4 Key results

Figure 2 shows a typical spectral fit. All features of the measured spectrum are remarkably well represented by the modelling. Bivariate linear interpolation was used to transfer the model parameters, predicted fluxes etc. onto the grid of 1 arcsec pixels. Figure 3 displays maps of the ionisation age and temperature of the cool NEI component. This component is dominant in the line spectrum including Fe-L emission. The temperature distribution of the hot component is similar to (but not the same as) the cool component but with a temperature range 2-6 keV. The hot component is responsible for all the Fe-K emission and also dominates the continuum above 4 keV.

Figure 3: Spectral fit parameters for the cool component, ionisation age left-hand panel and temperature right-hand panel. The contour indicates the region with good statistics and low scattering.

Figure 4 shows the ionisation age of the hot NEI component and the interstellar column density.

Figure 4: Ionisation age of the hot component and the interstellar column density. The contour indicates the region with good statistics and low scattering.

These plots demonstrate the amazing variability in the spectrum over the face of the remnant. The column density does exhibit some correlation with the surface brightness of the bright knots of the remnant presumably because of parameter coupling in the spectral fitting process. The $N_{\rm H}$fitting is particularly sensitive to modelling of the O VIII emission 0.6-0.8 keV and Fe-L lines 1.0-1.5 keV. The mean column density is $1.5\times10^{22}$ cm^-2 while the range is $1.0{-}2.5\times10^{22}$ cm^-2. The variation of interstellar column density over the face of the remnant has previously been mapped by Keohane et al. (1996) using radio data. The distribution in their map is similar to Fig. 2 with high column density in the West due to a molecular cloud but the overall range of their column density derived from the equivalent widths of HI and OH is smaller, $1.05{-}1.26\times10^{22}$ cm^-2.

Figure 5 is a montage of abundance maps. Again we see considerable variations over the remnant. The Fe-L distribution comes from the cool component while the Fe-K and Ni are derived exclusively from the hot component.

Figure 5: Abundance maps for the elements included in the spectral fitting. All are plotted on the logarithmic scale indicated by the bar at the bottom.

The distributions of Si, S, Ar and Ca, which are all oxygen burning products, are similar and distinct from carbon burning products, Ne and Mg, and Fe-L. Figure 6 shows the variation in the ratios S/Si, Ar/Si and S/Si with respect to the abundance of Si. On the one hand these ratios clearly vary over the remnant but on the other hand, for a Si abundance range spanning more than two orders of magnitude, these ratios remain remarkably constant. The thick vertical bars indicate the mean and rms scatter of the ratio values.

Figure 6: The variation in the abundance ratios of S/Si red, Ar/Si green and Ca/Si blue as a function of the Si abundance. The large error bars to the right indicate the mean and rms scatter for the three elements.

Line flux images were produced using an adaptive filter with a minimum beam count of 400 and maximum beam radius of 15 arcsec. The raw event images from each line energy band were smoothed and then multiplied by the ratio of the predicted line flux to line plus continuum flux ratio in order to estimate the line flux. Figure 7 shows the resulting line flux images colour coded with the Doppler velocity. The bottom left image is the colour coding used.

Figure 7: Doppler maps derived from Si-K, S-K and Fe-K emission lines. For each case the surface brightness of the line emission (after subtraction of the continuum) is shown colour coded with the Doppler velocity. The coding used is shown in the bottom left image.

The Doppler shifts seen in different areas of the remnant are very similar in the three lines. The knots in the South East are blue shifted and the knots in the North are red shifted. This is consistent with previous measurements, Markert et al. (1983), Holt et al. (1994), Vink et al. (1996). Moving from large radii towards the centre the shift generally gets larger as expected in projection. This is particularly pronounced in the North. At the outer edges the knots are stationary or slightly blue shifted. Moving South a region of red shift is reached indicating these inner knots are on the far side of the remnant moving away from us. The distributions of flux as a function of Doppler velocity are shown in Fig. 8. The distibutions for Si-K and S-K are very similar. The Fe-K clearly has a slightly broader distribution for the red shifted (+ve) velocities. The lower panel is the flux plotted in the Si velocity-S velocity plane showing the tight correlation between the Doppler shift measured for these lines. This plot was quite sensitive to small systematic changes in temperature, ionisation age or abundances in the spectral fitting since these can potentially have a profound effect on the derived Doppler velocities as indicated by the large values of $\Delta V_{\rm NEI}$ in Table 1.

Figure 8: Flux distributions of Si-K (red), S-K (green) and Fe-K (blue) as a function of measured Doppler velocity. The lower panel shows the flux distribution in the Si velocity-S velocity plane.

The X-ray knots of Cas A form a ring because the emitting plasma is confined to an irregular shell. We searched for a best fit centre to this ring looking for the position that gave the most strongly peaked radial brightness distribution (minimum rms scatter of flux about the mean radius). The best centre for the combined Si-K, S-K and Fe-K line image was 13 arcsec West and 11 arcsec North of the image centre (the central Chandra point source). Using this centre the peak flux occured at a radius of 102 arcsec, the mean radius was 97 arcsec and the rms scatter about the mean radius was 24 arcsec.

Given such a centre we can assign a radius to each pixel and using the Doppler velocity measured for each pixel we can map the flux into the radius-velocity plane. The result is shown in Fig. 9.