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Cosmological Implications of a Stellar Initial Mass Function that Varies with the Jeans Mass in Galaxies

Observations of star-forming galaxies at high-z have suggested discrepancies in the inferred star formation rates (SFRs) either between data and models, or between complementary measures of the SFR. These putative discrepancies could all be alleviated if the stellar IMF is systematically weighted toward more high-mass star formation in rapidly star-forming galaxies. Here, we explore how the IMF might vary under the central assumption that the turnover mass in the IMF, Mc, scales with the Jeans mass in giant molecular clouds (GMCs), M_J. We employ hydrodynamic and radiative transfer simulations of galaxies to predict how the typical GMC Jeans mass, and hence the IMF, varies with galaxy property. We then study the impact of such an IMF on the star formation law, the SFR-M* relation, submillimetre galaxies (SMGs), and the cosmic SFR density. Our main results are: The H2 mass-weighted Jeans mass in a galaxy scales with the SFR when the SFR is greater a few M_sun/yr. SPS modeling shows that this results in a nonlinear relation between SFR and Lbol, such that SFR Lbol^0.88. Using this model relation, the inferred SFR of local ULIRGs decreases by ~2, and that of high-z SMGs decreases by ~3-5. At z 2, this results in a lowered normalisation of the SFR-M* relation in better agreement with models, a reduced discrepancy between the observed cosmic SFR density and stellar mass density evolution, and SMG SFRs that are easier to accommodate in current hierarchical structure formation models. It further results in a Schmidt relation with slope of ~1.6 when utilising a physically motivated form for the CO-H2 conversion factor. While each of the discrepancies considered here could be alleviated without appealing to a varying IMF, the modest variation implied by assuming Mc M_J is a plausible solution that simultaneously addresses numerous thorny issues regarding the SFRs of high-z galaxies.