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Register a new userVariations of the stellar Initial Mass Function in Semi-Analytic Models: implications for the mass assembly of galaxies in the GAEA model
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Fabio Fontanot
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A wealth of observations recently challenged the notion of a universal stellar initial mass function (IMF) by showing evidences in favour of a variability of this statistical indicator as a function of galaxy properties. I present predictions from the semi-analytic model GAEA (GAlaxy Evolution and Assembly), which features (a) a detailed treatment of chemical enrichment, (b) an improved stellar feedback scheme, and (c) implements theoretical prescriptions for IMF variations. Our variable IMF realizations predict intrinsic stellar masses and mass-to-light ratios larger than those estimated from synthetic photometry assuming a universal IMF. This provides a self-consistent interpretation for the observed mismatch between photometrically inferred stellar masses of local early-type galaxies and those derived by dynamical and spectroscopic studies. At higher redshifts, the assumption of a variable IMF has a deep impact on our ability to reconstruct the evolution of the galaxy stellar mass function and the star formation history of galaxies.
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In this work, we investigate the implications of the Integrated Galaxy-wide stellar Initial Mass Function (IGIMF) approach in the framework of the semi-analytic model GAEA (GAlaxy Evolution and Assembly), which features a detailed treatment of chemical enrichment and stellar feedback. The IGIMF provides an analytic description of the dependence of the stellar IMF shape on the rate of star formation in galaxies. We find that our model with a universal IMF predicts a rather flat [$alpha$/Fe]-stellar mass relation. The model assuming the IGIMF, instead, is able to reproduce the observed increase of $alpha$-enhancement with stellar mass, in agreement with previous studies. This is mainly due to the fact that massive galaxies are characterized by larger star formation rates at high-redshift, leading to stronger $alpha$-enhancement with respect to low-mass galaxies. At the same time, the IGIMF hypothesis does not affect significantly the trend for shorter star formation timescales for more massive galaxies. We argue that in the IGIMF scenario the [$alpha$/Fe] ratios are good tracers of the highest star formation events. The final stellar masses and mass-to-light-ratio of our model massive galaxies are larger than those estimated from the synthetic photometry assuming a universal IMF, providing a self-consistent interpretation of similar recent results, based on dynamical analysis of local early type galaxies.
Recent studies proposed that cosmic rays (CR) are a key ingredient in setting the conditions for star formation, thanks to their ability to alter the thermal and chemical state of dense gas in the UV-shielded cores of molecular clouds. In this paper, we explore their role as regulators of the stellar initial mass function (IMF) variations, using the semi-analytic model for GAlaxy Evolution and Assembly (GAEA). The new model confirms our previous results obtained using the integrated galaxy-wide IMF (IGIMF) theory: both variable IMF models reproduce the observed increase of $alpha$-enhancement as a function of stellar mass and the measured $z=0$ excess of dynamical mass-to-light ratios with respect to photometric estimates assuming a universal IMF. We focus here on the mismatch between the photometrically-derived ($M^{rm app}_{star}$) and intrinsic ($M_{star}$) stellar masses, by analysing in detail the evolution of model galaxies with different values of $M_{star}/M^{rm app}_{star}$. We find that galaxies with small deviations (i.e. formally consistent with a universal IMF hypothesis) are characterized by more extended star formation histories and live in less massive haloes with respect to the bulk of the galaxy population. While the IGIMF theory does not change significantly the mean evolution of model galaxies with respect to the reference model, a CR-regulated IMF implies shorter star formation histories and higher peaks of star formation for objects more massive than $10^{10.5} M_odot$. However, we also show that it is difficult to unveil this behaviour from observations, as the key physical quantities are typically derived assuming a universal IMF.
In this work, we study the evolution of the mass-metallicity relations (MZRs) as predicted by the GAlaxy Evolution and Assembly (GAEA) semi-analytic model. We contrast these predictions with recent results from the VANDELS survey, that allows us to expand the accessible redshift range for the stellar MZR up to $zsim3.5$. We complement our study by considering the evolution of the gas-phase MZR in the same redshift range. We show that GAEA is able to reproduce the observed evolution of the $z<3.5$ gas-phase MZR and $z<0.7$ stellar MZR, while it overpredicts the stellar metallicity at $zsim3.5$. Furthermore, GAEA also reproduces the so-called fundamental metallicity relation (FMR) between gas-phase metallicity, stellar mass and star formation rate (SFR). In particular, the gas-phase FMR in GAEA is already in place at $zsim5$ and shows almost no evolution at lower redshift. GAEA predicts the existence of a stellar FMR, that is, however, characterized by a relevant redshift evolution, although its shape follows closely the gas-phase FMR. We also report additional unsolved tensions between model and data: the overall normalization of the predicted MZR agrees with observations only within $sim$0.1 dex; the largest discrepancies are seen at $zsim3.5$ where models tend to slightly overpredict observed metallicities; the slope of the predicted MZR at fixed SFR is too steep below a few ${rm M}_odot {rm yr}^{-1}$. Finally, we provide model predictions for the evolution of the MZRs at higher redshifts, that would be useful in the context of future surveys, like those that will be performed with JWST.
We present a method for investigating variations in the upper end of the stellar Initial Mass Function (IMF) by probing the production rate of ionizing photons in unresolved, compact star clusters with ages <~10 Myr and with different masses. We test this method by performing a pilot study on the young cluster population in the nearby galaxy NGC5194 (M51a), for which multi-wavelength observations from the Hubble Space Telescope are available. Our results indicate that the proposed method can probe the upper end of the IMF in galaxies located out to at least ~10 Mpc, i.e., a factor ~200 further away than possible by counting individual stars in young compact clusters. Our results for NGC5194 show no obvious dependence of the upper mass end of the IMF on the mass of the star cluster down to ~1000 M_sun, although more extensive analyses involving lower mass clusters and other galaxies are needed to confirm this conclusion.
We examine variations of the stellar initial mass function (IMF) in extreme environments within the formalism derived by Hennebelle & Chabrier. We focus on conditions encountered in progenitors of massive early type galaxies and starburst regions. We show that, when applying the concept of turbulent Jeans mass as the characteristic mass for fragmentation in a turbulent medium, instead of the standard thermal Jeans mass for purely gravitational fragmentation, the peak of the IMF in such environments is shifted towards smaller masses, leading to a bottom-heavy IMF, as suggested by various observations. In very dense and turbulent environments, we predict that the high-mass tail of the IMF can become even steeper than the standard Salpeter IMF, with a limit for the power law exponent $alphasimeq -2.7$, in agreement with recent observational determinations. This steepening is a direct consequence of the high densities and Mach values in such regions but also of the time dependence of the fragmentation process, as incorporated in the Hennebelle-Chabrier theory. We provide analytical parametrizations of these IMFs in such environments, to be used in galaxy evolution calculations. We also calculate the star formation rates and the mass-to-light ratios expected under such extreme conditions and show that they agree well with the values inferred in starburst environments and massive high-redshift galaxies. This reinforces the paradigm of star formation as being a universal process, i.e. the direct outcome of gravitationally unstable fluctuations in a density field initially generated by large scale shock-dominated turbulence. This globally enables us to infer the variations of the stellar IMF and related properties for atypical galactic conditions.
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