Deprojection analysis

Of course, the analysis presented in the previous section has not attempted to correct for projection effects; the observed emission from a particular annulus contains all of the projected foreground and background emission, thereby complicating the interpretation of these results.

Figure 8: Deprojection analysis of the Chandra/ACIS-S data for A4059. Panel (a) shows the results of fitting a single temperature plasma to the spectrum from each shell (filled squares), with the density determined from the emission measure assuming that the plasma uniformly fills the volume of the shell. The crosses show the results from the (projected) annular study of Section 3.4.2, with the density naively determined from the emission measure. In panel (b), an additional plasma component has been included in the deprojected study in those bins for which it makes a significant improvement to the goodness of fit (i.e., the inner two bins). It is assumed that the two components are in pressure equilibrium, have the same metallicity, and jointly fill the volume of the shell.

To address this complication, we have performed a spectral analysis of ``deprojected'' spectra. In detail, we deproject the cluster emission into eight shells assuming spherical symmetry using the projct model within the XSPEC spectral fitting package⁵. Clearly, any simple symmetry assumption will break down in the morphologically complex inner regions of A4059. However, we might hope to perform a deprojection analysis of this cluster beyond $30-40{\rm\thinspace kpc}$, where it is fairly regular.

With this deprojection in hand, we initially model the spectrum of each shell with an absorbed one-temperature mekal model in which the global abundance is a free parameter. The density of the plasma is determined from the plasma emission measure assuming that the plasma uniformly fills the volume of the shell. These results are reported in Fig. 8a; for comparison, we also show the results from fitting model-S to the spectra from the projected annuli (naively computing the density from the observed emission measure of the annulus). It can be seen that the single-temperature deprojection study reproduces the peak in metallicity at 30-40kpc. Within this radius, the spherical assumption clearly breaks downs and hence the deprojection is not to be trusted. Indeed, the leveling off of the ICM density, and the drop in ICM pressure within the centralmost bin is unphysical and almost certainly due to the morphological complexities associated with the radio-galaxy/ICM interaction.

In order to examine the possibility of multiphase gas, we add an additional temperature component to those deprojected spectra for which it is a significant improvement in the goodness of fit (employing the F-est with a 90% level confidence threshold). Only the inner two radial shells required a second temperature component (Fig. 8b). As in the case of the projected study, the central metallicity drop is removed by the addition of a second component.