Stellar mergers are common

The observed Galactic rate of stellar mergers or the initiation of common envelope phases brighter than M-V=-3 (M-I=-4) is of the order of similar to 0.5 (0.3) yr(-1) with 90 per cent confidence statistical uncertainties of 0.24-1.1 (0.14-0.65) and factor of similar to 2 systematic uncertainties. The (peak) luminosity function is roughly dN/dL proportional to L-1.4 +/- 0.3, so the rates for events more luminous than V1309 Sco (M-V similar or equal to -7 mag) or V838 Mon (M-V similar or equal to -10 mag) are lower at r similar to 0.1 and similar to 0.03/year, respectively. The peak luminosity is a steep function of progenitor mass, L proportional to M-2 (-) (3). This very roughly parallels the scaling of luminosity with mass on the main sequence, but the transients are similar to 2000-4000 times more luminous at peak. Combining these, the mass function of the progenitors, dN/dM proportional to M-2.0 + 0.8, is consistent with the initial mass function, albeit with broad uncertainties. These observational results are also broadly consistent with the estimates of binary population synthesis models. While extragalactic variability surveys can better define the rates and properties of the high-luminosity events, systematic, moderate depth (I greater than or similar to 16 mag) surveys of the Galactic plane are needed to characterize the low-luminosity events. The existing Galactic samples are only similar to 20 per cent complete, and Galactic surveys are (at best!) reaching a typical magnitude limit of less than or similar to 13 mag.