On the Lack of Evolution in Galaxy Star Formation Efficiency

Using reconstructed galaxy star formation histories, we calculate the instantaneous efficiency of galaxy star formation (i.e., the star formation rate divided by the baryon accretion rate) from $z=8$ to the present day. This efficiency exhibits a clear peak near a characteristic halo mass of 10^11.7 Msun, which coincides with longstanding theoretical predictions for the mass scale relevant to virial shock heating of accreted gas. Above the characteristic halo mass, the efficiency falls off as the mass to the minus four-thirds power; below the characteristic mass, the efficiency falls off at an average scaling of mass to the two-thirds power. By comparison, the shape and normalization of the efficiency change very little since z=4. We show that a time-independent star formation efficiency simply explains the shape of the cosmic star formation rate since z=4 in terms of dark matter accretion rates. The rise in the cosmic star formation from early times until z=2 is especially sensitive to galaxy formation efficiency. The mass dependence of the efficiency strongly limits where most star formation occurs, with the result that two-thirds of all star formation has occurred inside halos within a factor of three of the characteristic mass, a range that includes the mass of the Milky Way.