Because of the finite PSF of the XMM-Newton mirrors and their broad wings a significant flux that originates from one area of the sky is detected in a different area of the detector. If the source is uniform over the field then this effect isn't a major consideration, however if there are strong gradients in the emission and spectral parameters over the field then the effect can be significant. This is the case for many cooling flow clusters. SAS now includes a modification of the task arfgen to account for this “crosstalk”. The blue points in Figure 21 show the effect of the application of this modification to the determination of the temperature radial profile of Abell 1795. The effect is as should be expected with the central temperature being colder and the other inner annuli being hotter when crosstalk is included (the effect of the PSF spreading of the on-average cooler photons has been removed).

Figure 22: Radial profiles of the fitted temperatures for the annuli of the Abell 2205 cluster. Green points are from the fits to the data without accounting for the finite PSF. The red points are from refitting the data applying the crosstalk ARFs to account for flux from one region of the sky which due to the finite PSF appear in a different region of the detector.

Figure 22 shows similar results for the cluster of galaxies Abell 478 where the effect is much stronger.

Like with the model SPF component, the crosstalk contribution must be input as a separate model but its components will be linked to existing parameters. In the example below, the crosstalk model represents the contribution of the spectrum which originates in the $0.5'-1.0'$ annulus on the sky to the central $0.5'$ region of the cluster on the detector. The lines below associate the model parameters of the cluster emission from the annulus with the spectrum and RMF of the central region and the cross talk ARF. Specifically they link the spectral parameters of the cluster annulus thermal emission crosstalk.

resp  4:1 mos1S001-0-30.rmf                                           
arf   4:1 mos1S001-30-60-0-30.arf          
model  4:mycross1 con*apec*wabs
newpar mycross1:1 =  64
newpar mycross1:2 =  80
newpar mycross1:3 =  81
newpar mycross1:4 =  82
newpar mycross1:5 =  83
newpar mycross1:6 =  84

Figure 23: Radial profiles of the fitted temperatures for the annuli of the Abell 1795 cluster. Note that these results are from the CCF of 11 September 2008 and SAS V8 that are responsible for the lower values for the fitted temperatures than seen elsewhere. The green data are from the fits performed without accounting for the finite PSF. The blue data are from applying the crosstalk ARFs to account for flux from one region of the sky which due to the finite PSF appear in a different region of the detector. The red points are from applying the cross-talk arf calculation to the individual annuli.

The arfgen crosstalk calculations can also be used to improve the ARF calculations for individual regions. Run in its nominal mode using the extended source parameter turns off the encircled-energy calculation that for small regions can generate a significant over estimate of the effective area. Figure 23 shows the effect of using the arfgen cross-talk mode to calculate the ARFs for the individual annuli. (When the annuli are larger in area the effect is minor so for this test only the first two annuli were recalculated.) The effect is to enhance the cross-talk correction, which for a cooling-flow cluster is to lower the fitted temperature of the inner region and increase the fitted temperatures of the inner annuli. Care must be taken in choosing the bin sizes of the detector maps. If the binning is too coarse the ARF will be underestimated, which is a known feature of the method for calculating the cross-talk ARFs and not a bug. Figure 24 shows ARFs calculated for the innermost region using different bin sizes. A bin size of $1.5''$ produces close to the limiting value for the ARF, as does a bin size of $2.5''$. In general the bin size should be chosen so that the receiving region should have at least 300 pixels.

Figure 24: Calculated ARFs for the Abell 1795 cluster. The top curve is the ARF calculated using the standard arfgen method while the rest of the ARFs were calculated using the cross-talk mode of arfgen using different binnings for the detector maps. From the bottom the bin sizes were $7.5''$, $5.0''$, $3.75''$, $2.5''$, $1.5''$, and $1.0''$.