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The fitting process

We have taken into account vignetting corrections as well as the March 1992 version of the PSPC response matrix (see Paper I for further details about using this matrix). Moreover, we have taken into account the systematic errors of the adopted response matrix computed in the Appendix of Paper I by adding them in quadrature to the statistical errors. This procedure is required because of the high number of counts in the PSPC spectral channels. In the fitting process, we let tex2html_wrap_inline750 and tex2html_wrap_inline802 vary, as well as the normalization that provides directly a measure of emission measure and, less directly (see below), an estimate of plasma density. Moreover, we have included as a free parameter the hydrogen column density Ntex2html_wrap_inline930. We have considered the PSPC channels in the range 3-30, since channels 31-34 (corresponding to energies in the range 2.02-2.48 keV) have too few counts for the validity of the tex2html_wrap_inline700 statistics in the fitting (see Figure 3 as an example). With this choice, the number of degrees of freedom is 24.

This parametric fit approach is expected to give reliable results since: (i) the high statistics of our data allows us to determine parameters with quite small uncertainties (see Table 2); (ii) line strengths in the X-ray domain are strongly dependent on the ionization time (Figure 1; see also Brinkmann 1988) and this effect on the spectrum is measurable even with a low energy resolution detector like the ROSAT PSPC (Bocchino 1993). Since the results of the fitting procedure in some cases depend on the initial parameters guess, we have taken care of doing several trials with different starting points for the fitting to avoid convergence to local minima.

In summary, if we adopt the 95% confidence level (i.e. tex2html_wrap_inline934 with 24 degrees of freedom), the model is acceptable in 21 spatial bins, most of which are located around positions g3 and e6 (Region E,F, and G in Paper I), whereas is rejected in the remaining 27 bins, like d3, b5, d5 (Region C, H and A in Paper I). In the tex2html_wrap_inline700 map (Figure 2b), we show only those spatial bins where our STNEI model is acceptable; the remaining bins are not displayed.

In Figure 3, we show spectra and best-fit STNEI models for two sample bins where we found acceptable tex2html_wrap_inline700 values (e6, tex2html_wrap_inline940 counts; c7, tex2html_wrap_inline942 2600 counts) but different parameter values (T=0.15 keV, tex2html_wrap_inline878 in e6 and T=0.21 keV, tex2html_wrap_inline876 in c7). The unfolded model spectra are also shown in the right-hand panels, and indicate the different contribution from the line emission to the total X-ray emissivity in the two cases. In Figure 4, we show an example of spectrum which could not be fitted successfully (d3, 15200 counts): in this bin our model underestimates the observed spectrum in the 0.6-1.0 keV energy range, and this characteristic is common also to other spectra with unacceptable tex2html_wrap_inline700 values.

In Table 2 we summarize the statistical errors associated to T and tex2html_wrap_inline906, computed at the 99% confidence level in the case of two interesting parameters (Lampton, Margon & Bowyer 1976).


next up previous
Next: Results Up: Data Analysis Previous: Spatial grid resampling

Fabrizio Bocchino
Wed Jan 15 13:20:09 MET 1997