Potential contributions of Pop III and intermediate-mass Pop II stars to cosmic chemical enrichment

We propose a semi-analytic model that is developed to understand the cosmological evolution of the mean metallicity in the Universe. In particular, we study the contributions of Population III (Pop III) and Population II (Pop II) stars to the production of $\mathrm{Fe,~Si,~Zn, ~Ni,~P, ~Mg, ~Al, ~S, ~C, ~N}$, and $\mathrm{~O}$. We aim to quantify the roles of two different models in the chemical enrichment of the Universe. The first model (A) considers both stars with Pop III and Pop II yields. For the second model (B), the yields involved are only for Pop II stars. We start by describing the cosmic star formation rate (CSFR) through an adaptation of a scenario developed within the hierarchical scenario of structure formation with a Press-Schechter-like formalism. We adapt the formalism to implement the CSFR to the standard chemical evolution scenario to investigate the course of chemical evolution on a cosmological basis. Calculations start at redshift $z\sim 20$, and we compare the results of our two models with data from damped Lyman-$\alpha$ systems (DLAs), and globular clusters (GCs). Our main results find that metal production in the Universe occurred very early, quickly increasing with the formation of the first stars. When comparing results for [Fe/H] with observations from GCs, yields of Pop II stars are not enough to explain the observed chemical abundances, requiring stars with physical properties similar those expected from Pop III stars. Our semi-analytic model can deliver consistent results for the evolution of cosmic metallicities. Our results show that the chemical enrichment in the early Universe is rapid, and at redshift $\sim 12.5$, the metallicity reaches $10^{-4}\, Z_{\odot}$ for the model that includes Pop III stars. In addition, we explore values for the initial mass function (IMF) within the range $[0.85, 1.85]$.