Is the solar convection zone in strict thermal wind balance?

¹ Laboratoire AIM, CEA/DSM-CNRS-Université Paris Diderot, IRFU/SAp, 91191 Gif-sur-Yvette, France e-mail: sacha.brun@cea.fr
² LUTH, Observatoire de Paris, CNRS-Université Paris Diderot, Place Jules Janssen, 92195 Meudon, France
³ Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
⁴ Centre for Basic Sciences, University of Mumbai, Mumbai 400098, India

Received: 22 August 2009
Accepted: 14 October 2009

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 . 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.