Implications of a variable IMF for the interpretation of observations of
  galaxy populations
  We investigate the effect of a metallicity-dependent stellar initial mass
function (IMF), as deduced observationally by Martin-Navarro et al. (2015c), on
the inferred stellar masses and star formation rates (SFRs) of a representative
sample of 186,886 SDSS galaxies. Relative to a Chabrier IMF, for which we show
the implied masses to be close to minimal, the inferred masses increase in both
the low- and high-metallicity regimes due to the addition of stellar remnants
and dwarf stars, respectively. The resulting galaxy stellar mass function
(GSMF) shifts toward higher masses by 0.5 dex, without affecting the high-mass
slope (and thus the need for effective quenching). The implied low-redshift SFR
density increases by an order of magnitude. However, these results depend
strongly on the assumed IMF parametrisation, which is not directly constrained
by the observations. Varying the low-end IMF slope instead of the high-end IMF
slope, while maintaining the same dwarf-to-giant ratio, results in a much more
modest GSMF shift of 0.2 dex and a 10 per cent increase in the SFR density
relative to the Chabrier IMF. A bottom-heavy IMF during the late, metal-rich
evolutionary stage of a galaxy would help explain the rapid quenching and the
bimodality in the galaxy population by on the one hand making galaxies less
quenched (due to the continued formation of dwarf stars) and on the other hand
reducing the gas consumption timescale. We conclude that the implications of
the observational evidence for a variable IMF could vary from absolutely
dramatic to mild but significant.
