The quest to find the first stars has driven astronomers across cosmic time, from hopes to identify their signatures in their heyday at cosmic dawn to deep searches for their remnants in our local neighborhood. Such work crucially relies on robust theoretical modelling to understand when and where we expect pristine star formation to have occurred and survived. To that end, here we introduce an analytic bathtub for cosmic dawn, the abcd model, to efficiently trace the formation of the first stars from their birth through the first billion years of our universe’s history, jointly following star formation out of pristine and metal-enriched gas over time. Informed by the latest theoretical developments in our understanding of star formation in molecular cooling halos, metal mixing, and early galaxies, we expand pre-existing minimal models for galaxy formation to include Population III stars and many of the processes - both internal and environmental - affecting their evolution, while remaining fast and interpretable. With this framework, we can bridge the gap between numerical simulations and previous semi-analytic models, as we self-consistently follow star formation in dark matter halos from the minihalo era through the epoch of reionization, finding that, under plausible physical conditions, pristine star formation can persist at a high level in the presence of Pop II star formation down to z∼5, but is limited to the most massive halos. We highlight areas of theoretical uncertainty in the physics underpinning Pop III star formation and demonstrate the effects of this uncertainty first on individual star formation histories and subsequently bracketing the range of global star formation levels we expect. Finally, we leverage this model to make preliminary observable predictions, generating forecasts for high- z luminosity functions, transient rates, and the 21-cm global signal.
Hegde et al. (2025) studied this question.