the flat field under evaluation is 9 5 and the typical RMS variation for star locations is 1 2 In other words the all sky photometry method for evaluating a flat field 1s s
232. with an exoplanet transit Consider another survey candidate example P 2 4 days length 2 6 hours J K 0 60 Referring to the graph again we find that the longest possible transit is 2 1 hours The survey s reported length of 2 4 hours is too long These transit numbers are incompatible with an exoplanet transit and we may suspect that this is an eclipsing binary that is blended with another nearby star An EB blending situation can lead to an incorrect J K for the star undergoing transit so it is still possible that 112 APPENDIX B SELECTING TARGET this candidate is an exoplanet but since there are so many more EB blending situations than exoplanet transit situations the odds favor the EB blending interpretation and an observer should be wary of investing time in observing such a candidate CENTRAL TRANSIT LENGTH VS PERIOD amp J K 4 0 3 8 3 6 3 4 3 2 3 0 2 8 4 0 3 5 3 0 45 50 2 5 2 0 1 5 PERIOD DAYS Lx hr 2 5 24 23 20 tein Lt siens 18 1 6 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 8 J K Figure B 01 Central transit length Lx versus J K star color and orbital period Although Appendix D contains an extensive treatment of concepts for fitting LCs to exoplanet transit models I will give a brief description here of the concepts underlying this figure Main sequence stars which comprise 90 of all stars have sizes and masses tha
233. xes of references stars produced by seeing variations will be different from image to image The effect of this upon a light curve is to merely increase RMS scatter In other words there won t be any systematic effects that would change the shape of the light curve This is my reason for including variable seeing in this chapter as noise I don t know of any study analogous to that by Dravin s et al 1993 that can be used to predict the magnitude of noise introduced to a light curve by seeing variations For the moment let s simply treat it as an unknown small effect and if empirically determined RMS scatter requires invoking something unknown we can consider seeing variations to be a candidate for explanation Comparing Observed with Predicted RMS Scatter For the 2007 04 15 observations I measured an RMS scatter of 2 63 mmag for a one hour period How does this compare with the total errors calculated in the previous sections Here s the list 1 55 mmag Poisson noise 0 36 mmag Aperture pixel noise 2 12 mmag Scintillation noise mmag Unidentified sources of noise seeing noise etc 2 65 mmag Total noise predicted 2 63 mmag Measured noise The agreement is acceptable especially considering the uncertainties The most variable of these components is scintillation noise The amplitude of scintillation can 93 CHAPTER 15 STOCHASTIC ERROR BUDGET change by a factor two during the course of minutes and night to nig
234. y which star is varying at the times when the survey cameras detect small fades from a group of stars in the camera s low resolution photometry aperture If a star is found that varies less than 30 mmag it may be an exoplanet and additional observations would then be required If the amateur light curves are compatible with the exoplanet hypothesis a professional telescope will be used to measure radial velocity on a few dates for the purpose of measuring the mass of the object orbiting in front of the bright star A low mass for the secondary almost assures that it is an exoplanet although careful additional observations and model fitting will be done by the professionals to confirm this If you re on the team of amateur observers contributing to follow up observations that lead to an exoplanet discovery you will be smiling for days with a secret that can t be shared until the official announcement is made Appendix B is included for amateurs on a team charged with wide field camera follow up observations Whenever the night sky promises to be clear and calm the amateur observer will have many observing choices I suspect that amateur exoplanet observers will eventually form specialty groups with some specializing in each of the following possible areas OOT searches for new exoplanets Trojan transit searches BTE timing anomalies produced by another exoplanet in resonant orbit Transit depth versus filter band Search for transits by nominal NTE

EXOPLANET OBSERVING FOR AMATEURS

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