The stellar initial mass function of early-type galaxies from low to high stellar velocity dispersion: homogeneous analysis of atlas3D and Sloan Lens ACS galaxies

Abstract

We present an investigation about the shape of the initial mass function (IMF) of early-type galaxies (ETGs), based on a joint lensing and dynamical analysis, and on stellar population synthesis models, for a sample of 55 lens ETGs identified by the Sloan Lens ACS (SLACS) Survey. We construct axisymmetric dynamical models based on the Jeans equations which allow for orbital anisotropy and include a dark matter halo. The models reproduce in detail the observed HST photometry and are constrained by the total projected mass within the Einstein radius and the stellar velocity dispersion (σ) within the SDSS fibers. Comparing the dynamically-derived stellar mass-to-light ratios (M * /L) dyn , obtained for an assumed halo slope ρ h ∝ r −1 , to the stellar population ones (M * /L) Salp , derived from full-spectrum fitting and assuming a Salpeter IMF, we infer the mass normalization of the IMF. Our results confirm the previous analysis by the SLACS team that the mass normalization of the IMF of high σ galaxies is consistent on average with a Salpeter slope. Our study allows for a fully consistent study of the trend between IMF and σ for both the SLACS and ATLAS 3D samples, which explore quite different σ ranges. The two samples are highly complementary, the first being essentially σ selected, and the latter volume-limited and nearly mass selected. We find that the two samples merge smoothly into a single trend of the form log α = (0.38 ± 0.04) × log(σ e /200 km s −1 ) + (−0.06 ± 0.01), where α = (M * /L) dyn /(M * /L) Salp and σ e is the luminosity averaged σ within one effective radius R e . This is consistent with a systematic variation of the IMF normalization from Kroupa to Salpeter in the interval σ e ≈ 90 − 270 km s −1 .

Implications of Galaxy Buildup for Putative IMF Variations in Massive Galaxies

“…This is consistent with observational studies that also show substantial scatter in the reported IMF-σ relations (Cappellari et al 2012;Conroy & van Dokkum 2012b;Posacki et al 2015). For example, based on dynamical modeling of ETGs in the ATLAS 3D project, Cappellari et al (2013) report a 1σ scatter of »0.12 dex (or 32%) in their derived relation between IMF mismatch parameter and velocity dispersion.…”

“…Surprisingly, observations over the past few years of more distant stellar populations suggest deviations from the universal IMF inferred in the Local Group. Several independent methods have been implemented to study the IMF in unresolved stellar populations, including (1) dynamical studies where stellar population synthesis (SPS) mass-to-light ratios are compared to dynamically derived mass-to-light ratios (e.g., Dutton et al 2011;Cappellari et al 2012Cappellari et al , 2013Conroy & van Dokkum 2012b;Conroy et al 2013;Martín-Navarro et al 2015c), (2) absorption-line studies where spectral features either sensitive or anti-sensitive to dwarf stars provide the constraints (e.g., Cenarro et al 2003;Ferreras et al 2013;La Barbera et al 2013;Spiniello et al 2014;McConnell et al 2016), and (3) lensing studies where SPS masses are compared to masses derived from gravitational lensing (e.g., Ferreras et al 2008Ferreras et al , 2010Auger et al 2010;Treu et al 2010;Thomas et al 2011;Posacki et al 2015;Leier et al 2016).…”

The Initial Mass Function in the Nearest Strong Lenses from SNELLS: Assessing the Consistency of Lensing, Dynamical, and Spectroscopic Constraints

“…) samples define very consistent σ−M/L relations, and the SNELLS lenses lie below both (Figure 2, and see Posacki et al 2015). The lensing properties of the SNELLS galaxies are also not unusual: 0.97 e 2 SIE s s á ñ = , consistent with the SLACS lenses.…”

“…These include the use of new isochrones from the MIST project (Choi et al 2016), a new spectral library based on observations from IRTF , and new age-and metallicity-dependent response The SNELLS results are shown with dark matter contributions from the EAGLE simulations ("L+EAGLE") or from joint lensing and dynamical modeling ("L+D"). For the SLACS points, we use M * /L r from Posacki et al (2015) and approximate the luminosity evolution to z=0 using the V-band evolution from Auger et al Bottom panel: the IMF mass factor α (Equation (1)) is compared among the same samples. The SLACS results, and the linear relation from the combined ATLAS 8 functions.…”

“…The halo is parameterized with a generalized NFW (i.e., a gNFW) dark matter halo (see Equation(2) of Newman et al 2013a). The scale radius is fixed to r s =30 kpc, following Treu et al (2010) and Posacki et al (2015). Our constraints are located well within r s , so the density profile is effectively a power law ρ DM ∝r − α .…”