The stellar initial mass function of early-type galaxies from low to high stellar velocity dispersion: homogeneous analysis of ATLAS 3D and Sloan Lens ACS galaxies

We present an investigation about the shape of the initial mass function (IMF) of early-type galaxies (ETGs), based on a joint lensing and dynamical analysis, and on stellar population synthesis models, for a sample of 55 lens ETGs identified by the Sloan Lens Advanced Camera for Surveys (SLACS). We construct axisymmetric dynamical models based on the Jeans equations which allow for orbital anisotropy and include a dark matter halo. The models reproduce in detail the observed Hubble Space Telescope photometry and are constrained by the total projected mass within the Einstein radius and the stellar velocity dispersion (\u3c3 ) within the Sloan Digital Sky Survey fibres. Comparing the dynamically-derived stellar mass-to-light ratios (M 17/L)dyn, obtained for an assumed halo slope \u3c1h 1d r 121, to the stellar population ones (M 17/L)Salp, derived from full-spectrum fitting and assuming a Salpeter IMF, we infer the mass normalization of the IMF. Our results confirm the previous analysis by the SLACS team that the mass normalization of the IMF of high-\u3c3 galaxies is consistent on average with a Salpeter slope. Our study allows for a fully consistent study of the trend between IMF and \u3c3 for both the SLACS and atlas3D samples, which explore quite different \u3c3 ranges. The two samples are highly complementary, the first being essentially \u3c3 selected, and the latter volume- limited and nearly mass selected. We find that the two samples merge smoothly into a single trend of the form log\u3b1 = (0.38 \ub1 0.04) 7 log(\u3c3e/200kms 121) + ( 12 0.06 \ub1 0.01), where \u3b1 = (M 17/L)dyn/(M 17/L)Salp and \u3c3e is the luminosity averaged \u3c3 within one effective radius Re. This is consistent with a systematic variation of the IMF normalization from Kroupa to Salpeter in the interval \u3c3 e 48 90\u2013270 km s 121