, <Fe> and H
, and the mass-to-light ratios (M/L). Single stellar population models from Vazdekis et al. were used to transform from the measured line indices and M/L ratios to mean ages and mean metal abundances ([Mg/H] and [Fe/H]). The non-solar abundance ratios [Mg/Fe] were taken into account by assuming that for a given age and iron abundance, a [Mg/Fe] different from solar will affect the Mg index but not the M/L ratio or the indices. The derived ages and abundances are the luminosity weighted mean values for the stellar populations in the galaxies.
By comparing the mean ages derived from the Mg-H diagram to those derived from the Mg-M/L diagram, we estimate the variations of the fraction of dark matter. Alternatively, the difference between the two estimates of the mean age may be due to variations in the initial mass function or to any non-homology of the galaxies.
The distributions of the derived mean ages and abundances show that there are real variations in both the mean ages and in the abundances. We find an intrinsic rms scatter of [Mg/H], [Fe/H] and [Mg/Fe] of 0.2 dex, and an intrinsic rms scatter of the derived ages of 0.17 dex. The magnesium abundances [Mg/H] and the abundance ratios [Mg/Fe] are both strongly correlated with the central velocity dispersions of the galaxies, while the iron abundances [Fe/H] are uncorrelated with the velocity dispersions. Further, [Mg/H] and [Fe/H] are strongly anti-correlated with the mean ages of the galaxies. This is not the case for [Mg/Fe].
We have tested whether the slopes of the scaling relations between the global parameters for the galaxies (the Mg-
relation, the <Fe>- relation, the H- relation and the Fundamental Plane) are consistent with the relation between the ages, the abundances and the velocity dispersions. We find that all the slopes, except the slope of the Fundamental Plane, can be explained in a consistent way as due to a combination between variations of the mean ages and the mean abundances as functions of the velocity dispersions. The slope of the Fundamental Plane is "steeper" than predicted from the variations in the ages and abundances.
Because of the correlation between the mean ages and the mean abundances, substantial variations in the ages and the abundances are possible while maintaining a low scatter of all the scaling relations. When this correlation is taken into account. the observed scatter of the scaling relations is consistent with the rms scatter in derived the ages and abundances at a given velocity dispersion.
Accepted for publication in Monthly Notices of the Royal Astronomical Society (MNRAS)
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Ruth A. Kneale / web@gemini.edu / February 19, 1999