A low-mass cut-off near the hydrogen burning limit for Salpeter-like initial mass functions in early-type galaxies

We conduct a detailed investigation of the properties of the stellar initial mass function (IMF) in two massive early-type lens galaxies with velocity dispersions of 245 and 325 km s -1 , for which both Hubble Space Telescope imaging and X-Shooter spectra are available. We compare the inferences obtained from two fully independent methods: (i) a combined gravitational lensing and stellar dynamics (L&D) analysis of the data sets employing self-consistent axisymmetric models and (ii) a spectroscopic simple stellar population (SSP) analysis of optical line-strength indices, assuming single power-law IMFs. The results from the two approaches are found to be in agreement within the 1 uncertainties. Both galaxies are consistent with having a Salpeter IMF (power-law slope of x = 2.35), which is strongly favoured over a Chabrier IMF (x = 1.8), with probabilities inferred from the joint analysis of 89 and 99 per cent, respectively. Bottom-heavy IMFs significantly steeper than Salpeter (x 3.0) are ruled out with decisive evidence (Bayes factor B > 1000) for both galaxies, as they exceed the total mass derived from the L&D constraints. Our analysis allows, for the first time, the inference of the low-mass cut-off of the IMF (M low ). Combining the joint L&D and SSP analyses of both galaxies, we infer an IMF slope of x = 2.22 0.14, consistent with Salpeter IMF and a low-mass limit M low = 0.13 0.03 M , just above the hydrogen burning limit.