# Extended Source Analysis with ASCA

## T. Takahashi^{1,2}, M. Markevitch^{1,6},

Y. Fukazawa^{2}, Y. Ikebe^{2,3},

Y. Ishisaki^{2}, K. Kikuchi^{4},

K. Makishima^{2}, Y. Tawara^{5},

and ASCA Image analysis working group

###
^{1} Institute of Space and Astronautical Science

^{2} Dept. of Physics, Univ. of Tokyo

^{3} Riken

^{4} Dept. of Physics, Tokyo Metropolitan Univ.

^{5} Dept. of Physics, Nagoya Univ.

^{6} Moscow

takahasi@astro.isas.jaxa.jp

ASCA mirrors have a wide energy- and position-dependent point spread function (PSF), which must be accurately taken into account to fully utilize the spectro-imaging capability of the telescope. Below we discuss effects of the PSF, how it was calibrated, and how it can be included in the analysis of the extended sources.

**
Figure 1:** Cyg X-1 smoothed images from GIS2 at *theta*=8', at soft
and hard energies. A plus marks the optical axis position. Circles contain 90%
of all photons within the 16' radius in each image; they are of 6' radius for
the soft image and 10' for the hard image. At higher energy, the PSF has wider
outskirts.

**
Figure 2:** Smoothed 0.5-10 keV images of Cyg X-1 at different focal plane
positions: (1) off-axis distance *theta*=2', (2) *theta*=13',
and (3) *theta*=17'. Contours are logarithmically spaced. The PSF
position dependence is strong -- the image becomes more distorted at greater
off-axis distances.

Naïve methods of extended source analysis (e.g., fitting spectra from the
concentric rings around the cluster center, with the XRT ancillary response
calculated for each ring individually) do not work with ASCA (Takahashi et al.
1994). For clusters with relatively small angular sizes which are within the
GIS field of view, the outer rings, however large, inevitably have a
non-negligible energy-dependent contribution of the flux from the inner
brighter parts. For example, for a symmetric cluster with *a*x=1.2' and
beta=0.62 divided into concentric rings 0'-4'-8'-12', the flux in the outer
ring is in fact dominated by that scattered from the inner cluster part.
Fractions of the flux from the inner, middle and outer rings in the sky are
(0.94, 0.06, 0.002) in the inner image ring, (0.55, 0.42, 0.04) in the second
ring, and (0.33, 0.29, 0.39) in the outer ring for E=2.5 keV, respectively,
while for E=10 keV, the respective fractions are (0.93, 0.06, 0.004), (0.57,
0.39, 0.04), and (0.48, 0.25, 0.27). These numbers show that even though the
image rings are much larger than the PSF half-power diameter, flux from the
inner cluster regions can be extremely important in the outer rings. One also
notices that the sign of the energy dependence of these fractions is such that,
if these effects are not accounted for, the outer part of an isothermal cluster
would look hotter, as is seen in Figure 3 which shows a temperature profile of
the simulated isothermal cluster obtained by a naïve method ignoring the
PSF effects. To take this scattering into account, an accurate two-dimensional
energy-dependent model of the mirror PSF should be included in the analysis.
Eventually, such a model will be created using the upgraded raytracing code. In
the meantime, we suggest to use a model obtained by interpolation between a set
of actual GIS Cyg X-1 images as described below.

**
Figure 3:** A simulated isothermal symmetric cluster with *a*x=1' and
beta=0.55 is divided into concentric rings, whose spectra are fit
individually ignoring the PSF scattering. Different symbols correspond to
different true temperatures. The cluster is simulated using the PSF model
reconstructed from Cyg X-1 images (see text). A spurious temperature increase
outward arises because the PSF is wider at higher energies.

**
Calibration of the PSF**

To calibrate the mirror PSF, we have used the observations of Cyg X-1 performed in November 1993, November 1994 and May 1995 at several offset positions. This source is bright and hard and provides sufficient statistics to obtain high quality GIS images in the narrow energy intervals. Utilizing the 5' relative misalignment between the two GIS mirrors, the obtained pointings sample the PSF for a total of 13 focal plane positions. GIS detector images from these observations with the corrected attitude, in 10 energy intervals for each pointing, are available via anonymous ftp from

`
ftp.astro.isas.ac.jp: /asca/calibration/xrt/data/image/*`

together with a `README` file which has more details. Table 1 lists
focal plane coordinates sampled by these observations. Figure 4 schematically
shows these positions and those for which the PSF can be modeled assuming the
mirror symmetry. A star tracker accident occurred during the November 1994 run,
but it was possible to restore the images from the affected observations
without any loss of quality, tracking the satellite motion using Cyg X-1
itself. The result of this accident is that the PSF we have from the images
corresponds to positions averaged over a few-arcmin region of the focal plane
due to the source motion in the detector coordinates, for the pointings for
which a range of coordinates is given in Table 1. This should have a negligible
effect on the results comparing to other uncertainties.

The work is underway to tune the raytracing to reproduce the obtained Cyg X-1
images. In the meantime, a reasonable approximation of the PSF at any focal
plane position and energy can be obtained by direct interpolation between these
images, assuming that the four mirrors are identical and symmetric. A fortran
function `make_psf.f` which linearly interpolates between these Cyg X-1
images and outputs a 1'-resolution PSF model image for a given energy and focal
plane position is available at

`
ftp.astro.isas.ac.jp: /asca/calibration/xrt/data/make_psf/*`

together with the dataset it reads. The limitations and the systematic errors introduced by this method of modeling the PSF are described below.

pointing | GIS* | theta | phi
| averaged over | |
---|---|---|---|---|---|

arcmin | deg | theta | phi | ||

0 | 2 | 8.1 | 215 | ||

0 | 3 | 5.8 | 251 | ||

1 | 2,90deg | 1.6 | 92 | 1.0-2.0 | 80-110 |

1 | 2,180deg | 1.9 | 189 | 1.0-2.8 | 170-200 |

1 | 3 | 3.8 | 350 | 3.0-5.2 | 330-10 |

2 | 2 | 17.2 | 252 | 15-19 | 250-260 |

2 | 3 | 17.1 | 268 | 15-19 | 260-270 |

3 | 2 | 1.8 | 4 | 1.2-2.2 | 345-15 |

3 | 3 | 6.3 | 351 | 6.0-6.8 | 345-355 |

4 | 2 | 17.0 | 141 | 16.5-17.5 | 138-145 |

4 | 3 | 12.8 | 130 | 12.5-13.1 | 128-135 |

5 | 2 | 12.9 | 248 | ||

5 | 3 | 12.7 | 270 | ||

6 | 2 | 10.0 | 247 | ||

6 | 3 | 10.0 | 276 |

*Pointing 1, GIS2 observation was divided into 2 pieces with the average
*phi* around 90deg. and 180deg. and the rest was excluded.

**
Figure 4:** Sampled points of the focal plane. The center of the figure
corresponds to *theta*=0, and *phi* is calculated from the
`det x` axis counterclockwise looking up. Filled symbols represent
actual Cyg X-1 positions in the GIS2 and GIS3 images. Using symmetries, the
whole usable GIS FOV is covered (open circles), with the off-axis distance
increment of about 3-5' and the position angle increment of about 30deg.

**
**

**
**

**
Limitations of the PSF model based on Cyg X-1**

GIS images of Cyg X-1 are a superposition of the effects of the mirror PSF, the GIS detector PSF, the GIS supporting grid and spacecraft jittering. The procedure used to fix the attitude trouble is applied to all Cyg X-1 pointings, so that the spacecraft jittering is corrected with an accuracy better than that in other observations. A positive effect of this accident is smearing of the supporting grid shadows for most of the pointings. Although the grid shadow is still visible in the Cyg X-1 images, experience shows that ignoring it has a negligible effect on the derived results.

The GIS detector PSF is believed to be a Gaussian independent of the coordinate
(although dependent on energy, steeply widening below 2 keV and slightly
widening above 8 keV). It has a FWHM of 1' at 2 keV and can be safely ignored
when the regions of interest are of several arcminutes in size. For the GIS
data analysis, one doesn't have to worry about it at all since it is present in
both the data and the PSF model under discussion. However, the SIS detector has
no additional blurring and the PSF model we discuss is not directly applicable
for SIS analysis. Cyg X-1 is too bright to observe it with SIS. As a temporary
solution (before the upgraded raytracing has solved all these problems for
good), we suggest modelling the PSF using the GIS Cyg X-1 images which have
been smoothed to compensate for the energy dependence of the GIS blurring, and
smooth the SIS data to the resolution of the PSF model. There is a non-smoothed
set of the Cyg X-1 images for use with the GIS, and a set of images smoothed to
the final resolution of Gaussian sigma=0.5' for use with SIS, supplied with
the `make_psf` function. SIS cluster images should be smoothed to the
same final resolution sigma=0.5' before collecting the spectra. This can be
done by literally smoothing the images in each energy band. Alternatively,
without extracting data images in each energy interval, it can be done by
smoothing some kind of a mask image applied to the event file when collecting
the spectrum of a given region, which before smoothing would consist of 1 and 0
in the pixels inside and outside the region of interest. Work is underway to
model the PSF using less bright sources for which the SIS data are available.

In Figure 5, radial brightness profiles of the PSF image generated by
interpolation between the Cyg X-1 images are compared with those of 3C273. The
profiles are consistent at the energies above 2 keV, but Cyg X-1 always appears
to be considerably wider than a point source at the lower energies, which is
not an effect of the interpolation nor the mirror asymmetry. The reason is not
fully understood at the moment; it may be intrinsic to Cyg X-1 or be connected
to its extreme brightness. Therefore,* the PSF model based on Cyg X-1 can
only be used above 2 keV.*

The maximum off-axis distance for which Cyg X-1 images were obtained (and
therefore the model under discussion can be used) is 17'. The model ignores the
differences between the four mirrors and significant irregularities of each
mirror, which introduces a systematic error ~ 5% (sigma) in the predicted
flux from a several-arcminute-wide ring centered on the point source.
Comparison of the model with the real 2-dimensional images shows that for
integration regions other than concentric rings (for example, segments of the
ring), the error is greater because of the ignored mirror asymmetries and might
be reasonably taken as ~ 15% (1sigma). For a given region, this systematic
error should be conservatively assumed the same for all energies (that is, 100%
correlated between different energy channels). *We recommend avoiding
integration regions smaller and rings narrower than a few arcmin*.

Poissonian errors in the Cyg X-1 images are generally negligible compared to other errors, but may become significant for small integration regions, far off axis, and at the highest energies because of the poorer statistics.

**
Extended source analysis**

As is mentioned above, PSF scattering has to be taken into account when analyzing extended sources, by simultaneous fitting of the spectra from different image regions. It is implemented in the two ways described below.

**
1. Method utilizing Monte-Carlo instrument simulator**

The ASCA instrument simulator, originally developed for calibration of the
detector components of ASCA by the `SimASCA` working group, has been
extensively used to simulate the apparent temperature distribution and
brightness profile for clusters of galaxies observed with GIS and SIS (e.g.,
Ikebe et al. 1995). In the simulator, the XRT PSF is modeled either by
interpolating between the Cyg X-1 images or by using the ray-tracing program.
In this method, X-ray photons from a model cluster are passed through programs
simulating the instruments (XRT, GIS and SIS) to produce a photon list which
can be analyzed in exactly the same manner as real data (e.g., using
`xselect`, etc.) The photon list can be compared to the real images or
real spectra from different regions and the model parameters can be fit to
reproduce the data. The complicated detector characteristics, such as details
of the PSF and the pile-up effect of the SIS, can be treated correctly by the
Monte-Carlo method. This scheme has been applied to the Centaurus and Fornax
clusters by Ikebe (1995) in his PhD thesis, and to A1795 and 3A0336+09 by
Ohashi (1995). A sufficient number of model photons, say, 5-10 times more than
in the actual data, should be generated so that the statistical fluctuations of
the simulated data would not significantly affect the goodness of

the fit between the actual data and the model. The number of photons obtained in a typical cluster observation is 10^5, so that one needs to generate ~10^6 events, which takes a few tens of minutes on an Alpha workstation for one set of the model parameters. Figure 6 shows a simulated brightness distribution (two beta-models), fitted to the GIS image of the Fornax cluster with the galaxy NGC1399.

**
Figure 5:** Comparison of radial brightness profiles of the PSF model based
on Cyg X-1 with those of 3C273, for the position *theta*=4.7' and
*phi*=41deg.. The model is wider at the energies below 2 keV. A similar
effect is observed by comparing brightness profiles of Cyg X-1 and another
point source observed at the same position with the same detector, therefore,
it is not an effect of the interpolation or of the mirror differences.

**
Figure 6:** Simulated image of the Fornax cluster including its cD galaxy NGC
1399, using the Monte-Carlo scheme. The X-ray volume emissivity is modeled as a
sum of two beta-models whose parameters are fitted to the actual GIS data
(from Ikebe 1995).

**
2. Generalization of the scheme with telescope ancillary response**

Another way is to modify the standard spectral fitting procedure, in which one
includes the source geometry and the effective area energy- and
position-dependencies in the telescope ancillary response file (ARF), to
include the mirror scattering (Markevitch et al. 1995). Denoting a projected
sky image of the emission measure of the *i*-th model region (either two-
or three-dimensional) as *mi*, its spectrum as *si*(*E*) (where
*E* is in keV), the total number of the model regions as *M*, an
operation of summing the flux over the *j*-th detector image region as
*Rj* (including in it the SIS gaps and the GIS grid for clarity), a
spectrum from the *j*-th detector image region as *dj*(*E'*)
(where *E'* is in channels), the total number of the detector image
regions as *N*, the linear operation of multiplying by the mirror
effective area plus PSF scattering, which converts a model brightness
distribution into that in the detector plane, as *P*(*E*), and
convolution of the spectrum with the coordinate-independent detector spectral
response including the detector efficiency, as *D*, we have

The telescope response transform,
,
which for a given energy converts the spectra of the model regions to the
fluxes in the detector image regions, *d* = *DTs*, is thus an
*M* x* N* matrix that includes the geometry of the source and the
integration regions, vignetting and PSF scattering -- an analog of what a
commonly used ARF contains, but a matrix instead of a single number. The
least-squares solution *s* is searched by iterations. If there is no PSF
scattering and no projection, *T* is diagonal and everything is reduced to
the standard scheme with separate fitting. If *mi* can be fixed or
reasonably simply parametrized (for example, a ROSAT image is available or a
symmetric brightness profile can be assumed), *T*(*E*) can be
calculated once before performing the fit (which involves time-consuming
two-dimensional convolutions with the position-dependent PSF), after which only
the spectral parameters and maybe relative normalizations of the model spectra
need to be fit, each iteration involving only the convolution with the small
(for reasonable *M* and *N*) matrix *T*. Figure 7 shows a
two-dimensional temperature map of A2319 (Markevitch 1995) obtained using a
ROSAT image as a brightness template. In this case, *T* was a 13 x 13
matrix containing contributions of 13 model regions to the corresponding 13
image regions. To fit a beta-model density profile parameters in addition
to the temperatures, one can calculate the transform *T* for the narrow
radial model shells assuming uniform emission measure throughout the cluster,
and later recalculate the normalization for each shell in each iteration
according to the values of *ax* and beta, taking advantage of
linearity of all the involved operations. Errors in the fitted model parameters
may be estimated by Monte-Carlo simulation, adding random deviations to the
data and deviations representing systematic errors to the *T* matrix, and
rerunning the fit. Using this scheme on an Alpha workstation, to obtain the
temperature map shown in Figure 7 took about 30 min and to calculate errorbars
took another day.

For both schemes described above, for evaluation of goodness of the fit, PSF
systematic errors may be included in the *chi^2*
value, for example, by adding 5% or 15% of the model flux (selectively, perhaps
only to those components of the model flux which correspond to the non-diagonal
elements of *T*) in quadrature to the statistical error of the data.

Both methods are implemented (although not in the `ftools` form), and
the programs are available from the authors of this article.

Figure 7: Temperature map of A2319, obtained using the modified ARF method (from Markevitch 1995).

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References**

Ikebe Y., 1995, PhD thesis, Univ. of Tokyo

Ikebe Y., et al., 1995, Hakone ASCA meeting

Ikebe Y., et al., 1995, in preparation

Markevitch, M. 1995, Hakone ASCA meeting

Markevitch, M., et al. 1995, *ApJ*, in press

Ohashi, T., 1995, Proceedings of the 17th Texas Symposium on Relativistic Astrophysics

Takahashi, T. et al. 1994, "Why we need another Cyg X-1 observation", ASCA
internal report,
`ftp.astro.isas.ac.jp: /asca/report/xrt_US.ps`

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