Are the total mass density and the low-mass end slope of the IMF anticorrelated?

We conduct a detailed lensing, dynamics and stellar population analysis of nine massive lens early-type galaxies (ETGs) from the X-Shooter Lens Survey (XLENS). Combining gravitational lensing constraints from HST imaging with spatially-resolved kinematics and line-indices constraints from Very Large Telescope (VLT) X-Shooter spectra, we infer the low-mass slope and the low cut-off mass of the stellar initial mass function (IMF): $x_{250}=2.37^{+0.12}_{-0.12}$ and $M_{\mathrm{low}, 250}= 0.131^{+0.023}_{-0.026}\,\mathrm{M}_{\odot }$ , respectively, for a reference point with σ⋆ ≡ 250 km s−1 and R eff ≡ 10 kpc. All the XLENS systems are consistent with an IMF slope steeper than Milky Way-like. We find no significant correlations between IMF slope and any other quantity, except for an anticorrelation between total dynamical mass density and low-mass IMF slope at the 87 per cent CL [dx/d log (ρ) = $-0.19^{+0.15}_{-0.15}$ ]. This anticorrelation is consistent with the low-redshift lenses found by Smith et al. that have high velocity dispersions and high stellar mass densities but surprisingly shallow IMF slopes.