2 Simulation of X-ray images

The simulations are essential to understand and qualify the behavior of the different detection and analysis packages. We have developed a simulation program that generates X-ray images for given exposure times with extended and point-like objects. It takes into account the main instrumental characteristics of XMM-Newton and the total sensitivity of the three EPIC instruments. The procedure is fast and flexible and is made of two independent simulation tasks: object generation (positions, fluxes, properties) and instrumental effects. A possibility to apply the instrumental response directly over images is also implemented, especially useful when one wants to use sky predictions from numerical simulations (cf. Pierre et al. 2000).

A summary of the simulated images parameters are given in Table 1.

 

 

Table 1: The general parameters for the simulated images

Parameter
Image scale	$4\hbox {$^{\prime \prime }$ }$/pixel
Image size	$512\times512$
Exposure time	10 ks & 100 ks
Energy bands	[0.5-2] & [2-10] keV
PSF on axis	$6\hbox {$^{\prime \prime }$ }$ (FWHM)
	$15\hbox {$^{\prime \prime }$ }$ (HEW)
Total background (pn+2MOS)
[0.5-2] keV	1.78 10-5 cts/s/pixel
	0.0041 cts/s/arcmin2
[2-10] keV	2.4 10-5 cts/s/pixel
	0.0055 cts/s/arcmin2

The point-like sources are assumed to be AGNs or QSOs with a power law spectrum with a photon index of 2 and flux distribution following the $\log N-\log S$ relations of Hasinger et al. (1998, 2001) and Giacconi et al. (2000) in the two energy bands.

The PSF model is derived from the current available calibration files. On-board PSF data is generally in very good agreement with the previous ground based calibrations (Aschenbach et al. 2000). We must stress that the model PSF is an azimuthal average and in reality, especially for large off-axis angles, its shape can be very distorted. However, in the analytic model (Erd et al. 2000), the off-axis and energy dependences are not available yet. This is not crucial, as the energy dependence in the bands used is moderate and we confine all the analysis inside $10\hbox {$^\prime $ }$ from the centre of the field-of-view where the PSF blurring is negligible.

The extended objects are modeled by a $\beta$-profile (Cavaliere & Fusco-Femiano 1976) with fixed core radius $r_{\rm c}=250\,h^{-1}$kpc and $\beta=0.75$. A thermal plasma spectrum (Raymond & Smith 1977) is assumed for different temperatures, luminosities and redshifts.

The source spectra (extended and point-like) are folded with the spectral response function for the total sensitivity of the three XMM-Newton EPIC instruments (MOS1, MOS2 and pn with thin filters) by means of XSPEC (Arnaud 1996) to produce the count rates in different energy bands. The actual choice of the energy bands is not important for this comparison study, although some objects can be more efficiently detected in particular energy ranges.

As an example, we show in Table 2 (available on line) the resulting count rates for extended sources assuming that they represent an average cluster of galaxies.

The background in the simulations includes realistic background values derived from the XMM-Newton in-orbit measurements in the Lockman Hole (Watson et al. 2001).

The calculated count rates for the objects and the photons of the background are subject to the vignetting effect - some photons are lost due to the smaller telescope effective area at given off-axis angle, depending on the incoming photon's energy. We have parametrized the vignetting factor - the probability that a photon at an off-axis angle $\theta$ to be observed - as polynomials of fourth order in two energy bands: [0.5-2] and [2-10] keV, using the latest XMM-Newton on-flight calibration data. For example, a photon at $\theta=10\hbox{$^\prime$ }$ has a 53% chance of being observed in [0.5-2] keV and 48% in [2-10] keV.

Further instrumental effects such as quantum efficiency difference between the CCD chips, the gaps between the chips, out-of-time events, variable background, pile-up of the bright sources are not taken into account - their inclusion is not relevant for our main objective.