Dynamical masses of brightest cluster galaxies II: constraints on the
  stellar IMF
  We use stellar and dynamical mass profiles, combined with a stellar
population analysis, of 32 brightest cluster galaxies (BCGs) at redshifts of
0.05 $\leq z \leq$ 0.30, to place constraints on their stellar Initial Mass
Function (IMF). We measure the spatially-resolved stellar population properties
of the BCGs, and use it to derive their stellar mass-to-light ratios
($\Upsilon_{\star \rm POP}$). We find young stellar populations ($<$200 Myr) in
the centres of 22 per cent of the sample, and constant $\Upsilon_{\star \rm
POP}$ within 15 kpc for 60 per cent of the sample. We further use the stellar
mass-to-light ratio from the dynamical mass profiles of the BCGs
($\Upsilon_{\star \rm DYN}$), modelled using a Multi-Gaussian Expansion (MGE)
and Jeans Anisotropic Method (JAM), with the dark matter contribution
explicitly constrained from weak gravitational lensing measurements. We
directly compare the stellar mass-to-light ratios derived from the two
independent methods, $\Upsilon_{\star \rm POP}$ (assuming some IMF) to
$\Upsilon_{\star \rm DYN}$ for the subsample of BCGs with no young stellar
populations and constant $\Upsilon_{\star \rm POP}$. We find that for the
majority of these BCGs, a Salpeter (or even more bottom-heavy) IMF is needed to
reconcile the stellar population and dynamical modelling results although for a
small number of BCGs, a Kroupa (or even lighter) IMF is preferred. For those
BCGs better fit with a Salpeter IMF, we find that the mass-excess factor
against velocity dispersion falls on an extrapolation (towards higher masses)
of known literature correlations. We conclude that there is substantial scatter
in the IMF amongst the highest-mass galaxies.
