Rotation rate of the solar core as a key constraint to magnetic angular momentum transport in stellar interiors

Context. The internal rotation of the Sun constitutes a fundamental constraint when modelling angular momentum transport in stellar
interiors. In addition to the more external regions of the solar radiative zone probed by pressure modes, measurements of rotational
splittings of gravity modes would offer an invaluable constraint on the rotation of the solar core.
Aims. We study the constraints that a measurement of the core rotation rate of the Sun could bring on magnetic angular momentum
transport in stellar radiative zones.
Methods. Solar models accounting for angular momentum transport by hydrodynamic and magnetic instabilities were computed
for different initial velocities and disc lifetimes on the pre-main sequence to reproduce the surface rotation velocities observed for
solar-type stars in open clusters. The internal rotation of these solar models was then compared to helioseismic measurements.
Results. We first show that models computed with angular momentum transport by magnetic instabilities and a recent prescription for
the braking of the stellar surface by magnetized winds can reproduce the observations of surface velocities of stars in open clusters.
These solar models predict both a flat rotation profile in the external part of the solar radiative zone probed by pressure modes and
an increase in the rotation rate in the solar core, where the stabilizing effect of chemical gradients plays a key role. A rapid rotation
of the core of the Sun, as suggested by reported detections of gravity modes, is thus found to be compatible with angular momentum
transport by magnetic instabilities. Moreover, we show that the efficiency of magnetic angular momentum transport in regions of
strong chemical gradients can be calibrated by the solar core rotation rate independently from the unknown rotational history of the
Sun. In particular, we find that a recent revised prescription for the transport of angular momentum by the Tayler instability can be
easily distinguished from the original Tayler-Spruit dynamo, with a faster rotating solar core supporting the original prescription.
Conclusions. By calibrating the efficiency of magnetic angular momentum transport in regions of strong chemical gradients, a determination of the solar core rotation rate through gravity modes is of prime relevance not only for the Sun, but for stars in general, since
radial differential rotation precisely develops in these regions during the more advanced stages of evolution.