The gravitational potential of DM halos facilitated the formation of the coolant H2 within baryonic gas, allowing it to cool and collapse. The evolution of the collapse is dominated by the chemistry involved. The dominant chemical processes that complicate the collapse are three-body H2 formation heating, collision-induced emission cooling and H2 collisional dissociation. The collapse becomes adiabatic at the formation of the pre-stellar core at 10−4 g cm−3, although this may happen at 10−6 g cm−3 if stellar feedback is considered (Machida & Nakamura, 2015). Due to the lack of dust and metals in the early Universe, the Jeans length continues to decrease as the gas collapses, all the way down to the formation of the pre-stellar core. This corresponds to an increase in density of 10 orders of magnitude from the first stellar core in present-day star formation when the gas becomes stable to fragmentation. The Pop III IMF is disputed among authors, but most recent studies agree that the gas fragments to form a group of stars within the halo. In Prole et al. (2022a) we performed a resolution study to show that these discrepancies are largely due to the difference in resolution adopted by these studies. We have shown that failure to resolve the Jeans length at the pre-stellar core density (0.01-0.1 au) results in underestimated fragmentation behaviour in the gas. The lower core masses that we produce when we increase our resolution effects how these stars interact with their environments through increased main sequence lifetimes, reduced contribution to reionisation, and ending their lives as Type II SN instead of a pair-instability explosion. We also noted that a number of cores are ejected from the system with masses low enough that they should have survived until the present day, and may be observable. This raises questions into the pollution of Pop III stars with metals throughout their lifetimes as an explanation for the lack of Pop III observations.
Magnetic fields have been shown to prevent fragmentation in present-day star formation simulations, increasing stellar masses. It is natural to expect that this may be the case in primordial star formation also. If this is the case, it would soften the resolution criteria discovered in Prole et al. (2022a). The main differences between magnetic fields in primordial times and the present day is their structure. The galactic magnetic field present today is uniform over the scales concerned with star formation. These highly ordered fields can provide a coherent magnetic tension force over large scales. Primordial magnetic fields go through the small-scale turbulent dynamo and are therefore expected to have small-scale structure described by a k3/2 power spectrum, where the magnetic energy increases towards smaller spatial scales. Despite this, the magnetic pressure is isotropic and can therefore provide extra support against the fragmentation caused by gravitational collapse at Jeans scales at the highest densities. In Prole et al. (2022b) we investigated whether primordial magnetic fields could reduce Pop III disc fragmentation. Since amplification via the small-scale turbulent dynamo is dependent on resolution (which is inherently finite in simulations), we opted to bypass the amplification process and introduce a fully saturated (maximum strength) magnetic field late into a non-magnetised collapse. We created the field by generating a random vector field from the k3/2 power spectrum and applied it to the central region of the collapse before the formation of the disc. We have shown that the small-scale fields do not reduce disc fragmentation or prevent the degree of fragmentation from increasing when the maximum density of the simulations is increased. As the inclusion of magnetic fields into these simulations greatly increases the computational cost without changing the results, we concluded that magnetic fields are not necessary in Pop III star formation simulations
The radiation that Pop III stares emits interacts with their environments in different ways. Photons with energies above the hydrogen ionisation limit go towards forming a HII region around the star, while photons below this limit are free to escape the halo and penetrate nearby halos. Lyman-Werner (LW) band photons photodissociate H2 in nearby halos, preventing star formation until the halo gains sufficient mass through mergers so that the outer layers can self-shield the inner H2 and form stars. While cosmological simulations have confirmed that the mass of halos required to form stars increases as the strength of the LW field is increased, these simulations lack sufficient resolution to resolve star formation within the halo. How the increasing halo masses effects the Pop III IMF is therefore unclear from cosmological simulations. In Prole et al. (2023) we performed zoom-in simulations around halos from the cosmological simulations of Schauer et al. (2021), resolving the formation of the pre-stellar core and following the fragmentation of the gas for hundreds of years after (see figure). While the mass accreted onto sink particles by the end of the simulations was not correlated with initial mass of the halo or the mass of gas that managed to initially form enough H2 to collapse, the accreted mass was correlated to the mass of the inner molecular core. Crucially, the mass of the molecular core was not correlated with the initial mass of the halo. The IMFs were almost identical across the LW field strengths, suggesting that the Pop III IMF may be invariant with halo mass and is therefore the same wherever we look in the early Universe, until the formation of Pop II stars.
