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1. Tasks Superflat Fringes Smoothii Process SUPERFLAT le 256 Clear scripts Start Defaults Abort superfiat data Use unsmoothed SUPERFLAT le 7 Defringe data Adjust gains le 1 subtract SUPERFLAT FT Rescale fringe model r Messages ra _ Chop Nod sky subtraction Pattern 0110 Jd invert _ Merge sequence IR Number of groups 3 eji Collapse correction Configure r Commands Jparallel_manager sh create illumfringe para sh home prak1 all fp0_270114 images SDSS1650 4251 R Jparallel manager sh process science illum para sh home prakl all fpo 270114 images SDSS1650 4251_R Jparallel manager sh process science fringe para sh home prakl all fpo 270114 images SDSS1650 4251_R OFCS Enz an casoHouiM A ANA Figure 15 The Superflatting PG F 4 The SUPERFLATTING processing group F 4 1 Smooth SUPERFLAT create fringe model This step smoothes the SUPERFLAT that was created previously yielding an illumination correc tion that can be used to superflat the data The difference between the smoothed and the un smoothed SUPERFLAT gives the fringing model The illumination correction images are called SCIENCE i illum fits whereas the fringing models are named SCIENCE i fringe fits How to redo the task Just rerun Previous results will be overwritten F 4 2 Superflatting This step superflats your data by dividing each frame by the illumination correction How
2. Caused by the expansion of the Universe a set of comoving observers sees the recession of sur rounding objects The corresponding velocity is v de Sr H r 5 where r az and H t a is the Hubble parameter a measure of the cosmic expansion rate The observed velocity difference hence reads Av v r Ar v r H a Ar 6 From this distance velocity relation one concludes that objects surrounding the observer recede the more distant the faster Eq 6 specialised to today results in the local Hubble law Ves Ho D 7 where Hp H to is the Hubble constant and D the distance between object and observer This rela tion was observationally confirmed by Hubble in 1929 thereby proving the expansion of the Universe The Hubble constant assigns a size scale to the Universe its precise measurement still being one of the primary goals of observational cosmology today The expansion history of the Universe is typically parameterised in terms of the Hubble parameter NA HH 5 HG Qa t malt 1 Nm Q4 Mya t Q4 8 which depends on the different contribution of radiation Q matter Qm and vacuum energy Qa to the total energy content of the Universe Qi and where the curvature contribution 1 Qu Q4 0 0 for K 0 While Qm and Q4 are both of order unity Q 5 107 can be neglected at the present epoch Hence we will drop this term in the following text
3. A 1 General information e Start up Start a csh terminal by double clicking on the Desktop icon csh Change to your A 2 directory via cd fpdir photometry Then enter iraf 9 to start iraf in the current directory indicated by the dot Note The dot at the end of the command line above may seem negligible but is of utmost importance If it asks you to enter a terminal type choose xgterm This will open a new shell and a special ds9 display associated to it Within the iraf shell you can change between directories as usual using cd For all iraf tasks you can get online help by entering help taskname In order to recycle commands previously entered use the e command in combination with the up down keys Usually tasks can be run with various parameters l hese can often be set using extra command line elements but a more elegant way is given by entering epar taskname which will allow you to see the possible parameters and directly set them Use the up down keys to change to the line of the parameter of interest and enter the new value You can save and exit by entering q display To display an image enter disp imageABC fits 1 where the number specifies the ds9 frame In case only a fraction of the full frame is displayed enter set stdimage imt5 and again disp To display a multilayer image write its name and layer as disp image fits 9 A 3 imexam For image examination enter imexa
4. 3 1 2 Distances In an expanding universe distances change with time Given that objects are also not observed instantly but along a backward light cone one has to construct distance measures related to actual observables Suppose one knows the physical diameter 2R of a source at redshift z which is observed to have an angular diameter In Euclidean space one would then measure the distance to this source to be D 2R 9 where all angles are assumed to be small Accordingly one defines the angular diameter distance as exactly this ratio Dang 2 2R 0 a z fx w 9 where the final expression follows from eq 1 by letting d and ds 2R Furthermore we can define the angular diameter distance Dang 21 22 of a source at redshift z2 seen by an observer at redshift 21 lt zg as Dang 21 22 a 22 fx w z2 w z 10 which can be rewritten using eqs 1 3 8 and the fact that for light rays cdt a dw as 1 dz amp f Diss 2 8 fK x M CENSURE UE GER IO a 1 29 Ho 21 95 O E E EN Distances used in the gravitational lensing theory below always refer to the angular diameter distance Another distance measure relates the observed flux S of a source to its luminosity L For a known luminosity the distance to the source can be determined as Dium 2 A 5 gt 12 which is called the luminosity distance In a non expanding flat space this measurement would yield the same result as tha
5. a k a the dispersion spectrum Note that the method has to be used with caution when dealing with the flux normalization of the light curves The mean magnitude of the data points of both light curves must be made equal prior to calculating the dispersion function However the required normalization factors are often determined from the light curves themselves also in this case Formally this is done by adding a correction Am to one of the light curves Ideally this normalization ought to be done on the exact same portion of the intrinsic light curve of the quasar Therefore one actually does not only estimate 7 from the data but also the magnitude shift Am between the two light curves so that D D A Am The best guesses for these two parameters will be those values that minimize the dispersion spectrum In order to estimate the correct magnitude shift and time delay one can use the following procedure First get a rough estimate of the magnitude shift Am and obtain the minimum value D2 A1 Am1 of the dispersion function as well as the position A1 of this minimum Now assume that the true minimum of the dispersion spectrum is somewhere in the vicinity of this first guess Therefore one now slightly changes the magnitude shift between the two light curves to Ama and estimates a new time delay Aa and a new minimum value D As Ama and so on In this way the A Am plane is explored by looking at different rows with fixed Am Finall
6. minimum number of connected pixels and the extent pixels of the smoothing kernel This is the default method and useful for all exposures where the largest object is significantly smaller than the field of view of the detector How to redo the task Just rerun Old results will be overwritten 60 Configure sky subtraction Model the sky v Subtract a constant sky DMIN SIZE Manual override individual exposures DT 1 10 256 Get estimates Smoothing with SExtractor 5 2 Load Save Clear wv Smoothing with a Gaussian Fill Show mode Mode f Info Use all chips From each chip AG Show mosaics only Region with empty sky optional RAL xmin Du RA2 xmax J iso or Choose statistics or ymin DEC 2 ymax Defaults Cancel OK Figure 21 The configuration window for manual sky subtraction F 7 2 Coaddition The coaddition goes in three steps First global information about the data set is obtained and the reduction settings are made accordingly Then the SCIENCE images and their associated WEIGHTs are resampled Lastly the resampled images are combined 61 THELI parameter settings Processing group Coaddition Coaddition Reference RA Reference DEC Identification string Coadd these chips Coadd this FILTER R f ad Coadd image size x y Bul laa Pixel scale EE Sky position angle deg From image EE Edge smoot
7. 1 1 3 135 385 0 9 3 142 386 1 3 3 146 415 12 3 150 406 0 9 3 152 367 1 0 3 154 407 0 9 3 159 364 1 1 3 163 315 1 7 3 166 425 1 0 3 169 393 1 1 3 171 430 1 5 3 173 298 I 3 175 300 1 1 3 189 265 Lal 3 191 360 1 1 3 193 304 1 3 3 195 252 1 0 3 203 314 1 4 3 209 256 1 0 3 213 256 1 0 3 216 310 1 7 mag cA mag B op magstar 5 Ostar 5 0 273 0 006 2 244 0 016 0 175 0 013 0 291 0 002 2 241 0 011 0 166 0 004 0 282 0 004 2 268 0 012 0 177 0 008 0 287 0 002 2 273 0 007 0 167 0 003 0 276 0 001 2 264 0 006 0 178 0 002 0 264 0 001 2 300 0 006 0 176 0 001 0 279 0 004 2 231 0 011 0 172 0 008 0 267 0 002 2 252 0 007 0 175 0 003 0 253 0 003 2 254 0 018 0 174 0 005 0 249 0 002 2 301 0 010 0 173 0 003 0 248 0 002 2 244 0 008 0 177 0 003 0 222 0 003 2 317 0 011 0 189 0 006 0 234 0 002 2 284 0 008 0 172 0 004 0 233 0 001 2 275 0 006 0 168 0 002 0 230 0 001 2 279 0 006 0 178 0 001 0 208 0 007 2 236 0 023 0 172 0 012 0 215 0 003 2 255 0 018 0 167 0 004 0 194 0 006 2 246 0 018 0 166 0 012 0 217 0 002 2 239 0 007 0 170 0 004 0 186 0 001 2 345 0 007 0 173 0 002 0 189 0 003 2 198 0 010 0 167 0 007 0 166 0 003 2 190 0 010 0 183 0 007 0 149 0 006 2 189 0 018 0 163 0 011 46 3 219 281 3 221 234 3 224 209 3 232 187 3 246 163 3 248 138 3 254 125 3 256 135 3 261 115 3 271 109 3 273 103 3 277 104 3 281 106 3 283 100 3 430 540 3 434 546 3 461 499 3 475 491 3 482 443
8. 6 5 Take a series of 10 to 20 exposure pairs i e take two exposures for each exposure time with exposure times from close to 0 sec to this maximum exposure time Later you will work with the difference of these image pairs In regions where the curve deviates from linearity you should choose a denser spacing of the data points Note Do not increase the exposure times step by step but order them in a random way This way you avoid systematic effects e g by the non stability of the flat field lights T 6 6 For each exposure time measure the signal level in a uniformly illuminated area that covers at least 100 x 100 pixels You can do this with imstats image999999 fits s xmin xmax ymin ymax where xmin etc define the area of interest T 6 7 Plot signal level vs exposure time and determine the slope see Fig 8 and the point where non linearity sets in at home 35 Detector linearity Figure 8 Typical linearity diagram for the Enzian CCD all numbers removed The signal extends into the nonlinearity regime Your diagram should have more points to better identify the signal level where bending ie nonlinearity starts Limit your fit to the linear part of the diagram Draw the residuals Signal Exposure Time T 6 8 To determine the full well capacity of the detector more precisely we make use of the fact that at full well charge spills over into adjacent pixels T his reduces the overa
9. Figure 19 Configuration dialogue for Scamp F 6 3 Astro photometry Here you can choose between three methods Scamp Astrometrix and Shift only The latter determines only relative astrometric offsets and relative photometric zeropoints It does not care for sky position angles or absolute sky coordinates It can not handle mosaicing and only works for single chip data It requires a reasonable overlap of sources between exposures This method is most useful if you work with images that show just one or a few objects It serves as a fall back solution if the other two solutions fail for whatever reason Scamp usually fast and Astrometrix usually slower on the other hand are the entire opposite They calculate the linear offsets between the reference pixel CRPIX and the reference coordinates CRVAL as well as two dimensional distortion polynomials of higher order There is no difference in running them on a single chip or on a multi chip camera In the latter case the solution is for the entire mosaic The results of the astrometry step regardless of the method chosen will be written to a headers subdirectory inside SCIENCE Configuration We recommend to use Scamp for this experiment You can run it in its default configuration with one small modification the degree of the distortion polynomial should be set to 1 instead of 3 as there are not many sources in our data that can be used for distortion correction All other parameters
10. Glossary A a A x EA Be oe A RS ERA ed 4 3 Im ge Ted ctUlou us o Dor ome Poe Ee ee ne eek e 4 3 1 Step one bias subtraction 22 2 ee 4 3 2 Step two flat fielding manner 4 3 3 Step three masking weighting m aa Er we SS quee e x 4 3 4 Step four astrometric calibration 2e 4 3 5 Step five sky subtraction 2 2 2 2 22s 4 3 6 Step Six co addiblon uuo oeu a eee da a De a a EN o E UR 4 4 Photometry and photometric calibration 2 2 oaa a 4 4 To Magnitudes u 8 ea mpm i RR ene at hes a A a Ee de d 4 4 2 Deblending photometry rs 4 4 9 Noise statistics u 2 5 ara ud ep dug ERR domo en dm A 4 4 4 Photometric calibration rs Practical part I Image reduction photometry and lensing analysis Di Datareduction sete See pue a G fe rm iter Hop E aaah os ou ME in EE 5 1 2 Raw image inspection oaoa e e on s 5 1 3 Reduction of the SDSS1650 4251 R band data o 5 2 PSF extraction for SDSS1650 4251 o 5 3 SDSS1650 4251 Component fitting e 5 4 Time delay estimation less sors 5 5 Lensing analysis at home ao a ar eo d d o0 IU 6 Hj BE o a W Practical part II Measurement of CCD properties bad weather tasks 6 1 Detector system gain and noise a a 6 2 Detector linearity and full well capacity a 03 lt Dark Currente esr man i acr A Era e A e Dad ets Practical part III Night time
11. can use the following commands respectively imstats fits dfits fits fitsort EXPTIME T 5 6 Now look at the science frames Which image defects are visible What is changing between the exposures T 5 7 As for the bias frame compute the background value rms value in an area without bright objects also here note down the area used Why does the estimate differ from the value found for the bias frame 5 1 3 Reduction of the SDSS16504 4251 R band data In this subsection you will perform the data reduction for the source SDSS1650 4251 Here only images from one filter R are used Go to the images sub directory and start the data reduction package with the command theli Note The theli manual Chapters 4 6 11 is a useful reference when carrying out the image reduction However it is too extensive for this course we therefore provide you with all the necessary information in a shortened version of the manual which is found in Appendix F TASKS Following Appendix F describe the performed image reduction in detail in your report as well as answering the questions below In the Appendix each two numbered headline corresponds to a pro cessing group PG see the App F for explanation and each three numbered headline corresponds to tasks inside the PG For each of these tasks you have to tick a box next to the same line in the GUI before clicking Start to execute the tasks The tasks in the GUI not mentioned in
12. contained in the last line of LIST The size MFWHM of the objects se lected is given in the 11th column of LIST Only objects with MFHWM MAX FWHM STACK are used to create the stacked PSF The script creates several output files cut scale fits images correspond to the individual cut outs all registered onto the same sub pixel image centroid and scaled to have the same flux Note The last of these files is the cut out of your lens system e cut star stack scale fits is the stacked PSF Inspect cut star stack scale fits to ensure that you have no contribution from neighbouring stars Using imexam measure the FWHM of the stacked image which you can compare to the single stars and create contour and surface plots options e and s 30 T 5 21 For the subsequent component fitting choose either one of the single star PSFs or the stacked one as model Give reasons for your decision 5 3 SDSS1650 4251 Component fitting In spite of the blended quasar images it is nonetheless possible to derive reasonable photometry using component fitting In this step you will measure the fluxes of the lensed images as well as their separation Due to the finite resolution of the data components with small angular separation are difficult to decompose The decomposition is done by fitting the positions and fluxes of different components simulta neously using the 2 D fitting program galfit As detailed in the galfit manual it is a
13. de where s6test is your Uni Bonn account and then ssh prak1 fprak1 right computer Or ssh prak2 fprak2 left computer To copy data you can copy it first from fprakl or fprak2 to cipservl and from there to your local machine via assuming logged in into fprak1 scp FILE TO COPY s6test cipserv1 note that the is required and then assuming logged in into your own computer scp s6test cipservi astro uni bonn de FILE_TO_COPY note that the is required If you want to copy one or more directories please use scp r instead of scp If you want to store a few screen shots e g when doing image inspection these can be created using xv amp right mouse click grab autograb If you don t want to save the whole window you can use display click grab enter 2 then click grab after 2 s the cursor will change and you can frame what you would like to save click on an already existing file otherwise it won t be saved as long as it is not a png file it won t be overwritten click Format gt PNG Select gt Save Now you can change the image name in a normal terminal window to whatever you d like to call it To save a whole fits file use ds9 see below File gt Save image as For creating plots you can use gnuplot see App C 5 1 2 Raw image inspection In fpdir go to the sub directory images which contains sub directories with bias frames BIAS flat field frames FLAT
14. estimate for the subtracted sky background SKY which should be really small for the background subtracted images the number of pixels N an ellipticity ELLIP and position angle PA computed from second brightness moments the peak value PEAK and the fitted Moffat A 4 imarith Use this task to perform an arithmetic image computation of the type imarith operandi op operand2 result where operandi and operand2 can be image names or numbers Allowed operators op are wen 7 min and max The result is written to the image result A 5 Image sections Tasks expecting image files as input accept image sections in addition Image sections are specified as xmin xmax ymin ymax and appended to the image file name like disp image123 300 660 440 900 2 Display a subsection of image123 fits imstat image425 300 399 440 539 Calculate statistics for a 100 x 100 pixel subsection A 6 Image templates Many iraf tasks can work on multiple images as input or output This is useful if the same task e g imstat or imarith has to be performed for a series of images Multiple images are specified by image templates Image templates can be combined with image sections This option may help during the CCD experiment imstat imagel image2 Comma separated file names no spaces Wild characters are allowed 42 imstat image3 300 399 440 539 imstat will be applied to the corresponding sub section of image30 im
15. image then choose a higher pair of thresholds such as 10 10 or 40 15 or even 100 20 THELI has been used successfully with the latter parameters even for extremely crowded fields such as the Magellanic Clouds or exposures taken near the galactic centre The object catalogues created are saved in SCIENCE cat How to redo the task Just rerun Old catalogues in SCIENCE cat will be overwritten 57 THELI parameter settings Astrom Photom 3 Create source cat DETECT_THRESH DETECT_MINAREA DEBLEND MINCON Minimum FWHM Maximum FLAG Min of objects Background level Data is well sampled but plagued with hot pixels Defaults this page Cancel Defaults all pages OK Figure 18 Configuration for the catalogue creation 58 THELI parameter settings tox Processing group Astrom Photom 4 Astro photometry Scamp Astrometrix POSANGLE_MAXERR deg 20 POSITION MAXERR arcmin 20 PIXSCALE_MAXERR factor I a DISTORT DEGREES az FGROUP_RADIUS deg 1o CROSSID RADIUS arcsec 25 ASTREF WEIGHT 10 SN_THRESHOLDS low high 5 20 Add DISTORT GROUPS DEGREES Additional DISTORT KEYS a ASTRINSTRU_KEY FR PHOTINSTRU_KEY FILTER STABILITY_TYPE INSTRUMENT E MOSAIC_TYPE README UNCHANGED 4 which FOCAL PLANE Use default FP f Match flipped images lt lt gt gt Defaults this page Cancel Defaults all pages oK 4
16. is amplified by v2 according to standard error propagation x TASKS The determination of the gain k is now pretty straightforward Two frames with identical exposure time should be all you need Try to get a signal level of about 30000 ADU Remember that all the values read from the images are after A D conversion i e a transformation of eq 51 must be used instead o 4 02 02 02 53 tot d RON d e d prnu d and the factors of eq 52 converted accordingly T 6 1 Use imstats to determine signal levels and noise The image region you use for these statistics should have a uniform illumination and cover at least 100 x 100 pixels Use ic to calculate the difference frame in the following way ic p 32 1 42 IMAGE1 IMAGE2 gt difference fits where IMAGE1 2 are replaced by the filenames of the two images you want to subtract from each other The name of the output file is arbitrary The option p 32 is needed to ensure calculation in 32 bit floating point format with correct support of negative numeric values unprocessed raw data is usually stored in 16 bit integers T 6 2 Find and discuss the photon noise the PRNU noise and the PRNU factor fprnu at home T 6 3 Determine the gain at home 6 2 Detector linearity and full well capacity TASKS T 6 4 From previous experience estimate an exposure time that would theoretically bring the signal level close to 65 000 ADU Take an exposure to verify your estimate T
17. light curve 16 4 Background knowledge Observations 4 1 Observations in optical astronomy This section summarises some important facts and concepts concerning observations in optical astro nomy which are relevant for the lab course 4 1 1 Telescope optics Figure 5 Schematic light path in a Cassegrain telescope The AIfA 50cm telescope is a reflector of the Cassegrain type The in falling light first meets the concave parabolic primary mirror 1 to be then re reflected by the convex hyperbolic secondary mirror 2 The rear focus A of the secondary is placed in the focus of the primary mirror such that the light is collimated in the convex focus of the secondary B via an opening in the larger mirror see Fig 5 Thus the detector is placed behind the primary Due to the folding of its optical path the Cassegrain system allows for a compact construction Details of the actual system can be found at http www astro uni bonn de astroclub The light distribution in the image plane resulting from an apparently point like source star is termed point spread function PSF In the idealised diffraction limited case the PSF of a circular aperture is given by the Airy disc Using the Rayleigh criterion for spatial resolution a telescope of primary aperture D at a wavelength A is in principle capable of resolving structure with an angular separation of A A8 1 227 39 However due to the effects of Earth s atm
18. observations 7 1 Asteroids observations with the 50cm telescope 2 nn rn T2 PREPARATORY TASKS 202 005 amp been a m Bo ae RH RUSO x ARS References An iraf primer A l General information r 1 mute a oder ee ee a AJ display om A d RUE FUE a Bala ta a Be a ALB MOM eia Boe we RES Rena n XI e ae po eee DU ee Rus xa AA mari Ghy o4 Bay ee Boe A sedium and s pues a ten a tenet e A D Image sections cs are A A Oe d E o RUBER A EE A A6 Imag templates cosan nagsi garroa S Rx EUR Gs ee CR RR E RR EUN PSF component fitting with galfit Using gnuplot Time delay estimation with tdel Using the camera control software CCDSoft 5 with the SBIG STL6303E camera THELI user manual lab course short version F 1 The INITIALISE processing group F 1 1 Pipeline Settings 2s B12 Data directories x e 2 ius mee ors De du ac Di DRA F 2 The PREPARATION processing group 2 sls ee F 2 1 Split FITS correct header suos yo pb ok Rr Oo b RR BC Va F 3 The CALIBRATION processing group F 3 1 Process biases darks ua su Rr Leto ev ek dh edt dtd ds ts F 3 2 Process flats MANDATORY e A AA ER deg F 3 3 Calibrate data ic 24 8 dee are re YR eq ou uice eR RI TA F 4 The SUPERFLATTING processing group sooo a a F 4 1 Smooth SUPERFLAT create fringe model len F 4 2 SuperHatbmng iia her o Tee ae um Parvi RU euis ih re R3 Defnngsing a nee eb Ee ie e WR ES EG eei RR gos RE EN F 5 The WEIGHTING pro
19. of making the processing software disregard these corrupt data is to mask the incorrect pixels by assigning them a certain value This value is then recognised by the software programs and the pixels are hence neglected The mask files contain information about areas that should be masked out these areas being set to a fixed value typically 0 There are two types of mask files global masks and individual masks A global mask is a mask file which is applied to all frames in the case of more than one CCD one global mask is made for each chip and contains information about bad pixels in the CCD The individual masks contain information that is varying from exposure to exposure like cosmic rays hot pixels 22 and other CCD defects It is also possible to create individual masks manually by looking at each exposure and defining areas to be masked out At the creation of the final masks for each exposure the global masks are taken as input for each frame adding to it the information from the individual masks and the manually created ones The masks are then taken into consideration during the astrometric calibration in Sect 4 3 4 ignoring the pixels whose corresponding mask value equals 0 By creating the mask files using the normalised flat field image as input image the mask files will contain information about the exposure time in addition to masked areas turning them into weight images and not just mask files Upon co addition of all scie
20. sh home prak1 all fp0_270114 images SDSS1650 4251 R OFC Jcreate scamp sh home prak1 all fpO_270114 images SDSS1650 4251 R OFCSF Jcreate stats table sh home prak1 all fpo 270114 images SDSS1650 4251 R OFCSF headers Jcreate absphotom coadd sh home prak1 all fp0_270114 images SDSS1650 4251 R JENZIAN_ W CAsoHOl 1M PB Figure 17 The Astrom Photom PG How to redo the task Old results will be overwritten when a new reference catalogue is retrieved F 6 2 Create source cat Here we extract source catalogues from all images The detection characteristics can be fine tuned by means of the configuration dialogue Fig 18 Parameter configuration DETECT_THRESH is the detection threshold in sigma of the sky background noise and DETECT_MINAREA is the minimum number of connected pixels above that threshold The latter depends on the seeing and the pixel scale of your instrument Three more parameters that usually do not need to be modified are available too Fig 18 If you leave a field empty then the default value will be used No warning message will be printed General tips for the catalogue creation The WEIGHT maps created previously are taken into account in the catalogue creation process guaranteeing a clean catalogue that is largely free from spurious detections If the image quality is good you can have both DETECT THRESH and DETECT MINAREA as low as 5 5 If you have many hundreds or thousands of sources in an
21. stacking all science images into one making sure that each object falls onto the same pixels the final image will contain higher S N values than each image alone It is therefore desirable to use only one image that covers the whole field of interest while carrying out the analysis The master image is made from combining all available data from the same region of the sky By applying the corresponding astrometric solution to each individual frame all the images are mapped onto the sky and combined into one final master image After the science images are processed the exact same procedure is applied to the corresponding weight images creating a master weight image This can later be fed to SExtractor when carrying out object detection in the master science image and SExtractor will then weight the detections accordingly 4 4 Photometry and photometric calibration 4 4 1 Magnitudes The apparent brightness of a source in optical astronomy is called its magnitude The same word is used for the unit in which it conventionally is expressed An object showing an intrinsic brightness distribution J x y in your image plane will under the PSF x y of the imaging system appear as the convolution I9 s y Pot s y B x y x eee ey vary 40 y of the intrinsic distribution and the PSF In the case of a CCD the object s instrumental flux can be expressed by a sum over the counts Iz in all relevant pixels covered by it
22. the point where they cross the lens plane travelling in straight lines in between Born approximation A mass distribution that fulfills this condition is called geometrically thin lens For a given source its apparent angular position in the sky 0 its true position 8 and the scaled deflection angle a are related through the lens equation B 0 a 0 14 We can relate angles to physical distances by using n ae Das amp 15 where Dg n D and amp is the true deflection angle General Relativity predicts for a point like lens of mass M and a light ray with impact parameter E the true deflection angle AGM a we 16 which is twice as large as predicted by Newtonian gravity Source Plane Das Ds Lens plane Da Observer Figure 1 Sketch of a gravitational lens Note that angles are exaggerated in reality sina tana c a 1 Superposition for the mass distribution in the lens plane yields 4G 24 amp nn E a gt ee O 17 c le eP where X is the surface mass density at and E is the impact parameter for X Defining the convergence X D40 x 0 20 18 Ver as the dimensionless surface mass density scaled with the critical surface mass density c Ds Xu zn LE 19 a 7 G DD 19 we can rewrite the scaled deflection angle as 0 0 d 0 0 20 gt p 10 06 which is now given purely in terms of observabl
23. the red lights up Starting the program e Start Autoslew Click on the earth symbol to deactivate the tracking If you want to take flatfields or the remove the mirror covers click on position 2 e Start CCDSoft 5 program establishing link to the camera or any other camera control program installed that you might know better e Choose Camera Setup e In dialog box set Set Camera to SBIG STL Large Format Cameras Set Filter Wheel to SBIG Internal STL CFW Click on Temperature gt and set Temperature regulation to On Make sure that Fan on is activated Set Temperature setpoint C to your desired temperature Make sure that the desired temperature is reached before you continue and that the cooling power given in percent in the field Temperature does not exceed 80 then Taking frames e Choose Camera gt Take Image Choose the settings as you need exposure time binning frame type reduction type and filter Subframe should be deactivated and Bin should be 1x1 if not other stated If needed you can also take a series of images and choose a delay between two exposures After clicking Take Image or Take Series the camera will do the integration followed by the readout while the image is displayed simultaneously 48 F THELI user manual lab course short version General description of the GUI and its eleme
24. to redo the task Click the re do arrow and re run F 4 3 Defringing If you want to defringe your data you must have superflatted your data previously by a smoothed SUPERFLAT the illumination correction This task scales the fringing models according to the sky background of your exposures in relation to the SUPERFLAT and then subtracts the rescaled fringe model How to redo the task Click the re do arrow and re run 55 THELI GUI v 2 3 3 Edit Settings View Status Miscellaneous Delete Help Initialise Preparation Calibration Superflatting Weighting Astrom Photom Coaddition r Tasks ei _ Debloom images Saturation threshold 55000 Clear scripts Start Defaults Abort _ Create binned preview Configure r Messages F Create global weights Configure T Create WEIGHTs Configure _ Distribute target sets Minimum overlap 1000 parallel_manager sh create global weights para sh home prak 1jall fpo_270114 images FLAT R norm SDSS1650 4251_R Jtransform ds9 reg sh home prak1 all fpO_270114 images SDSS1650 4251 R parallel manager sh create weights para sh home prak1 all fp0_270114 images SDSS1650 4251_R OFCSF Figure 16 The Weighting PG F 5 The WEIGHTING processing group F 5 1 Create globalweights The normalised FLAT is taken and has bad pixels replaced by zero values Whether a pixel is bad is determined by one or more threshold pairs which refer to the normalised F
25. variance of the simulated sample of time delays The file DispFctns base MCprob tab contains the probability distribution of the time delay values as obtained by the Monte Carlo method Columns 1 time delay 2 probability 45 Description Some initial guess for the time delay Minimum time delay that is probed by tdel Maximum time delay that is probed by tdel Number of linear bins between Delay_ Min and Delay Max Minimum magnitude shift between the two light curves probed in step 2 Maximum magnitude shift between the two light curves probed in step 2 Number of steps between mmag Min and mmag Max Shall MC errors be computed If 0 the dispersion spectra are written to the subdirectory disp Number of Monte Carlo realizations in step 3 Required relative accuracy for the estimation of the mean magnitudes in step 1 Required relative accuracy for the estimation of the time delay in step 1 Defines a gap to be no data for more than MinGapLength days Minimum number of pairs of data points If UseMC is set to 0 this is the basename of the dispersion spectrum output files Table 2 Keywords in the tdel parameter file Keyword Type Delay_guess number Delay_Min number Delay Max number Delay nbin integer mmag Min number mmag Max number mmag nbin integer UseMC 0 or 1 NMC integer Mag FracAcc number Del FracAcc number MinGapLength number MinPairs number DispFctns base string HJD seeing 3 133 412 1 5 3 134 362
26. with the T HELI pipeline If single chip images are given only the FITS header will be updated This reduction step will be applied automatically to all subdirectories that are specified in the Initialise PG How to redo the task Delete all split images in the corresponding directories and move back the images from the ORIGINALS directory 51 Edit Settings View Status Miscellaneous Delete Help Initialise Preparation calibration Superfiatting weighting Astrom Photom Coaddition Tasks Data is in the main directory Clear scripts Start _ Sort data using FITS key Abort Data is in the individual directories Only raw data are allowed in the directories for the splitting F Split FITS correct header Configure Chips going to scratch _ Create links Scratch directory Jprocess split ENZIAN CAS QGHOLI 1M sh home prak1 all fp0_270114 images BIAS Jprocess split ENZIAN CAS QHOLI 1M sh home prak1 all fp0_270114 images FLAT R process split ENZIAN CASQHOLI 1M sh home prak1 all fp0_270114 images SDSS1650 4251_R Figure 12 The Preparation PG F 3 The CALIBRATION processing group F 3 1 Process biases darks Combines all BIASes in the BIAS subdirectory set in the Initialise PG The more BIASes you have the better your master BIAS will be and the smaller the calibration noise that is introduced into your SCIENCE images We recommend to use at least 10 BIASes Overscans are corr
27. 2 161 2 156 0 018 0 009 0 015 0 009 0 035 0 013 0 013 0 005 0 029 0 014 0 020 0 014 0 016 0 012 0 009 0 019 0 009 0 012 0 011 0 011 0 012 0 009 0 018 0 012 0 006 0 007 0 011 0 020 0 005 0 008 0 007 0 007 0 015 0 026 0 008 0 007 0 012 0 008 0 018 0 155 0 179 0 166 0 168 0 142 0 114 0 160 0 173 0 178 0 183 0 176 0 191 0 167 0 164 0 135 0 143 0 150 0 179 0 149 0 168 0 153 0 171 0 151 0 168 0 183 0 171 0 168 0 194 0 179 0 176 0 160 0 167 0 165 0 172 0 181 0 177 0 188 0 165 0 180 0 008 0 003 0 010 0 005 0 026 0 007 0 007 0 003 0 017 0 009 0 013 0 007 0 011 0 008 0 003 0 009 0 005 0 008 0 004 0 008 0 009 0 006 0 012 0 007 0 003 0 004 0 006 0 014 0 001 0 005 0 004 0 003 0 010 0 019 0 002 0 003 0 009 0 005 0 013 E Usingthe camera control software CCDSoft 5 with the SBIG STL6303E camera Equipment e SBIG STL6303E camera head power supply power cable USB cable e observing computer Getting started e Start the observing computer if not yet started e Login as user Astro Hook up the camera to power supply Connect the camera to one of the USB plugs e Switch on the camera power supply during boot procedure camera fan will start running e Switch on the telescope power supply gray box on the computer Wait until
28. 3 500 415 3 507 348 3 508 403 3 511 303 3 517 383 3 524 391 3 533 412 3 540 345 3 542 323 3 552 291 3 556 295 3 559 280 3 564 295 3 570 247 3 575 323 3 576 264 3 578 275 3 581 284 3 611 225 3 613 201 Table 3 Photometry of SDSS1650 and of reference star 5 table taken from Vuissoz et al 2007 The Julian date cor responds to HJD 2 450 000 days The five points marked by an asterisk are not used by the authors in the determination 1 6 1 0 12 1 1 1 3 1 5 0 9 1 0 1 5 1 3 1 2 1 0 1 4 1 2 0 9 0 8 0 9 0 9 1 1 1 3 1 0 0 9 1 0 0 8 0 9 1 6 1 0 1 1 0 9 0 9 1 0 1 3 1 0 1 3 1 0 1 2 12 12 1 5 0 151 0 178 0 140 0 215 0 133 0 172 0 156 0 188 0 203 0 191 0 163 0 190 0 146 0 146 0 167 0 175 0 166 0 175 0 177 0 206 0 177 0 199 0 172 0 163 0 194 0 193 0 194 0 172 0 201 0 204 0 181 0 228 0 192 0 198 0 211 0 189 0 190 0 188 0 175 of the time delay 0 004 0 002 0 005 0 003 0 013 0 004 0 004 0 001 0 011 0 005 0 007 0 004 0 006 0 004 0 002 0 007 0 003 0 004 0 002 0 004 0 005 0 003 0 007 0 004 0 002 0 002 0 003 0 007 0 001 0 003 0 002 0 001 0 005 0 010 0 001 0 002 0 005 0 003 0 007 47 2 198 2 241 2 228 2 198 2 148 2 054 2 139 2 181 2 153 2 167 2 117 2 179 2 151 2 129 2 078 2 088 2 138 2 120 2 124 2 147 2 106 2 222 2 153 2 146 2 118 2 002 2 124 2 132 2 149 2 185 2 134 2 300 2 094 2 084 2 195 2 133 2 176
29. 75 2 45 0 010 image008071 1 530 12 524 55 524 71 9 71 1 78 2 29 0 025 image008072 1 538 09 532 65 532 80 9 78 1 80 2 53 0 040 Figure 23 The dialogue for obtaining image statistics 62 ImageMagick statistics png Sky background Seeing u o o Mode ADU u u u A Ud9 A io to gt 00 o 2 d 4 5 amp 7 Image Transparency T T T T T T Relative ZP mag Figure 24 Example for statistics plot How it works Clicking on the Get statistics PushButton will retrieve the statistics This can take a while and the GUI will not allow any other action during this time may change in a future release The table obtained will automatically be stored in the directory you specified The name of this file will include the name filter if such a filter was put If the table is obtained a second time with an identical filter the old file will be overwritten without warning You can manually save the table to a different file name or load a previously created table If the Create source cat and Astrometry processing steps were done as well seeing and relative photometric zeropoints will be shown as well respectively That requires the presence of a cat and or a headers directory in the specified path 63
30. Advanced lab course in physics at Bonn University Optical astronomy and gravitational lensing Conducted at the Argelander Institut f r Astronomie Written by Alex Bohnert Xinzhong Er Jan Hartlap Karianne Holhjem Holger Israel Benjamin Joachimi Dominik Klaes Elisabeth Krause Emilio Pastor Klaus Reif Mischa Schirmer and Tim Schrabback Version February 07 2014 Contents 1 Overview 2 Preparation 3 Background knowledge Theory 3 1 Cosmology sa os nut Gee xe X Lus x ERR RED E Ree doi REGE 3 1 1 Cosmic expanslOh un sa m x3 sons RR GR ROPA aa 3 525 Distances sx Lex Wr Bo en dr UN eh us ENS Roue ROG N TRAE Te Rx d 9 2 QUASAIS 2 sse untere ue Sepe dua du EN Re Re deines eu E E 3 3 Gravitational Lensing on on nn nn 3 9 1 Lensiequatiof c wu uet PS ar Bm eee op is 33 27 Strong lensing s e osos Ron eR Ru eU Sg RS SOROR A oS ETE S RU 3 3 3 Pime Delay i ees ponen xS m oem a de RR UU EUR te UTR A 3 3 4 The SIS Singular Isothermal Sphere gA Hgo measurement a a A we a AUR Nus wu OUR FUE RE IE 3 5 Time delay measurement 2 2 2 2245242 rs 3 6 PREPARATORY TASKS le ss Background knowledge Observations 4 1 Observations in optical astronomy 4 4s lees ATA Telescop optics oos 2s a m ha a Leis RALF a a 4 1 2 Seeing and Airmass 29m Room hoop a REUS EUR E nd 4 1 8 Coordinate Systems 4 2 COOBXdetectorsg s a A A A A A A a Ne ee ADAL
31. Afterwards you will measure the brightness of the different quasar images in your calibrated data Cross correlating these values with estimates from other observation dates you will be able to determine the time delay between the different light paths which can be used to constrain the Hubble parameter for a given lens model 2 CCD properties and observations AIfA Bonn 0 5 day 1 night Depending on the weather conditions you will either measure different properties of our CCD camera during day time or observe asteroids using the 50cm Cassegrain telescope on the roof Given the variable weather conditions in Bonn clear nights are only foreseeable for a few days if at all Once you have passed the oral exam for the first part data reduction your tutor will let you know if the weather prospects are sufficiently good about 2 days before an observation Depending on your schedule due to e g other experiments you can then observe or try to observe later Still an adaption of your schedule to the weather conditions may be necessary In case the night is almost completely clear you may observe for your personal interests talk to your tutor about this Furthermore it is at the moment also possible to combine the observations for the lab course S263 Star clusters so that you need only one night for both lab courses If no observation is possible then the bad weather tasks measurment of CCD properties have to be performed In an
32. Appendix F you should ignore as they are not mandatory and we will not use them in this course 27 T 5 8 Initialise App F 1 e Enter your group name LOG file name and click on Reset to erase parameter settings by other people e Set of CPUs to 2 e Select ENZIAN CASGHOLL 1M from the list of professional instruments e Click Clear dirs then fill in the directory names skipping DARK OFFTARGET and STANDARD Fill in the full path as main path which you get by typing pwd in the shell If all paths are corrected all boxes will turn into a dark green If one box is marked red the directory does not exist so please check your path s again T 5 9 Preparation App F 2 e Make sure the images are correctly sorted into sub directories according to bias flat and science exposures e Using the command dfits image999999 fits look at the header of one of the images a Correct the headers according to App F 2 and look at the new header information in the same image as above Has the header changed In case how T 5 10 Calibration App F 3 e Follow App F 3 in creating co added bias and flat field frames When calculating the superflat you need to adjust the Superflat parameters Use DT 1 0 DMIN 10 SIZE 256 and a Median combination for the superflat The Window size should be set to 0 Note that the superflat is calculated from the science images after they are bias and flat field calibrated and
33. Delay In the case of multiple images the light rays for the different images have different paths from the source to the observer leading to different light travel times The difference in path can be divided into two contributions the geometrical time delay and the potential time delay The first part comes from the bending of the light ray caused by gravity while the second one is induced by the travel through a gravitational potential However the use of the Fermat potential enables us to treat the problem in a more elegant way In order to derive the time delay from two different images we start from a fiducial situation where the time delay is zero and define an observer plane parallel to the lens and source planes If we displace the observer infinitesimally the increase of the time delay will be d c t 9 d 26 where dd is the displacement of the observer from the reference point and Y 0 8 9 g om 0 are two images of the source We can now relate the infinitesimal observer displacement to 12 a k 9 Source Plane f VAN Das e 2 E o E SL lt Fiducial image av c he A e Lens Plane A I front E Da 1 7 ACA MA Q al dt i Observer Plane Figure 3 Left a Sketch of the relation between an observer s angular displacement and the equivalent of the source Right b Sketch of the infinitesimal time delay due to the displacement of the observer an equivalent displa
34. Delay guess see Table 2 and computes the mean magnitudes only from the overlap region of the reference and shifted light curve These means are used to obtain a refined delay estimate which in turn is used to refine the mean magnitudes etc The accuracies required to stop the iteration are set by the parameter file keywords Mag_FracAcc and Del FracAcc Usually this first step will not yet yield the true time delay because it minimizes a potentially very noisy dispersion spectrum directly It is therefore highly susceptible to this noise and may get stuck somewhere in a false minimum i e a noise feature 2 In the second step the magnitude shift Am between the two light curves having subtracted the means determined in step 1 is varied this is controlled by the keywords mmag Min mmag Max and mmag nbin Note that this is equivalent to varying the means of both curves individually For each value of Am the program computes the dispersion spectrum D A Am and per forms a second order polynomial fit to smooth out the noise From the fit the minimum value Dminl Amin Am and the corresponding time delay Amin are determined These values are stored for each Am so that we obtain the function DminlAmin Am Next we find the value of Am which minimizes Dyin Amin Am The last thing we have to do is to look up the corresponding stored value of the time delay to obtain our final result Since the dispersion spectra are well approximated by a p
35. LAT itself How to redo the task Just re run F 5 2 Create WEIGHTS All cosmics hot pixels and other chip defects are detected on an image by image basis in this step How to redo the task Just re run F 6 The ASTROM PHOTOM processing group F 6 1 Astrometric reference catalogue Retrieving a catalogue from the web This is the default state Select the nearest web server and your catalog of choise SDSS if possible You can control the limiting magnitude of the objects retrieved in the catalogue s magnitude system and therefore their number density The catalogue will be retrieved around the reference coordinates taken from the fits header within the radius specified The catalog will be downloaded automatically once you start source detection After you have inserted the correct values click on Get catalog 56 Edit Settings View Status Miscellaneous Delete Help Initialise Preparation Calibration Superflatting Weighting Astrom Photom Coaddition Tasks fenomenit Ra from header Mag limit reference dc gt a Clear scripts Start taloq from DEC J from header Radius 5 AN Defaults Abort WEB France aj SDSS DR7 f Messages Get catalog _ Absolute photometry indirect Configure ej _ Absolute photometry direct Configure Create source cat Configure T Astro photometry Scamp 4 Configure Update header Restore header parallel_manager sh create astromcats para
36. _X where X denotes the filter name and science frames named after the target 26 and filter The images consist of 1k x 2k pixels with pixel scale 07177 and have all been taken using the Enzian camera at the Hoher List 1m telescope in Cassegrain focus TASKS using the SDSS1650 4251 R band data T 5 1 Visually inspect the bias and flat field frames using ds9 ds9 image999999 fits amp When ds9 starts up select Scale zscale If you want to compare several frames you can use Frame new and open the new image here If not the entire frame is shown you can change the zoom via zoom T 5 2 Judging from the images what is the average bias level How does this vary across the field of view What are the small white dots hint look at several frames T 5 3 For one bias frame identify an area with little large scale variation not too close to the edges and compute the background rms value in this area using imstats image999999 fits s xmin xmax ymin ymax Note down the area used as you will use the same area in later tasks What is the source of the noise in the image T 5 4 What structures are visible in the flat field What are the donuts What are the sharp struc tures T 5 5 Look at the flat field frames and compare their mean values to the exposure time How and why does the ratio between the two change To measure the mean value of the images and to access their exposure times stored in the FITS headers you
37. age39 if the images ex ist replaces a whole string not only a single character like imstat image36 135 fits Applies to image361 image363 image365 The is needed to make clear that it s not an image section imstat allmyflats 1st Note the allmyflats 1st is a file contain ing one image file name per line imstat will be performed for all those images imstat Oflats lst gt flats stat Pipes the output into a file which may be used imstat image fits e g as input for a graphics program imarith Cop1 1st op Cop2 1st result 1st Templates work on input and output The number of file names in opi lst op2 1st result 1st have to be identical Before using image templates check first with the section command This will show how iraf re solves the template section image36 135 fits Will just output a list of three file names B PSF component fitting with galfit The program galfit is steered via an input parameter file which is provided for you already in the form needed First control parameters are specified indicated by capital letters Then one can define an arbitrary number of fit components each of them specified by several parameters indicated by numbers For our purposes three such components are given two PSFs and the sky background You specify several initial guesses e g for the position of the PSFs For each of these initial values a flag has to be set If it is 1 then the correspond
38. ained in the preparatory tasks in Sect 3 6 x TASKS T 5 32 Calculate the velocity dispersion of the lens galaxy from the measured image separation De termine the projected mass of the lens inside the Einstein radius For these calculations assume the currently accepted value of the Hubble constant Comment on your results T 5 33 The lens galaxy is unobservable by HOLIGRAIL To determine the Hubble constant explicitly more information than the image separation is needed for instance the flux ratio of the images where we assume that it is identical to the absolute value of the magnification ratio which you calculated from theory Compute the position of the lens galaxy and Ho Carefully keep track of potential minus signs stemming from originally negative image positions or negative magnification ratios T 5 34 The lens galaxy of SDSS1650 was observed with the 3 5m telescope at the Kitt Peak National Observatory by Morgan et al 2003 Figure 7 illustrates the resulting object positions Com ment on why the results you obtained above cannot be realistic hint The SIS is an axisym metric lens model amp Figure 7 Sketch of the true ob A G B ject positions in SDSS1650 drawn e C to scale A and B denote the quasar images G stands for the lens galaxy 33 6 Practical part II Measurement of CCD properties bad weather tasks These measurements are carried out at the 50cm telescope during day time All experiments are perfor
39. arabola only near the minimum it is necessary that you adjust the minimum and maximum time delay that is probed To do so call tdel with the parameter file keyword UseMc set to 0 This will skip step 3 and write the dispersion functions and the polynomial fits to the files disp DispFctns base n where n is the number of the Am bin for which the computation was done Columns 1 time delay 2 measured dispersion function 3 fit Using these files you can check by eye if you have chosen Delay Min and Delay Max properly This is done with gnuplot plotting columns 2 and 3 in the same window and comparing When you have found a good interval for the fit restart tdel now with UseMc set to 1 Make sure that you do not try to fit a noise minimum To avoid this check if there are other minima of similar amplitude relative to the large scale trend in the dispersion spectrum If so you have most likely found a noise feature 3 Step three is concerned with the estimation of error bars on the time delay For this the program uses a Monte Carlo strategy We assume that the measured light curves are the true ones i e noise free and create mock measurements by adding Gaussian noise to each data point The dispersion of the Gaussian is the photometric error as given in the input light curve file For each of these mock light curves the time delay is estimated as described in step 2 This procedure is repeated NMC times The program then computes mean and
40. are forbidden transitions they have long decay lifetimes and are very narrow resulting in fringing patterns in most I band science frames Depending on the CCD fringing can also show up in other bands the most common being the R band As opposed to the dark night sky that is dominated by emission lines the reflected sunlight dominating the twilight sky has a continuum spectrum and the fringing will therefore not appear in the twilight flats As the fringe pattern is an additive effect it must be subtracted from the science images The master sky flat is used to obtain a fringe model This is done by smoothing the flat with a large smoothing kernel typically 256 pixels and then subtracting this smoothed image from the original master sky flat creating a frame containing only the additive fringes This fringe model is then subtracted from the science images to obtain images fully corrected for pixel to pixel variations Although the main purpose of flat fielding is to get rid of pixel variations in the CCD the process will also compensate for possible dust specks present on the dewar window or the filter The dust specks if any are visible as darker doughnuts since they are not on the CCD surface and therefore out of focus 4 3 3 Step three masking weighting Bad pixels and columns are likely to cause problems during the analysis and lead to incorrect results if they are not dealt with properly during the calibration process A simple way
41. art is carried out at the Argelander Institut f r Astronomie in Bonn You will reduce and analyse an existing set of gravitational lens observations 5 1 Data reduction 5 1 1 Setup Log in on the lab course computer Username and password will be provided by the tutor Double click on the Desktop icon S261 startup which will create a new working directory fpdir for you comprising all data you need Please store ALL files you create in this directory or its sub directories Please be aware that if you later reset your dataset all data in the subfolder images might be deleted There are two ways to work with the file system The first possibility is to use a shell icon Terminal or also Bash fpdir is a sub directory of the user home directory Note that the majority of commands that you will execute in the following have to be typed in a shell Equivalently you can double click on the folder fpdir on the Desktop and handle your file system similar to Windows Explorer For your report you may want to store data images etc on a USB stick Plug your stick and if it is not automatically mounted type mount usbdisk Via cd usbdisk you now have access to the directories on your stick Before unplugging type umount usbdisk You also have access to both computers via the server cipservl astro uni bonn de The username is your Uni Bonn username so to log in into one of the machines type from home ssh s6test cipservi astro uni bonn
42. as A 24 u det A 25 3 3 2 Strong lensing An important characteristic of strong lensing is the possible occurrence of multiple images for a given source as well as strong magnification and distortion which is not important in our context In the following we will describe how a single source can have multiple images Classification of images Consider the Fermat potential 7 8 0 Fixing 8 and assuming normal conditions det A Z 0 a vanishing gradient of 7 corresponds to a solution of the lens equation and hence indicates an image position 0 One can now classify the images by the type of extremum of 7 e Minima det A gt 0 trA gt 0 e Maxima det A gt 0 trA lt 0 e Saddle points det A 0 This helps in deciding whether there are yet more images to a source than already known If we assume that two images are identified as minima of the Fermat potential we know immediately that there will also be at least one image of the saddle point type 11 Critical curves and caustics Critical curves are those points in the image plane where the mag nification diverges det A 0 In the simplest case radially symmetric lens and perfect alignment this is a circle with radius Op in general critical curves are smooth and closed The mapping of a critical curve onto the source plane is called a caustic Caustic curves are also closed but not necessarily smooth The odd number theorem If a source has a large o
43. ble to fit light profiles with many different analytic functions which aim at modelling different types of galaxies However since each observed quasar image can be approximated by a point source convolved with the PSF you will use galfit only in a very simple manner x TASKS T 5 22 First re add the sky background that has been subtracted during the reduction process in case you wonder why this is necessary see Sect 1 2 of the galfit manual You can use the following procedure In the image directory SDSS1650 4251_R obtain their sky values using imstats OFCSF fits Calculate the average of the modes given in the second output column As the coadded image is normalised to an exposure time of 1 second you must divide this average value by the exposure time of the images which can be seen in the FITS header using dfits OFCSF fits fitsort EXPTIME Add the sky background value to the stamp of the lens system This can be achieved on the command line using ic 1 SKY VALUE stamp image gt new stamp image where you have to insert your sky value and corresponding file names T 5 23 Create a backup copy of the parameter file galfit input located in the directory fpdir photometry before you edit anything in it For example cp galfit input galfit input backup Very often galfit crashes because unsensible input is provided in several places In that case you can revert to a fresh copy of the backup file T 5 24 Replace all do
44. can be left unchanged How to redo the task Just rerun Old results in SCIENCE headers will be overwritten 59 Edit Settings View Status Miscellaneous Delete Help Initialise Preparation Calibration Superflatting Weighting Astrom Photom Coaddition r Tasks Clear scripts Configure in this directory full path parallel_manager sh create skysub para sh home prak1 all fp0_270114 images SDSS1650 4251_R OFCSF Jprepare coadd swarp sh home prak1 all fp0_270114 images SDSS1650 4251 R OFCSF sub parallel_manager sh resample coadd swarp para sh home prak1 all fpo_270114 images SDSS1650 4251_R Jresample filtercosmics sh home prak1 all fpo 270114 images SDSS1650 4251 R Jperform coadd swarp sh home prakl all fpo 270114 images SDSS1650 4251 R Jupdate coadd header sh home prak1 all fpo 270114 images SDSS1650 4251_R OFCSF Figure 20 The Coaddition PG F 7 The COADDITION processing group F 7 1 Sky subtraction Configuration This step subtracts objects above certain user provided thresholds from the image From the remaining sky an estimate is determined The Configure dialog Fig 21 presents you with the following options lab course here we present only the option we are going to use Automatic sky modelling Ina first pass SExtractor is run to remove all objects from the image The result is then smoothed and subtracted To this end you must provide the usual detection threshold
45. cement of the source Given a fixed lens position the angular displacement of the observer is related to that of the source by dg dn 27 Nm D za 0 gU making use of D z4 0 1 za Da and the already mentioned relation dy D d we can then describe the time delay directly from the lens and source position dc 1 za rap 28 ds From the lens equation 8 0 Vw we find 2 6 48 d 6 8 0 46 auto a E 70 0 29 Integrating eq 26 we then find the time delay At eAt 8 1 24 E r 8 4 8 80 8 30 where 04 5 give the two image positions for which the time delay is calculated Inserting eq 11 into eq 30 we see that the time delay is to first order proportional to the inverse Hubble Constant Intuitively this can be understood from the sketch and description given in Fig 4 3 3 4 The SIS Singular Isothermal Sphere A simple model to describe the mass distribution of a galaxy acting as a lens is the singular isothermal sphere SIS 2 oy p r Cpe 31 which is fully characterised by the velocity dispersion oy Integration along the line of sight yields the surface mass density 2 Oy This model cannot be used for very small or large radii as the density p diverges as r 0 and the mass M r pr r is infinite for r oo nonetheless it is a reasonable model if it is truncated at a maximum radius and not used to describe the very centre of a lens 13 Figure 4 S
46. cessing group F 5 1 Create globalweights Coon nn b 5 2 Create WEIGHTS ici se BU dap ER a Pa So Ge US E e F 6 The ASTROM PHOTOM processing group a F 6 1 Astrometric reference catalogue aa F 6 2 Create source Cat 2 22 oo F 6 3 Astro photometry 2 o e ess sse F 7 The COADDITION processing group Fm1 Sky subtraction 2 4 i3 cc nue e Te Ei eee REE ROM RE ERR UB e dA E 7 2 Coaddition Rec eme a ee RU AD eub ee a 34 34 35 36 38 38 39 40 41 41 41 41 42 42 42 43 43 44 48 F 8 Image statistics 1 Overview This experiment will introduce you to modern astronomical observation and data analysis techniques Using data from the 1m telescope at Hoher List Observatory you will obtain calibrate and analyse imaging data of multiply lensed quasars in gravitational lensing systems which can be used to estimate the mass of the lensing galaxy and place constraints on the expansion rate of the Universe the Hubble parameter The data taken by you in the observation part will be added to a database of a large monitoring campaign Therefore you have the chance to contribute to an ongoing scientific programme The experiment is split into two parts 1 Data reduction and analysis AIfA Bonn 1 day This part is done at the Argelander Institut f r Astronomie in Bonn Here you will process and calibrate an existing set of images step by step using the software package THELI
47. critical part of the data reduction the astrometric matching of the dithered frames In order to achieve good results use the following settings For the astrometric reference catalog select Web France the SDSS DR7 reference catalog mag limit 22 and radius 5 which should provide you with 350 objects For Create source cat select a rather low detection threshold of DETECT THRESH 20 enter the value in units of i e just 2 above the local background for DETECT_MINAREA 10 connected pixels Leave the remaining parameters as they are by default The astrometric matching should be done with Scamp In the configuration dialog click on Defaults this page and then set DISTORT DEGREES 1 After Scamp has been configured start the calculation Once it is done you will find a plots directory with a number of check plots For example the file fgroups 1 png displays the image positions on the sky You can look at it with display fgroups 1 png You do not need to comment on it in your report T 5 14 Coaddition App F 7 In this step the frames are sky subtracted and co added according to the astrometric solution computed in the previous step and normalised to an exposure time of 1 second For the Sky subtraction choose the Automatic sky modelling with DT 1 DMIN 10 SIZE 256 and Smoothing with SExtractor For the coaddition activate the additional outlier rejection by setting the outlier thres
48. e angles Note that the critical surface mass density is not a constant but depends on the distances or redshifts of the lens and the source respectively If a 10 lens system has a surface mass density larger than the critical value amp gt 1 multiple solutions for the lens equation are possible leading to multiple images By means of the identity V In 0 0 0 we can define the deflection potential Y0 vo amp 8 In 8 21 The use of this quantity is motivated because it encloses all information of the mass distribution of the lens By means of the deflection potential the following relations can be derived 0 VO 2 8 Av 8 22 For a better understanding further reading of the references is advised From the deflection potential a further scalar function the Fermat potential can be derived 0 B 5 8 0 0 23 The solutions for the lens equation eq 14 are the stationary points of this potential With this function we can determine the number of solutions images for a certain lens geometry and certain properties such as the parity of each image The differential deflection of light leads to a change in flux and the distortion of images by grav itational lensing These effects are quantified by the Jacobian matrix of the lens mapping defined as E 7 In terms of the Jacobian matrix the magnification u of an image which is the ratio of lensed over un lensed flux is given
49. e sky falling onto a pixel more than once and hence avoid having important data fall on bad pixels in all the images It also means that a star will not be in the same place in any of the images when the dithering is done properly By using the median to make a combined image from all the science exposures it is possible to obtain an image frame free from stars and galaxies and this can then be used as a superflat If the variations in pixel values are multiplicative the science frames should be divided by the master sky flat as was done during normal flat fielding However if these variations are additive a fringe model should be made and the defringing method used Determining between additive and multiplicative variations is a task difficult even for the most experienced observer One hint is that fringes see below occuring in the image is often an additive effect Fringing is the pattern of fringes occurring on a CCD image from observations of monochromatic light The fringes are caused by interference between light waves reflecting within the CCD or long wavelength light passing through the CCD and reflecting back into it The spectral regime of the I band contains strong narrow emission lines which is the reason for the large amount of fringing that is usually seen in band exposures The night sky emission lines present in Earth s upper atmosphere are mainly attributed to OH transitions and are powered by sunlight during the day Since they
50. ected and trimmed How to redo the task Just run it a second time F 3 2 Process flats MANDATORY Combines all FLATs in the FLAT subdirectory A FLAT correction is very useful even if the camera appears to be illuminated very homogeneously This is because the FLAT does not only correct for vignetting effects but also for different sensitivities on a pixel to pixel basis The more FLATs you have the better the master FLAT will be and the smaller the calibration noise you introduce into your SCIENCE images We recommend at least 10 FLAT exposures The FLAT exposures are debiased overscan corrected and scaled to the highest mode in the stack before combination How to redo the task Just re run it a second time F 3 3 Calibrate data Images are overscan corrected debiased and flat fielded If suitable a SUPERFLAT is calculated from the data as well 52 Edit Settings View Status Miscellaneous Delete Help Initialise Preparation Calibration Superfiatting weighting Astrom Photom Coadaition r Tasks Configure _ Do not apply BIAS DARK Bi Nonlinearity _Sontigure_ _ Do not apply FLAT correction Clear scripts Start He ax Defaults Abort Process darks uae aT groups Length _ Spread sequence IR 3 12 min max e F calibrate data a I Create SUPERFLAT Use DARK m Commands Jparallel manager sh process bias para sh nome prak1 all fpO_270114 images BIAS parall
51. ed back thus restoring the original state before any processing has been launched If no ORIGINALS subdirectory is present nothing will be deleted Clear dirs Clears all LineEdits 50 THELI GUI v 2 3 3 Edit Settings View Status Miscellaneous Delete Help Initialise Preparation Calibration Superflatting Weighting Astrom Photom Coaddition Settings m Select instrument LOG file name Load U N SUREE REY test Reset ofcPus 2 E io Bee Data diskspace warning sooms f Gui style 2 6 E y User defined Home diskspace warning 100 MB 2 NFRAMES 49 a ACAMGWHT ALFOSC NOT ALTAU16M VYSOSO6 homejprak1 all fpo l4jimages Restore ALL CFH12K CFHT ae TC al a HIR ONUG Dolores TNG r Data directories Restore ORIG EFDSCZOS GM EMMI_BIMG NTT AT Restore onis EMMI RILDGNTT _ ENZIAN CASQGHOLI 1M Science SDSIG N Restore ORIG oue FORS1_1CCD VLT ae Ree onic FORS1_2CCD VLT FORS2_1CCD VLT Standard Restore ORIG FORS2_2CCD VLT GMOS GEMINI NORTH GMOS GEMINI SOUTH GPC1 PS1 GROND_IRIM MPGESO GROND_OIMG MPGESO HAWKI VLT Fully process OFFTARGET data as well Clear dirs Figure 11 The Initialise PG F 2 The PREPARATION processing group F 2 1 Split FITS correct header The main job of this task is to split multi extension FITS files into single chips thus allowing for parallel processing It also writes a new FITS header conformed
52. el_manager sh process flat para sh home prak1 all fpO 270114 images BIAS FLAT R J parallel manager sh process science para sh home prak1 all fpO_270114 images BIAS FLAT R SDSS1650 4251 R parallel manager sh create norm para sh home prakl all fpO 270114 images FLAT R parallel manager sh create superflat para sh home prak1 all fpO 270114 images SDSS1650 4251_R Disk 196 713626 MB left A Figure 13 The Calibration PG If you decide to calculate a SUPERFLAT from this data then activate the Calculate SUPERFLAT CheckBox The parameter configuration dialogue appears Alternatively you can bring it up with the Configure PushButton Superflat parameters Here you determine how objects in the images are detected and which method is used for image combination The left field takes the detection threshold DT per pixel given in units of sigma of the sky background noise The middle field takes the minimum number of connected pixels DMIN above DT which make up an object The smaller both values are the fainter the objects you mask The right field accepts the size of the convolution kernel for the sky background Its effect is very minor at this stage and you do not have to worry about it A good starting point for optical data is 1 0 5 250 depending on the flatness of the image and the detector size If your images exhibit strong fringing then you can no longer use very low detection thresholds since then the fring
53. er support such as a dialogue containing an overview of the functionality of the various GUI elements Furthermore you can access this document as well the general pipeline documentation or a rather technical paper analysing the performance of THELI e If the GUI expects some parameters as input it will highlight the according fields for you with a red background colour etc The colour coding is explained in detail in the following subsection e Each reduction step you run dumps all programme and script output into the SCRIPTLOG You can access these for each PG separately under View in the menu bar 49 L Use unsmoothed SUPERFLAT _ use OFFTAF Correct your data with an unsmoothed SUPERFLAT instead of a smoothed one Number of groups MIN along 3 12 G6 xC y Figure 10 A tooltip appears whenever you hover with the cursor over certain GUI elements F 1 The INITIALISE processing group F 1 1 Pipeline Settings The LOG file Imagine you start working on a new R band data set of NGC 1234 then NGC1234_R would qualify as a nice LOG name Enter it in the corresponding field then click on the Reset PushButton This will flush the GUI from all settings that might be left over from a previous reduction run Parameters in the GUI and the LOG are set to meaningful default values If the LOG entered does not yet exist it is created at this moment It is automatically updated or created if not yet existing if you swi
54. es themselves are detected as objects and thus removed from the SUPERFLAT In this case one can no longer calculate a fringing model from the SUPERFLAT We recommend to use a high S N threshold if strong fringing is present Try starting with 5 0 5 250 in this case With near IR detectors DT and DMIN often must be increased to 10 in order to not mask features in the very inhomogeneous sky background If one or more of those three LineEdits is left empty then the default values will be used without warning You can choose between a median and a mean combination for the SUPERFLAT The median delivers a more stable result for a small number of stacked images whereas the mean has lower noise when more images are stacked How to redo the task Click on the little arrow next to the Calibrate data task Then activate the task again and re run 53 THELI parameter settings Rejecting nlow and nhigh pixels from a stack Overscan Bias Dark Flat Superflat Calibrate data r Superflat parameters MI DT DMIN SIZE J 1 0 10 256 Median 4 Window size 0 _J FILTER Defaults this page Cancel Defaults all pages oK Figure 14 Configuration for the outlier rejection during image stacking and the creation of a SU PERFLAT 54 THELI GUI v 2 3 3 Edit Settings View Status Miscellaneous Delete Help Initialise Preparation calibration Superflatting weighting Astrom Photom Coaddition
55. ffset from the line of sight from the observer to the lens almost no lensing will occur It is easy to see that in this case there will be only one image This will not change as long as the mapping between source and image plane is invertible in other words until the source moves across a caustic In this case an image pair is created or destroyed if we move in the other direction Since we started with one image it is clear that there will always be an odd number of images However normally at least one of them is highly de magnified so it may not always be feasible to find all images to a source Most of the systems observed appear as doubly or quadruply imaged Fig 2 provides an illustration of the odd number theorem Figure 2 Sketch illustrating time delays and the odd number theorem The wave fronts emitted by the source are deformed by the gravitational poten tial of the deflector Furthermore the light rays A B and C travel different distances so that there is a time delay between the three images of the source An image appears if a wave front passes through the position of the observer in this case it happens three times Irrespective of the complexity of the structure of the wave front the observer is out side the wave front before and inside the wave front afterwards which implies that the wave front passes necessarily an odd number of times from P Schneider lecture notes S Observer 3 3 3 Time
56. hat the Universe is homogeneous on large scales These considerations are summarized under the term the cosmological principle It has been shown by Robertson and Walker in the 1920 s that within the framework of General Relativity the metric for a spatially homogeneous and isotropic universe can be written as ds c dt a t dw f2 w d0 sin 0dv 1 where t is cosmic time and a t the cosmic scale factor which describes the isotropic expansion and is normalised such that today t to a to 1 Recall that the metric of Minkowski space is given as ds c dt dz dx dx The radial coordinate w is defined comoving which means that distances do not scale with the expansion but refer to values today 0 and y are the angular coordinates on a unit sphere The space time curvature K specifies IR sin VKw K gt 0 fk w 4 w K 0 2 7 sinh V Ku K lt 0 where K 0 corresponds to a flat geometry which seems to be consistent with current observations Due to the cosmic expansion the wavelengths of photons are increased We define the redshift of a source as P Aobs Aem 3 em where Agps Altops and Aen Altem are the wavelenghts at time of observation and emission respectively The above relation is directly related to the scale factor by 1 altem 1 2 4 This means that a source at redshift z 1 is observed at a time when the Universe was half of its current size a 1 2
57. he noise low is one of the reasons why we coadd frames instead of just increasing the exposure time 4 4 4 Photometric calibration To calibrate the photometry of an image means to relate the instrumental magnitudes the amount of light measured in the frame to a set of known photometric data Photometric calibration therefore needs to take into account all atmospheric effects influencing the flux measured by the detector From a practical point of view the complexity of the calibration applied to a set of data are determined by the quantity and quality of information which can be inferred from calibration data The most simplistic ansatz is to ignore everything but an offset between instrumental magnitudes and magnitudes from the literature for a set of standard stars Mealib Minstr Z 44 Such a quantity Z to be determined by some fitting technique is called the photometric zeropoint For example if you measure a magnitude Minstr 4 0 mag for a standard star of which you know the calibrated magnitude Mealib 3 0 mag from the literature you have to apply the zeropoint correction Z 1 0 mag to all magnitudes you measure Since for this experiment we are only interested in flux ratios corresponding to magnitude differ ences we do not rely on an exact photometric calibration http users obs carnegiescience edu peng work galfit README pdf 25 5 Practical part I Image reduction photometry and lensing analy sis This p
58. he output device needs to be modified by typing Set term postscript eps enhanced set output test eps followed by replot or the plotting command Note that plots will only appear in the specified output device It is not possible to write a plot into a file and onto the screen at the same time To reset the plotting device to the screen type set term x11 A more comprehensive explanation of the various gnuplot commands can be found by either typ ing help in the gnuplot shell or go to the web page http ti6web lanl gov Kawano gnuplot index e html D Time delay estimation with tdel Syntax tdel input light curve parameter file All parameters of the program are set in a parameter file see fpdir timedel tdel param replace all dots before application For a description of all the keywords see Table 2 The input light curves must be given as an ASCII table with 5 white space separated columns the first being the observation time second and third the magnitudes and corresponding errors for image 1 fourth and fifth column the same for image 2 like f ex fpdir timedel timedel_sorted dat The resulting time delay with error is reported in the shell tdel implements the estimation of the time delay as described in Sect 5 4 using a three step procedure 44 1 In the first step a first estimate of the mean magnitudes of the two light curves is obtained This is done iteratively the program starts with a time delay guess of A
59. he scaling of the x y axis to logarithmic type set log x y this change will only show up in the plot after typing replot T he same is true for other commands that affect the plot but do not involve the plot command To switch back to linear scaling simply type unset log x y An even simpler way is to hold the mouse over the axis and press shift L The scaling can be modified by means of commands like set xscale 0 10 replace x by y for the ordinate axis In order to zoom into your plot just click your right mouse button drag a rectangle and click the right mouse button again Type a on the plot window to return to the automatic scaling A function may be entered as f x a x 2 b x c d sin x To fit this function to a data set the coefficients a b c and d must be assigned arbitrary starting values after which fit f x data file via a b c d will perform a least squares fit on the data by adjusting the specified coefficients Note that for a linear fit no initial guess is necessary Plotting more than one dataset or data and the fitted function is also possible plot data file using 3 5 f x In order to add further plots replace plot by replot in the commands given above If commands are too long to fit on one line entering a backslash 1 before pressing enter will allow the use of the next line for further input By default gnuplot prints plots on the screen To create a postscript file with the plot t
60. he signal level in question 4 3 Image reduction This chapter describes how to reduce a set of images T he image reduction is done to remove instru mental signature and improve the signal to noise S N in the data before extracting any scientific information Much of the information given here is taken from Handbook of CCD Astronomy Howell 2000 in particular Chapter 4 but also some from Chapters 3 and 5 in which a more thorough introduction to CCDs and data reduction can be found The image reduction software package THELI will be used throughout this course and the user manual can be downloaded from http www astro uni bonn de mischa theli html 20 4 3 1 Step one bias subtraction For each image taken the CCD electronics are set up to provide a positive offset value called the bias level This is done to avoid negative counts in the output image Calibration measurements of the bias level and its uncertainty are usually made using one or both of two processes the use of overscan regions and bias frames Bias frames are made by taking exposures of 0 000 seconds The shutter remains closed and the image is just a readout of the unexposed CCD This way the read noise level of the CCD is determined and a median bias frame is then to be subtracted from the images in order to create a bias corrected image The median bias frame should be made as the median of 10 or more bias frames in order to capture all the statistical varia
61. hen selecting asteroids for measurement is their apparent angular speed choose those that do not move much more than the average FWHM z 3 normally for our telescope during the time required to detect them Calculate the maximum exposure time for an object that moves with an angular speed of 60 minute needed to record it as a point source and not as a trail Assume that the FWHM is zz 3 Would you be able to detect an 18th magnitude asteroid moving with this apparent velocity Find out the apparent angular velocity and magnitude of the asteroid 2005YU55 on 2011 11 09 at 05 00 UT Would one be able to observe it using the AIfA telescope at the time What about 2011 11 09 at 19 00 UT How large could the apparent position error of an asteroid be if you used a geocentric observer to generate your ephemeris instead of the C60 observatory code Bonn coordinates 39 References Freedman W L Madore B F Gibson B K et al 2001 ApJ 553 47 Morgan N D Snyder J A amp Reens L H 2003 AJ 126 2145 Oguri M 2007 ApJ 660 1 Pelt J Kayser R Refsdal S amp Schramm T 1996 A amp A 305 97 Spergel D N Bean R Dor O et al 2007 ApJS 170 377 Vuissoz C Courbin F Sluse D et al 2007 A amp A 464 845 40 A An iraf primer iraf is a huge publicly available package for astronomical image reduction and analysis Here we only summarise a few iraf tasks which you need for the analysis
62. herwise you run the risk of fitting noise minima Before tdel explores the magnitude shifts it 32 registers both light curves to an average magnitude of 0 so it is sensible to choose mmag Min and mmag max symmetrically around 0 The range covered by mmag Min and mmag_max should correspond to the error you assume is made by taking averages of light curves that are shifted with respect to each other If you wonder how many bins to take Delay_nbin mmag nbin ask yourself how detailed you want to sample your range of parameters The number of MC realizations should be chosen large enough so that you can clearly recognize the form of the resulting probability distribution Choose MinGapLength such that the single obvious gap is securely detected 5 5 Lensing analysis at home In order to determine the Hubble constant a sufficiently determined model of the lens has to be known We choose the Singular Isothermal Sphere SIS the most realistic model which can still be treated completely analytically The background quasar of SDSS1650 has a redshift of z 1 547 while the lens galaxy is located at zg 0 577 Morgan et al 2003 By means of eq 11 the corresponding angular diameter distances can be calculated Again for the standard cosmological model ie Qm 0 3 O4 0 7 the integration in eq 11 can only be performed numerically resulting in w za 0 4985 c Ho and w z 1 039 c Ho In the following make use of the results you obt
63. hing length mosaics EE Maximum image seeing ri peek Minimum relative zeropoint BEER Threshold Clustersize Border width Outlier rejection 4 Resampling kernel LANCZOS3 Projection Al Ys Celestial type EQUATORIAL Combine type WEIGHTED lt lt gt gt Defaults this page Cancel Defaults all pages OK ZA Figure 22 The configuration window for the coaddition F 8 Image statistics Calling Image statistics from the Miscellaneous pull down menu presents you with the dialog shown in Fig 23 Image directory Specify here the path to the images for which you want to obtain some statistics Name filter This is a string for filtering a subset of images out of all files in the specified directory For example it can simply be something like AXOFCS fits If left empty all images fits in the directory will be considered Image statistics oOx Directory with images homejprak1 a 2 2 16 251_R Clear all Select image Close Name filter e g OFC fits OFCSF fits Image statistics Background seeing transparency Area for background estimation AN RER EHI Get statistics xmin xmax ymin ymax 3 arcsec y pixel Abort image008067 1 474 43 469 52 469 75 9 47 1 1 2 27 0 024 image008068 1 492 63 487 53 487 46 10 11 1 73 2 41 0 022 image008069 1 504 76 499 20 499 00 9 54 1 75 2 54 0 008 image008070 1 557 15 551 32 551 42 9 75 1
64. hold to 4 All other fields can be left empty After co addition inspect the co added frame SDSS1650 4251_R coadd_ filtername coadd fits Inspect and describe the co added weight image coadd weight fits How does it correlate with coadd fits Compute the noise rms for the deepest stacked area highest weight of the image Find such an area about 100 x 100 pixel or more without bright objects and compute the rms again using imstats coadd fits s xmin xmax ymin ymax Compare the result to the noise estimate from a single exposure What do you measure and what did you expect Can you explain the result 5 2 PSF extraction for SDSS1650 4251 Copy the co added image into the directory fpdir photometry and proceed from there 29 x TASKS T 5 15 T 5 16 T 5 17 T 5 18 T 5 19 T 5 20 Identify the target which is located at the J2000 coordinates RA 16550 43 45 DEC 42 51 49 00 The lens system SDSS1650 4251 by now you should have understood where this name comes from consists of two quasar images plus a lensing galaxy which is too faint to detect in our data The images have a separation of the order of typical seeing conditions and are therefore blended Use the iraf task imexam see App A to identify stars how do they differ from galaxies and measure the seeing FWHM in pixels and arcseconds How does the target differ from the stars mexam Are there any signs that this light distri bution is com
65. ht travels compared to vertical in fall For an angular distance z from the zenith it can in good approximation be computed such that a 1 for an object at the zenith and formally a oo at the horizon c wb as Q sz 4 1 3 Coordinate systems Astronomers make use of different coordinate systems to quantify the positions of celestial objects which in different ways take into account Earth s motion The most common system for identifying and cataloguing sources is the equatorial system pro jecting the grid of terrestrial latitudes and longitudes from the centre of Earth onto the sky The declination is defined in analogy to latitude in geography The North polar star is in approximate extension of the rotation axis of the Earth having a declination of 6 90 while the projection of the South Pole is defined to have 6 90 Right ascension o is the equivalent to longitude Its zero point is the vernal equinox point the position of the Sun at March equinox Right ascensions are expressed as times ranging from 0 hours to 24 hours due to their close connection to the rotation of the Earth Subsequently subdivisions are given as time minutes and seconds rather than angular minutes and seconds If you want to know where to point your telescope to find an object on the sky given the time and your location on Earth the hour angle t is a useful replacement for a At culmination when the object reaches its highest elevation in the S
66. imited The maximum number of electrons fitting into a single pixel is called full well capacity or simply full well Typical scientific CCDs have a full well of the order of 100 000 e If the charge level is approaching full well the signal is getting nonlinear and charge starts spilling over into adjacent pixels This is the well known blooming effect 19 Linearity CCD detectors are highly linear devices They are linear over the full dynamic range of 104 to 10 Deviations from linearity are usually in the 40 596 range for a well behaved system Stability This has several aspects i As a piece of silicon a CCD is geometrically very stable This is of great importance e g for any kind of astrometry ii It keeps its performance over years without degradation Exceptions are detectors which are exposed to e g damaging radiation like in space applications where all CCDs suffer from high energy protons iii Despite its high sensitivity at the lowest light levels a CCD is very insensitive to over exposure A less advantageous property of CCDs is dark current At room temperature dark current fills CCD pixels to their saturation level within a minute or even less Therefore astronomical CCDs are always cooled Cooling is done thermo electrically with closed cycle systems or by liquid nitrogen The used CCD uses a thermoelectric cooling 3060x2040 pixels CCD temperature difference about 30 C With this experiment some basic p
67. ing parameter is varied during the fit if it is 0 it is held constant Details about the parameters you have to edit can be found in Table 1 Keyword Type Description A string Cut out image of the lens system B string Name of the resulting output image block D string Cut out rescaled and sky subtracted PSF image H 4 integers Image region to fit xmin xmax ymin ymax PSF 1 2 integers Centroid position of the PSF in pixels PSF 3 integer Total magnitude only relative values between the two PSF s are rele vant SKY 1 number Sky background in ADU Table 1 Keywords to be adjusted in the galfit parameter file C Using gnuplot Gnuplot is a command line tool for plotting data as well as mathematical functions To start it simply type gnuplot into a shell It expects data to be in ASCII format ordered in columns separated by spaces tabs or comma The decimal separator is If there are lines within the file like a header which should be ignored by gnuplot put a st in front 43 Like regular shells the gnuplot shell features a history function arrow up shows the last com mand s and tab completion for filenames Unix commands may be called from the gnuplot shell To take a look at a data file simply type 1ess data file To plot the data in in column 3 against column 5 of data file type plot data file using 3 5 In case you would like the data points to be connected add with lines to the command If you want to set t
68. is camera The dark current Igark here given in e pix s increases exponentially with temperature T according to E Idark quie e TBT 54 where E 1 16eV is the silicon band gap energy kg 8 62 10 eV K is the Boltzmann constant and c is a detector specific constant The gain of the CCD is k 1 4 e ADU unbinned or k 2 3e ADU binned 36 x TASKS Start your measurements at room temperature Switch on the cooling nonetheless in order to stabilise the temperature which is achieved if T varies only within 0 2 Stability is only guaranteed if the cooling power does not exceed approximately 8596 of its maximum Note that this camera does not have an overscan nor can you choose an exposure time less than 0 12s T 6 9 T 6 10 T 6 11 Write down a procedure to determine the dark current measured in ADU pix s and the possibly temperature dependent bias level at a given temperature without making use of image manipulation merely analysing images taken with different exposure times For image statistics you should use the command imstats image999999 fits s xmin xmax ymin ymax on a suitably large contiguous area without hot pixels Is the mean the mode or the median the best measure for these purposes Measure the dark current as a function of temperature between room temperature and T 10 C Make use of the rule of thumb that the dark current level decreases by a fac tor of 2 for ever
69. ith the Earth in the next few dozen years For detailed instructions on telescope and camera control see the document Telescope manual During daytime you should make a plan for the night optimising the number of targets to observe Ideally they should be observed at as high elevations as possible low airmass to get best seeing conditions Create visibility plots showing elevation as a function of time which will be very useful for planning and e g rearranging your observation plans Calibration frames are not essential for this part of the laboratory but taking them will increase your chances of detecting a faint object Usually asteroids are observed in the R or V Jonson Bessel filters for obtaining consistent photometry The main goal you want to achieve is to get a few observations 3 5 frames for one asteroid then move to the next target and so on coming back later to the same ones as you should attempt to follow the asteroid on as much as possible of its orbit This way the uncertainty in the orbital elements will be greatly decreased than for only a few minutes long orbital arc Before arriving at the telescope you should have read the telescope manual and have a written observing plan for the night order of objects ephemeris and exposure times As accurate time is essential for this type of observations syncronize the telescope computer clock with an internet time server ahead of starting to take data see preparatory tasks Wri
70. ketch of a gravitational lensing system with quasar Q lens L and observer B in two universes with different Hubble Constants The redshifts image positions and flux ratios are the same for both cases The only difference is given by the time delay which is proportional to the ab solute scale of the system and hence the inverse Hubble Constant adapted from the monograph by Schneider 2007 Small H A characteristic angular scale of an axisymmetric lens is given by the Einstein radius 95 defined as the angle inside which the mean of the convergence is unity As a consequence the projected mass inside dx can be written as M 0 lt 0g 162 DX 33 For an SIS the Einstein radius reads Tv A Das Bou 2 i 34 poene 34 3 4 Ho measurement The Hubble Space Telescope Key Project has determined the Hubble Constant with 10 uncer tainty to 72 3 7 kms Mpc statistical and systematic errors see Freedman et al 2001 us ing Cepheid stars as distance estimators in nearby galaxies Making the strong assumption that the geometry of the Universe is exactly flat the three years results from the WMAP satellite study ing the angular fluctuations in the Cosmic Microwave Background radiation consistently yield Ho 73 x 3 kms Mpc Spergel et al 2007 Given the fundamental role of Ho in cosmology further high precision measurements of Ho are of great importance to independently confirm these results and ideal
71. ll noise and a sharp drop in noise becomes visible see Fig 9 Unfortunately near full well additional fixed pattern noise similar to the PRNU appears Its origin is not well understood This additional noise makes the expected noise drop less obvious but it can be removed in the same way as the PRNU noise by taking the difference of two images with identical exposure time This is why you have taken pairs of images Create difference images from your image pairs using imarithm Image templates see App A 6 may simplify the task to do similar calculations for a series of images Plot the variance in the difference images vs the signal level of individual images log log Identify the point where the variance starts decreasing Create a fit to the linear part to determine the gain k more precisely With this value calculate the full well capacity at home Photon Transfer Curve Figure 9 A photon transfer curve variance vs signal is used to determine the full well capacity Near full well charge starts to spread into neighbouring pixels resulting in a rapid decrease of the pixel to pixel variance log variance log Signal 6 3 Dark current You will examine the amount of dark current and the dependence of dark current on temperature for a typical astronomical CCD You will use a thermo electrically cooled SBIG STL6303E App E gives a short introduction to the camera control software ccdops used with th
72. ly placing more stringent constraints The measurement of time delays between different quasar images in strong lens systems provides a completely independent and purely geometric approach to constrain Ho If the lensed quasar varies in brightness the observed variation will be shifted by the time delay between the individual images Hence regular monitoring of such a lens system can reveal its time delays For given redshifts and angular image positions these delays scale with the absolute size of the source lens observer system see eq 30 and are thus Hg exact for a flat metric see eq 11 In return measured time delays can be used to constrain Ho if a good model for the lensing galaxy can be found At the time of writing time delays have been published for 17 gravitational lens systems with a total number of 100 known strong lens systems While constraints on Hp from individual systems are often limited by degeneracies with the radial mass profile estimates from a larger ensemble seem to be promising see Oguri 2007 who finds Ho 68 6 stat 8 sys kms Mpc from 16 measured time delays In order to increase the accuracy of these estimates large monitoring campaigns such as COSMOGRAII are currently conducted to measure time delays for a larger number of lens systems aiming at statistical errors at the percent level In addition to Ho estimates from a large ensemble of systems individual time delays are very useful to c
73. m which offers a variety of options to investigate an image Move the cursor to the ds9 frame and activate it by clicking on its border Then move the cursor to your object of interest and press one of the following keys this list is not complete e perform aperture photometry and a Moffat fit see below e e show a contour plot http iraf noao edu 41 e r show a radial profile e s show a surface plot e I show the line profile e c show the column profile e q quit imexam When imexam performs aperture photometry it refines the object centroid By default it also iteratively refines the aperture radius It is important that you change both of these parameters otherwise your relative photometry will be screwed up To do so you need to change the imexam parameter file which you can do by entering epar rimexam Set iterati 1 typing a new value will overwrite the old one In addition you need to change the aperture radius radius to a fixed number of pixels A good guess for that radius would be the mean stellar FWHM but test the impact of modifying the parameter When doing relative photometry the value has to be kept fixed for all objects within the image To save the changes and exit the editing window do CTRL D When doing the analysis imexam provides you with the object position COL LINE a magnitude computed with an arbitrary uncalibrated zero point of 25 RMAG the total flux in the aperture FLUX an
74. med with the detector system mounted at the telescope Light comes from a screen or an illuminated section of the dome just in front of the telescope aperture 6 1 Detector system gain and noise The ratio k between the amount of charge in a CCD pixel and the corresponding digital number after A D conversion is often called the detector gain given in e ADU The errors of e g stellar photometry can only be properly calculated if intensities are given in units of electrons e7 Therefore the gain k must be known The determination does not depend on any calibrated reference source Instead it can be derived based on the assumption that photon or electron numbers are described by Poisson statistics i e in a detector area with constant flat illumination the variance o of the pixel to pixel fluctuation equals the average number of electrons per pixel N N o 45 For the corresponding numbers after A D conversion Ne a and ce a where Ne kNea 46 and o ko 4 47 we have EN koe 4 48 and so a 49 Ted Thus to obtain the gain the average signal level and the variance has to be determined in a well exposed area of the detector and the above formula need just be applied In principle this is true Unfortunately there are usually two other noise components in the data which have to be separated or taken into account First the read out noise RON already mentioned in the introduction and second the
75. nce frames the weight images are co added too Information about the exposure time of each pixel is hence preserved for later analysis which is very useful during object detection in the final co added science image In addition the individual weight images are taken into account upon the photometric calibration 4 3 4 Step four astrometric calibration The pixel detector coordinates and the sky coordinates normally do not have a simple relation It is therefore necessary to perform a mapping from pixel coordinates onto a planar projection of the sky To make the astrometric calibration correct it is important that the exposures are oriented North up and East to the left In this process an astrometric reference catalogue is needed which is retrieved from the internet here we use SDSS R6 The objects in the images have to be identified with those in the reference catalogue achieving an acurate pixel to sky mapping To this end the sources in the images must be detected By defining several detection thresholds like signal to noise and the minimum number of connected pixels that comprise an object this can be done using SExtractor The individual masks created in Sect 4 3 3 are taken into account when creating these source catalogues guaranteeing a clean catalogue largely free from spurious detections An astrometric solution is calculated using the Scamp software package It calculates linear offsets between the reference pixel in each expo
76. nts Main elements and nomenclature The main window consists of two main parts e a menu bar at the top of the window and e a dialogue with a tabbed menu We will refer to the seven tab menues of the latter as processing groups PG for short These are e Initialise e Preparation Calibration Superflatting Weighting e Astrom Photom e Coaddition and contain the various reduction steps or other settings The data is reduced by making some initial settings in the first processing group tell the software where the data is which instrument was used etc and then one works his way through the remaining six PGs Integrated Help system A very extensive help layer has been integrated that comes in various active and passive forms e On the lowest level there are simple tool tips that are displayed when you hover with your mouse button over a specific PushButton or other element unless the meaning of those is obvious see Fig 10 e More extensive help for the various PGs and reduction steps is available under Help What s this The cursor will change to a question mark Move it anywhere into a GroupBox with the reduction steps to obtain general information of what is happening in this particular PG Or click on the CheckBox of a particular reduction step to obtain more detailed information for this task such as if this step is mandatory or optional and if you have to provide any parameters e The Help menu provides you with furth
77. o provided by the CCD control electronics CCD detectors are common on all astronomical telescopes world wide and are used in all kinds of instruments They have almost completely replaced other detector types like photographic plates tubes or photo multipliers Its properties make the CCD the ideal detector for astronomical observa tions in the visual 350nm to about 1000nm Some of these properties are Quantum efficiency QE Photon energies and the band gap energy of silicon are such that each photon can produce one electron Quantum efficiency is the ratio of produced electrons to the number of photons hitting the detector surface QEs of top grade CCDs are above 9096 over a significant wavelength range Photographic material is almost a factor of 100 less sensitive QE is the most important aspect of detector sensitivity Another one is noise Read out noise RON When an empty CCD is read out there is nevertheless a small scatter in signal level from pixel to pixel The standard deviation of this scatter is called read out noise Its source is amplifier noise occurring on the CCD and in the electronics The RON limits ultimately the detector sensitivity at low signal levels At high signal levels the photon shot noise dominates RON is usually measured in units of electrons e It s normally pretty low 5e to 15e In very low noise systems it may even be below 5e Saturation level full well The charge capacity of CCD pixels is l
78. on compact radio structure and strong y ray emission 3 3 Gravitational Lensing According to General Relativity light propagates along the null geodesics of the space time metric defined by ds 0 see eq 1 Assuming a weak gravitational field this is valid except in the surroundings of a black hole the theory can be heavily simplified as is done below A typical situation considered in gravitational lensing is sketched in Fig 1 where a mass concentration at distance Dg deflects light rays from a source at distance Dg If the extent of the deflecting mass along the line of sight is much smaller than both Dg and the distance Dg from the deflector to the source the actual light rays can be replaced by two straight lines with a deflection angle which depends on the mass distribution of the deflector and the impact vector of the light ray 3 3 1 Lens equation In this context we describe light by rays which will be deflected by the mass they encounter on their way from the source to the observer This mass distribution will be called the lens hereafter For the applications studied here the distances source lens and lens observer are much larger than the sizes of the source and the lens along the line of sight This implies two things first we will always work in the small angle approximation Second we can assume that source and lens are enclosed in parallel planes source plane and lens plane and that light rays are just affected in
79. onstrain the radial mass profile of the lensing galaxies if an externally estimated value for Ho e g See the CASTLES gravitational lens data base http www cfa harvard edu castles nttp www cosmograil org 14 from the HST key project is assumed Comparing this to the visible light profile the contribution of dark matter can be estimated 3 5 Time delay measurement A simple but efficient and well tested way to calculate time delays from observed light curves is the minimum dispersion method As a first step a guessed value is chosen for the time delay The light curve of one quasar image denoted by A t is taken as a reference and the other one B tz is shifted by all the time delays to be tested in an arbitrarily long interval around the initial guess value The light curve is assumed to be sampled at a discrete number of times tg where k 1 N Pairs of data points are formed by a point of the reference curve and its nearest corresponding neighbor in the shifted version of the second light curve After correcting for the fact that the two light curves may have different mean magnitudes one computes for each pair the difference in magnitude between the two points The best guess estimator for the time delay 7 is then that value of A which minimizes the sum over all pairs of the squared differences N D A Alte B te Y 35 kc where A is the time shift and D is the dispersion function
80. orbital elements become large enough to be unreliable Compare the uncertainties for obtained using only three consecutive observations and for the entire arc you observed during the night For more information about astrometry and orbit determination you can check Methods of orbit determination by Pedro Ramon Escobal chapters 1 6 1 and 6 2 and To measure the sky by Frederick Chromey section 4 6 7 2 PREPARATORY TASKS You are asked to do the following tasks before the observations They should improve your under standing of the theory and provide results needed for the observation P 7 5 P 7 6 P 7 7 P 7 8 The first step in taking the position measurements is planning which objects are to be observed To do this use MPCs planning tool at http scully cfa harvard edu cgi bin neaobs cgi filling in the appropriate parameters take care that your objects are brighter than mag nitude 19 above the horizon and not close to the Sun or the Moon for the C60 observatory code If there are no objects returned or too few also try the Observing List Customizer at at http www minorplanetcenter net iau lists Customize html selecting Dates Of Last Observation Of NEOs and eventually Dates Of Last Observation Of Unusual Minor Planets you would want to observe objects for which the position has not been measured in a long time with a larger uncertainty in their position Another factor to which you have to pay attention w
81. osphere described next the actual resolution is much lower for actual ground based telescopes 4 1 2 Seeing and Airmass For ground based astronomical observations Earth s atmosphere has to be considered as part of the optical system leading to numerous effects Most importantly turbulence in the atmosphere leads to variations of the refractive index on short spatial and temporal scales This results in a blurring and scintillation of the PSF which no longer is an Airy disc but has a more complicated shape which to some extent can be represented by a Gaussian in two dimensions a better approximation is given by the Moffat profile The size of such a stellar image as given by the full width at half maximum FWHM of the Gaus sian is called the seeing of the image and measures the actual resolution in a particular observation The less turbulent the atmosphere the higher the resolution and thus the data quality that can be 17 achieved For Bonn a seeing of 2 arcsec is a good value while in excellent locations like Hawaii or the Atacama desert 0 6 arcsec are common The best possible observing conditions are achieved near the zenith where the length of the light path through the atmosphere is minimal On the contrary extinction and disturbing seeing effects get worse for observations at lower elevations These effects are often expressed in terms of the objects airmass which tells you through how much atmosphere column density the lig
82. outh its hour angle is 0 h In general it is defined as the time elapsed since the last culmination running through all values from 0 h to 24 h and S W N E S in one day To connect right ascension and the hour angle we define the sidereal time to be O t a Only dependent on your longitude its practical meaning is that at e g O 18 h sidereal time objects with right ascension a 18 h are culminating 4 2 CCD detectors CCDs are silicon based two dimensional pixel detectors The physical mechanism of light detection in a CCD is the photoelectric effect Silicon responds to photons over a wide wavelength range from the near infrared to the soft x ray Here we restrict ourselves to the visible light Light distributions imaged on a CCD are converted to and represented by a corresponding distribution of charge packets which are collected and held in 3 dim potential wells the well known pixels Pixel sizes are typically between 10u and 20u To measure the amount of charge in each of the packets they have to be transported across the full detector surface to an output amplifier which is usually located at one of the four corners of the detector surface At the amplifier charge packets are converted to volts with typical conversion gains of 1 5 V e Amplification of these signals and conversion to digital numbers occurs in the CCD control electronics In order to transport charge packets across the detector surface potential barrie
83. posed of two objects In order to perform component fitting photometry you need to extract a good Point Spread Function PSF model using stars in the image which are quasi point sources and hence provide an estimate for the possibly position dependent PSF Create PSF models for at least 5 single stars and a stack This can be done using the shell script create psf csh in the following way create psf csh DIR IMAGE LIST RADIUS MAX FWHM STACK Words printed in CAPITALS are variables and must be replaced by reasonable values Please read the following explanations CAREFULLY If the script crashes or doesn t work it is most likely because you provided wrong input e DIR is the directory in which the image IMAGE is located and where it puts the cut outs e LIST is an ASCII file containing the output from imexam created with the option When creating LIST please exclude the first line with column labels but include all stars which are brighter why than the lens system check the FLUX value Include the lens system itself in the last line as you will need a cut out of it for the component fitting Sect 5 3 e RADIUS is half the side length of the square which is cut out It has to be large enough to include the outer wings of the stellar light profiles but small enough to exclude contami nation from neighbouring objects e MAX FWHM STACK is the maximum size of the PSF allowed It must be smaller than the size of the lens system
84. quick start manual only for further reading http users obs carnegiescience edu peng work galfit README pdf In addition you need to know basic Linux shell commands cd cp mv rm mkdir ls pwd Topics of examination e Cosmology Expansion of the Universe Hubble constant measures of distance e Gravitational lensing Lens equation geometry of strong gravitational lensing multiple images fundamental quantities as e g Einstein angle etc e Active galactic nuclei Basic properties relevance for gravitational lensing e Time delay measurements Estimation of the Hubble Parameter from time delays minimum dispersion method singular isothermal sphere SIS and its properties e Basic telescope design Cassegrain telescope telescope resolution e Properties of astronomical CCD cameras Types of CCDs charge transfer principle noise con tributions quantum efficiency saturation level linearity stability e CCD calibration Bias dark flat superflat astrometric and photometric calibration co addition e Observational basics Sky coordinates sidereal time hour angle magnitudes filters seeing airmass 3 Background knowledge Theory 3 1 Cosmology Numerous observational results consistently show that the Universe started with a hot Big Bang about 13 7 Gigayears ago and since then has been expanding and cooling down The nuclei of hydrogen 75 helium 25 and to a low fraction lithium formed within the fi
85. roperties of a typical CCD detector relevant for astronomical observations shall be quantified e g gain noise behaviour linearity saturation level full well dark current The same detector is then taken to perform the astronomical observations 4 2 1 Glossary Here some terms are explained that will be used in the following sections BIAS When an empty CCD is read out one will still get positive numbers This is due to a DC offset that is added in the electronics to keep any fluctuations noise in the conversion range of the A D converter This level is called BIAS level or just BIAS Signal levels mentioned in the following sections are always with respect to this BIAS level A BIAS frame or BIAS image is obtained when the unexposed detector is read out Overscan When shifting the charge packets from the serial register this process is continued beyond the last packet i e additional empty packets are read out This is usually done for about 20 to 50 pixels These are called overscan pixels and they represent the BIAS level In the final image they appear as a dark bar besides the image area ADU This is an acronym for Analog Digital Unit It s used as a unit for the digital numbers produced by the A D conversion process I e you may say I find a BIAS level of 345 ADU As 16 Bit converters are used values between 0 ADU and 65 535 ADU are possible Noise Noise always means the standard deviation of t
86. rs in transport direction can be manipulated This is done by applying appropriate voltage waveforms to an array of electrodes so called gates spanning across the detector surface The transport is divided in two alternating phases parallel shift and serial shift During parallel shift the whole charge image is shifted by one row data time which brings the lowest row into an extra register of similar pixels the serial register During the following horizontal transport only charge in the the serial register is 3We observe from the northern hemisphere 18 1 3 co0000000000000 e0000000000000 H Figure 6 CCD structure and read out principle Top left A 2048x2048 pixel CCD This CCD type is also available for the experiment Centre Microscopic view of the detector corner with the output amplifier structure In the upper left hand corner a part of the image area is still visible The square pointed to by the arrow covers one 15u x 15u pixel Between the image area and the three white bars at the right hand side is the serial register which extends by another 16 pixels downward towards the output amplifier The bright lines and bars are the aluminised clock lines Bottom right Schematic representation of the charge transport mechanism in a CCD shifted one pixel at a time towards the output amplifier Pixels are shifted detected and digitised ata rate of about 30 kHz Voltage waveforms for charge transport are als
87. rst 15 minutes At an age of 370000 years the Universe had cooled down sufficiently for protons and electrons to combine and form hydrogen atoms With the disappearance of free electrons the scattering cross section for photons was strongly reduced so that from this point on they could travel almost freely through the expanding Universe These photons can now be observed as the Cosmic Microwave Background CMB radiation which has an almost perfect black body spectrum with a temperature of 2 73K Density fluctuations which probably originate from quantum fluctuations in the very early phase grew during the cosmic expansion driven by the gravitational pull of the mostly dark matter to form the complex structures galaxies galaxy clusters etc we observe today 3 1 1 Cosmic expansion Despite the wealth of structure one can observe in the night sky the distribution of galaxies is relatively uniform on scales larger than about 200 Mpc as can be seen in galaxy surveys Taking into account that the visible Universe has a radius of several Gigaparsecs 1parsec 1pc z 3 x 101 m the simplifying assumption of isotropy on large scales is therefore justified Further support comes from the isotropy of the CMB radiation In generalization of the Copernican Principle one postulates that the position of Earth in the Universe is not special from others so that large scale isotropy should also be found by every other observer from which one can conclude t
88. s image I obs 75 y ginstr Nodo 41 Ty The difference in magnitudes between two sources is defined by the ratio of their observed fluxes S and 5 in the following way Am m ma 100 logio 42 2 Note that following this definition fainter sources have higher magnitudes While it is relatively easy to compare fluxes connecting your observations to a referential zero point can be a challenging task In practice this relies on the observation of standard stars whose magnitudes are well known 4 4 2 Deblending photometry In the case of an isolated object meaning that its point spread function is not significantly overlapping with any other bright noticeable source eq 41 can be applied in a straight forward way In this aperture photometry you sum up the counts found in all pixels within a certain radius around your object s centre and subtract from that the number of background counts you would have measured in case your source wasn t there This second important step is usually done by measuring the background flux in an empty ring the annulus around the object Our task however is more complicated because we aim at disentangling the flux contributions of two sources very close to each other such that their PSFs strongly overlap For the pixels measuring the signal of both sources there is no way to tell for the single photo electron if it was triggered 6In the case of an ideal point source this
89. s there a large gap in the observations T 5 29 Estimate the time delay for the real data set of SDSS1650 as given in Table 3 Use as input file timedel_sorted dat Consult also App D and the comments on the choice of parameters given below Set UseMC to 0 and examine the generated dispersion spectra and the quality of the corresponding fits Where is the absolute minimum of the dispersion spectrum in the two dimensional parameter plane Make sure that you do not try to fit a noise minimum To avoid this check if there are other minima of similar amplitude relative to the large scale trend in the dispersion spectrum If so you have most likely found a noise feature A nice check is to plot columns 1 vs 3 on top of columns 1 vs 2 from the dispersion spectrum file to check how the fit corresponds to the data T 5 30 If you have found a configuration that yields reliable fits set UseMC to 1 and rerun tdel to get your final time delay estimate and its error What does the probability distribution of the time delay look like Don t forget to report the parameters you chose T 5 31 How realistic are the error bars determined by the Monte Carlo method at home In the beginning choose Delay_Min and Delay_Max relatively wide The dependence of the quality of your results on the initial guess Delay guess is only small If at a later stage you have got an idea where your final time delay will be keep Delay_Min and Delay Max wide nonetheless because ot
90. s used in calibration to make up for the slightly different gain or quantum efficiency QE value of each pixel in the CCD when compared to its neighbours To flatten each pixels relative response to the incoming light the object frames are divided by a flat field frame The ideal flat field image would be an exposure with uniform illumination of every pixel in order to obtain the internal variations of the pixels within the CCD preferably by a light source that has a similar spectral energy distribution to that of the object images The number of counts in a flat field exposure should be slightly less than half the amount that leads to saturation Also for each filter used for the science exposures a new flat field image should be made as the pixel response to incoming light is wavelength dependent Before being used in calibration the flat field image needs to be normalised to an average value of 1 This means that a pixel with a normalised value less than 1 have a smaller value than it would have had if all the pixels had reacted in the same way By dividing the object image by the flat field image the corresponding pixel value in the object frame will increase and the pixel variations will be evened out There are several ways of obtaining a flat field image all of which involve a bright light source giving a CCD calibration image of high S N ratio One way to acquire a flat field image is by taking dome flats This is done by illuminating the tele
91. scope dome from the inside and taking short exposures as not to saturate the CCD The flats are then averaged together to form a co added master flat field image to be used for calibrations Sky flats are obtained by taking exposures during evening and or morning twilight The sky flats often give better results than dome flats and are therefore usually preferred The reason for this is that the dome is difficult to illuminate uniformly as opposed to the twilight sky which is quite smoothly lit during twilight leading to all the pixels in the CCD being more likely to receive the 21 same amount of light in a sky flat One problem with sky flats arises from bright stars visible in the image However these stars can be avoided from appearing in the co added master flat field image by dithering between exposures and using the median rather than the average value of each pixel upon co addition The advantage of dome flats is that they can always be obtained even during daytime For both methods five to ten flats from each filter should be obtained in order to get a master flat field image of the quality required for proper image reduction In addition to the flat fielding described above the use of a superflat a co added master sky flat is necessary in the case where normal flat fielding does not flatten the pixels properly For each exposure the telescope is slightly displaced each time This dithering is done in order to avoid the same region of th
92. so called Pixel Response Non Uniformity PRNU noise PRNU noise is a pixel to pixel fluctuation which comes from the fact that the QE is not exactly identical for every pixel which is also the reason why one calibrates the data by flat field images The CCD production process leads to tiny differences among the individual pixels These differences are imprinted on the detector Thus the signal difference between say two adjacent pixels is proportional to the signal level and the PRNU standard deviation Oprnu increases linearly with signal level N as well Oprnu Nefprnu gt 50 where fprnu is the detector dependent characteristic PRNU factor fprnu is typically of the order of 0 01 Together the total noise standard deviation is Otot V TRON c2 sn y 51 Otot V Tron Ne Ne fd 52 34 or Obviously the PRNU term may dominate the noise at high signal levels depending on fprnu As an example let s assume the PRNU factor to be form 0 01 Then at an average signal level of 10 000 electrons both contributions photon noise and PRNU noise are exactly the same 10000 0 01 100007 Above 10 000 electrons PRNU noise dominates Fortunately the PRNU is imprinted on the detector and thus the corresponding fluctuations in two frames with the same signal level are the same Taking the difference of those two frames removes the PRNU completely while the remaining noise contributions are preserved as in eq 51 that
93. sure and the reference coordinates on sky offsets are due to dithering and in addition determines two dimensional distortion polynomials to correct for telescope distortion and other effects due to filters atmospheric refraction thermal expansion or e g mechanical strain The accurate astrometric solution for each frame guarantees that they can be mapped onto each other with high precision 4 3 5 Step five sky subtraction During exposures the CCD not only collects light from the target of interest but also receives radiation from the background sky In addition there will be ADU counts from undetected objects moonlight and sky glow together forming a background level in the CCD image that needs to be accounted for By determining this background level and removing it from the image only the source flux will remain The usual way of modelling the sky or background is to first remove all objects in one frame and then smooth the image with a specified kernel width This sky image is then subtracted from the original frame Different techniques are used when dealing with extended objects covering large fractions of the CCD or when very low surface brightness objects are observed which might be mistaken as a background feature and removed by the modelling with THELI this is already done during the header correction in the Preparation processing group this will not be the case in this course 23 4 3 6 Step six co addition By
94. t from the angular diameter distance but in general Diss 2 1 2 Dang 2 1 2 fx w 13 3 2 Quasars Quasars QUASi stellAR radio sources are active galactic nuclei AGN with luminosities exceeding those of typical galaxies by large factors up to 10 and more making them easily visible over large distances They were roughly a thousand times more numerous at redshift 2 5 than they are today It is most widely believed that the power for AGNs comes from accretion of matter onto super massive black holes up to several 10 solar masses where a significant fraction of the gravitational energy is released as radiation The fact that quasars show variability on timescales of days to years indicates that the radiating region must be very compact light days which is a strong argument for the black hole explanation In optical bands the variability amplitude of the quasar over human timescales is in the order of lt 10 Incomplete evidence suggests that the variability amplitude on the most easily observed timescales increases toward shorter wavelengths with factors of two often seen in the X rays A small subset of AGNs varies much more strongly even in the optical band In some cases fluctuations of a factor of two have been seen from night to night and cumulative changes of factors of 100 have occurred over year timescales High variability is also strongly correlated with three other properties high degree of polarisati
95. tch to any other PG or shut down the GUI The LOG will contain all reduction steps parameter and GUI settings you have done or chosen for a particular data set Choose a new LOG name if you reduce a different data set If you leave this field empty and start processing anyway the LOG will be named noname Whenever you launch THELI it will read the LOG that was used last updates all GUI elements and internal variables correspondingly and switches to the PG that was active when you closed your last T HELI session You can continue with your reduction at the point where you left it the last time LOGs are usually stored in qt and linked to theli reduction logs The previous path may vary depending on your Qf installation You will never have to touch a LOG file apart from loading an old one into the GUI F 1 2 Data directories The LineEdit fields collected in this GroupBox tell THELI where the data is that you want to process You specify the main directory path hereafter maindir that contains everything followed by the names of the subdirectories that contain the BIASes FLATs etc All fields do not accept blank characters as input in addition the subdirectories do not accept a slash You only need to specify those subdirectories which you actually need Restore ORIG This deletes all data in the corresponding directory apart from the very raw data that has been moved into the ORIGINALS subdirectory The ORIGINALS data is play
96. te a brief documentation of your work including planning of observations calibration frames focusing procedure and results observed targets observation procedure and possible anomalies x TASKS T 7 1 Take all needed calibration frames T 7 2 Observe the asteroids according to your own schedule T 7 3 To measure the positions one could use Astrometrica http www astrometrica at a free software running under Windows or any other astrometry software such as THELI a configura tion file for Astrometrica is also provided It is important for the next step that the measure ments are complying with the MPC format see also http www minorplanetcenter net 5http www astro uni bonn de astroclub AIfA telescope manual pdf 38 T 7 4 iau info Astrometry html After reducing the data and obtaining the positions and magni tudes one should submit the resulting text file by sending it attached in an email to mpc cfa harvard edu your tutor will do that for you this way your observations would be scientific measurements also used for research Finding the orbital elements using your data can be easily done using a free software called FindOrb see http www projectpluto com findorb htm for which you only need to input your measurements file Check your results against the official orbital elements for the asteroids you observed see http www minorplanetcenter net iau Ephemerides Ephem rbEls html After how long the errors in your
97. that the superflat is only calculated at this stage not applied to the images a What is happening in the co addition processes b Inspect the newly created co added bias and flat field frames using ds9 How do they differ from the initial bias and flat field exposures c As done for a single bias frame compute the noise dispersion rms in the same area of the co added bias frame as for the single bias frame note that the orientation of the image has changed Does the rms change according to your expectations d What is the minimum value in the normalised flat field use stats lt FLAT R norm 1 fits Why is dithering important e What structures do you see in the superflat SDSS1650 4251_R SDSS1650 4251_R_1 fits T 5 11 Superflatting App F 4 e Process and apply superflat and fringe model to the data according to App F 4 Use a smoothing kernel of size 256 for the superflat leave the smoothing scale for the fringe image empty e Inspect the created fringe model SDSS1650 4251_R SDSS1650 4251_R_1_fringe fits and the illumination correction SDSS1650 4251_R SDSS1650 4251_R_1_illum fits the latter is simply the superflat minus the fringe model a How large are the remaining corrections given by the illumination correction 28 b Are the fringes properly removed T 5 12 Weighting App F 5 Create the weights needed for your data T 5 13 Astrometry Photometry App F 6 You are now at the most
98. the separation of these images Calculate the magnification ratio of the two images of the SIS lens as a function of 04 and 0g by employing eq 25 and by taking into account that for axial symmetry B dp det A 37 0 d en Note that the sign of the magnification denotes the parity of an image i e an image with negative magnification is mirror inverted with respect to the source Consequently the resulting magnification ratio may be negative its absolute value being the flux ratio of the considered images Derive the time delay for an SIS lens as a function of 04 and Op What does the minimum dispersion estimator as described above assume about the functional form of the light curve between two data points How could one improve on that Show that the dispersion function can be approximated near the minimum i e close to the true time delay by a parabola optional A method alternative to the minimum dispersion approach for time delay estimation makes is the correlation method Define the cross correlation of two light curves m t and ma t by C A J dt mi ma t A 38 Prove that the cross correlation between two light curves is maximized if the lag A is equal to the time delay 7 use the Cauchy Schwarz inequality Assume that the light curves are given by m t s t n t and ma t s t T na t where s t is the intrinsic light curve of the quasar and n t is the measurement noise in the i th
99. tions Due to statistical rejection when combining the median bias frame will also be free from cosmic rays read noise variations and random fluctuations that will appear in a single bias frame The use of bias frames is important when the CCD has a two dimensional structure in the bias level Overscan strips are produced with every readout of a CCD frame and are additional columns and or rows of pixels located next to the exposed frame These pixels hence capture the bias level in each frame and are important when dealing with a CCD camera known to have a varying bias level As the bias level varies throughout the night the median value of the overscan stripes must be subtracted from all images first including the individual bias frames The overscan strips are then cut away from all frames the frames are trimmed The bias frames are combined to a median bias frame which is then subtracted from the images to remove the bias structure completely Dark frames are also exposures taken with the shutter closed but the CCD is exposed for a time period equal to the longest exposure time used in the science images These frames measure the dark current thermal noise in the CCD As CCDs are usually cooled with liquid nitrogen LN2 they reach temperatures in which the dark current is essentially negligible which means that the need of dark frames strongly depends on the camera in use 4 3 2 Step two flat fielding A flat field image i
100. ts in galfit input by numbers or file names and ONLY the dots delete NO spaces and leave all parameters already given unchanged see Table 1 in App B The image region to fit parameter H can be the whole cut out area determined in Sect 5 2 Note that the pixel coordinates must be given relative to the cut out not the original full frame and you must provide two different sets of coordinates Since absolute photometry is not needed in this case only the magnitude difference between the two components is of relevance and the zeropoint is set to an arbitrary value Pixels are counted starting from the value 1 and must be given as integers no floating points T 5 25 Run galfit galfit galfit input When the program shows the prompt type q The galfit output files are a log file and an image block The log file fit log contains a list of parameters used in the fit Every time you run galfit its output will be appended to fit log i e you find the latest solution at the 31 end of this file The image block named after keyword B contains 4 images an empty HDU 1 the original HDU 2 modelled HDU 3 and residual image HDU 4 T 5 26 Inspect the different layers in the image block using the skycat programme The residual image should not contain any structure If necessary repeat the fitting procedure with modified input parameters Looking at the log file calculate the magnitude difference and the flux ratio between the
101. two images and finally give the image separation T 5 27 Is it possible to explain the light distribution of SDSS1650 4251 by just one object Create a parameter file with just one PSF object plus sky background and rerun the fit to confirm or reject 5 4 Time delay estimation If the fluxes of the quasar images are obtained for a large number of epochs the time delay between the two images can be estimated In the following the minimum dispersion method is introduced a simple and effective way to determine time delays Details about this method can be found for instance in Vuissoz et al 2007 and Pelt et al 1996 where it was applied to the gravitational lens systems SDSS1650 4251 and QSO0957 561 respectively Since several years of observations are necessary to arrive at a reasonable time delay we use the data of Vuissoz et al 2007 in the following An electronic version of the data already in the form needed for the programs used is available in fpdir timedel timedel_sorted dat The columns given are 1 HJD 2 mag A 3 oq 4 mag B 5 op similar to Table 3 App 3 though not containing all the columns Note that the first column denotes the Julian date which is measured in days In the same directory you find the complete data set timedel complete dat and a TFX version timedel tex tex x TASKS T 5 28 Visually inspect the light curves using gnuplot see App C Can you recognize the time delay by eye sight Why i
102. will be a two dimensional Dirac distribution 24 by a photon from the one or the other object In addition commonly used methods of background estimation wil go wrong and extremely wrong here A more sophisticated approach is needed for dealing with the photometry of blended i e mixed signals from these sources Several algorithms and programs exist for photometrising blended objects Many of them fit a predefined function for each source to their combined two dimensional brightness distribution The flux of the objects is calculated from the model parameters We perform this kind of fitting photometry using the galfit software see Section 5 3 The galfit manual will also provide you with further information 4 4 3 Noise statistics For a deeper understanding of photometry it is necessary to understand how photometric noise origi nates and behaves statistically For any single photon emitted by an astronomical source the proba bility p of hitting the detector surface during an exposure is tiny But as the number n of emitted photons is large a stochastic stream of on average u n p photons will be detected In such a situation the probability of detecting r photons is given by the Poisson distribution Tau Eee 43 Its standard deviation as a measure of uncertainty in the measurement is o J u meaning that if you quadruple the exposure time the signal to noise ratio of the detected sources will double Keeping t
103. y the minimum of all the row minima D2 A Amy is determined the corresponding value of A is then the best estimate of the time delay 7 The accuracy of this time delay estimate is determined by means of a Monte Carlo method The data point magnitudes of the light curves are assumed to be the means of a random Gaussian dis tribution which has a width according to the photometric measurement errors Random values are drawn from this distribution and on this modified data the algorithm described above is run a large number of times The resulting distribution of time delay results should be approximately Gaussian distributed from which mean and error of the final time delay estimate can be read off A program tdel to perform this algorithm using the minimum dispersion method including the Monte Carlo part is provided see App D 15 3 6 PREPARATORY TASKS You are asked to do the following tasks before the lab course They should improve your understanding of the theory and provide results needed for the lensing analysis P 3 1 P 3 2 P 3 3 P 3 4 P 3 5 P 3 6 P 3 7 Calculate the deflection potential v 0 and the scaled deflection angle of an SIS lens Take into account axial symmetry which simplifies eq 21 to v 8 2 a 0501 la s 36 Solve the lens equation 14 Provided that the source lies within the Einstein radius you should find two solutions 04 and 0p both defined as positive angles What is
104. y case if you find this exciting and want to do more observations you are invited to join our Astroclub team on a regular basis 2 Preparation For this experiment you need background knowledge from different astronomical fields We summarise most of the theory needed for the examination in Sections 3 and 4 For further reading we suggest e Basics A Unsold B Baschek Der neue Kosmos Einf hrung in die Astronomie und Astrophysik Springer 1999 P Schneider Extragalactic Astronomy and Cosmology An Introduction Springer 2007 e Gravitational lensing cosmology P Schneider Extragalactic Astronomy and Cosmology An Introduction Springer 2007 P Schneider Introduction to Gravitational Lensing and Cosmology http www astro uni bonn de peter SaasFee html T Padmanabhan AIP Conf Proc 843 111 166 2006 astro ph 0602117 e Astronomical observations and data reduction M Schirmer CCD data reduction http www astro uni bonn de mischa datareduction html S Howell Handbook of CCD Astronomy 2000 Chapters 1 5 In any case read at least Chapters 2 and 3 Appendix F is a shortened version of the THELI user manual http www astro uni bonn de theli gui index html If you would like more extensive reading than what the Appendix gives the original user manual will provide you with this However the manual is not mandatory reading e Photometry and fitting C Peng Galfit
105. y drop in temperature of 6 Verify the dependence between temperature and dark current given by eq 54 and determine the constant c Calculate the expected dark current level at T 25 C i e a temperature at which this type of CCD is typically used Under the assumption that the dark current properties of the detector at the 1m telescope do not differ considerably from those investigated here is dark current a matter of concern for HOLIGRAIL observations 3T 7 Practical part III Night time observations General remarks e To find object coordinates magnitudes of nearby reference stars or finder charts some very useful web pages are SIMBAD http simbad u strasbg fr ALADIN http aladin u strasbg fr 7 1 Asteroids observations with the 50cm telescope The purpose of this part of the experiment is to measure the positions of a few Near Earth Asteroids NEAs Potentially Hazardous Asteroids PHAs or Virtual Impactors VIs and submit the mea surements to the IAUs Minor Planet Center which centralizes such observations Also using these observations you will determine the orbital elements of an asteroid and compare them to the catalogue values Measuring the positions of asteroids with an uncertain orbit newly discovered or with too few observations might help in fixing their orbital elements and prevent them from becoming lost In the case of PHAs and NEAs it could also help determine the probability of an impact w

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