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Subsections


10. Spatial Analysis

10.1 Introduction

In this chapter we describe in more detail image extraction and the structure of the image files. We will also address some issues relating to attitude reconstruction, image deconvolution, exposure maps, and extended source analysis. In this chapter we also show you how to get started using the image display and analysis program XIMAGE.


10.2 Extracting Images

Once the data have been screened and the desired filters set, simply type extract image at the XSELECT prompt. This command initiates the extractor, which applies whatever GTIs and filters are in place to the current events list. The extractor creates a temporary file which is deleted on exiting XSELECT unless saved. Use the save image command, giving the name of the image file as the argument. Although this procedure is as straightforward as it sounds, please note the following.

For the detector-specific properties of GIS and SIS images, please consult chapters 3 and 4 respectively.


10.3 Image Files

It is not necessary to know all about ASCA image files in order to use them. However, it is a good idea to be familiar with their basic structure and contents.

Compared with ASCA spectral files, image files are much simpler. They comprise only the primary header (containing keywords, some of which are used by SAOimage and XIMAGE) and the primary image array (containing the actual image data). Some of the important keywords in the primary header of both detector and SKY image files are:

NAXIS1 - Length of data axis 1 (number of X or DETX pixels)
NAXIS2 - Length of data axis 2 (number of Y or DETY pixels)
IMGBIN - Image binning factor
EXPOSURE - Exposure in seconds (sum of GTIs used for extraction)
RA_NOM - Right Ascension (decimal degree) of target from Observation Plan
DEC_NOM - Declination (decimal degree) of target from Observation Plan
DROLLANG - Mean roll angle (decimal degree)
CRPIX1 - X axis reference pixel
DRPIX1 - DETX axis reference pixel
CRPIX2 - Y axis reference pixel
DRPIX2 - DETY axis reference pixel
CRVAL1 - Sky coord of X reference pixel (degree)
CRVAL2 - Sky coord of Y reference pixel (degree)
CDELT1 - X axis increment (degree)
CDELT2 - Y axis increment (degree)
DRDELT1 - DETX axis increment (degree)
DRDELT2 - DETY axis increment (degree)
CROTA2 - Roll angle (degree)

Unlike SKY image files, detector image files have non-zero values of CROTA2 which gives the rotation of the Spacecraft Y axis from the detector to the SKY coordinate system. In addition, detector image files have an extra pair of keywords:

OPTIC1 - DETX pixel of the telescope optical axis.
OPTIC2 - DETY pixel of the telescope optical axis.

The primary header of a FITS image file can be displayed on the screen using the FTOOL fdump. The image data themselves can be converted to ASCII and displayed on the screen with the FTOOL fimgdmp.

To convert pixel coordinates from one mission to another, please follow the instructions for multi-mission region filters in §7.10.


10.4 Attitude Reconstruction

Here, attitude reconstruction means the conversion of detector coordinates to SKY coordinates. For ASCA, this conversion is done as part of the standard processing by the ASCA Data Facility: data delivered to PIs and in the ASCA archive therefore carry SKY coordinates - except for the non-imaging GIS MPC and SIS FAST modes.

The accuracy of the reconstruction depends on two things, the pointing stability of the spacecraft and the accuracy of the reconstruction algorithm itself.


10.4.1 Pointing Stability

The ASCA spacecraft can rotate about all three of its axes at a maximum rate of 0.15 degrees per second. At the end of a maneuver, when the target has been acquired, the spacecraft settles into a stable attitude. The Attitude Control System (ACS) has been performing as follows:

Pointing stability:
  Z-axis, 3-sigma                                         5 arcsec
  Around Z-axis, 3-sigma                                 20 arcsec

Post-maneuver settling time:                        15-20 minutes


10.4.2 Reconstruction Algorithm

The attitude reconstruction algorithm is embodied in an FTOOL called ascalin which, as mentioned above, is normally run by the ADF rather than by the user. It takes as input the attitude file, the data file (events list), gain history file and telescope definition file.

The typical error circle for ASCA is $\sim 40$ arcsec. A more thorough explanation is given in the article `The ASCA Source Position Uncertainties', ASCANews, #4.


10.5 Exposure Maps

An exposure map gives the net exposure time per SKY pixel for a given observation. It is used to normalize the associated sky count map to derive counts per seconds per pixel. This is useful for generating exposure corrected surface brightness sky maps.

The FTOOL ascaexpo is a powerful tool used to generate exposure maps for both SIS and GIS observations. ascaexpo uses the header information in an events file, the telescope definition file, and the attitude file to produce an exposure map in SKY coordinates. This takes into account the attitude reconstruction, and includes, for the GIS, the detector geometry, and for the SIS, the chip arrangement, area discrimination, and hot/flickering pixel (for files run through the program CLEANSIS). Note that removal of SIS telemetry-saturated events is dealt with in §5.4.5.

Warning! If none (the default) is given as an input to the question: Input ASCA instrument map filename (or NONE) [] ascaexpo assumes a uniform detector efficiency and adds attitude jitter to it. In order to generate an exposure map, a detector efficiency map has to be used as an input. The FTOOL ascaeffmap generates such map. This method takes into account the observed spectral distribution, the mirror response, and the instrument efficiency to estimate a flat-field. There are several potential pitfalls while using ascaeffmap. First it is essential to check the range of PHA given as input. In particular, one should exclude all channels below 0.7 keV (for the GIS) and make sure that the upper limit is not above 10 keV. Because ascaeffmap uses the grouped channels, it can be useful to check the screen output while the program is running. This is because the GIS has no effective area below 0.7 keV but there are events with PHA/PI corresponding to lower energies than that due to the low energy tail of the response. If those value are included while running ascaeffmap, the program strongly biases the efficiency map. To avoid being dominated by the low energy contribution from the background, the PHA file used as an input to the program should be extracted from a region covering all the source, but not all the detector. If the PHA is dominated by the background, ascaeffmap will not produce an accurate result. If XRT effective area is included in the computation, the output of ascaeffmap is in cm$^2$. When the output of ascaeffmap is given as a input to ascaexpo, the hidden parameter imath has to be set to mul on the command line (look at the help page of ascaexpo).

To generate an appropriate flat-fielded image, a detector efficiency map can be used as an input to ascaexpo. The FTOOL ascaeffmap is available to estimate the detector/mirror efficiency based on user parameters germane to a particular analysis. This method takes into account the observed spectral distribution, the mirror response, and the instrument efficiency to estimate a flat-field. The output map from ascaeffmap can be given as input to ascaexpo.

Below is a typical session using ascaexpo, complete with running annotations. Symbols at the beginning of each line denote the following.

(>) inputs to ASCAEXPO
(<) outputs from ASCAEXPO
(o) running comments

Use fhelp ascaexpo for additional details, features, and limitations.


10.5.1 Example ASCAEXPO Session

ascaexpo_V0.9a


    o First we input the various files and options:

> Input ASCA science file filename[] ad42000000s000202h.evt


    o A single modally merged events file.

> Input ASCA telescope definition filename (or CALDB)[] s0_teldef_070294.fits


    o If you have the CALDB installed, you may enter 'caldb' to 
      automatically read in the correct telescope definition file,
      otherwise use the `tel_def' file which came with your data (in the 
      `aux' directory).

> Input ASCA attitude filename (or DEFAULT/NONE)[] fa940529_2031.2020
   
    o If `none' is entered, a fixed aspect will be performed (using 
      the FTOOL FIXEDASP; see help file for details).

> Input ASCA rate filename (or NONE)[] none

    o Only option available thus far.
> Input ASCA instrument map filename (or NONE)[] none

    o Entering `none' creates an internal instrument map based on the 
      events file observing mode.

    o Or, input the output file from ascaeffmap.

> Output exposure map filename (or DEFAULT)[] default

    o Output exposure map, `default' will append `.expo' to events filename.
       
> Output instrument map filename (or DEFAULT/NONE)[] default

    o Output instrument map, `default' will append `.inst' to events filename.

    o If it is not necessary to output this map, use the `none' option.

> Output sky image filename (or DEFAULT/NONE)[] default

    o Output sky image map, `default' will append `.sky' to events filename.

    o If it is not necessary to output this map, use the `none' option.

    o This SKY image map will be a perfect match to the exposure map!

> Maximum attitude deviation (arcsecs)[4] 1

    o This option allows you to trade off speed for accuracy. The attitude 
      file typically contains records every 2 seconds (but depends on the
      bit rate).

    o For each step though the attitude file, ASCAEXPO generates a temporary 
      exposure map for that interval and attitude. This map is then added to 
      the summed exposure map.     

    o It is very slow to build up an exposure map for every step in 
      the attitude file. ASCAEXPO allows three methods to speed up the 
      processes.
        
      1) Enter -N to skip N attitude file records between exposure map updates.
      
      2) Enter X to skip records until the attitude deviated by more than
         X arcmin from the last exposure map update.

      3) Use a smaller image size with the `rebin' option below.

    o To use the full accuracy available in the attitude file, i.e.
      to build up the exposure map for each step in the attitude file,
      select -1.

> Integer image rebin factor (-1 for default)[] -1

    o You may wish to rebin the output image. Choosing -1 will 
      rebin SIS maps by a factor of 4, and by unity for the GIS.

> Pixel convention offset for CRPIX of output images[] 0.5

    o This option allows for none-standard image CRPIX pixel conventions.
    o Enter a number between 0.0 and 1.0; normally 0.5.

<   reading data file: ad42000000s000202h.evt
<   reading   gti ext: STDGTI
<   reading    hp ext: HOT_PIXELS
<   reading  cal file: s0_teldef_070294.fits

    o Now ASCAEXPO displays each steps as it goes...

    o For the SIS, the events file header info, GTI and HOT_PIXELS extension 
      data are read in.

    o Then the Telescope Definition File is read.

<   making an inst map...

    o If appropriate, creates the instrument map.

< SIS AREA DISC ENABL          ON

<              CHIP:            0           1           2           3

< CCD POWER  ON/OFF:          OFF          ON         OFF         OFF
< AREA DISC  IN/OUT:          OUT          IN          IN          IN
< AREA DISC H START:            6         226           6         316
< AREA DISC H  STOP:          425         300         200         425
< AREA DISC V START:            2         220           2           2
< AREA DISC V  STOP:          422         294         150         112

   o Display the SIS AREA DISCRIMINATION state and values.

<    writing inst file: ad42000000s000202h.evt.imap

   o If appropriate, writes out the instrument map.


<    reading att  file: fa940529_2031.2020

   o Just read in the attitude file.

<    making a sky image...
<    writing sky image: ad42000000s000202h.evt.sky

   o If appropriate, creates and writes out the sky image.

<    making an exposure map...

< Aspect RA/DEC/ROLL :      308.1400      41.0414     297.8467
< Mean   RA/DEC/ROLL :      308.1349      41.0176     297.8467
< Pnt    RA/DEC/ROLL :      308.1489      41.0613     297.8467

   o Analysed the coordinates system.

< Image rebin factor :             4
< Attitude Records   :         75032
< Hot Pixels         :            19
< GTI intervals      :            65
< Total GTI (secs)   :      7228.517

   o Display file information.

< Max attitude excursion (arcsecs) :         1.000

   o Display attitude excursion option.

<   0 Percent Complete: Total/live time:        0.0000000       0.0000000
<  10 Percent Complete: Total/live time:      812.0728760     812.0728760
<  20 Percent Complete: Total/live time:     1552.5705566    1552.5705566
<  30 Percent Complete: Total/live time:     2255.6794434    2255.6794434
<  40 Percent Complete: Total/live time:     3344.9746094    3344.9746094
<  50 Percent Complete: Total/live time:     3754.4421387    3754.4421387
<  60 Percent Complete: Total/live time:     4429.9404297    4429.9404297
<  70 Percent Complete: Total/live time:     5138.4086914    5138.4086914
<  80 Percent Complete: Total/live time:     5855.1186523    5855.1186523
<  90 Percent Complete: Total/live time:     6583.0859375    6583.0859375
< 100 Percent Complete: Total/live time:     7228.5229492    7228.5229492

   o ASCAEXPO is now computing the exposure map. For convenience the
     percentage completed is displayed.

< Number of attitude steps  used:          496
< Number of attitude steps avail:        18685
< Mean RA/DEC pixel offset:      -67.1511     -90.6348

   o ASCAEXPO has completed the exposure map. It used 496 attitude steps
     out of 18685 available in the file. That is because (a) the events file
     contains a subset of the time in the attitude file, and (b) we skipped
     over records in the file by choosing the `max attitude excursion'
     option.

   o The Mean RA/DEC pixel offset is the average deviation of the attitude 
     from the pointing direction of this file.

<    writing expo file: ad42000000s000202h.evt.expo

   o Write out the final exposure map

<    closing attitude file...
<    closing data file...

   o Close up shop....


10.5.2 HINTS on running ASCAEXPO and using its products


10.6 The ASCA PSF

In order to understand how to do spatial and extended source analysis with ASCA data, it is necessary to understand the properties of the Point Spread Function (PSF) and how it was calibrated both on the ground and inflight. The PSF describes, for photons of a given energy, $E$, the two-dimensional spatial distribution of count rates due to a point source.

The PSF of the ASCA X-ray telescopes (XRT) has a relatively sharp core (FWHM of $\sim 50$ arcsec) but broad wings (half-power diameter of 3 arcmin). In general the XRT PSF is a function of energy, the angle from the optical axis and also the azimuthal angle about the source position. The energy dependence is such that core of the PSF is sharper at lower energies. In addition, the GIS has its own PSF which is comparable in width to that of the XRT but with a different shape (a Gaussian with $\sigma ~ 30$ arcsec at  6 keV and a $1/\sqrt(E)$ dependence). The intrinsic spatial broadening of the SIS is negligible compared to that of the XRT.

In the early part of the ASCA mission the XRT PSF that was used was based on ray-tracing results. The PSF was then fine-tuned using observations of Cyg X-1 placed at different points in the focal plane. The current XRT PSF files can be obtained by anonymous FTP from ftp://legacy.gsfc.nasa.gov/ in the directory

/caldb/data/asca/xrt/bcf.

At the time of going to press the PSF file in use is xrt_psf_v2_0.fits and the associated XRT effective area file is xrt_ea_v2_0.fits. The calibration images of Cyg X-1 can be obtained from the same place in the directory

/caldb/data/asca/xrt/bcf/psf

Check the `README' for details.

A problem with the Cyg X-1 PSF calibration is that the source is thought to be extended below $\sim 2$ keV and this may introduce errors of the order of $\sim 10\%$. More details can be found in Kunieda et al., ASCANews, #3 in which the azimuthal calibration of the PSF is discussed. The azimuthal properties of the ASCA PSF are not as well understood as the azimuthally-averaged properties so that circular data-extraction regions currently give the most accurate results.

Further PSF calibration observations are planned, this time of Her X-1 which is thought to be a point source even at soft energies. Consult the Web page `Calibration Uncertainties' for the latest information (§1.7).


10.7 Extended Sources and Spatio-Spectral Analysis

From the above, it should be clear that the analysis of extended source using ASCA data is non-trivial. For extended sources, the astrophysical implications of the broad PSF are complicated and not easy to deal with. If you are analyzing an extended source, then please note the following effects which, if not taken into account, could lead to spurious scientific results. It is important to realize that these effects are not calibration uncertainties or instrumental defects, but features intrinsic to the design of the XRT which emphasizes effective area as much as angular resolution.

  1. When ascaarf is used to make an ARF for a point source, XRT effective area and PSF calibration files are used to generate the ancillary response file. If the `extended source' option is utilized, the count distribution in the WMAP of the spectral file is used as the template for the spatial counts distribution (thus, the `extended source' computation is actually faster than the point-source option). The extended-source option is inherently an approximation. A more accurate method is to generate an ARF using a ray-tracing code to simulate the real data. This requires either finding the true, intrinsic spatial distribution of the source by trial and error or using a ROSAT image as a surface-brightness template for ray-tracing. However, an important point to bear in mind is that ROSAT covers a much soft X-ray energy band than ASCA so the spatial structure in the ROSAT band may be very different to that in the ASCA band.

  2. The XRT PSF has a sharp core and broad wings. If your extended source has a brightness distribution which is peaked on the same scale as the PSF, then the outer parts of the image will contain a significant proportion of counts from the core. For example, the moderate redshift cluster A2218 has a core radius of about 1 arcmin. If the image is divided into annulli (3 arcmin wide centered on the core) then the second annulus (between 3 and 6 arcmin) will contain more emission from the cluster core than from those parts of the cluster which actually lie in the central 3 arcmin circle.

  3. The effect described above will be compounded by telescope vignetting if the core of your object is close to the optical axis of the XRT.

  4. The XRT scatters high-energy X-rays more than low-energy X-rays. In other words, the PSF broadens with increasing energy. One consequence of this effect is to introduce spurious (outwardly increasing) temperature gradients in isothermal distributions. If there is a negative temperature gradient present, that gradient will appear to be reduced. The GIS has its own intrinsic energy-dependent PSF, although the energy dependence is in the opposite sense to that of the XRT.


10.7.1 Spatio-Spectral Analysis

In view of the above, it should be clear by now that any combined spatial and spectral analysis on extended source is highly non-trivial. There are many cases where it is nevertheless necessary: the determination of X-ray temperature maps of clusters of galaxies, for example, or the detection of a non-thermal contribution to the spectrum of a supernova remnant.

The two most accurate methods which have been developed so far, are described in an article ASCANews, # 3, by Takahashi et al. It is beyond the scope of this document to describe these in detail but essentially the two methods can be summarized as follows.

1. Simulate the real data, either with trial, theoretical temperature and brightness distributions, and/or using ROSAT data (again, bear in mind that the ROSAT energy band is sufficiently different from that of ASCA that the spatial distribution in the two bandpasses may be different). The photons produced can be analyzed in exactly the same manners as the real data (e.g., using xselect, etc.). The input model is then modified to reproduce the data. It is necessary to simulate 5 to 10 times more photons than the real data so to minimize the statistical fluctuations of the simulated data. This method has been applied to the Centaurus and Fornax clusters by Ikebe (1995, PhD thesis, University of Tokyo) and to A1795 and 3A0336+09 by Ohashi (1995, Proceedings of the 17th Texas Symposium on Relativistic Astrophysics).

2. Another way is to modify the spectral fitting procedure to include the mirror scattering. This method transforms the telescope response transform into a matrix which includes all the information about the source geometry and integration regions, vignetting and PSF scattering. When there is no PSF scattering, the matrix is diagonal and all is reduced to the standard scheme. Errors are estimated with Monte-Carlo simulations. The reader is urged to read Markevitch (1996, ApJ, 465, L1) in which temperature maps were made for four clusters using ASCA data.


10.8 Merging Observations

In the case of several observations of a large extended source, it is possible to merge the data to map the totality of the source. A program called fmosaic is available to do just so, as part of the ASCA package of HEAsoft. The fmosaic program is an FTOOL inspired by an existing program written by E. Churazov, M. Gilfanov, and A. Finoguenov. fmosaic creates a mosaic of several observations and take correctly into account, both the energy and the spatial binning of the data files. The user specifies the center of the image to be created, the image size (in arcmin) and the energy range of photons to be included in the final image. A mosaic of the background and exposure map, using the same image definition, can be generated as an option.

To create an image mosaic of the observations and nothing else, the input file must consist of 2 columns containing the name of the event files and of the RMF file associated respectively (to allow for energy range selection). WARNING! if the rmf file and the event file are not binned the same way, fmosaic will stop).

Options: There are two ways to generate a mosaic background map. One is to generate blank files for each observation and fill the third column of the input file with the name of this background file. These files can be generated using mkgisbgd and the newest files in the CALDB directory or they can be "private" background maps generated with some user-defined routine. This is the prefered mode.

The other option is to use the default option and access the old CALDB background files. For the moment the files accessed through CALDB options are still the ones under the /94may/ directory and not the newest ones (see Chapter 8). In this case, the input file's third column should contain the name of the MKF file associated with each observation. The MKF file is used in the case of the ASCA to derive the rigidity histogram and then assigning the same weight to the background files found in CALDB.

The exposure maps associated with each observation are computed with the program (ascaexpo) and combined later. Their name is given either in the third or the fourth column, depending if a mosaic of the background is generated or not.


10.9 Image Deconvolution

The deconvolution of images is also non-trivial. Application of the `Lucy-Richardson' method to ASCA data, as well as a description of the XRT performance can be found in Jalota, L., Gotthelf, E.V., and Zoonematkermani, S. 1993, SPIE 1945, 453. The method is able to resolve two point sources of equal intensity, $\sim 30$ arcsec apart. An example of the method applied to actual ASCA data of Cas A can be found in Holt, S. S., Gotthelf E. V., Tsunemi, H., Negoro, H., 1994, PASJ, 46, L151.

There is also a deconvolution routine available in IDL called max_entropy. Given the similarity of the XRT PSF with the original, uncorrected PSF of the Hubble Space Telescope, users might also want to check out some of the early HST imaging papers.


10.10 Getting Started with XIMAGE

XIMAGE is a powerful and versatile image display and analysis program. It is fully documented, with an extensive manual and on-line help. The User's Guide can be obtained by consulting the URL

http://heasarc.gsfc.nasa.gov/docs/xanadu/ximage/ximage.html.

Note that while spectral work is more accurate with image manipulation in detector coordinates, image analysis is more accurate in SKY coordinates. The following, which covers XIMAGE basics, is a very brief guide to get you started. Note that many XIMAGE commands have several qualifiers to extend their function: please use the on-line help to find out about them.


next up previous contents
Next: 11. APPENDICES Up: ASCA ABC Guide Previous: 9. TEMPORAL ANALYSIS   Contents
Michael Arida 2002-10-22