Impact of Population III homogeneous stellar evolution on early cosmic reionisation

Context: Population III (Pop III) stars may be fast rotating. An expected consequence of fast rotation is strong internal mixing that deeply affects their evolutionary tracks in the Hertzsprung-Russell diagram and hence their ionising power. aims: We investigate the impact on the ionising power of Pop III stars in an extreme case of internal mixing, the one leading to chemically homogeneous evolution (CHE). In that situation, during the main sequence phase, the star keeps the same chemical composition from its center to its surface. Homogeneous stars have larger effective temperatures and luminosities than stars evolving non-homogeneously and thus are stronger ionising sources. Methods: The stellar evolution models are based on $n=3$ polytropes with a time varying hydrogen mass fraction. The ionisation model employs the self-similar champagne flow solution from Shu et al. (2002), as well as numerical simulations for the stochastic treatment of star clusters over a grid of redshifts and halo masses. Results: We find that haloes containing chemically homogeneous stars have an escape fraction of ionising photons about twice that of haloes containing classical Pop III stars. By extrapolating the high-$z$ ionisation history powered by Pop III stars (at $z\gtrsim 15$) to the post-reionisation epoch, we derive the Thomson scattering optical depth $\tau$, which is compared with the value measured by $\textit{Planck}$. We find that $\tau$ is overproduced by $\sim1.5- 5\sigma$, when all Pop III stars evolve homogeneously. This indicates that CHE is unlikely to be realised in the majority of Pop III stars, although the present study cannot exclude that a fraction of them undergoes CHE. Conclusions: Fast rotation might have a significant impact on the ionising budget of Pop III stars, and thus on early cosmic reionisation.