Is the solar convection zone in strict thermal wind balance?

Abstract

Context. The solar rotation profile is conical rather than cylindrical as it could be expected from classical rotating fluid dynamics (e.g. Taylor-Proudman theorem). Thermal coupling to the tachocline, baroclinic effects and latitudinal transport of heat have been suggested to explain this peculiar state of rotation. Aims. To test the validity of thermal wind balance in the solar convection zone using helioseismic inversions for both the angular velocity and fluctuations in entropy and temperature. Methods. Entropy and temperature fluctuations obtained from 3D hydrodynamical numerical simulations of the solar convection zone are compared with solar profiles obtained from helioseismic inversions. Results. The temperature and entropy fluctuations in 3D numerical simulations have smaller amplitude in the bulk of the solar convection zone than those derived from seismic inversions. Seismic inversion provides variations of temperature from about 1 K at the surface to up to 100 K at the base of the convection zone while in 3D simulations they are of an order of 10 K throughout the convection zone up to 0.96 R . In 3D simulations, baroclinic effects are found to be important to tilt the isocontours of Ω away from a cylindrical profile in most of the convection zone, helped by Reynolds and viscous stresses at some locations. By contrast the baroclinic effect inverted by helioseismology is much larger than what is required to yield the observed angular velocity profile. Conclusions. The solar convection does not appear to be in strict thermal wind balance, Reynolds stresses must play a dominant role in setting not only the equatorial acceleration but also the observed conical angular velocity profile.

Differential rotation of main-sequence dwarfs and its dynamo efficiency

“…Balbus et al 2009). Similar results on the Taylor–Proudman balance are provided by 3D numerical simulations (Miesch et al 2006; Brun, Antia & Chitre 2010).…”

Characterizing the feedback of magnetic field on the differential rotation of solar-like stars

“…Hydro simulations show stronger gradients than the MHD cases in agreement with the overall large angular velocity contrast. Figure 9 shows the temper- The presence of gradients in temperature and entropy leads to a mismatch of the iso-surfaces of mean density and pressure that is named baroclinicity and appears in the vorticity equation (Zahn, 1992;Miesch et al, 2006;Brun et al, 2010). The baroclinic term contributes to breaking Taylor constraint of a cylindrical mean flow yielding more complex (conical) angular velocity profiles (Kitchatinov & Ruediger, 1995).…”

Convective differential rotation in stars and planets – I. Theory

“…More recently, and in part owing to dramatic improvements in observational capabilities, differential rotation has garnered substantial theoretical attention. Some authors argue that thermal wind balance and entropy gradients dominate the solar rotation profile (Miesch et al 2006;Balbus & Schaan 2012), while others have called this into question (Brun et al 2010;Brun & Toomre 2002). Observations suggest that the thermal wind term is substantial, though there remain uncertainties as to its precise contribution (Caccin et al 1976;Rast et al 2008;Teplitskaya et al 2015).…”