The stellar initial mass function of early type galaxies from low to high stellar velocity dispersion: homogeneous analysis of ATLAS$^{\rm 3D}$ and Sloan Lens ACS galaxies

TL;DR

This study investigates how the initial mass function (IMF) varies with stellar velocity dispersion in early-type galaxies, using lensing, dynamical modeling, and stellar population synthesis to reveal a systematic trend from Kroupa to Salpeter IMFs.

Contribution

It provides a homogeneous analysis combining lensing and dynamical models with stellar populations to characterize IMF variations across different galaxy samples and velocity dispersions.

Findings

IMF normalization correlates with stellar velocity dispersion.

High $\sigma$ galaxies have IMFs consistent with Salpeter.

A smooth trend of IMF variation from Kroupa to Salpeter is observed.

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 \textit{HST} photometry and are constrained by the total projected mass within the Einstein radius and the stellar velocity dispersion ($\sigma$) within the SDSS fibers. Comparing the dynamically-derived stellar mass-to-light ratios $(M_*/L)_{\rm dyn}$, obtained for an assumed halo slope $\rho_{\rm h}\propto r^{-1}$, to the stellar population ones $(M_*/L)_{\rm pop}$, 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 $\sigma$ galaxies is consistent on average with a Salpeter slope. Our study allows for a fully consistent study of the trend between IMF and $\sigma$ for both the SLACS and \ATLAS samples, which explore quite different $\sigma$ ranges. The two samples are highly complementary, the first being essentially $\sigma$ 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 $\log\alpha =(0.38\pm0.04)\times\log(\sigma_{\rm e}/200\,\mathrm{km~s}^{-1})+(-0.06\pm0.01)$, where $\alpha=(M_*/L)_{\rm dyn}/(M_*/L)_{\rm pop}$ and $\sigma_{\rm e}$ is the luminosity averaged $\sigma$ within one effective radius $R_{\rm e}$. This is consistent with a systematic variation of the IMF normalization from Kroupa to Salpeter in the interval $\sigma_{\rm e}\approx90-270\,\mathrm{km~s}^{-1}$.