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

Abstract

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 = 10 11 − 10 12 M ⊙ ). The addition of high-precision strong lensing estimates of the total mass allows us to gain further insights into their internal structure: i) the average slope of the total mass density profile (ρ tot ∝ r −γ ′ ) is γ ′ = 2.078 ± 0.027 with an intrinsic scatter of 0.16 ± 0.02; ii) γ ′ correlates with effective radius (r e ) and central mass density, in the sense that denser galaxies have steeper profiles; iii) the dark matter fraction within r e /2 is a monotonically increasing function of galaxy mass and size (due to a mass-dependent central cold dark matter distribution or to baryonic dark matter -stellar remnants or low mass stars -if the IMF is non-universal and its normalization increases with mass); iv) the dimensional mass M dim ≡ 5r e σ 2 e/2 /G is proportional to the total (lensing) mass M re/2 , and both increase more rapidly than stellar mass M * (M * ∝ M 0.8 re/2 ); v) 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 populations effects; vi) 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 re/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.

Planck’s dusty GEMS

“…Such low-mass stars are difficult to observe directly. However, the best estimates currently available, including those based on direct spectral tracers of lowmass stars, favor bottom-heavy IMFs consistent with Salpeter or even steeper slopes (Auger et al 2010;Conroy et al 2013;Sonnenfeld et al 2017;, which are also consistent with our results. These IMFs should scale with galaxy mass, but not with redshift (Sonnenfeld et al 2017); this is consistent with mainly passively evolving stellar populations since redshifts z = 1-2.…”

“…The mass profiles of massive galaxies at low redshift suggest that dark matter contributes at most 10 % to the total mass out to 6-7 kpc (Auger et al 2010;Conroy et al 2013) and probably less in our source at z = 1.5, owing to gradual dark-matter assembly (Macciò et al 2008). The non-detection of the dust continuum with ALMA (C17) also rules out masses of cold molecular and atomic gas above on the order of 10 9 M (1 % of M lens ), for a simple scaling with the range of gas-to-dust ratios between 40 and 100, as measured by C15.…”

Cosmological constraints from the double source plane lens SDSSJ0946+1006

“…The latter point is not a significant concern here, since the highest redshift source has an impact parameter with respect to the z = 0.609 source that is more than three times larger than the Einstein radius θ E s1 . Similarly, the power-law description for the central total mass density distribution is motivated by the absence of any correlation between the power-law indices and radii of strong lenses (e.g., Koopmans et al 2006Koopmans et al , 2009Auger et al 2010), as well as the power-law behaviour of the total mass distribution over a large range of scales from the ensemble weak lensing mass profile of lenses (Gavazzi et al 2007) and mass profiles of massive X-ray-bright galaxies (Humphrey & Buote 2010). Furthermore, Suyu et al (2013) have explicitly modelled one time delay gravitational lens, RX J1131-1231, with both a power-law and a stars-plus-dark matter model and find no significant difference in the cosmographic inference between the two models when stellar kinematics are included in the modelling; a similar analysis for J0946 is under way.…”

Stellar masses calibrated with micro-lensed quasars

“…• For a galaxy with a proxy velocity dispersion of 266 km/s and an effective radius of 6.17 kpc, average for the Auger et al (2010) sample, the calibrated fractional stellar surface mass density peaks at a value of 1.10 at 0.074r e , as shown in Figure 3. At 1.5r e , the typical Einstein radius for our lens systems, the stellar mass fraction is 0.25.…”