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 sigma(e), 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 sigma. We use this correlation to estimate a dynamical or IMF-corrected stellar mass, M-*(alpha JAM), from M-* and sigma(e) for a sample of 6 x 10(5) Sloan Digital Sky Survey (SDSS) galaxies for which spatially resolved kinematics is not available. We also compute the 'virial' mass estimate k(n, R) R-e alpha(2)(R)/G, where n is the Sersic index, in the SDSS and ATLAS(3D) 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 ATLAS(3D) sample varies weakly with n: (sigma(R)/sigma(e)) = (R/R-e)(-gamma(n)). The resulting stellar mass functions, based on M-*(alpha JAM) and the recalibrated virial mass, are in good agreement. Using a Fundamental Plane-based observational proxy for sigma(e) 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.