Several recent observational studies have concluded that the initial mass function ( IMF ) of stars varies systematically with galaxy properties such as velocity dispersion .
In this paper , we investigate the effect of linking the circular velocity of galaxies , as determined from the Fundamental Plane and Tully-Fisher relations , to the slope of the IMF with parameterizations guided by several of these studies .
For each empirical relation , we generate stellar masses of \sim 600,000 SDSS galaxies at z \sim 0.1 , by fitting the optical photometry to large suites of synthetic stellar populations that sample the full range of galaxy parameters .
We generate stellar mass functions and examine the stellar-to-halo mass relations using sub-halo abundance matching .
At the massive end , the stellar mass functions become a power law , instead of the familiar exponential decline .
As a result , it is a generic feature of these models that the central galaxy stellar-to-halo mass relation is significantly flatter at high masses ( slope \sim - 0.3 to -0.4 ) than in the case of a universal IMF ( slope \sim - 0.6 ) .
We find that regardless of whether the IMF varies systematically in all galaxies or just early types , there is still a well-defined peak in the central stellar-to-halo mass ratio at halo masses of \sim 10 ^ { 12 } M _ { \odot } .
In general , the IMF variations explored here lead to significantly higher integrated stellar densities if the assumed dependence on circular velocity applies to all galaxies , including late-types ; in fact the more extreme cases can be ruled out , as they imply an unphysical situation in which the stellar fraction exceeds the universal baryon fraction .