Predicting a single-temperature fit to multicomponent thermal plasma spectra

Observed X-ray spectra of hot gas in clusters, groups, and individual galaxies are commonly fit with a single-temperature thermal plasma model, although the beam may contain emission from components with different temperatures. Recently, Mazzotta et al. pointed out that thus derived T-spec can be significantly different from commonly used definitions of average temperature, such as emission-weighted or emission measure -weighted T, and found an analytic expression for predicting Tspec for a mixture of plasma spectra with relatively hot temperatures (T greater than or similar to 3 keV). In this paper, we propose an algorithm that can accurately predict T-spec in a much wider range of temperatures (T greater than or similar to 0.5 keV) and for essentially arbitrary abundances of heavy elements. This algorithm can be applied in the deprojection analysis of objects with the temperature and metallicity gradients, for correction of the point-spread function (PSF) effects, for consistent comparison of numerical simulations of galaxy clusters and groups with the X-ray observations, and for estimating how emission from undetected components can bias the global X-ray spectral analysis.