Journal Article

A simple model for solar isorotational contours

Steven A. Balbus

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 395, issue 4, pages 2056-2064
Published in print June 2009 | ISSN: 0035-8711
Published online May 2009 | e-ISSN: 1365-2966 | DOI:
A simple model for solar isorotational contours

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The solar convective zone, or SCZ, is nearly adiabatic and marginally convectively unstable. But, the SCZ is also in a state of differential rotation, and its dynamical stability properties are those of a weakly magnetized gas. This renders it far more prone to rapidly growing rotational baroclinic instabilities than a hydrodynamical system would be. These instabilities should be treated on the same footing as convective instabilities. If isentropic and isorotational surfaces coincide in the SCZ, the gas is marginally (un)stable to both convective and rotational disturbances. This is a plausible resolution for the instabilities associated with these more general rotating convective systems. This motivates an analysis of the thermal wind equation in which isentropes and isorotational surfaces are identical. The characteristics of this partial differential equation correspond to isorotation contours, and their form may be deduced even without precise knowledge of how the entropy and rotation are functionally related. Although the exact solution of the global SCZ problem in principle requires this knowledge, even the simplest models produce striking results in broad agreement with helioseismology data. This includes horizontal (i.e. quasi-spherical) isorotational contours at the poles, axial contours at the equator and approximately radial contours at mid-latitudes. The theory does not apply directly to the tachocline, where a simple thermal wind balance is not expected to be valid. The work presented here is subject to tests of self-consistency, among them the prediction that there should be a good agreement between isentropes and isorotational contours in sufficiently well-resolved large-scale numerical magnetohydrodynamics simulations.

Keywords: convection; instabilities; MHD; Sun: helioseismology

Journal Article.  6217 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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