Radiative feedback on supermassive star formation: the massive end of the Population III initial mass function

Abstract

ABSTRACT Supermassive stars with masses of M* ≃ 104–105 M⊙ are invoked as possible seeds of high-redshift supermassive black holes, but it remains under debate whether their protostar indeed acquires sufficient mass via gas accretion overcoming radiative feedback. We investigate protostellar growth in dynamically heated atomic cooling haloes (ACHs) found in recent cosmological simulations, performing three-dimensional radiation hydrodynamical simulations that consider stellar evolution under variable mass accretion. We find that one of the ACHs feeds the central protostar at rates exceeding a critical value, above which the star evolves in a cool bloating phase and hardly produces ionizing photons. Consequently, the stellar mass reaches M* ≳ 104 M⊙ unimpeded by radiative feedback. In the other ACH, where the mass supply rate is lower, the star evolves almost as a hot main-sequence star, emitting intense ionizing radiation. Then, the stellar mass growth is terminated around 500 M⊙ by photoevaporation of the circumstellar disc. Our simulations provide a formula of the final stellar mass determined either by stellar feedback or their lifetime as a function of the mass supply rate from the parent cloud. Combining the results with the statistical properties of star-forming clouds in high-redshift quasar progenitor haloes, we construct a top-heavy mass distribution of primordial stars over M* ≃ 100–105 M⊙, approximately following a power-law spectrum of ${\propto} M_\ast ^{-1.3}$. Their black hole remnants would be further fed via the dense debris disc, powering ‘milliquasars’ with a bolometric luminosity of Lbol ≳ 1043 erg s−1.