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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.