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Modeling the surface brightness distribution of stars is of prime importance to interpret observations. Nevertheless, this remains quite challenging for cool stars as it requires one to model the MHD turbulence that develops in their convective envelope. In Paper I, the effect of the Coriolis acceleration on the surface heat flux has been studied by means of hydrodynamic simulations. In this paper, we aim to investigate the additional effect of dynamo magnetic fields. We focus on an envelope thickness that is representative of either a $\sim0.35~M_\odot$ M dwarf, a young red giant star or a pre-main sequence star. We performed a parametric study using numerical MHD simulations of anelastic convection in thick rotating spherical shells. For each model, we computed the mean surface distribution of the heat flux, and examined the leading-order effect of the magnetic field on the obtained latitudinal luminosity profile. We identify three different regimes. Close to the onset of convection, while the first unstable modes tend to convey heat more efficiently near the equator, magnetic fields are shown to generally enhance the mean heat flux close to the polar regions (and the tangent cylinder). By progressively increasing the Rayleigh number, the development of a prograde equatorial jet was previously shown to make the equator darker when no magnetic field is taken into account. For moderate Rayleigh numbers, magnetic fields can instead inverse the mean pole-equator brightness contrast (which means going from a darker to a brighter equator when a dynamo sets in) and finally induce a similar regime to that found close to the onset of convection. For more turbulent models with larger Rayleigh numbers, magnetic fields alternatively tend to smooth out the brightness contrast. This general behavior is shown to be related to the quenching of the surface differential rotation by magnetic fields., Comment: Accepted in A&A - Acceptance date: 04/03/2024

Stably stratified layers are present in stellar interiors (radiative zones) as well as planetary interiors - recent observations and theoretical studies of the Earth's magnetic field seem to indicate the presence of a thin, stably stratified layer at the top of the liquid outer core. We present direct numerical simulations of this region, which is modelled as an axisymmetric spherical Couette flow for a stably stratified fluid embedded in a dipolar magnetic field. For strong magnetic fields, a super-rotating shear layer, rotating nearly 30% faster than the imposed rotation rate difference between the inner convective dynamo region and the outer boundary, is generated in the stably stratified region. In the Earth context, and contrary to what was previously believed, we show that this super-rotation may extend towards the Earth magnetostrophic regime if the density stratification is sufficiently large. The corresponding differential rotation triggers magnetohydrodynamic instabilities and waves in the stratified region, which feature growth rates comparable to the observed timescale for geomagnetic secular variations and jerks. In the stellar context, we perform a linear analysis which shows that similar instabilities are likely to arise, and we argue that it may play a role in explaining the observed magnetic dichotomy among intermediate-mass stars., Comment: 18 pages, 6 figures. Accepted for publication in GAFD

Observations of low-mass stars reveal a variety of magnetic field topologies ranging from large-scale, axial dipoles to more complex magnetic fields. At the same time, three-dimensional spherical simulations of convectively driven dynamos reproduce a similar diversity, which is commonly obtained either with Boussinesq models or with more realistic models based on the anelastic approximation, which take into account the variation of the density with depth throughout the convection zone. Nevertheless, a conclusion from different anelastic studies is that dipolar solutions seem more difficult to obtain as soon as substantial stratifications are considered. In this paper, we aim at clarifying this point by investigating in more detail the influence of the density stratification on dipolar dynamos. To that end, we rely on a systematic parameter study that allows us to clearly follow the evolution of the stability domain of the dipolar branch as the density stratification is increased. The impact of the density stratification both on the dynamo onset and the dipole collapse is discussed and compared to previous Boussinesq results. Furthermore, our study indicates that the loss of the dipolar branch does not ensue from a specific modification of the dynamo mechanisms related to the background stratification, but could instead result from a bias as our observations naturally favour a certain domain in the parameter space characterized by moderate values of the Ekman number, owing to current computational limitations. Moreover, we also show that the critical magnetic Reynolds number of the dipolar branch is scarcely modified by the increase of the density stratification, which provides an important insight into the global understanding of the impact of the density stratification on the stability domain of the dipolar dynamo branch.

Numerical modelling of convection driven dynamos in the Boussinesq approximation revealed fundamental characteristics of the dynamo-generated magnetic fields and the fluid flow. Because these results were obtained for an incompressible fluid, their validity for gas planets and stars remains to be assessed. A common approach is to take some density stratification into account with the so-called anelastic approximation. The validity of previous results obtained in the Boussinesq approximation is tested for anelastic models. We point out and explain specific differences between both types of models, in particular with respect to the field geometry and the field strength, but we also compare scaling laws for the velocity amplitude, the magnetic dissipation time, and the convective heat flux. Our investigation is based on a systematic parameter study of spherical dynamo models in the anelastic approximation. We make use of a recently developed numerical solver and provide results for the test cases of the anelastic dynamo benchmark. The dichotomy of dipolar and multipolar dynamos identified in Boussinesq simulations is also present in our sample of anelastic models. Dipolar models require that the typical length scale of convection is an order of magnitude larger than the Rossby radius. However, the distinction between both classes of models is somewhat less explicit than in previous studies. This is mainly due to two reasons: we found a number of models with a considerable equatorial dipole contribution and an intermediate overall dipole field strength. Furthermore, a large density stratification may hamper the generation of dipole dominated magnetic fields. Previously proposed scaling laws, such as those for the field strength, are similarly applicable to anelastic models. It is not clear, however, if this consistency necessarily implies similar dynamo processes in both settings., Comment: 14 pages, 11 figures

Context: Large-scale magnetic fields resulting from hydromagnetic dynamo action may differ substantially in their time dependence. Cyclic field variations, characteristic for the solar magnetic field, are often explained by an important omega-effect, i.e. by the stretching of field lines due to strong differential rotation. Aims: The dynamo mechanism of a convective, oscillatory dynamo model is investigated. Methods: We solve the MHD-equations for a conducting Boussinesq fluid in a rotating spherical shell. For a resulting oscillatory model, dynamo coefficients have been computed with the help of the so-called test-field method. Subsequently, these coefficients have been used in a mean-field calculation in order to explore the underlying dynamo mechanism. Results: Although the rather strong differential rotation present in this model influences the magnetic field, the omega-effect alone is not responsible for its cyclic time variation. If the omega-effect is suppressed, the resulting alpha^2-dynamo remains oscillatory. Surprisingly, the corresponding alpha-omega dynamo leads to a non-oscillatory magnetic field. Conclusions: The assumption of an alpha-omega mechanism does not explain the occurrence of magnetic cycles satisfactorily.