WVT BINNING - Physics & Astronomy
Contents
1. Perform the binning with target signal to noise of 5 targetSN 5d0 wvt_image signal noise targetSN binnedimage snbin snbin binnumber binnumber Save the distribution of SN over the field of view remember that binnumber starts at 1 snbin 0 snbin mwrfits snbin binnumber abinned_snr fits 6 2 External Interactive Controls 6 2 1 FILE plotit all A good way to check the progress of the adaptive binning algorithm is to have graphical output on the way see also the PLOTIT keyword If you decide that you want to plot the iteration steps create a file in the current directory with the name plotit A simple way to do this is to issue the command touch plotit in a shell Remove the file if you want to stop plotting This is useful when you want to decide if stopping the binning algorithm prematurely will give you useful results see also stopmenow 6 2 2 FILE stopmenow all Sometimes it is useful to be able to stop the algorithm manually In cases where computing time is an issue you need to shut down the system etc If you want to terminate the iteration at the next possible time simply create a file named stopmenow in the current directory e g touch stopmenow If necessary you can resume the stopped session later with the help of the RESUME and SAVE_ALL keywords 35 Chapter 7 Sample Output 7 1 Text Output The following example uses a subse2. shouldn t be used for the final analysis since changes in the fractional contribution 18 of the background as well as energy dependent features of the exposure map can introduce unreal artifacts In this simpler case the S N ratio is reduced to S N IN 3 5 rev Car rev CB Example 3 4 2 Background corrected flux hardness ratios A better way to compute hardness ratios is to use background and exposure corrected fluxes instead of counts In our example we will use a flat background for each band However we could have used a spatially dependent background model or a blank sky image as well see also 82 4 19 Example Chapter 4 WVT_PIXELLIST Binning of pixel lists YET TO COME Include example from IFS data by Cappellari and Copin 21 Chapter 5 Spectral maps with SHERPA CIAO In this chapter I will briefly describe how to use WVT_BINNING to generate two dimensional maps of spectral parameters I will focus on the most common application in X ray astronomy namely the creation of temperature maps However the scripts are completely general and can be easily modified for the use with any spectral parameter e g metallicity absorption etc The cookbook section will give a brief overview about how to apply the scripts to a typical example The following section gives detail on how to use each script individually and explains its functionality This chapter is not intende
3. Cp Ek Bk 2 7 Ny 04 E2 0 2 8 There are various possibilities for how to find such a background The easiest way is to use blank sky fields normalized to the appropriate exposure time These images can either be subtracted directly or a fit can be used alternatively uniform background tilted plane etc Another option is to use a local background on the same chip derived from source free regions or a surface brightness profile fit 12 Example 2 4 4 Isolating components of linear combinations of images In X ray astronomy images are often composed of various components that contribute in spectrally distinct ways to the total image Thus the image can be considered as a linear combination of these components A good example is the X ray emission of elliptical galaxies where one is often faced with the problem of removing the contribution of unresolved point sources to the diffuse emission We will use this particular example to demonstrate the capabilities of the binning algorithm although it can easily be generalized to other problems To remove the contribution of unresolved point sources we use the fact that the hot gas and point sources contribute differently to the soft and the hard bands Let Fs and Fy represent the background subtracted and exposure map corrected 13 soft and hard images We can express both in terms of the unresolved point source emission P the gas emission G and their respectiv
4. a look at the raw counts image C Due to the sparse nature of X ray data it is in most cases necessary to bin the data in order to gain some kind of insights about the spatial distribution Here the signal and noise per pixel are defined as follows Sk Ch 2 2 M VO 2 3 WVT_IMAGE will correctly compute the signal and noise in the bins according to equation P T Thus after simplifying equation P 1 the S N per bin can be expressed as S N Y Cs 2 4 kevV 10 and binning to a constant target S N is equivalent to binning to a constant number of counts per binf Crarget S N target Example 2 4 2 Binning of exposure corrected flux images If one is interested in removing artifacts in the counts image due to instru ment structures such as node boundaries or chip edges one should use the exposure map Ej In order to convert counts to physical units of photons sec cm arcsec one has to divide by the exposure map and the effective exposure time Sh Cr Er 2 5 Ny y Cr Er 2 6 1This is one of the few cases where you can make use of the keyword GERSHO see 1 3 for more details For examples on how to use exposure maps please refer to the official CIAO website 11 Example 2 4 3 Binning of background corrected images Let s assume a spatially variable background Bj across the image that you know with a lo accuracy og Then you can define the signal and noise in as Sk
5. the field of view this keyword is essential otherwise you will attempt to bin empty regions 32 Example 6 1 10 CTSIMAGE WVT_IMAGE WVT_XRAYCOLOR Optional input two dimensional image same size as the signal and noise images containing the counts per pixel Often necessary for very sparse X ray data where some pixels can contain no counts In certain cases you can then artificially have a high S N value for these empty pixel e g when you subtract two background corrected components example remove the point source contribution in ellipticals or compute X ray colors Supply the counts image in order to avoid that the bin ning algorithm produces bins without any counts In case of producing a color image from two distinct X ray bands one should supply the combined counts image of both bands as this image gives information about where the signal is located Example 6 1 11 BINNUMBER all Optional output size Nyizeis for WVT_PIXELLIST and WVT_BINNING nz ny for WVT_IMAGE and WVT_XRAYCOLOR that contains the indices of the bin distribution The labels range from 1 to Npins 0 is reserved for pixels outside the field of view as specified by the MASK keyword Example 6 1 12 SNBIN all Optional output vector size Npins that keeps track of the S N for all indi vidual bins In conjunction with BINNUMBER see s6 1 11 this can be used to create a map of the S N distribution 34 Example
6. Adaptive Binning with Weighted Voronoi Tesselations WVT_BINNING User s Manual Steven Diehl July 2005 2005 Steven Diehl All rights reserved Preface This manual is intended to give a hands on introduction on how to use the main features of the adaptive binning technique WVT_BINNING Throughout the doc ument we will denote all pixel indices with the letters k and l Bins will be denoted with 7 and j to avoid confusion Accordingly the signal and noise per pixel will be denoted as S and Nz respectively In addition we will also use the slightly different calligraphic characters for bins S and Nj All bins will be abbreviated with the letter V Each chapter of this manual is divided into several sections starting with a general description of the required input parameters followed by some examples Among those we start with the easiest case and increase in complexity but also cor rectness toward the end The last chapter contains a general description of keywords which can improve the performance of the algorithm The examples in this manual use various procedures or functions from the Astro IDL library which is available at http idlastro gsfc nasa gov homepage html Table of Contents Preface Mable of Contents 1 Desciption of the adaptive binning method WVT_BINNING 3 WVT_IMAGE Intensi binning of X ray images 2 eneral Description 2 2 1 SIGNAL mput requred 22 2 N
7. Example Run wvt_image and save everything in wvt_image signal noise targetSN binnedimage save_all save_all Save the structure save_all in a fits file mwrfits save_all abinned_data fits Have a look at the RESUME keyword to find out to restart from this point 6 1 5 RESUME all Set this keyword if you want to start from an existing WVT which is uniquely defined by the vectors XNODE YNODE and SNBIN The WVT iteration scheme will be applied to the supplied WVT and the values overwritten with the final output If you are using one of the interfaces WVT_IMAGE WVT_XRAYCOLOR or WVT_PIXELLIST you should use this keyword in conjunction witht the structure SAVE_ALL Example 6 1 6 KEEPFIXED all Optional input vector containing x and y coordinates of bin generators that you want to keep fixed in their position The binning algorithm will move all other bins around as usual The size of this vector should be 2 of fixed bins Example use Keep one bin fixed on the center of a galaxy Example 6 1 7 CENTER WVT_IMAGE WVT_XRAYCOLOR Optional input vector size 2 containing x and y values for the center If this keyword is not supplied 0 0 will be assumed as the center and the algorithm will start at the highest S N pixel in the bin accretion step If the center is given bin accretion will start at the center For work with pixel lists WVT_BINNING or WVT_PIXELLIST the X and Y coord
8. MAX AREA Tall 2 2220 6 1 9 MASK WVT_IMAGE WWT_XRAYCOLOR 22 222200 6 1 10 CTSIMAGE WVT_IMAGE WWT_XRAYCOLOR 6 1 11 BINNUMBER Mo 6 1 12 SEN all cb recorra as es o 2 1 BIER plotit Jalli s s s 2 eo 2 amp A oe dm een a a 6 2 2 FILE stopmenow all u s4 4 3 22 2e bse coh a een edad ext QU PpUA 2 0a wu a dai wR ei a D VULPUL s e ach a a ds a a ew 8s A D D D A ici eh 17 17 17 18 20 21 21 23 23 25 26 27 28 28 28 28 29 29 29 30 30 30 31 32 33 33 34 34 34 35 35 37 39 40 41 41 42 Chapter 1 Desciption of the adaptive binning method WVT_BINNING 1 1 Modified bin accretion Show pictures of example after bin accretion 1 2 Redistribute unbinned pixels Show pictures of example after redistribution 1 3 WVT iteration Show pictures of example after WVT is done S N distribution Wait with this chapter until the paper is done completely since it will be mostly the same text to describe the method Chapter 2 WVT_IMAGE Intensity binning of X ray images 2 1 General Description WVT_IMAGE provides an interface to WT_BINNING to produce adaptively binned X ray images These can be raw counts exposure and or background corrected im ages The algorithm operates directly on 2 dimensional images and has a straight forward basic syntax WVT_IMAGE signal noise targetSN binnedimage Although WVT_IMAGE will w
9. OISE mput requied 2 2 3 TARGETSN imput required 2 2 4 BINNEDIMAGE Joutput required 2 2 5 XNODE YNODE WEIGHT Joutput optional BER RR 2 4 Applications 2 22 EEE nn nn 2 4 4 solating components of linear combinations of images WVT_XRAYCOLOR Binning ot Hardness Ratios O eneral Description 5 3 1 SIGNAL Input required 3 2 2 NOISE mput required 0 8 2 3 SIGNAL2 mput required 8 2 4 NOISE2 Input required 8 2 5 TARGETSN mput required 8 2 6 BINNEDIMAGE Joutput required 3 2 7 _XNODE YNODE WEIGHT loutput optional A DADD m OD V O oo o N N E N 15 15 16 16 16 16 16 16 16 17 O Prescription to compute signal to nolsq nn 9 4 Applications 22 2 Co m nn 4 WVT_PIXELLIST Binning of pixel lists 5 Spectral maps with SHERPA CTIAO Pi TOO es cond AR ne ee en O Details of Single Stepg m nn be We eg eee ee ee OP tee Be BOE We Bee ie 3 9 2 WVT_TEMPERATUREMAP Create the binning and extract event list 6 Detailed description ot parameters 7 O K d BEL POO alll ooo aa re ee ee e re ee ee ee 6 1 3 GERSHO WVI_BINNING WVT_IMAGE WVT_PIXELLIST 6 1 4 SAVE ALL WVT IMAGE WT_XRAYCOLOR WWT PIXELLIST 6 1 5 RESUME All ee ieh 6 1 6 KEEPFIXED IA 2222202 6 1 7 CENTER WVT_IMAGE WVIT_XRAYCOLOR 22 22 222 onen 6 1 8
10. TUREMAP Create the binning and extract event lists wvt_temperaturemap pro is actually an IDL batch file rather that a pro cedure or function The reason for this is that you can execute it from within an 26 automated script with the simple command idl queue wvt_temperaturemap The queue option ensures that idl automatically waits for a license to be available before starting so you avoid the interactive question to wait for a license The default setup is such that WVT_TEMPERATUREMAP reads in the counts im age cts fits and bins it to a constant signal to noise per bin value of 30 This corresponds to binning to 900 30 counts per bin The sophistication of your spec tral model determines what the value should be in your situation In spectral fitting it is recommended to bin the spectrum within Sherpa to a minimum of 20 counts later i e 900 counts would correspond to about 45 spectral bins This will decrease depending on your background contribution to the counts If you want to take the background into account edit wvt_temperaturemap pro see chapter B for more detail After binning the program will automatically save the results and split the evt2 fits file up into several files The files with the names evt2 fits X contain the evt lists for the bins X The corresponding evt2 fits X BACKSCAL files have the BACKSCAL factor i e the relative size of the bin X needed by Sherpa to get the normalization of the s
11. WVT_XRAYCOLOR signal signal2 noise noise2 targetSN binnedimage The complete more flexible syntax with all keywords 88 is given here WVT_XRAYCOLOR signal signal2 noise noise2 targetSN binnedimage xnode ynode weight snbin snbin mask mask ctsimage ctsimage binnumber binnumber binvalue binvalue center center plotit plotit resume resume save_all save_all max_area max_area keepfixed keepfixed Depending on your specific background values for the soft and hard band and their respective uncertainties it could happen that you create artificially high 16 S N values in pixels that contain no counts To avoid these artifacts always supply the counts image CTSIMAGE of the combined bands See for more details 3 2 Main Parameters 3 2 1 SIGNAL input required A two dimensional image containing the signal per pixel for band A The image can be background subtracted or exposure map corrected as long as the NOISE image reflects this 3 2 2 NOISE input required Two dimensional image same size as SIGNAL containing the noise associ ated with each pixel sqrt variance for band A 3 2 3 SIGNAL2 input required The equivalent to SIGNAL for band B 3 2 4 NOISE2 input required The equivalent to NOISE for band B 3 2 5 TARGETSN input required The desired signal to noise ratio in the final 2D binned data A TARGETSN between 4 10 is standard for X
12. al distribution of bins each bin colored differently The crosses indicate the locations of the bin generators The bottom panel shows the signal to noise distribution of the final bins excluding those with less than 2 pixels in size as well as those reaching MAX_AREA in size 38 E ne game sal a Mars o EE oil ad ar a or TS ART 20 10 0 10 20 pixel 80 60 2 L o u 40 4 o 2 L 4 E 5 H J Z 20F 0 ti of ti 0 20 40 60 80 100 S N Figure 7 1 Top Bin distribution bin colors are random Bottom signal to noise distribu tion excluding bins with less than 2 pixel and bins approaching MAX_AREA 39 Chapter 8 Caveats e The bin accretion algorithm is based on a neighbor search to increase speed Thus bins are not able to cross gaps in the data e g due to chip boundaries readout streaks etc in the bin accretion stage e The algorithm can run rather slowly for large images with large bins We rec ommend the use of the keyword MAX_AREA in this case e The functions ADD_SIGNAL and ADD_NOISE are part of the wrappers WVT_IMAGE WVT_XRAYCOLOR and WVT_PIXELLIST and not compatible with each other So you have to recompile the program you want to use first to make sure you use the correct function The wrappers have checks built in to warn you and will exit if you use incorrect functions 40 Bibliography M Cappellari a
13. d to explain the usage of CIAO Sherpa or S lang tools or scripts The intention is rather to give you an example on how one can use the spatial binning for spectral fitting using these systems A basic familiarity with all the former languages will be necessary to modify these scripts to suit your needs You might also decide to trust me and use them as a black box The scripts were written and tested with CIAO 3 1 and CALDB 2 28 on a Sun Ultra80 station running SunOS 5 8 They might be compatible with other unix systems or CIAO versions though I cannot guarantee its proper functionality there 5 1 Cookbook Before you start using the scripts it is necessary to follow the general setup that this script requires First the event2 file should be in the working directory and 22 named evt2 fits There should also be a mask file mask fits that contains 1 for good data and 0 for bad data Look at the examples in chapter 2 for ideas on how to create such a mask One should also have the bad pixel file in the directory or a parallel primary or secondary directory for the CIAO script acis_set_ardlib to find it You will also need a copy of your ciao csh in CIAO bin in this directory 23 5 2 Details of Single Steps 5 2 1 General setup The temperature map script requires the following files to be present in the working directory e evt2 fits The file containing the event 2 list of X ray photons For computa tional rea
14. e softness ratios y and 0 Fr P 2 10 The uncontaminated gas image is then given by de Es 5 Fu 2 11 For more details and instructions on how to determine the constants gamma and delta with spectral models please refer to Diehl and Statler 2005 If we use the gas image G as our signal Sp we have to define the noise accordingly Depending on your specific background values for Fs and Fp and their re spective uncertainties it could happen that you create artificially high S N values in pixels that contain no counts To avoid these artifacts always supply the counts image of the combined bands CTSIMAGE See for more details S Gr 2 12 1 7 EN N 4 0 2 2 13 k un CHR 14 Example 15 Chapter 3 WVT_XRAYCOLOR Binning of Hardness Ratios 3 1 General Description Another useful tool in X ray astronomy is the generation of so called color maps An X ray color is generally defined as the quotient between the fluxes in two different bands A and B Depending on the choice of energy bands this hardness ratio map can be used as diagnostics for temperature gradients or photoelectric absorption features for example Sanders and Fabian 2001 A general discussion about the physical interpretation of these maps and an appropriate choice of bands can be found in 2000 for example The basic required syntax to use WVT_XRAYCOLOR successfully is as follows
15. inates should already have the center coordinates subtracted 6 1 8 MAX_AREA all Optional scalar specifying a maximum bin size in square pixels We gen erally recommend the use of this keyword bins Essential in cases where there is 31 essentially no signal in a certain region otherwise the empty bins will eat into the region with signal or if spatial resolution is more important than a smooth S N distribution This boundary is only approximate but bins stay in general within a few percent Attention In area where the bin size hits MAX_AREA the algorithm does no longer enforce a uniform S N anymore Thus be careful when interpreting the resulting images Always interpret in conjunction with the output S N map see also SNBIN keyword Example Adaptively bin the signal with a maximum bin size of a circle with a radius of approximately 25pixel max_area pi 25 2 WVT_IMAGE signal noise targetSN binnedimage max_area max_area snbin snbin binnumber binnumber Create an S N map from the bin distribution and its associated S N values sn_image snbin binnumber 1 6 1 9 MASK WVT_IMAGE WVT_XRAYCOLOR Optional input two dimensional image same size as the signal and noise images The MASK specifies which pixels should be included in the WVT binning algorithm Valid pixels have to be designated as 1 excluded pixels as 0 integer or byte If your detector does not fill
16. ire higher TARGETSN 30 100 depending on the spectral model used For integral field spectroscopy a TARGETSN of 50 per bin may be a reasonable value to extract stellar kinematics information from galaxy spectra In general the higher TARGETSN is the fewer bins will be computed and thus the lower the resolution will be 2 2 4 BINNEDIMAGE output required The final binned image will have the same size as the input image SIGNAL 2 2 5 XNODE YNODE WEIGHT output optional The locations of the WVT bin generators together with the associated weights for the WVT This set of three 3 parameter values is sufficient to recon struct the complete binning scheme and or to apply it to different data sets This represents the most efficient way to save and or distribute the binning structure 2 3 Prescription to compute signal to noise WVT_IMAGE assumes that the signal to noise ratio of a bin can be computed in the following manner A Sk TN Note If this is not the case for your type of data you have to adjust the functions ADD_SIGNAL and or ADD_NOISE as described in section A S N 2 1 2 4 Applications Although all of our examples are drawn from applications to X ray data we should emphasize that the algorithm is not restricted to X ray analysis but rather to any type of 2 dimensional data 2 4 1 Binning of X ray counts images The easiest way to get a first impression of X ray images is to have
17. nd Y Copin Adaptive spatial binning of integral field spectroscopic data using Voronoi tessellations MNRAS 342 345 354 June 2003 S Diehl and T S Statler An x ray gas fundamental plane for elliptical galaxies ApJ 2005 A C Fabian J S Sanders S Ettori G B Taylor S W Allen C S Crawford K Iwasawa R M Johnstone and P M Ogle Chandra imaging of the complex X ray core of the Perseus cluster MNRAS 318 1L65 L68 November 2000 J S Sanders and A C Fabian Adaptive binning of X ray galaxy cluster images MNRAS 325 178 186 July 2001 41 Appendix A WVT_GENERIC Adopting the binning algorithm to your needs A 1 General Description The structure of the main binning algorithm WVT_BINNING was held in a very general way in order to make the algorithm more flexible and applicable to a broader variety of problems The file wvt_generic pro contains a template on how to adjust the algorithm to your own needs It is also very instructive to have a look at wvt_image pro wvt_xraycolor pro and wvt_pixellist pro and to use them as guidance For WVT_BINNING all information that you need in order to calculate the combined signal of the bin has to be contained in a global variable named P P has to be a structure containing scalars and or vectors which are generally of length npixels The functions ADD_SIGNAL and ADD_NOISE determine how to compute the combined signal and noise for the bin The only parameter given t
18. o these function are the indices of the bin members locating the correct pixel properties in the arrays of P The next section will give you a hands on tutorial on how to implement this 42 A 2 Step by step Guide Step 1 The variable P In order to compute the signal to noise ratio of a bin one needs two types of information The properties of all pixels and the information on which pixels belong to the bin in question In step 1 we define a globally accessible structure P to deal with the first issue P stores all of the pixel properties and constants necessary to compute the signal to noise ratio of a bin COMMON DATAVALUES P P pixprop1 dblarr npix pixprop2 fltarr npix pixprop3 lonarr npix constant1 3 142d0 5 constant2 9L y A The number of tags here 5 as well as their names here pixpropl pixprop2 pixprop3 constant1 and constant2 are irrelevant and only used in the functions ADD_SIGNAL and ADD_NOISE which are defined by the user The structure should hold all the information that you need to add signal and noise correctly There is no limit on how much information P can contain and which nature it should be In this example the pixprop tags could describe pixel properties since they are vectors of length Npizers such as the flux counts noise or the exposure in each pixel Step 2 Define the function ADD_SIGNAL FUNCTION ADD_SIGNAL index COMMON DATAVALUES P RETURN total P
19. ork with only these few arguments it is far more flexible The complete syntax is the following WVT_IMAGE signal noise targetSN binnedimage xnode ynode weight snbin snbin mask mask ctsimage ctsimage binnumber binnumber binvalue binvalue center center plotit plotit resume resume save_all save_all max_area max_area gersho gersho keepfixed keepfixed quiet quiet For X ray data it is recommended always to supply the counts image CTSIMAGE 6 1 10 as well as the mask file MASK s6 1 9 2 2 Main Parameters Here is a short general description of the main parameters For a complete description of all the keywords please refer to chapter 6 or the IDL files directly Have a look at section DA 2 2 1 SIGNAL input required A two dimensional image containing the signal per pixel The image can be background subtracted or exposure map corrected as long as the NOISE image reflects this If the pixels are actually the apertures of an integral field spectrograph then the signal can be defined as the total flux in the spectral range under study for each aperture 2 2 2 NOISE input required Two dimensional image same size as SIGNAL containing the noise associ ated with each pixel sqrt variance 2 2 3 TARGETSN input required The desired signal to noise ratio in the final 2D binned data A TARGETSN between 4 10 is standard for X ray images a temperature map would requ
20. pectrum correct The program will also create a file called nbins dat that simply specifies the number of bins that were created 5 2 3 tempmap generic csh Fit a spectral model with Sherpa The main work is done by the C shell script tempmap generic csh and the S lang script fitsingletemp sl First the CIAO procedure dmextract is evoked to create a spectrum from the event list of the current bin The CIAO script acisspec is used to create the weighted ARF and RMF corresponding to the bin region If a file named use_one_rmf is present only the ARF and RMF of the first bin will be computed and used for all other bins in order to save time If this file is not present the ARF and RMF will be computed separately for each bin After this step the header of the spectrum file is automatically updated to include the correct BACKSCAL area ANCRFILE ARF and RESPFILE RMF keywords 27 fitsingletemp sl lets Sherpa automatically read in the bin source spec trum the background spectrum the response and parameter files Then it adap tively bins the spectrum to a minimum of 20 counts per spectral bin and fits an APEC newer version of MEKAL model to the spectrum by minimizing the x devi ation The temperature is then saved in the ascii file evt2 fits X temp its positive and negative lo error bounds in evt2 fits X tempcov Please note that so far there are no backup or restart features built in for non convergent fits For cases where
21. pixpropi index END This is the simplest example on how your ADD_SIGNAL function could look like This function takes the global variable P and adds up the pixel property pixprop1 of all bin members gt INDEX The recipe on how compute the signal can be as easy or complicated as is required by the specific problem This would be a real example if pixprop1 was something like a flux per pixel Step 3 Define the function ADD_NOISE The usage of ADD_NOISE is completely analogous to ADD_SIGNAL with the only difference that the combined noise of the bin should be returned In the example case the square root of the sum of all squares of pixprop2 similar to a real example of adding gaussian errors Step 4 Start WVT_BINNING Now we have everything set up to successfully start the adaptive binning All we have to do is to call the main binning program WVT_BINNING As you can see nothing has changed in the way WVT_BINNING is being used All we did was to introduce a new way to compute the signal to noise ratio of the bins We have to be sure that the correct functions ADD_SIGNAL and ADD_NOISE are precompiled and that we have the global variable P initiated
22. ray color images but will in general depend on what type of features you want to show As always the higher TARGETSN the fewer detail you will see 3 2 6 BINNEDIMAGE output required The final binned image will have the same size as the input images 17 3 2 7 XNODE YNODE WEIGHT output optional The locations of the WVT bin generators together with the associated weights for the WVT This set of three 3 parameter values is sufficient to reconstruct the complete binning scheme and or to apply it to different data sets 3 3 Prescription to compute signal to noise Here our signal consists of the hardness ratio of the two flux values We define Fa and Fg as the flux per pixel k in the bands A and B respectively Thus we can write our signal as MN wen Far u Rey FRE l The associated error in the hardness ratio can be expressed in terms of the noise in the individual bands N 5 Tar rev Tpk N ren Far ren Far If necessary these definitions can be extended for the general use of n different bands for more details refer to 2001 S 3 1 3 2 3 4 Applications 3 4 1 Count hardness ratios The easiest way to compute an X ray color map is to use simply count hard ness ratios between the counts in band A and B C4 and Cp respectively F S rev Far 3 3 N Fp me 1 1 Car NENA a pa This is good to get a first impression of the general structure of the target but
23. sons it might be useful to restrict the event list to the CCD that you are analysing e bpix fits Observation specific bad pixel file The acis_set_ardlib scripts will set the parameters for the RMF and ARF generators later which will need this information to function correctly 24 e cts fits The counts image that has to be analysed Here is an example on how to create this image from the evt2 file e mask fits File containing the mask for the field of analysis Here is an example on how to create a mask file from an exposure map and a CIAO region file e mark _bgd pi The background spectrum file This can be a extracted from a local background region on the same chip or taken from the Markevitch background compilation as shown in this example 25 e wvt_ pro The WVT binning suite of programs should be in the current di rectory or in a directory that is included in you IDLPATH variable e acis_set_ardlib CIAO script that sets parameters necessary for ARF and RMF generation e ciao csh A copy of your PATH_TO_CIAO bin ciao csh file e acisspec CIAO script that creates ARF and RMF e fitsingletemp sl Sherpa S lang script that does the automatic spectral fit ting e is file sl Sherpa S lang script that determines if a file exists or not e nh dat redshift dat Files that are used during fitting and contain the Galactic value for the column density and redshift of the target 5 2 2 WVT_TEMPERA
24. t of a Chandra observation of the Perseus cluster core The data are freely available on our WVT website in the package test_wvt_image tar gz In this section we will go through the example step by step and include all text output that you will see The optional graphical output is described in the following section This is the start of the binning process where each pixel gets its associated neighbor list computed Every 10000 steps you will get a line noting the progress of the procedure This is the output of the bin accretion step The columns denote the current number of the accepted bins the signal to noise value of the bin its size in pixels and the total fraction of pixels that have been binned After the bin accretion step all pixels of bad bins that didn t meet S N or roundness criteria are reassigned to its closest neighbor The modified Lloyd algorithm represents the heart of the algorithm where the binning scheme continuously tries to reach a more uniform and self consistent bin distribution Each iteration names the number and percentage of bins that have 37 switched bins It is often advisable to stop the algorithm before one of the convergence criteria is fulfilled to save computing time However this depends on your analysis goal 7 2 Graphical Output Figure 7 1 give an example on what a typical graphical output from WVT_BINNING looks like The top panel shows the two dimension
25. the fit converges onto a non physical solution i e where the temperature parameter bounds are stepped over or the fit didn t converge the temperature will be simply reported as 1 5 2 4 WVT_EVALTEMPERATUREMAP Generate the temperature map Again wvt_evaltemperaturemap pro is an IDL batch file that reads in the fitted temperature values from evt2 fits X temp and applies it to the saved binning scheme This creates the 2 dimensional temperature map tempmap fits 28 Chapter 6 Detailed description of parameters Most keywords are common to the main binning algorithm as well as their different interfaces The brackets indicate for which algorithm the keyword is valid 6 1 Keywords 6 1 1 PLOTIT all This keyword regulates the amount of graphical output during the session The default value is PLOTIT 0 i e no output Set this keyword to 1 either via PLOTIT 1 or PLOTIT to produce a plot of the two dimensional bin distribution and of the corresponding S N at the end of the computation A value of PLOTIT 2 will produce a similar plot after the bin accretion step Setting PLOTIT to 3 will result in renewing the plots after each iteration Having a file named plotit in the working directory has the same effect as setting PLOTIT 3 Note that plotting can significantly slow down the speed of the binning algorithm since WVT_BINNING operates on pixel lists Thus the plotting procedure is designed
26. to plot each pixels individually and can take rather long depending on the graphical capabilities of your machine 6 1 2 QUIET all By default the program shows the progress while accreting pixels and then while iterating the CVT QUIET 0 Set this keyword to avoid printing progess 29 results Be aware that the binning algorithm can run rather long in some cases depending on image size and bin sizes Having text output does not negatively affect the speed of the algorithm 6 1 3 GERSHO WVT_BINNING WVT_IMAGE WVT_PIXELLIST WVT_BINNINGis based on an algorithm based on unweighted centroidal Voronoi tesselations CVT 2003 which exploits a property of CVTs known as Gersho s conjecture If you set the GERSHO keyword the output will be very similar to the output of Cappellari amp Copin s code VORONOI_2D_BINNING except for some modifications in the bin accretion steps However be aware that Gersho s conjecture is only valid for strictly positive data where the S N adds in quadrature 6 1 4 SAVE_ALL WVT_IMAGE WVT_XRAYCOLOR WVT_PIXELLIST Set this keyword to a variable will be in structure format that holds all information that is necessary in order to restart the program from any given point Simply supply the SAVE_ALL output and set the RESUME keyword Its contents will be overwritten with the updated binning information at the end If this keyword is supplied all other input information will be ignored
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