A Simple Model for Solar Isorotational Contours

Abstract

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 instabilites. If isentropic and isorotational surfaces coincide in the SCZ, the gas is marginally (un)stable to {\em 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 midlatitudes. 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 good agreement between isentropes and isorotational contours in sufficiently well-resolved large scale numerical MHD simulations.

Final version: 21 pages, 4 figures, to appear in MNRAS; thorough revision, typos and minor errors corrected, expanded development and reordering of the material. Conclusions unchanged from original

References in corpus (1)

• MHD simulations of the magnetorotational instability in a shearing box with zero net flux. I. The issue of convergence

Cited by in corpus (28)

• Towards Realistic Progenitors of Core-Collapse Supernovae
• Anomalously Weak Solar Convection
• Beyond Mixing-length Theory: a step toward 321D
• Differential rotation of main-sequence dwarfs and its dynamo-efficiency
• High-resolution calculation of the solar global convection with the reduced speed of sound technique: II. Near surface shear layer with the rotation
• Astrophysical turbulence modeling
• Theory and simulations of rotating convection
• High S/N Keck and Gemini AO imaging of Uranus during 2012-2014: New cloud patterns, increasing activity, and improved wind measurements
• Convection Theory and Sub-photospheric Stratification
• On Differential Rotation and Convection in the Sun
• Differential rotation and meridional flow on the lower zero age main sequence: Reynolds stress versus baroclinic flow
• Global model of differential rotation in the Sun
• Rotation of Giant Stars
• Differential rotation of main-sequence dwarfs: predicting the dependence on surface temperature and rotation rate
• Revisiting the Sun's Strong Differential Rotation along Radial Lines
• Differential rotation in rapidly rotating early-type stars. I. Motivations for combined spectroscopic and interferometric studies
• Impact of MHD Turbulence on Thermal Wind Balance in the Sun
• A self-consistent model of the solar tachocline
• Differential Rotation in a 3D Simulation of Oxygen Shell Burning
• The Quest to Understand Supergranulation and Large-Scale Convection in the Sun
• Key Issues Review: Numerical studies of turbulence in stars
• Light or heavy supermassive black hole seeds: the role of internal rotation in the fate of supermassive stars
• Turbulent Mixing in Stars: Theoretical Hurdles
• Lorentz force mediation of turbulent dynamo transitions
• The effect of the tachocline on differential rotation in the Sun
• The 2D dynamics of radiative zones of low-mass stars
• Differential rotation in fully convective stars
• The stellar thermal wind as a consequence of oblateness