The imprint of the first stars on the faint end of the white dwarf luminosity function

Abstract: Population III stars are characterized by extremely low metallicities as they are thought to be formed from a pristine gas in the early Universe. Although the existence of Population III stars is widely accepted, the lack of direct observational evidence hampers the study of the nature of the putative stars. In this article, we explore the possibilities of constraining the nature of the oldest stars by using the luminosity function of their remnants -- white dwarfs. We study the formation and evolution of white dwarf populations by following star formation in a Milky Way-like galaxy using the semi-analytic model A-SLOTH. We derive the white dwarf luminosity function by applying a linear Initial-Final Mass Relation and Mestel's cooling model. The obtained luminosity function is generally in agreement with available observations and theoretical predictions -- with an exponential increase to a maximum of Mabs = 16 and a sudden drop for Mabs > 16. We explore the uncertainties of our model and compare them to the observational estimates. We adopt two different models of the initial mass function of Population III stars to show that the faint end of the luminosity function imprints the signature of Population III remnants. If the feature is detected in future observations, it would provide a clue to Population III stars and would also be an indirect evidence of low- to intermediate-mass Population III stars. We discuss the challenges and prospects for detecting the signatures.