Mapping the Gas Temperature Distribution in Extended X‐Ray Sources and Spectral Analysis in the Case of Low Statistics: Application toASCAObservations of Clusters of Galaxies

A simple method for mapping the temperature distribution in extended sources is developed for application to ASCA observations of galaxy clusters. Unlike the conventional approach to spatially resolved spectral analysis, this method does not require nonlinear minimization and is computationally fast and stable. Therefore, it can be implemented for a large number of regions or on a ne spatial grid. Although based on a Taylor expansion over the nonlinear parameter, the method is found to be accurate in many practical situations, the relative error for the temperature estimate being less than 2%4% when the plasma temperature exceeds D2 keV. This method is not intended to replace conventional spectral analysis but to supplement it, providing relatively fast and easy construction of temperature maps, which may be used as a guide to further detailed analysis of particularly interesting regions using conventional spectral tting.