Converging on the Initial Mass Function of Stars

Understanding the origin of stellar masses - the initial mass function (IMF) - remains one of the most challenging problems in astrophysics. The IMF is a key ingredient for simulations of galaxy formation and evolution, and is used to calibrate star formation relations in extra-galactic observations. Modeling the IMF directly in hydrodynamical simulations has been attempted in several previous studies, but the most important processes that control the IMF remain poorly understood. This is because predicting the IMF from direct hydrodynamical simulations involves complex physics such as turbulence, magnetic fields, radiation feedback and mechanical feedback, all of which are difficult to model and the methods used have limitations in terms of accuracy and computational efficiency. Moreover, a physical interpretation of the simulated IMFs requires a numerically converged solution at high resolution, which has so far not been convincingly demonstrated. Here we present a resolution study of star cluster formation aimed at producing a converged IMF. We compare a set of magnetohydrodynamical (MHD) adaptive-mesh-refinement simulations with three different implementations of the thermodynamics of the gas: 1) with an isothermal equation of state (EOS), 2) with a polytropic EOS, and 3) with a simple stellar heating feedback model. We show that in the simulations with an isothermal or polytropic EOS, the number of stars and their mass distributions depend on the numerical resolution. By contrast, the simulations that employ the simple radiative feedback module demonstrate convergence in the number of stars formed and in their IMFs.