Calibrated, cosmological hydrodynamical simulations with variable IMFs
  II: Correlations between the IMF and global galaxy properties
  The manner in which the stellar initial mass function (IMF) scales with
global galaxy properties is under debate. We use two hydrodynamical,
cosmological simulations to predict possible trends for two self-consistent
variable IMF prescriptions that respectively become locally bottom-heavy or
top-heavy in high-pressure environments. Both simulations have been calibrated
to reproduce the observed correlation between central stellar velocity
dispersion and the excess mass-to-light ratio (MLE) relative to a Salpeter IMF
by increasing the mass fraction of, respectively, dwarf stars or stellar
remnants. We find trends of MLE with galaxy age, metallicity and [Mg/Fe] that
agree qualitatively with observations. Predictions for correlations with
luminosity, half-light radius, and black hole mass are presented. The
significance of many of these correlations depends sensitively on galaxy
selection criteria such as age, luminosity, and morphology. For an IMF with a
varying high-mass end, some of these correlations are stronger than the
correlation with the birth ISM pressure (the property that governs the form of
the IMF), because in this case the MLE has a strong age dependence. Galaxies
with large MLE tend to have overmassive central black holes. This indicates
that the abnormally high MLE observed in the centres of some high-mass galaxies
does not imply that overmassive BHs are merely the result of incorrect IMF
assumptions, nor that excess M/L ratios are solely the result of overmassive
BHs. Satellite galaxies tend to scatter toward high MLE due to tidal stripping,
which may have significant implications for the inferred stellar masses of
ultracompact dwarf galaxies.
