We use high signal-to-noise spectroscopy for a sample of 232 quiescent galaxies in the Shapley Supercluster , to investigate how their stellar populations depend on velocity dispersion ( \sigma ) , luminosity and stellar mass .
The sample spans a large range in velocity dispersion ( 30–300 { km s ^ { -1 } } ) and in luminosity ( M _ { R } from –18.7 to –23.2 ) .
Estimates of age , total metallicity ( Z/H ) and \alpha -element abundance ratio ( \alpha /Fe ) were derived from absorption-line analysis , using single-burst models of Thomas and collaborators .
Using the Rose Ca ii index , we conclude that recent star-formation ( “ frosting ” ) events are not responsible for the intermediate ages observed in some of the galaxies .
Age , Z/H and \alpha /Fe are correlated positively with velocity dispersion , but we also find significant residual trends with luminosity : at given \sigma , the brighter galaxies are younger , less \alpha -enriched , and have higher Z/H .
At face value , these results might suggest that the stellar populations depend on stellar mass as well as on velocity dispersion .
However , we show that the observed trends can be reproduced by models in which the stellar populations depend systematically only on \sigma , and are independent of stellar mass M _ { * } .
For age , the observed luminosity correlation arises because young galaxies are brighter , at fixed M _ { * } .
For metallicity , the observed luminosity dependence arises because metal-rich galaxies , at fixed mass , tend also to be younger , and hence brighter .
We find a good match to the observed luminosity correlations with Age \propto \sigma ^ { +0.40 } , Z/H \propto \sigma ^ { +0.35 } , \alpha / { Fe } \propto \sigma ^ { +0.20 } , where the slopes are close to those found when fitting traditional scaling relations .
We conclude that the star formation and enrichment histories of galaxies are determined primarily by the depth of their gravitational potential wells .
The observed residual correlations with luminosity do not imply a corresponding dependence on stellar mass .