Dissecting the Red Sequence--I. Star Formation Histories of Quiescent Galaxies: The Color-Magnitude vs. the Color-Sigma Relation

We use a sample of ~16,000 non-emission line galaxies from the SDSS to investigate the physical parameters underlying the well-known color-magnitude and color-sigma relations. Galaxies are sorted in terms of velocity dispersions (sigma), luminosity (L), and color, and their spectra are stacked to obtain very high S/N mean spectra for stellar population analysis. This allows us to map mean luminosity-weighted ages, [Fe/H], [Mg/H], and [Mg/Fe] in sigma-L-color space. Our first result is that there are many different red sequences, with age, [Fe/H], [Mg/H], and [Mg/Fe] showing different amounts of slope and scatter when plotted versus sigma, L, or color. These behaviors are explained if the star formation histories of the galaxies populate a two-dimensional parameter space. One parameter is the previously well-known increase in age, [Fe/H], [Mg/H], and [Mg/Fe] with sigma. In addition to this, we find systematic variations at fixed sigma, such that more luminous galaxies are younger, more Fe-rich, but have lower [Mg/Fe] than their fainter counterparts. The main sigma trends support a paradigm in which more massive galaxies form their stars more rapidly and at earlier times than less massive galaxies. The trends at fixed sigma are consistent with scatter in the duration of star formation for galaxies at a given sigma. The co-variation of stellar population properties and L residuals at fixed sigma that we present here has a number of implications: it explains the differing behavior of stellar population indicators when investigated versus sigma as compared to L, and it reveals that L is not as efficient as sigma for indicating galaxy "size" in stellar population studies.