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 \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 Sérsic index , in the SDSS and ATLAS ^ { 3 D } 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 ^ { 3 D } 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 .
If the M _ { * } ^ { \alpha _ { JAM } } / M _ { * } - \sigma _ { e } correlation is indeed due to the IMF , and stellar mass-to-light gradients can be ignored , then our \phi ( M _ { * } ^ { \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 .
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 .