First tidal disruption events discovered by SRG/eROSITA: X-ray/optical properties and X-ray luminosity function at z<0.6

We present the first sample of tidal disruption events (TDEs) discovered during the SRG all-sky survey. These 13 events were selected among X-ray transients detected in the 0<l<180 deg hemisphere by eROSITA during its second sky survey (10 June - 14 December 2020) and confirmed by optical follow-up observations. The most distant event occurred at z=0.581. One TDE continued to brighten at least 6 months. The X-ray spectra are consistent with nearly critical accretion onto black holes of a few 10^3 to 10^8 M_Sun, although supercritical accretion is possibly taking place. In two TDEs, a spectral hardening is observed 6 months after the discovery. Four TDEs showed an optical brightening apart from the X-ray outburst. The other 9 TDEs demonstrate no optical activity. All 13 TDEs are optically faint, with Lopt/Lx<0.3 (Lopt and Lx being the g-band and 0.2-6 keV luminosity, respectively). We have constructed a TDE X-ray luminosity function, which can be fit by a power law with a slope of -0.6+/-0.2, similar to the trend observed for optically selected TDEs. The total rate is estimated at (1.1+/-0.5)10^-5 TDEs per galaxy per year, an order of magnitude lower than inferred from optical studies. This suggests that X-ray bright events constitute a minority of TDEs, consistent with models predicting that X-rays can only be observed from directions close to the axis of a thick accretion disk formed from the stellar debris. Our TDE detection threshold can be lowered by a factor of ~2, which should allow a detection of ~700 TDEs by the end of the SRG survey.