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 order 0.5 (0.3)/year with 90% confidence statistical uncertainties of 0.24-1.1 (0.14-0.65) and factor of 2 systematic uncertainties. The (peak) luminosity function is roughly dN/dL L^(-1.4+/-0.3), so the rates for events more luminous than V1309 Sco (M_V=-7 mag) or V838Mon (M_V=-10 mag) are lower at r~0.1/year and 0.03/year, respectively. The peak luminosity is a steep function of progenitor mass, L M^(2-3). This very roughly parallels the scaling of luminosity with mass on the main sequence, but the transients are ~2000-4000 times more luminous at peak. Combining these, the mass function of the progenitors, dN/dM 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>16 mag) surveys of the Galactic plane are needed to characterize the low luminosity events. The existing Galactic samples are only ~20% complete and Galactic surveys are (at best) reaching a typical magnitude limit of <13 mag.