Differential rotation in fully convective stars
Abstract
Under the assumption of thermal wind balance and effective entropy mixing in constant rotation surfaces, the isorotational contours of the solar convective zone may be reproduced with great fidelity. Even at this early stage of development, this helioseismology fit may be used to put a lower bound on the midlatitude radial solar entropy gradient, which is in good accord with standard mixing length theory. In this paper, we generalize this solar calculation to fully convective stars (and potentially planets), retaining the assumptions of thermal wind balance and effective entropy mixing in isorotational surfaces. It is found that each isorotation contour is of the form R^{2} = A + BΦ(r), where R is the radius from the rotation axis, Φ(r) is the (assumed spherical) gravitational potential, and A and B are constants along the contour. This result is applied to simple models of fully convective stars. Both solarlike surface rotation profiles (angular velocity decreasing toward the poles) as well as `antisolar' profiles (angular velocity increasing toward the poles) are modelled; the latter bear some suggestive resemblance to numerical simulations. We also perform exploratory studies of zonal surface flows similar to those seen in Jupiter and Saturn. In addition to providing a practical framework for understanding the results of largescale numerical simulations, our findings may also prove useful in dynamical calculations for which a simple but viable model for the background rotation profile in a convecting fluid is needed. Finally, our work bears directly on an important goal of the CoRoT programme: to elucidate the internal structure of rotating, convecting stars.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 May 2010
 DOI:
 10.1111/j.13652966.2010.16380.x
 arXiv:
 arXiv:1001.3542
 Bibcode:
 2010MNRAS.404.1263B
 Keywords:

 convection;
 hydrodynamics;
 Sun: helioseismology;
 Sun: rotation;
 stars: rotation;
 Astrophysics  Solar and Stellar Astrophysics
 EPrint:
 21 pages, 20 figures. Accepted for publication in MNRAS