The effects of surface fossil magnetic fields on massive star evolution: II. Implementation of magnetic braking in MESA and implications for the evolution of surface rotation in OB stars

The time evolution of angular momentum and surface rotation of massive stars is strongly influenced by fossil magnetic fields via magnetic braking. We present a new module containing a simple, comprehensive implementation of such a field at the surface of a massive star within the Modules for Experiments in Stellar Astrophysics (MESA) software instrument. We test two limiting scenarios for magnetic braking: distributing the angular momentum loss throughout the star in the first case, and restricting the angular momentum loss to a surface reservoir in the second case. We perform a systematic investigation of the rotational evolution using a grid of OB star models with surface magnetic fields ($M_\star=5-60$ M$_\odot$, $\Omega/\Omega_{\rm crit} =0.2-1.0$, $B_{\rm p} =1-20$ kG). We then employ a representative grid of B-type star models ($M_\star=5, 10, 15$ M$_\odot$, $\Omega/\Omega_{\rm crit} =0.2 , 0.5, 0.8$, $B_{\rm p} = 1, 3 ,10, 30$ kG) to compare to the results of a recent self-consistent analysis of the sample of known magnetic B-type stars. We infer that magnetic massive stars arrive at the zero age main sequence with a range of rotation rates, rather than with one common value. In particular, some stars are required to have close-to-critical rotation at the ZAMS. However, magnetic braking yields surface rotation rates converging to a common low value, making it difficult to infer the initial rotation rates of evolved, slowly-rotating stars.