2 Data analysis and preparation

2.1 Observations

A1413 was observed in Guaranteed Time for 29.4 ks during XMM-Newton revolution 182 (2000 December 16). Calibrated event files were provided by the XMM-Newton SOC. The MOS and pn data were obtained with the THIN1 and MEDIUM filters, respectively. For the pn data set, we extracted single events, which correspond to PATTERN 0, while for the MOS data sets PATTERNs 0-12 were selected.

Dedicated blank-sky data sets, which consist of several high-galactic latitude pointings with sources removed (Lumb 2002), were used as background for the whole of this analysis. These data sets are distributed as calibrated event files which have already been treated with the SAS. We extract the background events using the same PATTERN selection criteria as outlined above. In addition, we transformed the coordinates of the background file such that they were the same as for the A1413 data set. In this way we can ensure that all source/background products come from exactly the same regions of the detector, thus minimising detector variations.

2.2 Vignetting correction

The method described in Arnaud et al. (2001b) was used to correct spectra and surface brightness profiles for vignetting effects. Briefly, this method involves weighting each photon with energy (E), detected at position (x_j,y_j), by the ratio of the effective area at the detected position  A_xj,yj(E) to the central effective area  A_0,0(E).

The background data were treated in the same manner as the source. Note that the background component induced by cosmic rays (see below) is not vignetted, but since source and background observations are treated in the same way, the correction factor is the same and thus cancels.

2.3 Background subtraction

The XMM-Newton background, consisting of several components, is both time and energy-dependent, and so subtraction is a subtle process. Furthermore it is essential that the subtraction is done correctly, especially so for extended sources like clusters of galaxies, where background effects begin to play a role at large off-centre distances where the surface brightness declines approximately as r^-4 (e.g., Vikhlinin et al. 1999).

The soft proton background due to solar flares cannot be corrected for in the normal fashion (e.g., spectral subtraction) as it displays extreme temporal and flux variability, causing the spectrum to change rapidly with time. At the moment it can only be removed by excising all frames above a certain count-rate threshold, the main effect of which is to considerably reduce the effective exposure time. For these observations, the $3 \sigma$ threshold for each camera was calculated using the method described in Appendix A, and all frames not meeting this criterion were rejected. In practice the observation is very clean. Note however that the pn is considerably more sensitive to the flares. The final exposure times were 24 163 s, 24 567 s and 10 254 s for MOS1, MOS2 and pn cameras, respectively. The blank-sky backgrounds were cleaned using the same criteria.

The blank-sky background represents effectively the particle induced background, dominant in the hard X-ray band, which is, both spatially and temporally, relatively constant. Nevertheless, this background is variable at the $\sim$$10\%$-level, and so it is frequently necessary to normalise the background. We normalise these observations using the count rate in the (10-12) keV and (12-14) keV bands, for MOS and pn respectively, treating each camera separately. We varied the normalisation by $\pm$$10\%$ to assess any systematic uncertainties.

However, the blank-sky data set does not necessarily represent the cosmic X-ray background (CXB), because this is variable across the sky, especially the soft X-ray component (see Snowden et al. 1997). We use the method described in Pratt et al. (2001), and Arnaud et al. (2002) to correct for the difference of the CXB. An annular region external to the cluster emission (between 9' and 13' in this case) is used to estimate the local background. The normalised spectrum of the same region of the blank-sky background is then subtracted, giving a difference spectrum, which can then be scaled according to the size of any extraction region and subtracted directly from the source spectra. A similar procedure is applied to subtract the residual CXB component for the surface brightness profile (see Arnaud et al. 2002 for details).

In addition to the above, the pn data were corrected for "out of time events'', which occur when a photon hits the CCD during the read-out process in the imaging mode.