Abstract

The formation of the first stars in the Universe is regulated by a sensitive interplay of chemistry and cooling with the dynamics of a self-gravitating system. As the outcome of the collapse and the final stellar masses depend sensitively on the thermal evolution, it is necessary to accurately model the thermal evolution in high-resolution simulations. As previous investigations raised doubts regarding the convergence of the temperature at high resolution, we investigate the role of the numerical method employed to model the chemistry and the thermodynamics. Here we compare the standard implementation in the adaptive-mesh refinement code ENZO, employing a first-order backward differentiation formula (BDF), with the fifth-order accurate BDF solver DLSODES. While the standard implementation in ENZO shows a strong dependence on the employed resolution, the results obtained with DLSODES are considerably more robust, both with respect to the chemistry and thermodynamics, but also for dynamical quantities such as density, total energy or the accretion rate. We conclude that an accurate modelling of the chemistry and thermodynamics is central for primordial star formation.