The Sloan Lens ACS Survey. X. Stellar, Dynamical, and Total Mass Correlations of Massive Early-type Galaxies

We use stellar masses, surface photometry, strong-lensing masses, and stellar velocity dispersions (σ _e/2) to investigate empirical correlations for the definitive sample of 73 early-type galaxies (ETGs) that are strong gravitational lenses from the SLACS survey. The traditional correlations (fundamental plane (FP) and its projections) are consistent with those found for non-lens galaxies, supporting the thesis that SLACS lens galaxies are representative of massive ETGs (dimensional mass M _dim = 10¹¹-10¹² M _sun). The addition of high-precision strong-lensing estimates of the total mass allows us to gain further insights into their internal structure: (1) the average slope of the total mass-density profile ( ρ_tot∝ r^{-γ'}) is langγ'rang = 2.078 ± 0.027 with an intrinsic scatter of 0.16 ± 0.02; (2) γ' correlates with effective radius (r_e ) and central mass density, in the sense that denser galaxies have steeper profiles; (3) the dark matter (DM) fraction within r_e /2 is a monotonically increasing function of galaxy mass and size (due to a mass-dependent central cold DM distribution or due to baryonic DM—stellar remnants or low-mass stars—if the initial mass function is non-universal and its normalization increases with mass); (4) the dimensional mass M _dim ≡ 5r_e σ² _e/2/G is proportional to the total (lensing) mass M _{r_{e}/2}, and both increase more rapidly than stellar mass M _* (M _* ∝ {M}_{r_{e}/2}^{0.8}); (5) the mass plane (MP), obtained by replacing surface brightness with surface mass density in the FP, is found to be tighter and closer to the virial relation than the FP and the M_*P, indicating that the scatter of those relations is dominated by stellar population effects; (6) we construct the fundamental hyper-plane by adding stellar masses to the MP and find the M _* coefficient to be consistent with zero and no residual intrinsic scatter. Our results demonstrate that the dynamical structure of ETGs is not scale invariant and that it is fully specified by M _{r_{e}/2}, r_e , and σ _e/2. Although the basic trends can be explained qualitatively in terms of varying star formation efficiency as a function of halo mass and as the result of dry and wet mergers, reproducing quantitatively the observed correlations and their tightness may be a significant challenge for galaxy formation models.