Deciphering Solar Convection

Numerical modeling of solar and stellar convection, and by extension modeling of solar and stellar dynamos faces a surprising challenge. No hydrodynamic, magnetohydrodynamic, or radiative magnetohydrodynamic model of solar convection, if conducted in a sufficiently deep domain, achieves the velocity power spectrum implied by observations of the Sun. The horizontal velocity at low wavenumbers in the upper layers of the simulation domains is much too high, monotonically increasing to low wavenumber rather than rolling over at supergranular scales, as on the Sun. This reflects convective amplitudes at depth that are similarly too large, and results in equatorial differential rotation profiles in simulations of rotating spherical shells of opposite sign to those observed. The problem worsens in models with decreasing diffusivities, as the amplitudes of the convective motions increase. This has come to be known as the convective conundrum. Solving it is critical to understanding dynamo behavior on stars, which in turn is central to the assessment of the structure of the asterospheres in which their planetary companions are embedded. This paper examines what is known about solar convection in light of one possible underlying cause of the convective conundrum, that the deep interior of the Sun is even more nearly adiabatically stratified than our models suggest or can achieve. Correcting this in models will likely be difficult, but we point in some potentially fruitful directions.