Fragmentation-induced starvation in Population III star formation: a resolution study

The Population III initial mass function (IMF) is currently unknown, but recent studies agree that fragmentation of primordial gas gives a broader IMF than the initially suggested singular star per halo. In this study, we introduce sink particle mergers into AREPO, to perform the first resolution study for primordial star formation simulations and present the first Population HI simulations to run up to densities of 10(-6) g cm(-3) for hundreds of years after the formation of sink particles. The total number of sinks formed increases with increasing sink particle creation density, without achieving numerical convergence. The total mass in sinks remains invariant to the maximum resolution and is safe to estimate using low-resolution studies. This results in an IMF that shifts towards lower masses with increasing resolution. Greater numbers of sinks cause increased fragmentation-induced starvation of the most massive sink, yielding lower accretion rates, masses, and ionizing photons emitted per second. The lack of convergence up to densities two orders of magnitudes higher than all relevant chemical reactions suggests that the number of sinks will continue to grow with increasing resolution until H-2 is fully dissociated and the collapse becomes almost adiabatic at 10(-4) g cm(-3). These results imply that many Population III studies utilising sink particles have produced IMFs that have overestimated the masses of primordial stars, and underestimated the number of stars formed. In the highest resolution runs, sinks with masses capable of surviving until the present day had an ejection fraction of 0.21.