Population III star clusters: The connection between the rest-frame ultraviolet luminosity and the stellar initial mass function

The Initial Mass Function (IMF) of Population III (Pop III) star systems is one of the most heavily researched topics in high-redshift cosmology and astrophysics as it plays a crucial role in understanding the cosmic evolution. High-redshift galaxy luminosity functions at the rest-frame ultraviolet (UV) luminosity of 1500 Å can be employed to characterize Pop III stellar clusters, but in the present day, there is no simple prescription that relates this observable to the wide range of IMFs listed in the literature. In this project, we attempt to remedy this by performing population synthesis of a large grid of Pop III stellar models and identify an analytic mapping between the IMF properties and the time-dependent UV luminosity at 1500 Å per total stellar mass. Using recent evolutionary tracks of zero metallicity stars, we interpolate to high mass (2000 M ) and time (40 Myr) and identify a strong dependence of the ratio to the upper stellar mass limit Mmax. We parametrize this by creating two polynomial fits to the 10 kyr - 1 Myr and 1 Myr - 40 Myr age intervals respectively. The fits maintain accuracy of below 0.13 dex and provide a fast and flexible tool for studying Pop III stellar system formation and high-redshift observations.