Ultraviolet photon production rates of the first stars: Impact on the He II $λ$ 1640 Å emission line from primordial star clusters and the 21-cm signal from cosmic dawn

The first stars, the chemically pristine Population III, likely played an important role in heating the intergalactic medium during the epoch of cosmic dawn. The very high effective temperatures ($\sim 10^5$ K) predicted for the most massive Population III stars could also give rise to tell-tale signatures in the emission-line spectra of early star clusters or small galaxies dominated by such stars. Important quantities in modelling their observational signatures include their photon production rates at ultraviolet energies at which photons are able to ionize hydrogen and helium, dissociate molecular hydrogen and cause Lyman-$α$ heating. Here, we model the spectral energy distributions of Population III stars to explore how these key quantities are affected by the initial mass and rotation of Population III stars given a wide range of models for the evolution of these stars. Our results indicate that rotating Population III stars that evolve to effective temperatures $\sim 2\times 10^5$ K could potentially give rise to a very strong HeII 1640 emission line in the spectra from primordial star clusters, without requiring stellar masses of $\gtrsim 100\ \mathrm{M}_\odot$ indicated by previous models for non-rotating Population III stars. At the same time, the observable impact on 21-cm signatures from cosmic dawn and epoch of reionization from our set of rotating stars that evolve to $\sim 2\times 10^5$ K are modest, and produce potentially detectable features in the global 21-cm signal and 21-cm power spectrum for high Population III star formation efficiencies only.