Numerical tests of rotational mixing in massive stars with the new population synthesis code BONNFIRES

We use our new population synthesis code BONNFIRES to test how surface abundances predicted by rotating stellar models depend on the numerical treatment of rotational mixing, such as spatial resolution, temporal resolution, and computation of mean molecular weight gradients. In stellar evolution codes the process of transporting chemical species and angular momentum is usually approximated as a diffusion process. We find that even with identical numerical prescriptions for calculating the rotational mixing coefficients in the diffusion equation, different timesteps lead to a deviation of the coefficients and hence surface abundances. We find the surface abundances vary by 10-100% between the model sequences with short timestep of 0.001 Myr to model sequences with long timesteps of 0.1-1 Myr. Model sequences with stronger surface nitrogen enrichment also have longer main-sequence lifetimes because more hydrogen is mixed to the burning cores. The deviations in main-sequence lifetimes can be as large as 20%. Mathematically speaking, no numerical scheme can give a perfect solution unless infinitesimally small timesteps are used, which is computationally not practical. However, we find that the surface abundances eventually converge within 10% between modelling sequences with sufficiently small timesteps below 0.1Myr. The efficiency of rotational mixing depends on the implemented numerical scheme and critically on the computation of the mean molecular weight gradient. A smoothing function for the mean molecular weight gradient results in stronger rotational mixing. When comparing observations with detailed theoretical models made by stellar evolutionary codes or population synthesis codes such as BONNFIRES, deviations of surface abundances because of numerical treatments have to be considered carefully. Calibrations of rotational mixing parameters therefore depend on the chosen discretization schemes. If the discretization scheme or the computational recipe for calculating the mean molecular weight gradient is altered, re-calibration of mixing parameters may be required to fit observations. If we are to properly understand the fundamental physics of rotation in stars, it is crucial that we minimize the uncertainty introduced into stellar evolution models when numerically approximating rotational mixing processes.