  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.
