Effects of Multiphase Gas and Projection on X-ray Observables in Simulated Galaxy Clusters as Seen by eROSITA

The number density of galaxy clusters as a function of mass and redshift is a sensitive function of the cosmological parameters. To use clusters for cosmological parameter studies, it is necessary to determine their masses as accurately as possible, which is typically done via mass-observable scaling relations. X-ray observables can be biased by multiphase gas and projection effects, especially in the case where cluster temperatures and luminosities are estimated from single-model fits to all of the emission with a given radius. Using simulated galaxy clusters from a realistic cosmological simulation, we seek to determine the importance of these biases in the context of Spectrum-Roentgen-Gamma/eROSITA observations of clusters. We extract clusters from the Magneticum suite, and simulate eROSITA observations of these clusters using PHOX and SIXTE. We compare the fitted observables from these observations to those derived from the simulations. We fitted an intrinsically scattered $L_{\rm X}-T$ scaling relation to these measurements following a Bayesian approach with which we fully took into account the selection effects and the mass function. The largest biases on the cluster observables come from the inadequacy of single-temperature model fits to represent emission from multiphase gas, as well as a bias arising from cluster emission within the projected $r_{500c}$ along the line of sight but outside of the spherical $r_{500c}$. We find that the biases on temperature and luminosity due to the projection of emission from other clusters within $r_{500c}$ is small. We find that our simulated clusters follow a $L_{\rm X}-T$ scaling relation that has a broadly consistent but slightly shallower slope compared to the literature, and that the intrinsic scatter of $L_{\rm X}$ at given T is lower compared to the recent observational results where the selection effects are fully considered.