Critical accretion rates for rapidly growing massive Population III stars

Efforts to understand the origin and growth of massive black holes observed in the early Universe have spurred a strong interest in the evolution and fate of rapidly-accreting primordial (metal-free) stars. Here, we investigate the evolution of such Population III stars under variable accretion rates, focusing on the thermal response and stellar structure, the impact of the luminosity wave encountered early in the pre-main sequence phase, and the influence of accretion on their subsequent evolution. We employ the Geneva stellar evolution code and simulate ten models with varying accretion histories, covering a final mass range from 491 M$_{\odot}$ to 6127 M$_{\odot}$. Our findings indicate that the critical accretion rate delineating the red and blue supergiant regimes during the pre-main sequence evolution is approximately $2.5\times10^{-2} $M$_{\odot}$/yr. Once core hydrogen burning commences, the value of this critical accretion rate drops to $7.0\times10^{-3}$M$_{\odot}$/yr. Moreover, we also confirm that the Kelvin-Helmholtz timescale in the outer surface layers is the more relevant timescale for determining the transition between red and blue phases. Regarding the luminosity wave, we find that it affects only the early pre-main sequence phase of evolution and does not directly influence the transition between red and blue phases, which primarily depends on the accretion rate. Finally, we demonstrate that variable accretion rates significantly impact the lifetimes, surface enrichment, final mass and time spent in the red phase. Our study provides a comprehensive understanding of the intricate evolutionary patterns of Population III stars subjected to variable accretion rates.