Backtracing the internal rotation history of the

Context. HD 129929 is a slowly rotating β Cephei pulsator with a rich spectrum of detected oscillations, including two rotational multiplets. The asteroseismic interpretation revealed the presence of radial differential rotation in this massive star of ∼9.35 M⊙. The stellar core is indeed estimated to spin ∼3.6 times faster than the surface. The surface rotation was consequently derived as v ∼ 2 km s−1. This massive star represents an ideal counterpart to the wealth of space-based photometry results for main-sequence and evolved low-mass stars. Those latter stars have revealed a new, and often unexpected, picture of the angular momentum transport processes acting in stellar interiors. Aims. We investigate in a new way the constraints on the internal rotation of HD 129929, as a marker of the evolution of the internal rotation during the main sequence of a massive star. We test both hydrodynamic and magnetic instability transport processes of angular momentum. Methods. We used the best asteroseismic model obtained in an earlier work. We calibrated stellar models including rotation, with different transport processes, to reproduce that reference model. We then looked to determine whether one process is favoured to reproduce the rotation profile of HD 129929, based on the fit of the asteroseismic multiplets. Results. The impact of the Tayler magnetic instability on the angular momentum transport predicts a ratio of the core-to-surface rotation rate of only 1.6, while the recently revised prescription of this mechanism predicts solid-body rotation. Both are too low in comparison with the asteroseismic inference. The models with only hydrodynamic processes are in good agreement with the asteroseismic measurements. Strikingly, we can also get a constraint on the profile of rotation on the zero age main sequence: likely, the ratio between the core and surface rotation was at least ∼1.7. Conclusions. Transport of angular momentum by the Tayler magnetic instability is discarded for this star. The models with pure hydrodynamical processes reproduce the asteroseismic constraints. This result is specific to a slow rotator and has to be verified more generally in other massive main-sequence stars. Constraints on the rotation in earlier stages of this star also offer a new opportunity to test the impact of accretion during the pre-main sequence evolution