Dissecting the Red sequence. III. Mass-to-Light Variations in Three-dimensional Fundamental Plane Space

The fundamental plane (FP) of early-type galaxies is observed to have finite thickness and to be tilted from the virial relation. Both of these represent departures from the simple assumption that dynamical mass-to-light ratios (M{sub dyn}/L) are constant for all early-type galaxies. We use a sample of 16,000 quiescent galaxies from the Sloan Digital Sky Survey to map out the variations in M {sub dyn}/L throughout the three-dimensional FP space defined by velocity dispersion ({sigma}), effective radius (R{sub e}), and effective surface brightness (I{sub e}). Dividing M{sub dyn}/L into multiple components allows us to separately consider the contribution to the observed M{sub dyn}/L variation due to stellar population effects, initial mass function (IMF) variations, and variations in the dark matter fraction within one R{sub e} . Along the FP, we find that the stellar population contribution given some constant IMF (M{sub *,IMF}/L) scales with {sigma} such that M{sub *,IMF}/L {proportional_to} f({sigma}). Meanwhile, the dark matter and/or IMF contribution (M{sub dyn}/M {sub *,IMF}) scales with M{sub dyn} such that M{sub dyn}/M {sub *,IMF} {proportional_to} g(M{sub dyn}). This means that the two contributions to the tilt of the FP rotate the plane around different axes in the three-dimensional space. The observed tilt of the FP requires contributions from both, with dark matter/IMF variations likely comprising the dominant contribution. Looking at M {sub dyn}/L variations through the thickness of the FP, we find that M{sub dyn}/L variations must be dominated either by IMF variations or by real differences in the dark matter fraction with R{sub e} . This means that the finite thickness of the FP is due to variations in the stellar mass surface density within R{sub e} ({Sigma}{sub *,IMF}), not the fading of passive stellar populations. It therefore represents genuine structural differences between early-type galaxies. These structural variations are correlated with galaxy star formation histories such that galaxies with higher M{sub dyn}/M {sub *,IMF} have higher [Mg/Fe], lower metallicities, and older mean stellar ages. We discuss several physical mechanisms that might explain the observed co-variation between M {sub dyn}/M {sub *,IMF} and galaxy star formation histories. It is difficult to explain the observed enhancement of {alpha}-elements in lower-surface-brightness galaxies by allowing the IMF to vary. Differences in dark matter fraction can be produced