Strong Gravitational Lensing and the Stellar IMF of Early-type Galaxies
  Systematic variations of the IMF in early-type galaxies, and their connection
with possible drivers such as velocity dispersion or metallicity, have been
much debated in recent years. Strong lensing over galaxy scales combined with
photometric and spectroscopic data provides a powerful method to constrain the
stellar mass-to-light ratio and hence the functional form of the IMF. We
combine photometric and spectroscopic constraints from the latest set of
population synthesis models of Charlot & Bruzual, including a varying IMF, with
a non-parametric analysis of the lens masses of 18 ETGs from the SLACS survey,
with velocity dispersions in the range 200-300 km/s. We find that very
bottom-heavy IMFs are excluded. However, the upper limit to the bimodal IMF
slope ($\mu \lesssim 2.2$, accounting for a dark matter fraction of 20-30%,
where $\mu=1.3$ corresponds to a Kroupa-like IMF) is compatible at the
$1\sigma$ level with constraints imposed by gravity-sensitive line strengths. A
two-segment power law parameterisation of the IMF (Salpeter-like for high
masses) is more constrained ($\Gamma \lesssim 1.5$, where $\Gamma$ is the power
index at low masses) but requires a dark matter contribution of $\gtrsim 25\%$
to reconcile the results with a Salpeter IMF. For a standard Milky Way-like IMF
to be applicable, a significant dark matter contribution is required within
$1R_e$. Our results reveal a large range of allowed IMF slopes, which, when
interpreted as intrinsic scatter in the IMF properties of ETGs, could explain
the recent results of Smith et al., who find Milky Way-like IMF normalisations
in a few massive lensing ETGs.
