Predicting Single - Temperature Fit to Multi - Component 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 even though 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-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 which can accurately predict T spec in a much wider range of temperatures (T 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. 1. INTRODUCTION Temperature of the hot gas filling the volume of galaxy clusters and groups is the primary diagnostic of properties and physical processes in these objects. An incomplete list of applications includes the study of radiative cooling and feedback mechanisms in the cluster centers; distribution of heavy elements in the intracluster (ICM) and interstellar (ISM) media; estimation of the cluster mass either through the virial M − T relation or application of the hydrostatic equilibrium equation ICM temperature is usually measured by fitting its observed X-ray spectrum. Generally, the spectrum is integrated within a beam which contains several components with different T and metallicity. Current detectors, such as CCDs onboard Chandra and XMM-Newton, cannot spectrally separate emission from different components. Also, statistical quality in the vast majority of cases is insufficient to detect the presence of several emission components in the total spectrum. Therefore, single-temperature models are commonly fit to the integrated spectrum with the hope that the derived T is a representative average of the temperatures within the beam. Recently, Mazzotta et al. (2004) pointed out that the temperature derived from the X-ray spectral analysis, T spec , is significantly different from commonly used averages, such as the emission measure-weighted T EM (volume-averaged with weight w = ρ 2), or emission-weighted T E (w = ρ 2 Λ(T), where Λ(T) is the plasma emissivity per unit emission measure). The " …