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(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(dyn)/L throughout the three-dimensional FP space defined by velocity dispersion (sigma), effective radius (R(e)), and effective surface brightness (I(e)). Dividing M(dyn)/L into multiple components allows us to separately consider the contribution to the observed Mdyn/L variation due to stellar population effects, initial mass function (IMF) variations, and variations in the dark matter fraction within one Re. Along the FP, we find that the stellar population contribution given some constant IMF (M(*),(IMF)/L) scales with sigma such that M(*),(IMF)/L alpha f(sigma). Meanwhile, the dark matter and/or IMF contribution (M(dyn)/M(*),(IMF)) scales with M(dyn) such that M(dyn)/M(*),(IMF) alpha g(M(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(dyn)/L variations through the thickness of the FP, we find that M(dyn)/L variations must be dominated either by IMF variations or by real differences in the dark matter fraction with R(e). This means that the finite thickness of the FP is due to variations in the stellar mass surface density within R(e) (Sigma(*),(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(dyn)/M(*),(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(dyn)/M(*),(IMF) and galaxy star formation histories. It is difficult to explain the observed enhancement of a-elements in lower-surface-brightness galaxies by allowing the IMF to vary. Differences in dark matter fraction can be produced by variations in the conversion efficiency of baryons into stars or by the redistribution of stars and darkmatter through dissipational merging. The former explanation, specifically amodel in which some galaxies experience low conversion efficiencies due to premature truncation of star formation, provides a more natural explanation for the co-variation of M(dyn)/M(*),(IMF) and the observed stellar population properties.