The most massive Population III stars

Recent data from the James Webb Space Telescope suggest that there are realistic prospects for detecting the earliest generation of stars at redshift ~20. These metal-poor, gaseous Population III (Pop III) stars are likely in the mass range 10-1000 solar masses. We develop a framework for calculating the abundances of Pop III stars as well as the distribution of the most massive Pop III stars based on an application of extreme-value statistics. Our calculations use the star formation rate density from a recent simulation to calibrate the star-formation efficiency from which the Pop III stellar abundances are derived. Our extreme-value modelling suggests that the most massive Pop III stars at redshifts 10-20 are likely to be $\gtrsim10^3-10^4\,{\rm M}_\odot$. Such extreme Pop III stars were sufficiently numerous to be the seeds of supermassive black holes at high redshifts and possibly source detectable gravitational waves. We conclude that the extreme-value formalism provides an effective way to constrain the stellar initial mass function.