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Available data on the magnesium - velocity dispersion (Mg-sigma) relation for\~2000 early-type galaxies is collected and compared. As noted previously, theMg residuals from a fitted line are roughly Gaussian near the mean but have anasymmetric blue tail, probably from subpopulations of relatively young stars.We define statistics for scatter and asymmetry of scatter in the Mg dimensionand find impressive uniformity among data sets. We construct models of galaxyformation built to be as unbiased as possible toward the question of theimportance of mergers in the formation of early type galaxies. Theobservational constraints (Mg-sigma width, asymmetry, and mean Mg strength,plus mean age and width of abundance distribution) are severe enough toeliminate almost all of models. Among the casualties are: models with mergerrates proportional to (1+z)^n with n>0, models that assume early formationfollowed by recent drizzling of new stars, merger-only models where the numberof mergers exceeds ~80, merger-only models with less than ~20 mergers, andmodels with a cold dark matter power spectrum even with biasing included. Themost successful models were those with merger probability constant with time,with the number of mergers needed to form the galaxy around 40. These modelsare characterized by mean light-weighted ages of 7-10 Gyr (consistent withspectroscopic studies), a narrow abundance distribution, and a lookback timebehavior nearly indistinguishable from passive evolution of old stellarpopulations.Comment: 37 pages with 17 figures, AASTe

The Magnesium–Velocity Dispersion Relation and the Genesis of Early‐Type Galaxies