The Mg-$\sigma$ Relation of Elliptical Galaxies at Various Redshifts

The correlation between the Mg absorption index and the velocity dispersion (sigma) of local elliptical galaxies is very tight. Because the Mg absorption depends on both metallicity and age of the underlying stellar population the observed Mg-sigma relation constrains the possible variation in metallicity and age for a given velocity dispersion. For a time interval with no change in metallicity any variation of the Mg index is caused only by the aging of the stars. We have measured the Mg absorption and velocity dispersion of ellipticals in three clusters at a redshift of z=0.37 and established their Mg-sigma relation. For any given sigma, the measured Mg absorption is weaker than the mean value for local ellipticals. Since the evolution of bright cluster ellipticals between z=0.4 and today is most probably only `passive' this reduction in Mg can be attributed solely to the younger age of the stellar population. The small weakening of the Mg absorption of the distant galaxies compared to the local values implies that most of the stars in cluster ellipticals must have formed at high redshifts (z_f > 2...4). The Mg-sigma test is a very robust method to investigate the evolution of elliptical galaxies and has several advantages over traditional methods using luminosities. A remaining problem is the aperture correction necessary to calibrate observations of galaxies at different distances. Here, we show that our general conclusions about the epoch of formation still hold when aperture corrections are calculated assuming a dependence of the radial gradient of sigma on the galaxy's effective radius rather than assuming no dependence as was done in all previous studies