Zero Metallicity with Zero CPU Hours: Masses of the First Stars on the Laptop

Abstract

We develop an analytic model for the mass of the first stars forming in the center of primordial gas clouds as a function of host halo mass, redshift, and degree of rotation. The model is based on the estimation of key timescales determining the following three processes: the collapse of the gas cloud, the accretion onto the protostellar core, and the radiative feedback of the protostellar core. The final stellar mass is determined by the total mass accreted until the radiative feedback halts the accretion. The analytic estimation, motivated by the result of the full numerical simulations, leads to algebraic expressions allowing an extremely fast execution. Despite its simplicity, the model reproduces the stellar mass scale and its parameter dependences observed in state-of-the-art cosmological zoom-in simulations. This work clarifies the basic physical principles undergirding such numerical treatments and provides a path to efficiently calibrating numerical predictions against eventual observations of the first stars.