Average energy of the X-ray spectrum as a model-independent proxy for the mass of galaxy clusters

Temperature of the hot gas in galaxy clusters is known to be a reliable proxy for their total gravitating mass, allowing one to use spectroscopic X-ray observations for halo mass function measurements. Data of shallow wide area surveys, however, often precludes direct fitting of the X-ray spectra, given possible biases arising due to unresolved (multi-temperature) inner structure of the intracluster medium (ICM), projection effects and necessity of certain model assumptions to be made to allow for robust spectral fitting. We consider using a simple observable value - the average energy of the observed cluster X-ray spectrum - as a model-independent proxy for the ICM temperature, and consequently cluster's mass. We calibrate relation of this proxy to the cluster parameters using mock observations for a sample of 84 massive galaxy clusters extracted from the \textit{Magneticum} cosmological hydro simulations. We consider observational parameters corresponding to the all-sky survey observations by \textit{SRG/eROSITA}. Taking into account contributions of various background and foreground signals, average energy of the simulated X-ray spectra in the $0.4-7.0$ keV band is shown to be a stable indicator of the ICM temperature with $\sim10\%$ scatter and cluster's mass $M_{500}$ with a $\sim 20\%$ scatter. A database containing simulated X-ray images and their spectra (subtracted in several concentric rings) is publicly available.