Constraining the Initial-Mass Function via Stellar Transients

Abstract

The stellar initial-mass function (IMF) represents a fundamental quantity in astrophysics and cosmology, describing the mass distribution of stars from low to very-high masses. It is intimately linked to a wide variety of topics, including stellar and binary evolution, galaxy evolution, chemical enrichment, and cosmological reionization. Nonetheless, the IMF still remains highly uncertain. In this work, we aim at determining the IMF with a novel approach based on the observed rates of transients of stellar origin. We parametrize the IMF with a simple, but flexible, Larson shape, and insert it into a parametric model for the cosmic UV luminosity density, local stellar mass density, type Ia supernova (SN Ia), core-collapse supernova (CCSN), and long gamma-ray burst (LGRB) rates as function of redshift. We constrain our free parameters by matching the model predictions to a set of empirical determinations for the corresponding quantities, via a Bayesian Markov-Chain Monte Carlo method. Remarkably, we are able to provide an independent IMF determination, with characteristic mass $m_c=0.10^{+0.24}_{-0.08}\:M_{\odot}$, and high-mass slope $\xi=-2.53^{+0.24}_{-0.27}$, that is in accordance with the widely-used IMF parameterizations (e.g. Salpeter, Kroupa, Chabrier). Moreover, the adoption of an up-to-date recipe for the cosmic metallicity evolution, allows us to constrain the maximum metallicity of LGRB progenitors to $Z_{max}=0.12^{+0.29}_{-0.05}\:Z_{\odot}$. We also find what progenitor fraction actually leads to SN Ia or LGRB emission, put constraints on the CCSN and LGRB progenitor mass ranges, and test the IMF universality. These results show the potential of this kind of approach for studying the IMF, its putative evolution with galactic environment and cosmic history, and the properties of SN Ia, CCSN and LGRB progenitors, especially considering the wealth of data incoming in the future.