Until recently, X-ray spectra of cosmic X-ray sources were obtained using instruments like proportional counters and GSPC’s with moderate spectral resolution (typically 5–20 %). With the introduction of CCD detectors a major leap in resolution has been achieved (up to 2 %).
These X-ray spectra are usually analysed by a forward folding technique. First a spectral model appropriate for the observed source is chosen. This model spectrum is then convolved with the instrument response, represented usually by a response matrix. The convolved spectrum is compared to the observed spectrum, and the parameters of the model are varied in a fitting procedure in order to get the best solution.
This ”classical” way of analysing X-ray spectra has been widely adopted and is implemented e.g. in spectral fittting packages such as XSPEC (Arnaud, 1996) and SPEX (Kaastra et al., 1996).
When high resolution data are available (like in optical spectra), the instrumental broadening is often small compared to the intrinsic line widths. Instead of forward folding and fitting, at each energy the observed spectrum is divided by the nominal effective area (straightforward deconvolution).
Although straightforward deconvolution, due to its simplicity, seems to be attractive for high resolution X-ray spectroscopy, it might fail in several situations. For example, the grating spectrometers of EUVE have a high spectral resolution, but it is not possible to separate the spectral orders at the longer wavelengths. Therefore only careful instrumental calibration and proper modelling of the short wavelength spectrum can help. A similar situation holds for the low energy gratings of AXAF. For the RGS detector on board of XMM, 30 % of all line flux is contained in broad scattering wings due to the mirror and grating.
However, the application of ”standard” concepts, like a response matrix, is not at all trivial for these high resolution instruments. For example, with the RGS of XMM, the properly binned response matrix has a size of 120 Megabytes, counting only non-zero elements. This cannot be handled by most present day computer systems, if analysis packages like XSPEC or SPEX are applied to these data sets. Also, the larger spectral resolution enhances considerably the computation time needed to evaluate the spectral models. Since the models applied to AXAF and XMM data will be much more complex than those applied to data from previous missions, computational efficieny is important to take into acount.
For these reasons we critically re-evaluate the concept of response matrices and the way spectra are analysed. In fact, we conclude that it is necessary to drop the classical concept of a matrix, and to use instead a modified approach. First we evaluate the required binning for both the model and the data grid. We also show how to properly handle different features like redshift components, velocity broadening, absorption edges, etc. The proper treatment of these effects is critically intermixed with the overall accuracy of the spectral model.