VARIATIONS OF THE STELLAR INITIAL MASS FUNCTION IN THE PROGENITORS OF MASSIVE EARLY-TYPE GALAXIES AND IN EXTREME STARBURST ENVIRONMENTS

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, the peak of the IMF in such environments is shifted toward 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 alpha similar or equal to -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 parameterizations 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.