Stellar mass functions and implications for a variable IMF

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 ($M_{\ast }^{\mathrm{JAM}}/M_{\ast }$) correlates with ${\sigma }_e$, if $M_{\ast }$ 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, $M_{\ast }^{{\alpha }_{\mathrm{JAM}}}$, from $M_{\ast }$ 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${}^{3D}$ 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${}^{3D}$ sample varies weakly with $n$: $({\sigma }_R/{\sigma }_e)=(R/R_e{)}^{-\gamma (n)}$. The resulting stellar mass functions, based on $M_{\ast }^{{\alpha }_{\mathrm{JAM}}}$ and the recalibrated virial mass, are in good agreement. If the $M_{\ast }^{{\alpha }_{\mathrm{JAM}}}/M_{\ast }-{\sigma }_e$ correlation is indeed due to the IMF, and stellar M/L gradients can be ignored, then our $\varphi (M_{\ast }^{{\alpha }_{\mathrm{JAM}}})$ 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.

17 pages, 19 figures, 4 tables. Accepted for publication by MNRAS. Tables 1, C1 and C2 are provided as ancillary files

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