A semi-analytic approach to angular momentum transport in stellar radiative interiors

Abstract

We address the problem of angular momentum transport in stellar radiative interiors with a novel semi-analytic spectral technique, using an eigenfunction series expansion, that can be used to derive benchmark solutions in hydromagnetic regimes with very high Reynolds number (10^7 - 10^8). The error arising from the truncation of the series is evaluated analytically. The main simplifying assumptions are the neglect of meridional circulation and of non-axisymmetric magnetic fields. The advantages of our approach are shown by applying it to a spin-down model for a 1 M_sun main-sequence star. The evolution of the coupling between core and envelope is investigated for different values of the viscosity and different geometries and values of the poloidal field. We confirm that a viscosity enhancement by 10^4 with respect to the molecular value is required to attain a rigid rotation in the core of the Sun within its present age. We suggest that a quadrupolar poloidal field may explain the short coupling time-scale needed to model the observed rotational evolution of fast rotators on the ZAMS, while a dipolar geometry is indicated in the case of slow rotators. Our novel semi-analytic spectral method provides a conceptually simple and rigorous treatment of a classic MHD problem and allows us to explore the influence of various parameters on the rotational history of radiative interiors.