We determine an absolute calibration of stellar mass-to-light ratios for the densest \simeq 3 \% of early-type galaxies in the local universe ( redshift z \simeq 0.08 ) from SDSS DR7 .
This sample of \sim 4000 galaxies has , assuming a Chabrier IMF , effective stellar surface densities , \Sigma _ { e } > 2500 M _ { \odot } / { pc } ^ { 2 } , stellar population synthesis ( SPS ) stellar masses \log _ { 10 } ( M _ { SPS } / M _ { \odot } ) < 10.8 , and aperture velocity dispersions of \sigma _ { ap } = 168 ^ { +37 } _ { -34 } km s ^ { -1 } ( 68 % range ) .
In contrast to typical early-type galaxies , we show that these dense early-type galaxies follow the virial fundamental plane , which suggests that mass-follows-light .
With the additional assumption that any dark matter does not follow the light , the dynamical masses of dense galaxies provide a direct measurement of stellar masses .
Our dynamical masses ( M _ { dyn } ) , obtained from the spherical Jeans equations , are only weakly sensitive to the choice of anisotropy ( \beta ) due to the relatively large aperture of the SDSS fiber for these galaxies : R _ { ap } \simeq 1.5 R _ { e } .
Assuming isotropic orbits ( \beta = 0 ) we find a median \log _ { 10 } ( M _ { dyn } / M _ { SPS } ) = 0.233 \pm 0.003 , consistent with a Salpeter IMF , while more bottom heavy IMFs and standard Milky-Way IMFs are strongly disfavored .
Our results are consistent with , but do not require , a dependence of the IMF on dynamical mass or velocity dispersion .
We find evidence for a color dependence to the IMF such that redder galaxies have heavier IMFs with M _ { dyn } / M _ { SPS } \propto ( g - r ) ^ { 1.13 \pm 0.09 } .
This may reflect a more fundamental dependence of the IMF on the age or metallicity of a stellar population , or the density at which the stars formed .