Observed X-ray spectra of hot gas in clusters , groups , and individual galaxies are commonly fit with a single-temperature thermal plasma model even though the beam may contain emission from components with different temperatures .
Recently , Mazzotta et al .
pointed out that thus derived T _ { \text { spec } } can be significantly different from commonly used definitions of average temperature , such as emission- or emission measure-weighted T , and found an analytic expression for predicting T _ { \text { spec } } for a mixture of plasma spectra with relatively hot temperatures ( T \gtrsim 3 keV ) .
In this Paper , we propose an algorithm which can accurately predict T _ { \text { spec } } in a much wider range of temperatures ( T \gtrsim 0.5 keV ) , and for essentially arbitrary abundance of heavy elements .
This algorithm can be applied in the deprojection analysis of objects with the temperature and metallicity gradients , for correction of the 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 .