The Sun, Earth's star, is of fundamental interest for life on our planet and remains a source of many scientific mysteries. The motion in its interior is complex and involves diverse physical phenomena at many scales, from nuclear to astronomical. In this Colloquium the unusual flow of mass and energy inside the convective region of our yellow star is discussed.

Colloquium: Unusual dynamics of convection in the Sun

Recent advances in mean-field theory are reviewed and applications to the Sun, late-type stars, accretion disks, galaxies and the early Universe are discussed. We focus particularly on aspects of spatio-temporal non-locality, which provided some of the main new qualitative and quantitative insights that emerged from applying the test-field method to magnetic fields of different length and time scales. We also review the status of nonlinear quenching and the relation to magnetic helicity, which is an important observational diagnostic of modern solar dynamo theory. Both solar and some stellar dynamos seem to operate in an intermediate regime that has not yet been possible to model successfully. This regime is bracketed by antisolar-like differential rotation on one end and stellar activity cycles belonging to the superactive stars on the other. The difficulty in modelling this regime may be related to shortcomings in simulating solar/stellar convection. On galactic and extragalactic length scales, the observational constraints on dynamo theory are still less stringent and more uncertain, but recent advances both in theory and observations suggest that more conclusive comparisons may soon be possible also here. The possibility of inversely cascading magnetic helicity in the early Universe is particularly exciting in explaining the recently observed lower limits of magnetic fields on cosmological length scales. Such magnetic fields may be helical with the same sign of magnetic helicity throughout the entire Universe. This would be a manifestation of parity breaking.

Advances in mean-field dynamo theory and applications to astrophysical turbulence

Observations suggest that the large-scale convective velocities obtained by solar convection simulations might be over-estimated (convective conundrum). One plausible solution to this could be the small-scale dynamo which cannot be fully resolved by global simulations. The small-scale Lorentz force suppresses the convective motions and also the turbulent mixing of entropy between upflows and downflows, leading to a large effective Prandtl number (Pr). We explore this idea in three-dimensional global rotating convection simulations at different thermal conductivity (κ), i.e., at different Pr. In agreement with previous non-rotating simulations, the convective velocity is reduced with the increase of Pr as long as the thermal conductive flux is negligible. A subadiabatic layer is formed near the base of the convection zone due to continuous deposition of low entropy plumes in low-κ simulations. The most interesting result of our low-κ simulations is that the convective motions are accompanied by a change in the convection structure that is increasingly influenced by small-scale plumes. These plumes tend to transport angular momentum radially inward and thus establish an anti-solar differential rotation, in striking contrast to the solar rotation profile. If such low diffusive plumes, driven by the radiative-surface cooling, are present in the Sun, then our results cast doubt on the idea that a high effective Pr may be a viable solution to the solar convective conundrum. Our study also emphasizes that any resolution of the conundrum that relies on the downward plumes must take into account the angular momentum transport and heat transport.

Consequences of high effective prandtl number on solar differential rotation and convective velocity

It has recently been recognized that the convective velocities achieved in current solar convection simulations might be overestimated. The newly revealed effects of the prevailing small-scale magnetic field within the convection zone may offer possible solutions to this problem. The small-scale magnetic fields can reduce the convective amplitude of small-scale motions through the Lorentz-force feedback, which concurrently inhibits the turbulent mixing of entropy between upflows and downflows. As a result, the effective Prandtl number may exceed unity inside the solar convection zone. In this paper, we propose and numerically confirm a possible suppression mechanism of convective velocity in the effectively high-Prandtl number regime. If the effective horizontal thermal diffusivity decreases (the Prandtl number accordingly increases), the subadiabatic layer which is formed near the base of the convection zone by continuous depositions of low entropy transported by adiabatically downflowing plumes is enhanced and extended. The global convective amplitude in the high-Prandtl thermal convection is thus reduced, especially in the lower part of the convection zone via the change in the mean entropy profile, which becomes more subadiabatic near the base and less superadiabatic in the bulk.

Convective Velocity Suppression via the Enhancement of the Subadiabatic Layer: Role of the Effective Prandtl Number

Progress in the theory of stellar convection over the past decade is reviewed. The similarities and differences between convection in stellar envelopes and laboratory convection at high Rayleigh numbers are discussed. Direct numerical simulation of the solar surface layers, with no other input than atomic physics, the equations of hydrodynamics and radiative transfer is now capable of reproducing the observed heat flux, convection velocities, granulation patterns and line profiles with remarkably accuracy. These results show that convection in stellar envelopes is an essentially non-local process, being driven by cooling at the surface. This differs distinctly from the traditional view of stellar convection in terms of local concepts such as cascades of eddies in a mean superadiabatic gradient. The consequences this has for our physical picture of processes in the convective envelope are illustrated with the problems of sunspot heat flux blocking, the eruption of magnetic flux from the base of the convection zone, and the Lithium depletion problem.

Bridget O’Mara

Papers

Velocity amplitudes in global convection simulations: The role of the Prandtl number and near-surface driving