Implementation of stellar heating feedback in simulations of star cluster formation: effects on the initial mass function

Explaining the initial mass function (IMF) of stars is a long-standing problem in astrophysics. The number of complex mechanisms involved in the process of star cluster formation, such as turbulence, magnetic fields, and stellar feedback, make understanding and modelling the IMF a challenging task. In this paper, we aim to assert the importance of stellar heating feedback in the star cluster formation process and its effect on the shape of the IMF. We use an analytical sub-grid model to implement the radiative feedback in fully three-dimensional magnetohydrodynamical (MHD) simulations of star cluster formation, with the ultimate objective of obtaining numerical convergence on the IMF. We compare a set of MHD adaptive mesh refinement simulations with three different implementations of the heating of the gas: (1) a polytropic equation of state, (2) a spherically symmetric stellar heating feedback, and (3) our newly developed polar heating model that takes into account the geometry of the accretion disc and the resulting shielding of stellar radiation by dust. For each of the three heating models, we analyse the distribution of stellar masses formed in 10 molecular cloud simulations with different realizations of the turbulence to obtain a statistically representative IMF. We conclude that stellar heating feedback has a profound influence on the number of stars formed and plays a crucial role in controlling the IMF. We find that the simulations with the polar heating model achieve the best convergence on the observed IMF.