Approaches to Spectral Fitting

For data sets of high signal-to-noise and low background, where counting statistics are within the Gaussian regime, the data products above are suitable for analysis using the default fitting scheme in XSPEC, $\chi^2$-minimization. However, for low count rates, in the Poisson regime, $\chi^2$-minimization is no longer suitable. With low count rates in individual channels, the error per channel can dominate over the count rate. Since channels are weighted by the inverse-square of the errors during $\chi^2$ model fitting, channels with the lowest count rates are given overly-large weights in the Poisson regime. Spectral continua are consequently often fit incorrectly, with the model lying underneath the true continuum level.

This will be a common problem with most RGS sources. Even if count rates are large, much of the flux from these sources can be contained within emission lines, rather than the continuum. Consequently, even obtaining correct equivalent widths for such sources is non-trivial. There are two approaches to fitting low signal-to-noise RGS data, spectral rebinning and maximum-likelihood statistics. The correct approach would normally be to use an optimization of the two.