The most massive Population III stars

Recent data from the JWST suggest that there are realistic prospects for detecting the earliest generation of stars at redshift similar to 20. These metal-poor, gaseous Population III (Pop III) stars are likely in the mass range 10-10(3) M-circle dot. 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 < z < 20 are likely to be greater than or similar to 10(3) -10(4) M-circle dot. 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.