Abstract
The formation of the first stars and the subsequent population of X-ray binaries represents a fundamental transition in the state of the Universe as it evolves from near homogeneity to being abundant in collapsed structures such as galaxies. Due to a lack of direct observations, the properties of these stars remain highly uncertain. Here, by considering the impact of the first stars and their remnant X-ray binaries on the cosmological 21-cm signal, we demonstrate that upcoming observations have the potential to improve our understanding of these objects. We find that a 25 mK sensitivity measurement of the 21-cm global signal by a wide-beam radiometer, such as REACH, or 3,000 h of foreground avoidance observations of the 21-cm power spectrum by SKA-Low, could provide 3σ constraints on the mass distribution of the first stars. Such measurements will fill a critical gap in our understanding of the early Universe and aid in interpreting high-redshift galaxy observations.