Our understanding of solar convection is incomplete. A crucial gap is the unknown superadiabaticity in the solar convection zone, δ = ▽–▽ad. Global modes of oscillations in the inertial frequency range are sensitive to δ and serve as a novel tool to explore solar convection. Here, we address the forward problem where the superadiabaticity δ(r) varies with radius. We solve the 2.5D eigenvalue problem, considering the linearized equations for momentum, mass and energy conservation with respect to a realistic solar model. We find that the frequency and eigenfunction of the m = 1 high-latitude mode are influenced by δ in the lower convection zone. Our prescribed setup suggests that the superadiabaticity in the lower half of the convection zone is below 2.4×10-7 to reach a qualitative agreement with the observed eigenfunction.

The Sun is the archetype of magnetic star and its proximity coupled with very high accuracy observations has helped us understanding how solar-like stars (e.g with a convective envelope) redistribute angular momentum and generate a cyclic magnetic field. However most solar models have been so fine tuned that when they are applied to other solar-like stars the agreement with observations is not good enough. I will thus discuss, based on theoretical considerations and multi-D MHD stellar models, what can be considered as robust properties of solar-like star dynamics and magnetism and what is still speculative. I will derive scaling laws for differential rotation and magnetic energy as a function of stellar parameters, discuss recent results of stellar dynamo models and define the new concept of spot-dynamo, e.g. global dynamo that develops self-consistent magnetic buoyant structures that emerge at the surface.

Three-dimensional global modelling of turbulent convection coupled to rotation and magnetism within the Sun are revealing processes relevant to many stars. We study spherical shells of compressible convection spanning many density scale heights using the MHD version of the anelastic spherical harmonic (ASH) code on massively parallel supercomputers. The simulations reveal that strong magnetic fields can be realized in the bulk of the solar convection zone while still attaining differential rotation profiles that make good contact with helioseismic findings. We find that the Maxwell and Reynolds stresses present in such a turbulent layer play an important role in redistributing angular momentum, with the latter maintaining the differential rotation, aided by baroclinic forcing at the base of the convection zone which is consistent with a tachocline there. The dynamo processes generate strong non-axisymmetric and intermittent fields and weak mean (axisymmetric) fields, but do not possess a regular cyclic magnetism. The explicit inclusion of penetrative convection into the tachocline below is modifying such behavior, serving to build strong toroidal magnetic fields there that may yield more prominent mean fields that have the potential of erupting upward.