Determination of the mass distribution of the first stars from the 21-cm signal

Abstract

Properties of the first generation of stars [referred to as the Population III (Pop III) stars], such as their initial mass function (IMF), are poorly constrained by observations and have yet to converge between simulations. The cosmological 21-cm signal of neutral hydrogen is predicted to be sensitive to Lyman-band photons produced by these stars, thus providing a unique way to probe the first stellar population. In this paper, we investigate the impacts of the Pop III IMF on the cosmic-dawn 21-cm signal via the Wouthuysen-Field effect, Lyman-Werner feedback, Ly α heating, and cosmic microwave background heating. We calculate the emission spectra of star-forming haloes for different IMFs by integrating over individual metal-free stellar spectra, computed from a set of stellar evolution histories and stellar atmospheres, and taking into account variability of the spectra with stellar age. Through this study, we therefore relax two common assumptions: that the zero-age main-sequence emission rate of a Pop III star is representative of its lifetime mean emission rate, and that Pop III emission can be treated as instantaneous. Exploring bottom-heavy, top-heavy, and intermediate IMFs, we show that variations in the 21-cm signal are driven by stars lighter than 20 M⊙. For the explored models, we find maximum relative differences of 59 per cent in the cosmic-dawn global 21-cm signal, and 131 per cent between power spectra. Although this impact is modest, precise modelling of the first stars and their evolution is necessary for accurate prediction and interpretation of the 21-cm signal.