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 T_spec for a mixture of plasma spectra with relatively hot temperatures (T ≳ 3 keV). In this paper, we propose an algorithm that can accurately predict T_spec in a much wider range of temperatures (T ≳ 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.