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 \sim 0.5 ( 0.3 ) year ^ { -1 } with 90 % confidence statistical uncertainties of 0.24 – 1.1 ( 0.14 – 0.65 ) and factor of \sim 2 systematic uncertainties .
The ( peak ) luminosity function is roughly dN / dL \propto L ^ { -1.4 \pm 0.3 } , so the rates for events more luminous than V1309 Sco ( M _ { V } \simeq - 7 mag ) or V838 Mon ( M _ { V } \simeq - 10 mag ) are lower at r \sim 0.1 /year and \sim 0.03 /year , respectively .
The peak luminosity is a steep function of progenitor mass , L \propto M ^ { 2 - 3 } .
This very roughly parallels the scaling of luminosity with mass on the main sequence , but the transients are \sim 2000 - 4000 times more luminous at peak .
Combining these , the mass function of the progenitors , dN / dM \propto M ^ { -2.0 \pm 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 \mathrel { \raise 1.29 pt \hbox { $ > $ } \mkern - 14.0 mu \lower 2.58 pt \hbox { $ \sim$ } } 16 mag ) surveys of the Galactic plane are needed to characterize the low luminosity events .
The existing Galactic samples are only \sim 20 \% complete and Galactic surveys are ( at best ! )
reaching a typical magnitude limit of \mathrel { \raise 1.29 pt \hbox { $ < $ } \mkern - 14.0 mu \lower 2.58 pt \hbox { $ \sim$ } } 13 mag .