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Register a new userThe Cosmic Evolution of the IMF Under the Jeans Conjecture with Implications for Bottom-Heavy Ellipticals
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Desika Narayanan
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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. We find that at early times, energetic coupling between dust and gas drive warm conditions in the ISM, yielding bottom-light/top- heavy IMFs associated with large ISM Jeans masses for massive star-forming galaxies. Owing to the remnants of massive stars that formed during the top-heavy phases at early times, the resultant M/L_K(sigma) in massive galaxies at the present epoch is increased relative to the non- varying IMF case. At late times, lower cosmic ray fluxes allow for cooler ISM temperatures in massive galaxies, and hence newly formed clusters will exhibit bottom-heavy IMFs, further increasing M/L_K(sigma). Our central result is hence that a given massive galaxy may go through both top-heavy and bottom-heavy IMF phases during its lifetime, though the bulk of the stars form during a top-heavy phase. Qualitatively, the variations in M/L_K(sigma) with galaxy mass are in agreement with observations, however, our model may not be able to account for bottom-heavy mass functions as indicated by stellar absorption features.
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We tested the implementation of different IMFs in our model for the chemical evolution of ellipticals, with the aim of reproducing the observed relations of [Fe/H] and [Mg/Fe] abundances with galaxy mass in a sample of early-type galaxies selected from the SPIDER-SDSS catalog. Abundances in the catalog were derived from averaged spectra, obtained by stacking individual spectra according to central velocity dispersion, as a proxy of galaxy mass. We tested initial mass functions already used in a previous work, as well as two new models, based on low-mass tapered (bimodal) IMFs, where the IMF becomes either (1) bottom-heavy in more massive galaxies, or (2) is time-dependent, switching from top-heavy to bottom-heavy in the course of galactic evolution. We found that observations could only be reproduced by models assuming either a constant, Salpeter IMF, or a time-dependent distribution, as other IMFs failed. We further tested the models by calculating their M/L ratios. We conclude that a constant, time-independent bottom-heavy IMF does not reproduce the data, especially the increase of the $[alpha/Fe]$ ratio with galactic stellar mass, whereas a variable IMF, switching from top to bottom-heavy, can match observations. For the latter models, the IMF switch always occurs at the earliest possible considered time, i.e. $t_{text{switch}}= 0.1$ Gyr.
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