Stellar mass functions and implications for a variable IMF

TL;DR

This paper investigates how the initial mass function (IMF) varies with galaxy velocity dispersion and develops methods to estimate more accurate stellar masses for large galaxy samples, improving mass function measurements.

Contribution

It introduces a new approach to correct stellar mass estimates for IMF variations using galaxy velocity dispersion, enabling more accurate mass functions without spatially resolved data.

Findings

The $M_*^{ m ext{alpha}_{JAM}}$ mass estimate aligns well with virial mass calculations.

Applying an $n$-dependent correction improves virial mass estimates.

The derived stellar mass functions account for IMF variations across galaxy populations.

Abstract

Spatially resolved kinematics of nearby galaxies has shown that the ratio of dynamical- to stellar population-based estimates of the mass of a galaxy ($M_*^{\rm JAM}/M_*$) correlates with $\sigma_e$, if $M_*$ is estimated using the same IMF for all galaxies and the stellar M/L ratio within each galaxy is constant. This correlation may indicate that, in fact, the IMF is more dwarf-rich for galaxies with large $\sigma$. We use this correlation to estimate a dynamical or IMF-corrected stellar mass, $M_*^{\rm \alpha_{JAM}}$, from $M_{*}$ and $\sigma_e$ for a sample of $6 \times 10^5$ SDSS galaxies for which spatially resolved kinematics is not available. We also compute the `virial' mass estimate $k(n,R)\,R_e\,\sigma_R^2/G$, where $n$ is the Sersic index, in the SDSS and ATLAS$^{\rm 3D}$ samples. We show that an $n$-dependent correction must be applied to the $k(n,R)$ values provided by Prugniel & Simien (1997). Our analysis also shows that the shape of the velocity dispersion profile in the ATLAS$^{\rm 3D}$ sample varies weakly with $n$: $(\sigma_R/\sigma_e) = (R/R_e)^{-\gamma(n)}$. The resulting stellar mass functions, based on $M_*^{\rm \alpha_{JAM}}$ and the recalibrated virial mass, are in good agreement. If the $M_*^{\rm \alpha_{JAM}}/M_* - \sigma_e$ correlation is indeed due to the IMF, and stellar M/L gradients can be ignored, then our $\phi(M_*^{\rm \alpha_{JAM}})$ is an estimate of the stellar mass function in which $\sigma_e$-dependent variations in the IMF across the population have been accounted for. Using a Fundamental Plane based observational proxy for $\sigma_e$ produces comparable results. By demonstrating that cheaper proxies are sufficiently accurate, our analysis should enable a more reliable census of the mass in stars for large galaxy samples, at a fraction of the cost. Our results are provided in tabular form.