On the precision of X-ray source parameters estimated from ROSAT data

Abstract

The precision of the point source parameters, i.e. those for source position, source counts and source extension obtained via Maximum Likelihood Estimation from ROSAT data, is investigated. The various categories of error in X-ray observatories are identified. An analytic perturbation analysis is set forth. This means in the ROSAT case a perturbation analysis of the likelihood function with respect to the perturbed quantity being scrutinized. The background distribution and point spread function of the telescope-detector unit belong to these quantities. ROSAT observations are simulated and subjected to data analysis with the ROSAT software. The parameter space spanned by the point source parameters is explored in this way. Common summarizing statistics, namely mean value and standard error for the empirical distributions of the source parameters obtained in simulation runs, are taken as estimates for the unknown true precision counterparts. The precision for the errors of the source parameters as determined in the ROSAT data analysis are treated in the same way. In this sense, the source count imprecision is below 2 counts (for ROSAT typical sources and background), the directional positional precision below , and the source extent imprecision below for the ROSAT PSPC detector. For the HRI detector, the positional precision figures are better. An alternative approach to the precision issue by cross correlating the ROSAT All-Sky Bright Source Catalogue with the optical TYCHO star catalogue is taken in order to assess the over-all precision. Inference on the positional accuracy for the ROSAT sources along with the quality of the accompanying ROSAT position errors is made. The positional errors determined in this way are about larger than the simulation counterpart. This is in qualitative agreement with the surplus added for the random attitude errors and all other known or less well known error sources. In this sense, the catalogue positional errors are compatible with the positional precision found in the simulations.