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The Population III initial mass function (IMF) is currently unknown, butrecent studies agree that fragmentation of primordial gas gives a broader IMFthan the initially suggested singular star per halo. In this study we introducesink particle mergers into Arepo, to perform the first resolution study forprimordial star formation simulations and present the first Population IIIsimulations to run up to densities of 10-6g cm-3 for hundreds of years afterthe formation of sink particles. The total number of sinks formed increaseswith increasing sink particle creation density, without achieving numericalconvergence. The total mass in sinks remains invariant to the maximumresolution and is safe to estimate using low resolution studies. This resultsin an IMF that shifts towards lower masses with increasing resolution. Greaternumbers of sinks cause increased fragmentation-induced starvation of the mostmassive sink, yielding lower accretion rates, masses and ionising photonsemitted per second. The lack of convergence up to densities 2 orders ofmagnitudes higher than all relevant chemical reactions suggests that the numberof sinks will continue to grow with increasing resolution until H2 is fullydissociated and the collapse becomes almost adiabatic at 10-4g cm-3. Theseresults imply that many Population III studies utilising sink particles haveproduced IMFs which have overestimated the masses of primordial stars, andunderestimated the number of stars formed. In the highest resolution runs,sinks with masses capable of surviving until the present day had an ejectionfraction of 0.21.

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