Magnetic and rotational quenching of the $\Lambda$ effect

Context: Differential rotation in stars is driven by turbulent transport of angular momentum. Aims: To measure and parametrize the non-diffusive contribution to turbulent stress, known as $\Lambda$ 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 the turbulent Reynolds and Maxwell stresses. Magnetic fields are introduced by imposing a uniform large-scale field on the system. Turbulent transport coefficients pertaining to the $\Lambda$ effect are obtained by fitting. Results: The numerical results agree qualitatively with analytic ones at slow rotation and low Reynolds numbers. This entails that vertical (horizontal) transport is downward (equatorward). The existence of a significant meridional $\Lambda$ effect is confirmed. Large-scale vorticity generation is found at rapid rotation when the Reynolds number exceeds a threshold value. The $\Lambda$ 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 $\Lambda$ occurs at more rapid rotation (at lower field strength) in simulations than in theory. Conclusions: The current results largely confirm the earlier theoretical results but they also offer new insights: the non-negligible meridional $\Lambda$ 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 stars. The results regarding magnetic quenching are consistent with the strong decrease of differential rotation in recent semi-global simulations and highlight the importance of including magnetic effects in differential rotation models. (abridged)
Comment: 14 pages, 9 figures, version accepted to Astron. Astrophys