The SRG/eROSITA all-sky survey: X-ray scaling relations of galaxy groups and clusters in the western Galactic hemisphere

The soft X-ray telescope on board the SRG mission, eROSITA, has produced the largest sample to date of galaxy groups and clusters detected via their intracluster and intragroup medium emission. Scaling relations between the intrinsic properties of these systems provide valuable insight into their formation and evolution. In this work, we investigated the scaling relations between key physical properties, such as soft band X-ray luminosity, temperature, gas mass, and the low-scatter mass proxy Y X, for the galaxy groups and clusters detected in the first eROSITA All-Sky Survey (eRASS1). Our analysis fully accounts for selection effects and the redshift evolution of the observable distributions. We constructed a high-purity sample of 3061 galaxy groups and clusters spanning the redshift range of 0.05<z<1.07 and the mass range of 1.1 times10 13<M 500/ M <1.6 times10 15. This represents the largest sample to date used in scaling-relation analysis. The selection function, derived from state-of-the-art simulations of the eROSITA sky, is rigorously incorporated into our modeling. We report best-fit parameters -- normalization, slope, redshift evolution, and intrinsic scatter -- for a set of scaling relations: L X-T, L X-M gas, L X-Y X, as well as the M gas-T relation. Our best-fit models indicate that the slopes of the scaling relations significantly deviate from self-similar expectations, while the redshift evolution remains consistent with the self-similar model. The fits exhibit small statistical uncertainties, likely owing to the large sample size. Our results are in good agreement with previous observational studies that account for selection effects. For clusters with kT>3 keV, our inferred L X-T relation is consistent with simulation models that include strong or stronger AGN feedback.