Understanding the evolution of self-gravitating, isothermal, magnetized gas is crucial for star formation, as these physical processes have been postulated to set the initial mass function (IMF). We present a suite of isothermal magnetohydrodynamic (MHD) simulations using the GIZMO code, that resolve the formation of individual stars in giant molecular clouds (GMCs), spanning a range of Mach numbers found in observed GMCs. As in past works, the mean and median stellar masses are sensitive to numerical resolution, because they are sensitive to low-mass stars that contribute a vanishing fraction of the overall stellar mass. The { \em mass-weighted} median stellar mass $M_\mathrm{ 50}$ becomes insensitive to resolution once turbulent fragmentation is well-resolved. Without imposing Larson-like scaling laws, our simulations find $M_\mathrm{ 50} \propto M_\mathrm{ 0} \mathcal{ M}^{ -3} \alpha_\mathrm{ turb} \mathrm{ SFE}^{ 1/3}$ for GMC mass $M_\mathrm{ 0}$, sonic Mach number $\mathcal{ M}$, virial parameter $\alpha_\mathrm{ turb}$, and star formation efficiency $\mathrm{ SFE}=M_\mathrm{ \star}/M_\mathrm{ 0}$. This fit agrees well with previous IMF results from the RAMSES, ORION2, and SphNG codes. Although $M_\mathrm{ 50}$ has no significant dependence on the magnetic field strength at the cloud scale, MHD is necessary to prevent a fragmentation cascade that results in non-convergent stellar masses. For initial conditions and SFE similar to star-forming GMCs in our Galaxy, we predict $M_\mathrm{ 50}$ to be $>20 M_{ \odot}$, an order of magnitude larger than observed ($\sim 2 M_\odot$), together with an excess of brown dwarfs. Moreover, $M_\mathrm{ 50}$ is sensitive to initial cloud properties and evolves strongly in time within a given cloud, predicting much larger IMF variations than are observationally allowed. We conclude that physics beyond MHD turbulence and gravity are necessary ingredients for the IMF.
Categories: astro-ph.GA