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 the moving mesh code Arepo, to perform the first resolution study for primordial star formation simulations and present the first Population III simulations to run up to densities of 10-6 g cm-3 for hundreds of years after the formation of sink particles.
The maximum resolution of a simulation is set by the maximum density it is allowed to run to. When the gas density increases during gravitationally collapse, the Jeans length (the scale that structures can support themselves thermally against gravitational collapse) shrinks, and so the simulation mesh must refine to resolve these scales and prevent artificial instability. This process continues until the maximum density is reached and a sink particle is introduced to represent the densest gas on the smallest scales. In this resolution study, we vary the sink particle creation density from 10-10 – 10-6 g cm-3 and track the fragmentation behaviour of the gas and the resulting IMF.
We find that the total number of sink particles formed continues to increase with increasing sink particle creation density, without achieving numerical convergence. However, 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 ionising photons emitted per second. The lack of convergence up to densities 2 orders of magnitudes higher than all relevant chemical reactions suggests that the number of sinks will continue to grow with increasing resolution until H2 is fully dissociated and the collapse becomes almost adiabatic at 10-4 g cm-3. We also note that in the highest resolution runs, sinks with stellar masses capable of surviving until the present day had an ejection fraction of 0.21.
These results imply that many Population III studies utilising sink particles have produced IMFs which have overestimated the masses of primordial stars and underestimated the number of stars formed.