Magnetic and rotational quenching of the Λ effect

¹ Georg-August-Universität Göttingen, Institut für Astrophysik, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
e-mail: pkaepyl@uni-goettingen.de
² Leibniz-Institut für Astrophysik, An der Sternwarte 16, 14482 Potsdam, Germany
³ ReSoLVE Centre of Excellence, Department of Computer Science, Aalto University, PO Box 15400 00076 Aalto, Finland
⁴ Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
⁵ NORDITA, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden

Received: 21 December 2017
Accepted: 6 January 2019

Abstract

Context. Differential rotation in stars is driven by the turbulent transport of angular momentum.

Aims. Our aim is to measure and parameterize the non-diffusive contribution to the total (Reynolds plus Maxwell) turbulent stress, known as the Λ effect, and its quenching as a function of rotation and magnetic field.

Methods. Simulations of homogeneous, anisotropically forced turbulence in fully periodic cubes are used to extract their associated turbulent Reynolds and Maxwell stresses. The forcing is set up such that the vertical velocity component dominates over the horizontal ones, as in turbulent stellar convection. This choice of the forcing defines the vertical direction. Additional preferred directions are introduced by the imposed rotation and magnetic field vectors. The angle between the rotation vector and the vertical direction is varied such that the latitude range from the north pole to the equator is covered. Magnetic fields are introduced by imposing a uniform large-scale field on the system. Turbulent transport coefficients pertaining to the Λ effect are obtained by fitting. The results are compared with analytic studies.

Results. The numerical and analytic results agree qualitatively at slow rotation and low Reynolds numbers. This means that vertical (horizontal) transport is downward (equatorward). At rapid rotation the latitude dependence of the stress is more complex than predicted by theory. The existence of a significant meridional Λ effect is confirmed. Large-scale vorticity generation is found at rapid rotation when the Reynolds number exceeds a threshold value. The Λ effect is severely quenched by large-scale magnetic fields due to the tendency of the Reynolds and Maxwell stresses to cancel each other. Rotational (magnetic) quenching of Λ occurs at more rapid rotation (at lower field strength) in the simulations than in the analytic studies.

Conclusions. The current results largely confirm the earlier theoretical results, and also offer new insights: the non-negligible meridional Λ effect possibly plays a role in the maintenance of meridional circulation in stars, and the appearance of large-scale vortices raises the question of their effect on the angular momentum transport in rapidly rotating stellar convective envelopes. The results regarding magnetic quenching are consistent with the strong decrease in differential rotation in recent semi-global simulations and highlight the importance of including magnetic effects in differential rotation models.