Magnetic fields limit the mass of Population III stars even before the onset of protostellar radiation feedback

The masses of Population III stars are largely unconstrained since no simulations exist that take all relevant primordial star formation physics into account. We perform the first suite of radiation magnetohydrodynamics (RMHD) simulations of Population III star formation, with the POPSICLE project. Compared to control simulations that only include magnetic fields (MHD), protostellar ionizing and dissociating feedback, or neither, the RMHD simulation best resembles the MHD simulation during the earliest stages of collapse and star formation. In $5000\,\rm{yrs}$, the mass of the most massive star is $65\,\rm{M_{\odot}}$ in the RMHD simulation, compared to $120\,\rm{M_{\odot}}$ in simulations without magnetic fields. This difference arises because magnetic fields act against gravity, suppress mass transport, and reduce compressional heating. The maximum stellar mass of Population III stars is thus already limited by magnetic fields, even before accretion rates drop to allow significant protostellar radiative feedback. Following classical main sequence stellar evolution with MESA reveals that it is difficult to create Population III stars with masses larger than $600\,\rm{M_{\odot}}$ in typical dark matter minihaloes at $z \gtrsim 20$, with maximum stellar masses $\sim 100\,\rm{M_{\odot}}$ more likely due to expected negative feedback from both magnetic fields and stellar radiation. This work lays the first step in building a full physics-informed mass function of Population III stars.