Petri J. Käpylä

Context. Localised strengthening of the f mode precedes the emergence of active regions on the Sun by one to three days. While such an effect has also been demonstrated in highly simplified numerical models, those studies used a prescribed forcing function whose properties are different from those of a convectively driven flow. Aims. Our aim is to demonstrate magnetic effects on the f mode in convectively driven flows. Methods. We carried out non-linear simulations of convection with imposed magnetic fields at a range of depths. The power spectrum of the vertical velocity (with the depth and the horizontal wave vector kept fixed) took the form of a broad continuum with superposed peaks corresponding to various modes. We measured the mode amplitudes near the top of the domain. Results. Overall, if the continuum is modelled by a power law, its power law index is consistent with ω ⁻² (where ω is the angular frequency). We find that the f mode is strengthened when a super-equipartition magnetic field is imposed near the top of the domain. However, neither a magnetic field of equal strength near the bottom of the domain, nor an equipartition magnetic field near the top of the domain are seen to exert any significant effect. Conclusions. The magnetic effects we find are qualitatively consistent with those previously found in simplified numerical models. Future applications to observations should account for the fact that the observed effects are transient. Furthermore, we suggest that the continuum should be fit by a power law, rather than by unmotivated linear or polynomial fits.

Rotating anisotropic convection generates differential rotation in stellar convection zones. The main aim is to compute the non-diffusive contribution (Λ effect) to angular momentum transport---described by Reynolds stress---from rotating turbulent convection. Rotating hydrodynamic convection is simulated in Cartesian geometry at different latitudes and rotation rates. Large-scale flows are suppressed such that the Reynolds stress is due to non-diffusive effects. The radial angular momentum flux is downward (outward) for slow (fast) rotation. This is in contrast with prevailing theories in mean-field hydrodynamics, where the radial transport is always downward. The outward transport at rapid rotation is due to thermal Rossby waves that manifest as elongated large-scale convection cells near the equator. The horizontal angular momentum flux is always equatorward, with increasing concentration towards the equator as in earlier Cartesian studies. The magnitudes of the Λ effect coefficients are roughly an order of magnitude lower than in the case of anisotropically forced turbulence or in analytic theories. The current results highlight the tension between numerical simulations, widely used mean-field models, and solar observations. The mean-fields models have been remarkably successful in reproducing solar differential rotation but underlying assumptions regarding turbulence in these models seem to be at odds with 3D simulations. The current simulation results for the vertical (radial) angular momentum transport are in accordance with spherical shell simulations, where thermal Rossby waves are responsible for the generation of equatorial acceleration or solar-like differential rotation. Thermal Rossby waves are typically absent in the turbulence models of current mean-field theories, and they have not been unambiguously detected in the Sun.

We address the question whether the magnetorotational instability (MRI) can operate in the near-surface shear layer (NSSL) of the Sun and how it affects the interaction with the dynamo process. Using hydromagnetic mean-field simulations of α Ω-type dynamos in rotating shearing-periodic boxes, we show that for negative shear the MRI can operate above a certain critical shear parameter. This parameter scales inversely with the equipartition magnetic field strength above which α quenching set in. Like the usual Ω effect, the MRI produces toroidal magnetic field when the field is sufficiently strong. The work done by the Lorentz force is positive, so the magnetic field drives kinetic energy and not the other way around, as in a turbulent dynamo. This results in strong kinetic energy production and dissipation, which occurs at the expense of the magnetic energy. In view of the application to the solar NSSL, we conclude that the turbulent magnetic diffusivity may be too large for the MRI to be excited and that therefore only the standard Ω effect is expected to operate.

Mean-field dynamo theory, describing the evolution of large-scale magnetic fields, has been the mainstay of theoretical interpretation of magnetism in astrophysical objects such as the Sun for several decades. More recently, three-dimensional magnetohydrodynamic simulations have reached a level of fidelity where they capture dynamo action self-consistently on local and global scales without resorting to parametrization of unresolved scales. Recent global simulations also capture many of the observed characteristics of solar and stellar large-scale magnetic fields and cycles. Successful explanation of the results of such simulations with corresponding mean-field models is a crucial validation step for mean-field dynamo theory. Here the connections between mean-field theory and current dynamo simulations are reviewed. These connections range from the numerical computation of turbulent transport coefficients to mean-field models of simulations, and their relevance to the solar dynamo. Finally, the most notable successes and current challenges in mean-field theoretical interpretations of simulations are summarized.

Context. Large-scale magnetic fields of Ap/Bp stars are stable over long timescales and typically have simple dipolar geometries, leading to the idea of a fossil origin. These stars are also expected to have convective cores that can host strong dynamo action. Aims. Our aim was to study the interaction between the magnetic fields generated by the convective core dynamo of the star, and a dipolar fossil field reminiscent of observed magnetic topologies of Ap/Bp stars. Methods. We used numerical 3D star-in-a-box simulations of a 2.2 M_⊙ A-type star, where the core encompasses 20% of the stellar radius. As an initial condition, we imposed two purely poloidal configurations, both with a surface dipolar strength of 6 kG, and we explored different obliquity angles β (the angle between the magnetic and rotational axes), ranging from 0° to 90°. Results. The inclusion of a poloidal field where none of the magnetic field lines are closed inside the star, does not affect the core dynamo in a significant way. Dipolar configurations where all the field lines are closed inside the star can enhance the dynamo, producing a superequipartition quasi-stationary solution, where the magnetic energy is five times stronger than the kinetic energy. The enhanced core dynamos have typical magnetic field strengths between 105 and 172 kG, where the strength has an inverse relation with β. The strong magnetic fields produce an almost rigid rotation in the radiative envelope, and change the differential rotation of the core from solar-like to anti-solar. The only cases where the imposed dipoles are unstable and decay are those with β = 90°. In the rest of the cases, the core dynamos are enhanced and the surface magnetic field survives, keeping simple topologies as in the observations.

Mean-field dynamo theory, describing the evolution of large-scale magnetic fields, has been the mainstay of theoretical interpretation of magnetism in astrophysical objects such as the Sun for several decades. More recently, three-dimensional magnetohydrodynamic simulations have reached a level of fidelity where they capture dynamo action self-consistently on local and global scales without resorting to parametrization of unresolved scales. Recent global simulations also capture many of the observed characteristics of solar and stellar large-scale magnetic fields and cycles. Successful explanation of the results of such simulations with corresponding mean-field models is a crucial validation step for mean-field dynamo theory. Here the connections between mean-field theory and current dynamo simulations are reviewed. These connections range from the numerical computation of turbulent transport coefficients to mean-field models of simulations, and their relevance to the solar dynamo. Finally, the most notable successes and current challenges in mean-field theoretical interpretations of simulations are summarized.

Context. The paradigm of convection in solar-like stars is questioned based on recent solar observations. Aims. The primary aim is to study the effects of surface-driven entropy rain on convection zone structure and flows. Methods. Simulations of compressible convection in Cartesian geometry with non-uniform surface cooling are used. The cooling profile includes localised cool patches that drive deeply penetrating plumes. Results are compared with cases with uniform cooling. Results. Sufficiently strong surface driving leads to strong non-locality and a largely subadiabatic convectively mixed layer. In such cases the net convective energy transport is done almost solely by the downflows. The spatial scale of flows decreases with an increasing number of cooling patches for the vertical flows, whereas the maximum power for horizontal flows still occurs at largest scales. Conclusions. To reach the plume-dominated regime with a predominantly subadiabatic bulk of the convection zone requires significantly more efficient entropy rain than what is realised in simulations with uniform cooling. It is plausible that this regime is realised in the Sun but that it occurs on scales smaller than those resolved in current simulations. Current results show that entropy rain can lead to a largely mildly subadiabatic convection zone, whereas its effects for the scale of convection are more subtle.

Turbulent flows are known to produce enhanced effective magnetic and passive scalar diffusivities, which can fairly accurately be determined with numerical methods. It is now known that, if the flow is also helical, the effective magnetic diffusivity is reduced relative to the nonhelical value. Neither the usual second-order correlation approximation nor the various τ approaches have been able to capture this. Here we show that the helicity effect on the turbulent passive scalar diffusivity works in the opposite sense and leads to an enhancement. We have also demonstrated that the correlation time of the turbulent velocity field increases with the kinetic helicity. This is a key point in the theoretical interpretation of the obtained numerical results. Simulations in which helicity is being produced self-consistently by stratified rotating turbulence resulted in a turbulent passive scalar diffusivity that was found to be decreasing with increasing rotation rate.

Context. Early-type stars have convective cores due to a steep temperature gradient produced by the CNO cycle. These cores can host dynamos and the generated magnetic fields may be relevant in explaining the magnetism observed in Ap/Bp stars. Aims. Our main objective is to characterise the convective core dynamos and differential rotation. We aim to carry out the first quantitative analysis of the relation between magnetic activity cycle and rotation period. Methods. We used numerical 3D star-in-a-box simulations of a 2.2 M_⊙ A-type star with a convective core of roughly 20% of the stellar radius surrounded by a radiative envelope. We explored rotation rates from 8 to 20 days and used two models of the whole star, along with an additional zoom set where 50% of the radius was retained. Results. The simulations produce hemispheric core dynamos with cycles and typical magnetic field strengths around 60 kG. However, only a very small fraction of the magnetic energy is able to reach the surface. The cores have solar-like differential rotation and a substantial part of the radiative envelope has a quasi-rigid rotation. In the most rapidly rotating cases, the magnetic energy in the core is roughly 40% of the kinetic energy. Finally, we find that the magnetic cycle period, P_cyc, increases with decreasing the rotation period, P_rot, which has also been observed in many simulations of solar-type stars. Conclusions. Our simulations indicate that a strong hemispherical core dynamo arises routinely, but that it is not enough the explain the surface magnetism of Ap/Bp stars. Nevertheless, since the core dynamo produces dynamically relevant magnetic fields, it should not be neglected even when other mechanisms are being explored.

Previous studies have found that localized strengthening of the f mode recedes the emergence of active regions on the Sun by one day to three days. To help interpret these observations, we have performed nonlinear simulations of convection with imposed magnetic fields at different depths. We find that the f mode is strengthened when a super-equipartition magnetic field is imposed near the top of the domain. However, neither a magnetic field of equal strength near the bottom of the domain nor an equipartition magnetic field near the top of the domain have a significant effect. Our results suggest that the magnetic precursors of active regions are present near the surface of the Sun for much longer than would be expected if active regions were formed by flux tubes rising from deep within the convection zone. Application to observations should account for the fact that the effects we observe are transient.