Population III star formation in the presence of turbulence, magnetic fields and ionizing radiation feedback

Turbulence, magnetic fields and radiation feedback are key components that shape the formation of stars, especially in the metal-free environments at high redshifts where Population III stars form. Yet no 3D numerical simulations exist that simultaneously take all of these into account. We present the first suite of radiation-magnetohydrodynamics (RMHD) simulations of Population III star formation using the adaptive mesh refinement (AMR) code FLASH. We include both turbulent magnetic fields and ionizing radiation feedback coupled to primordial chemistry, and resolve the collapse of primordial clouds down to few au. We find that dynamically strong magnetic fields significantly slow down accretion onto protostars, while ionizing feedback is largely unable to regulate gas accretion because the partially ionized \ion{H}{ii} region gets trapped near the star due to insufficient radiative outputs from the star. The maximum stellar mass in the HD and RHD simulations that only yield one star exceeds $100\,\rm{M_{\odot}}$ within the first $5000\,\rm{yr}$. However, in the corresponding MHD and RMHD runs, the maximum mass of Population III star is only $60\,\rm{M_{\odot}}$. In other realizations where we observe widespread fragmentation leading to the formation of Population III star clusters, the maximum stellar mass is further reduced by a factor of few due to fragmentation-induced starvation. We thus conclude that magnetic fields are more important than ionizing feedback in regulating the mass of the star, at least during the earliest stages of Population III star formation, in typical dark matter minihaloes at $z \approx 30$.