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

<jats:title>ABSTRACT</jats:title> <jats:p>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° &lt; l &lt; 180° hemisphere by eROSITA during its second sky survey (2020 June 10 to December 14) 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 on to black holes of a few ×103 to $10^8\, \mathrm{ M}_\odot$, 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 nine TDEs demonstrate no optical activity. All 13 TDEs are optically faint, with Lg/LX &lt; 0.3 (Lg 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 disc 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.</jats:p>