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 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 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 the temperature estimate being less than 2%-4% when the plasma temperature exceeds similar to 2 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 fitting. Conventional spectral analysis in the case of moderate and low numbers of counts is discussed. A practical recipe for unbiased parameter estimation is suggested and verified in Monte Carlo simulations for commonly used spectral models. A simple modification of the chi(2) statistic (calculation of weights based 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 statistics (similar to 50-100 counts in the observed spectrum with several hundred channels).