The effect of the tachocline on differential rotation in the Sun

TL;DR

This paper develops a mathematical model to understand how the tachocline influences the Sun's differential rotation, revealing detailed features that match observations and suggesting a thermal wind balance in the convection zone.

Contribution

The paper introduces a new model linking tachocline dynamics to solar rotation patterns using entropy assumptions and quadrupolar stresses, providing detailed solutions matching observed contours.

Findings

Model reproduces observed tachocline isorotation contours

Quadrupolar structure is key to the rotation pattern

Supports thermal wind balance in the convection zone

Abstract

In this paper, we present a model for the effects of the tachocline on the differential rotation in the solar convection zone. The mathematical technique relies on the assumption that entropy is nearly constant ("well-mixed") in isorotation surfaces both outside and within the tachocline. The resulting solutions exhibit nontrivial features that strikingly resemble the true tachocline isorotation contours in unexpected detail. This strengthens the mathematical premises of the theory. The observed rotation pattern in the tachocline shows strong quadrupolar structure, an important feature that is explicitly used in constructing our solutions. The tachocline is treated locally as an interior boundary layer of small but finite thickness, and an explicit global solution is then constructed. A dynamical link can thus be established between the internal jump in the angular velocity at the tachocline and the spread of angular velocities observed near the solar surface. In general, our results suggest that the bulk of the solar convection zone is in thermal wind balance, and that simple quadrupolar stresses, local in radius, mediate the tachocline transition from differential rotation to uniform rotation in the radiative interior.