X-ray surface brightness and gas density profiles of galaxy clusters up to 3*R500c with SRG/eROSITA

Using the data of the SRG/eROSITA all-sky survey, we stacked a sample of ~40 galaxy cluster images in the 0.3--2.3 keV band, covering the radial range up to $10\times R_{\rm 500c}$. The excess emission on top of the galactic and extragalactic X-ray backgrounds and foregrounds is detected up to $\sim 3\times R_{\rm 500c}$. At these distances, the surface brightness of the stacked image drops below $\sim 1$% of the background. The density profile reconstructed from the X-ray surface brightness profile agrees well (within $\sim30$%) with the mean gas profile found in numerical simulations, which predict the local gas overdensity of $\sim$ 20--30 at $3\times R_{\rm 500c}$ and the gas fraction close to the universal value of $\frac{\Omega_b}{\Omega_m}\approx 0.15$ in the standard $\Lambda$CDM model. Taking at face value, this agreement suggests that up to $\sim 3\times R_{\rm 500c}$ the X-ray signal is not strongly boosted by the gas clumpiness, although a scenario with a moderately inhomogeneous gas cannot be excluded. A comparison of the derived gas density profile with the electron pressure profile based on the SZ measurements suggests that by $r\sim 3\times R_{\rm 500c}$ the gas temperature drops by a factor of $\sim$ 4--5 below the characteristic temperature of a typical cluster in the sample within $R_{\rm 500c}$, while the entropy keeps growing up to this distance. Better constraints on the gas properties just beyond $3\times R_{\rm 500c}$ should be possible with a sample larger than used for this pilot study.