2 Spectral fitting analysis

We divided a 5$^\prime$$\times$ 5$^\prime$ field of view of Cas A on a spatial grid containing 15$\times$15 pixels. This corresponds to a pixel size of $20{\hbox {$^{\prime \prime }$ }} \times 20{\hbox {$^{\prime \prime }$ }}$, slightly larger than the half-power beam width of XMM-Newton. Spectra were extracted using this grid and analysed on a pixel by pixel basis.

The spectral analysis was performed using the SRON SPEX (Kaastra et al. 1996) package, which contains the MEKAL code (Mewe et al. 1995) for modeling thermal emission. We find that, even at the $20{\hbox {$^{\prime \prime }$ }} \times 20{\hbox {$^{\prime \prime }$ }}$ level, one thermal component does not model the data sufficiently well, particularly in describing both the Fe-L and Fe-K emission. We therefore choose as a minimum for representative modelling two NEI components for the thermal emission. In addition we incorporated the absorption measure as a free parameter and also introduced two separate redshift parameters, one for each plasma component. The basic rationale behind a two component NEI model is that we expect low and high temperature plasma associated with a reverse shock and a blast wave respectively. While we obtain good fits using a two NEI model, we estimate that a contribution from a power law hard tail to the 4-6 keV continuum could be as high as 25$\%$. Since there is no evidence that the hard X-ray emission is synchrotron and its brightness distribution is very much in line with the thermal component (see Bleeker et al. 2001), we feel that our fitting procedure is justified. In other words the combined high and low temperature NEI components will provide a good approximation to the physical conditions that give rise to the line emission.

The low temperature plasma component in our model implicitly assumes that the ejecta material, which largely consist of oxygen and its burning products (Chevalier & Kirshner 1979), has been fully mixed regarding the contributing atomic species. In order to mimic a hydrogen deficient, oxygen rich medium we adopted a similar approach to that used by Vink et al. (1996), where they fixed the oxygen abundance of the cool component to a high value. We set the cool component abundances of O, Ne, Mg, Si, S, Ar and Ca to a factor 10000 higher than that of the hot component. It should be noted that 10000 is not a magic number, 1000 would suffice. The important point is that oxygen and the heavier elements are all dominant with respect to hydrogen so that oxygen rather than hydrogen is the prime source of free electrons in the plasma. The abundances of O, Ne, Mg, Si, S, Ar, Ca, Fe and Ni were allowed to vary over the remnant while the rest of the elemental abundances (He, C and N) were fixed at their solar values (Anders & Grevese 1989). Our model allows us to estimate the distribution over the remnant of the emission measure $n_{\rm e}n_{\rm H}V$, the electron temperature $T_{\rm e}$ and the ionisation age $n_{\rm e}t$ of the two NEI components as well as the distribution of the abundance of the elements (O, Ne, Mg, Si, S, Ar, Ca, Fe & Ni), the column density $N_{\rm H}$ of the absorbing foreground material, Doppler broadening of the lines and the redshift of the respective plasma components. Here $n_{\rm e}$ and $n_{\rm H}$ are the electron and hydrogen density respectively, V is the volume occupied by the plasma and t is the time since the medium has been shocked. The best fit model parameters were found and recorded for each pixel and it was thus possible to create maps of the various model parameters over the face of the remnant.