MAPPING THE GAS TEMPERATURE DISTRIBUTION IN EXTENDED X-RAY SOURCES AND SPECTRAL-ANALYSIS IN THE CASE OF LOW STATISTICS - APPLICATION TO ASCA OBSERVATIONS OF CLUSTERS OF GALAXIES

A simple method for mapping the temperature distribution in extended s ources is developed for application to ASCA observations of galaxy clu sters. 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 fine 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 th e temperature estimate being less than 2%-4% when the plasma temperatu re exceeds similar to 2 keV. This method is not intended to replace co nventional spectral analysis but to supplement it, providing relativel y fast and easy construction of temperature maps, which may be used as a guide to further detailed analysis of particularly interesting regi ons using conventional spectral fitting. Conventional spectral analysi s in the case of moderate and low numbers of counts is discussed. A pr actical recipe for unbiased parameter estimation is suggested and veri fied in Monte Carlo simulations for commonly used spectral models. A s imple modification of the chi(2) statistic (calculation of weights bas ed on the smoothed observed spectrum) yields nearly unbiased parameter estimates and correct confidence interval determination with no need for regrouping (binning) the energy channels even in the case of low s tatistics (similar to 50-100 counts in the observed spectrum with seve ral hundred channels).