We determine an absolute calibration of the initial mass function ( IMF ) of early-type galaxies , by studying a sample of 56 gravitational lenses identified by the SLACS Survey .
Under the assumption of standard Navarro , Frenk & White dark matter halos , a combination of lensing , dynamical , and stellar population synthesis models is used to disentangle the stellar and dark matter contribution for each lens .
We define an “ IMF mismatch ” parameter \alpha \equiv M _ { *, { Ein } } ^ { LD } / M _ { *, { Ein } } ^ { SPS } as the ratio of stellar mass inferred by a joint lensing and dynamical models ( M _ { *, { Ein } } ^ { LD } ) to the current stellar mass inferred from stellar populations synthesis models ( M _ { *, { Ein } } ^ { SPS } ) .
We find that a Salpeter IMF provides stellar masses in agreement with those inferred by lensing and dynamical models ( \langle \log \alpha \rangle = 0.00 \pm 0.03 \pm 0.02 ) , while a Chabrier IMF underestimates them ( \langle \log \alpha \rangle = 0.25 \pm 0.03 \pm 0.02 ) .
A tentative trend is found , in the sense that \alpha appears to increase with galaxy velocity dispersion .
Taken at face value , this result would imply a non universal IMF , perhaps dependent on metallicity , age , or abundance ratios of the stellar populations .
Alternatively , the observed trend may imply non-universal dark matter halos with inner density slope increasing with velocity dispersion .
While the degeneracy between the two interpretations can not be broken without additional information , the data imply that massive early-type galaxies can not have both a universal IMF and universal dark matter halos .