Stellar mass functions and implications for a variable IMF

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*JAM/M*|⁠) correlates with σe, the light-weighted velocity dispersion within its half-light radius, if M* is estimated using the same initial mass function (IMF) for all galaxies and the stellar mass-to-light ratio within each galaxy is constant. This correlation may indicate that, in fact, the IMF is more bottom-heavy or dwarf-rich for galaxies with large σ. We use this correlation to estimate a dynamical or IMF-corrected stellar mass, |M*^ α JAM|⁠, from M* and σe for a sample of 6 × 105 Sloan Digital Sky Survey (SDSS) galaxies for which spatially resolved kinematics is not available. We also compute the ‘virial’ mass estimate |k(n,R)\,Rₑ\,σ R²/G|⁠, where n is the Sérsic index, in the SDSS and ATLAS3D samples. We show that an n-dependent correction must be applied to the k(n, R) values provided by Prugniel & Simien. Our analysis also shows that the shape of the velocity dispersion profile in the ATLAS3D sample varies weakly with n: (σR/σe) = (R/Re)−γ(n). The resulting stellar mass functions, based on |M_*^ α JAM| and the recalibrated virial mass, are in good agreement. Using a Fundamental Plane-based observational proxy for σe produces comparable results. The use of direct measurements for estimating the IMF-dependent stellar mass is prohibitively expensive for a large sample of galaxies. By demonstrating that cheaper proxies are sufficiently accurate, our analysis should enable a more reliable census of the mass in stars, especially at high redshift, at a fraction of the cost. Our results are provided in tabular form.