The angular momentum transport by unstable toroidal magnetic fields

Abstract

We demonstrate with a nonlinear magnetohydrodynamic (MHD) code that angular momentum can be transported because of the magnetic instability of toroidal fields under the influence of differential rotation, and that the resulting effective viscosity may be high enough to explain the almost rigid-body rotation observed in radiative stellar cores. We only consider stationary, current-free fields, and only those combinations of rotation rates and magnetic field amplitudes which provide maximal numerical values of the viscosity. We find that the dimensionless ratio of the effective over molecular viscosity, ν T /ν, linearly grows with the Reynolds number of the rotating fluid multiplied by the square-root of the magnetic Prandtl number, which is approximately unity for the considered red subgiant star KIC 7341231. For the interval of magnetic Reynolds numbers considered -which is restricted by numerical constraints of the nonlinear MHD code -the magnetic Prandtl number has a remarkable influence on the relative importance of the contributions of the Reynolds stress and the Maxwell stress to the total viscosity, which is magnetically dominated only for Pm > ∼ 0.5. We also find that the magnetized plasma behaves as a non-Newtonian fluid, i.e., the resulting effective viscosity depends on the shear in the rotation law. The decay time of the differential rotation thus depends on its shear and becomes longer and longer during the spin-down of a stellar core.

Near-degeneracy effects on the frequencies of rotationally-split mixed modes in red giants

“…The main candidates invoked so far are internal gravity waves (Charbonnel & Talon 2005;Talon & Charbonnel 2008;Fuller et al 2014) and magnetic fields that either have a fossil origin (e.g., Gough & McIntyre 1998;Spada et al 2010;Maeder & Meynet 2014) or result from magneto-hydrodynamic (MHD) instabilities (e.g. Spruit 1999;Rüdiger et al 2015). However, the relative importance of these processes and the timescales over which they operate is still a matter of active debate.…”

“…More recently it has been shown that a similar conclusion can be drawn for intermediate-mass stars in the core-He burning phase, where an even milder radial differential rotation was observed, with core-envelope ratios around two . These novel observational constraints prompted new theoretical studies about the efficiency of angular momentum transport caused by internal gravity waves (Fuller et al 2014), MHD instabilities (Rüdiger et al 2015;Jouve et al 2015), or mixed modes themselves (Belkacem et al 2015b,a), but the question remains open.…”

Three-dimensional evolution of magnetic fields in a differentially rotating stellar radiative zone

“…It has also been used in the context of planetary interiors (Petitdemange et al 2008(Petitdemange et al , 2013 where a modified version of the MRI was shown to be able to operate in the magnetospheric force balance relevant to the Earth's core. In stellar physics, the MRI of a purely poloidal or purely toroidal field was studied using local stability criteria (Menou et al 2004;Masada et al 2006) or using global analysis in spherical (Arlt et al 2003) or cylindrical (Ogilvie & Pringle 1996;Rüdiger et al 2014Rüdiger et al , 2015 geometries, with a particular focus on the induced transport of angular momentum in the last two articles. However, considering the level of differential rotation and the presence of strong magnetic fields in various situations encountered in stellar radiative zones, this mechanism could have attracted more attention.…”

A hydrostatic MHD code for modeling stellar interiors

“…See Ibáñez-Mejía & Braithwaite (2015) for a discussion of this point. Braithwaite (2006) and Rüdiger et al (2015) find the mechanism in simulations. However, further numerical work is needed.…”

“…Differential rotation will wind up any seed field into a predominantly toroidal configuration, which is then unstable to an interchange instability (Tayler 1973), and in so decaying, a new poloidal field is produced that can be wound up anew by the differential rotation, thereby closing a dynamo loop (Spruit 2002). This dynamo process should result in transport of angular momentum and chemical elements in the radial direction, and a prescription for this has been implemented in some stellar evolution models (e.g., Heger et al 2005;Suijs et al 2008).…”