Abstract
We examine the cosmic evolution of a stellar initial mass function (IMF) in
galaxies that varies with the Jeans mass in the interstellar medium, paying
particular attention to the K-band stellar mass to light ratio (M/L_K) of
present-epoch massive galaxies. We calculate the typical Jeans mass using
high-resolution hydrodynamic simulations coupled with a fully radiative model
for the ISM, which yields a parameterisation of the IMF characteristic mass as
a function of galaxy star formation rate (SFR). We then calculate the star
formation histories of galaxies utilising an equilibrium galaxy growth model
coupled with constraints on the star formation histories set by abundance
matching models. Our main result is that at early times, energetic coupling
between dust and gas drive warm conditions in the ISM, and hence
bottom-light/top-heavy IMFs associated with large ISM Jeans masses for massive
star-forming galaxies. At late times, lower cosmic ray fluxes allow for cooler
ISM temperatures in massive galaxies, and hence bottom-heavy IMFs. Because the
massive stars (M >~ 1 Msun) formed during the top-heavy phases at early times
have all disappeared by today, the resultant M/L_K ratios in massive galaxies
at the present epoch is increased relative to the non-varying IMF case. A key
result is that a given galaxy may go through both top-heavy and bottom-heavy
phases during its lifetime. Quantitatively, the variations in M/L_K with galaxy
mass are slightly smaller than what is observed. Nonetheless, these results are
encouraging because they can, at least qualitatively, reconcile a bottom-light
IMF that would help explain a number of observations of massive high-z galaxies
with the bottom-heavy IMF inferred for the descendants of those galaxies today.
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