Survey of gravitationally-lensed objects in HSC imaging (SuGOHI). III.
  Statistical strong lensing constraints on the stellar IMF of CMASS galaxies
  Context: The determination of the stellar initial mass function (IMF) of
massive galaxies is one of the open problems in cosmology. Strong gravitational
lensing is one of the few methods that allow us to constrain the IMF outside of
the Local Group. Aims: The goal of this study is to statistically constrain the
distribution in the IMF mismatch parameter, defined as the ratio between the
true stellar mass of a galaxy and that inferred assuming a reference IMF, of
massive galaxies from the BOSS CMASS sample. Methods: We take 23 strong lenses
drawn from the CMASS sample, measure their Einstein radii and stellar masses
using multi-band photometry from the Hyper Suprime-Cam survey, then fit a model
distribution for the IMF mismatch parameter and dark matter halo mass to the
whole sample. We use a prior on halo mass from weak lensing measurements and
account for strong lensing selection effects in our model. Results: Assuming an
NFW density profile for the dark matter distribution, we infer a value
$\mu_{\mathrm{IMF}} = -0.04\pm0.11$ for the average base-10 logarithm of the
IMF mismatch parameter, defined with respect to a Chabrier IMF. A Salpeter IMF
is in tension with our measurements. Conclusions: Our results are consistent
with a scenario in which the region of massive galaxies where the IMF
normalization is significantly heavier than that of the Milky Way is much
smaller than the scales $5\sim10$~kpc probed by the Einstein radius of the
lenses in our sample, as recent spatially resolved studies of the IMF in
massive galaxies suggest. The MCMC chains describing the posterior probability
distribution of the model are available online, together with the code used to
obtain them.
