The Mg-sigma Relation and the Genesis of Early-Type Galaxies

Available data on the magnesium - velocity dispersion (Mg-sigma) relation for \~2000 early-type galaxies is collected and compared. As noted previously, the Mg residuals from a fitted line are roughly Gaussian near the mean but have an asymmetric blue tail, probably from subpopulations of relatively young stars. We define statistics for scatter and asymmetry of scatter in the Mg dimension and find impressive uniformity among data sets. We construct models of galaxy formation built to be as unbiased as possible toward the question of the importance of mergers in the formation of early type galaxies. The observational constraints (Mg-sigma width, asymmetry, and mean Mg strength, plus mean age and width of abundance distribution) are severe enough to eliminate almost all of models. Among the casualties are: models with merger rates proportional to (1+z)^n with n>0, models that assume early formation followed by recent drizzling of new stars, merger-only models where the number of mergers exceeds ~80, merger-only models with less than ~20 mergers, and models with a cold dark matter power spectrum even with biasing included. The most successful models were those with merger probability constant with time, with the number of mergers needed to form the galaxy around 40. These models are characterized by mean light-weighted ages of 7-10 Gyr (consistent with spectroscopic studies), a narrow abundance distribution, and a lookback time behavior nearly indistinguishable from passive evolution of old stellar populations.