Aims. The aim of this study is to explore the magnetic and flow properties of fully convective M dwarfs as a function of rotation period P-rot and magnetic Reynolds Re-M and Prandlt numbers Pr-M.Methods. We performed three-dimensional simulations of fully convective stars using a star-in-a-box set-up. This set-up allows global dynamo simulations in a sphere embedded in a Cartesian cube. The equations of non-ideal magnetohydrodynamics were solved with the PENCIL CODE. We used the stellar parameters of an M5 dwarf with 0.21 M-circle dot at three rotation rates corresponding to rotation periods (P-rot) of 43, 61, and 90 days, and varied the magnetic Prandtl number in the range from 0.1 to 10.<br />Results. We found systematic differences in the behaviour of the large-scale magnetic field as functions of rotation and Pr-M. For the simulations with P-rot = 43 days and Pr-M <= 2, we found cyclic large-scale magnetic fields. For Pr-M > 2, the cycles vanish and the field shows irregular reversals. In the simulations with P-rot = 61 days for Pr-M <= 2, the cycles are less clear and the reversal are less periodic. In the higher Pr-M cases, the axisymmetric mean field shows irregular variations. For the slowest rotation case with P-rot = 90 days, the field has an important dipolar component for Pr-M <= 5. For the highest Pr-M the large-scale magnetic field is predominantly irregular at mid-latitudes, with quasi-stationary fields near the poles. For the simulations with cycles, the cycle period length slightly increases with increasing Re-M.

Context. Late-type stars such as the Sun rotate differentially due to the interaction of turbulent convection and rotation.

Aims. The aim of the study is to investigate the effects of the effective thermal Prandtl number, which is the ratio of kinematic viscosity to thermal diffusivity, on the transition from anti-solar (slow equator, fast poles) to solar-like (fast equator, slow poles) differential rotation.

Methods. Three-dimensional hydrodynamic and magnetohydrodynamic simulations in semi-global spherical wedge geometry were used to model the convection zones of solar-like stars.

Results. The overall convective velocity amplitude increases as the Prandtl number decreases, in accordance with earlier studies. The transition from anti-solar to solar-like differential rotation is insensitive to the Prandtl number for Prandtl numbers below unity, but for Prandtl numbers greater than unity, solar-like differential rotation becomes significantly harder to excite. Magnetic fields and more turbulent regimes with higher fluid and magnetic Reynolds numbers help to achieve solar-like differential rotation in near-transition cases where anti-solar rotation is found in more laminar simulations. Solar-like differential rotation occurs only in cases with radially outward turbulent angular momentum transport due to the Reynolds stress at the equator. The dominant contribution to this outward transport near the equator is due to prograde propagating thermal Rossby waves.

Conclusions. The differential rotation is sensitive to the Prandtl number only for large Prandtl numbers in the parameter regime explored in this study. Magnetic fields have a greater effect on the differential rotation, although the inferred presence of a small-scale dynamo did not lead to drastically different results. The dominance of the thermal Rossby waves in the simulations is puzzling because they are not detected in the Sun. The current simulations are shown to be incompatible with the currently prevailing mean-field theory of differential rotation.

Eclipsing time variations in post-common-envelope binaries were proposed to be due to the time-varying component of the stellar gravitational quadrupole moment. This is suggested to be produced by changes in the stellar structure due to an internal redistribution of angular momentum and the effect of the centrifugal force. We examined this hypothesis and present 3D simulations of compressible magnetohydrodynamics performed with the PENCIL CODE. We modeled the stellar dynamo for a solar-mass star with angular velocities of 20 and 30 times solar. We included and varied the strength of the centrifugal force and compared the results with reference simulations without the centrifugal force and with a simulation in which its effect is enhanced. The centrifugal force causes perturbations in the evolution of the numerical model, so that the outcome in the details becomes different as a result of nonlinear evolution. While the average density profile is unaffected by the centrifugal force, a relative change in the density difference between high latitudes and the equator of ∼10−4 is found. The power spectrum of the convective velocity is found to be more sensitive to the angular velocity than to the strength of the centrifugal force. The quadrupole moment of the stars includes a fluctuating and a time-independent component, which vary with the rotation rate. As very similar behavior is produced in absence of the centrifugal force, we conclude that it is not the main ingredient for producing the time-averaged and fluctuating quadrupole moment of the star. In a real physical system, we thus expect contributions from both components, that is, from the time-dependent gravitational force from the variation in the quadrupole term and from the spin-orbit coupling that is due to the persistent part of the quadrupole.

Context. The ratio of kinematic viscosity to thermal diffusivity, the Prandtl number, is much smaller than unity in stellar convection zones.

Aims. The main goal of this work is to study the statistics of convective flows and energy transport as functions of the Prandtl number.

Methods. Three-dimensional numerical simulations of compressible non-rotating hydrodynamic convection in Cartesian geometry are used. The convection zone (CZ) is embedded between two stably stratified layers. The dominant contribution to the diffusion of entropy fluctuations comes in most cases from a subgrid-scale diffusivity whereas the mean radiative energy flux is mediated by a diffusive flux employing Kramers opacity law. Here, we study the statistics and transport properties of up- and downflows separately.

Results. The volume-averaged rms velocity increases with decreasing Prandtl number. At the same time, the filling factor of down-flows decreases and leads to, on average, stronger downflows at lower Prandtl numbers. This results in a strong dependence of convective overshooting on the Prandtl number. Velocity power spectra do not show marked changes as a function of Prandtl number except near the base of the convective layer where the dominance of vertical flows is more pronounced. At the highest Reynolds numbers, the velocity power spectra are more compatible with the Bolgiano-Obukhov k(-11/5 )than the Kolmogorov-Obukhov k(-5/3) scaling. The horizontally averaged convected energy flux ((F) over bar (conv)), which is the sum of the enthalpy ((F) over bar (enth)) and kinetic energy fluxes ((F) over bar (kin)), is independent of the Prandtl number within the CZ. However, the absolute values of (F) over bar (enth )and (F) over bar (kin) increase monotonically with decreasing Prandtl number. Furthermore, (F) over bar (enth) and (F) over bar (kin) have opposite signs for downflows and their sum (F) over bar (down arrow)(conv) diminishes with Prandtl number. Thus, the upflows (downflows) are the dominant contribution to the convected flux at low (high) Prandtl numbers. These results are similar to those from Rayleigh-Benard convection in the low Prandtl number regime where convection is vigorously turbulent but inefficient at transporting energy.

Conclusions. The current results indicate a strong dependence of convective overshooting and energy flux on the Prandtl number. Numerical simulations of astrophysical convection often use a Prandtl number of unity because it is numerically convenient. The current results suggest that this can lead to misleading results and that the astrophysically relevant low Prandtl number regime is qualitatively different from the parameter regimes explored in typical contemporary simulations.

Context. Main-sequence late-type stars with masses of less than 0.35 M-circle dot are fully convective.

Aims. The goal is to study convection, differential rotation, and dynamos as functions of rotation in fully convective stars.

Methods. Three-dimensional hydrodynamic and magnetohydrodynamic numerical simulations with a star-in-a-box model, in which a spherical star is immersed inside of a Cartesian cube, are used. The model corresponds to a 0.2 M-circle dot main-sequence M5 dwarf. A range of rotation periods (P-rot) between 4.3 and 430 d is explored.

Results. The slowly rotating model with P-rot=430 days produces anti-solar differential rotation with a slow equator and fast poles, along with predominantly axisymmetric quasi-steady large-scale magnetic fields. For intermediate rotation (P-rot=144 and 43 days) the differential rotation is solar-like (fast equator, slow poles), and the large-scale magnetic fields are mostly axisymmetric and either quasi-stationary or cyclic. The latter occurs in a similar parameter regime as in other numerical studies in spherical shells, and the cycle period is similar to observed cycles in fully convective stars with rotation periods of roughly 100 days. In the rapid rotation regime the differential rotation is weak and the large-scale magnetic fields are increasingly non-axisymmetric with a dominating m=1 mode. This large-scale non-axisymmetric field also exhibits azimuthal dynamo waves.

Conclusions. The results of the star-in-a-box models agree with simulations of partially convective late-type stars in spherical shells in that the transitions in differential rotation and dynamo regimes occur at similar rotational regimes in terms of the Coriolis (inverse Rossby) number. This similarity between partially and fully convective stars suggests that the processes generating differential rotation and large-scale magnetism are insensitive to the geometry of the star.

We test the sensitivity of hydrodynamic and magnetohydrodynamic turbulent convection simulations with respect to Mach number, thermal and magnetic boundary conditions, and the centrifugal force. We find that varying the luminosity, which also controls the Mach number, has only a minor effect on the large-scale dynamics. A similar conclusion can also be drawn from the comparison of two formulations of the lower magnetic boundary condition with either vanishing electric field or current density. The centrifugal force has an effect on the solutions, but only if its magnitude with respect to acceleration due to gravity is by two orders of magnitude greater than in the Sun. Finally, we find that the parameterisation of the photospheric physics, either by an explicit cooling term or enhanced radiative diffusion, is more important than the thermal boundary condition. In particular, runs with cooling tend to lead to more anisotropic convection and stronger deviations from the Taylor-Proudman state. In summary, the fully compressible approach taken here with the Pencil Code is found to be valid, while still allowing the disparate timescales to be taken into account.

We consider the effect of a subadiabatic layer at the base of the convection zone on convection itself and the associated large-scale dynamos in spherical wedge geometry. We use a heat conduction prescription based on the Kramers opacity law which allows the depth of the convection zone to dynamically adapt to changes in the physical characteristics such as rotation rate and magnetic fields. We find that the convective heat transport is strongly concentrated towards the equatorial and polar regions in the cases without a substantial radiative layer below the convection zone. The presence of a stable layer below the convection zone significantly reduces the anisotropy of radial enthalpy transport. Furthermore, the dynamo solutions are sensitive to subtle changes in the convection zone structure. We find that the kinetic helicity changes sign in the deeper parts of the convection zone at high latitudes in all runs. This region expands progressively towards the equator in runs with a thicker stably stratified layer.

Context. Differential rotation in stars is driven by the turbulent transport of angular momentum.

Aims. Our aim is to measure and parameterize the non-diffusive contribution to the total (Reynolds plus Maxwell) turbulent stress, known as the Lambda effect, and its quenching as a function of rotation and magnetic field.

Methods. Simulations of homogeneous, anisotropically forced turbulence in fully periodic cubes are used to extract their associated turbulent Reynolds and Maxwell stresses. The forcing is set up such that the vertical velocity component dominates over the horizontal ones, as in turbulent stellar convection. This choice of the forcing defines the vertical direction. Additional preferred directions are introduced by the imposed rotation and magnetic field vectors. The angle between the rotation vector and the vertical direction is varied such that the latitude range from the north pole to the equator is covered. Magnetic fields are introduced by imposing a uniform large-scale field on the system. Turbulent transport coefficients pertaining to the Lambda effect are obtained by fitting. The results are compared with analytic studies.

Results. The numerical and analytic results agree qualitatively at slow rotation and low Reynolds numbers. This means that vertical (horizontal) transport is downward (equatorward). At rapid rotation the latitude dependence of the stress is more complex than predicted by theory. The existence of a significant meridional Lambda effect is confirmed. Large-scale vorticity generation is found at rapid rotation when the Reynolds number exceeds a threshold value. The Lambda effect is severely quenched by large-scale magnetic fields due to the tendency of the Reynolds and Maxwell stresses to cancel each other. Rotational (magnetic) quenching of Lambda occurs at more rapid rotation (at lower field strength) in the simulations than in the analytic studies.

Conclusions. The current results largely confirm the earlier theoretical results, and also offer new insights: the non-negligible meridional Lambda effect possibly plays a role in the maintenance of meridional circulation in stars, and the appearance of large-scale vortices raises the question of their effect on the angular momentum transport in rapidly rotating stellar convective envelopes. The results regarding magnetic quenching are consistent with the strong decrease in differential rotation in recent semi-global simulations and highlight the importance of including magnetic effects in differential rotation models.

Context. Both dynamo theory and observations of stellar large-scale magnetic fields suggest a change from nearly axisymmetric configurations at solar rotation rates to nonaxisymmetric configurations for rapid rotation. Aims. We seek to understand this transition using numerical simulations. Methods. We use three-dimensional simulations of turbulent magnetohydrodynamic convection in spherical shell wedges and considered rotation rates between 1 and 31 times the solar value. Results. We find a transition from axi- to nonaxisymmetric solutions at around 1.8 times the solar rotation rate. This transition coincides with a change in the rotation profile from antisolar- to solar-like differential rotation with a faster equator and slow poles. In the solar-like rotation regime, the field configuration consists of an axisymmetric oscillatory field accompanied by an m = 1 azimuthal mode (two active longitudes), which also shows temporal variability. At slow (rapid) rotation, the axisymmetric (nonaxisymmetric) mode dominates. The axisymmetric mode produces latitudinal dynamo waves with polarity reversals, while the nonaxisymmetric mode often exhibits a slow drift in the rotating reference frame and the strength of the active longitudes changes cyclically over time between the different hemispheres. In the majority of cases we find retrograde waves, while prograde waves are more often found from observations. Most of the obtained dynamo solutions exhibit cyclic variability either caused by latitudinal or azimuthal dynamo waves. In an activity-period diagram, the cycle lengths normalized by the rotation period form two different populations as a function of rotation rate or magnetic activity level. The slowly rotating axisymmetric population lies close to what in observations is called the inactive branch, where the stars are believed to have solar-like differential rotation, while the rapidly rotating models are close to the superactive branch with a declining cycle to rotation frequency ratio and an increasing rotation rate. Conclusions. We can successfully reproduce the transition from axi- to nonaxisymmetric dynamo solutions for high rotation rates, but high-resolution simulations are required to limit the effect of rotational quenching of convection at rotation rates above 20 times the solar value.

Using simulations of slowly rotating stratified turbulence, we show that the alpha effect responsible for the generation of astrophysical magnetic fields is proportional to the logarithmic gradient of kinetic energy density rather than that of momentum, as was previously thought. This result is in agreement with a new analytic theory developed in this paper for large Reynolds numbers and slow rotation. Thus, the contribution of density stratification is less important than that of turbulent velocity. The a effect and other turbulent transport coefficients are determined by means of the test-field method. In addition to forced turbulence, we also investigate supernova-driven turbulence and stellar convection. In some cases (intermediate rotation rate for forced turbulence, convection with intermediate temperature stratification, and supernova-driven turbulence), we find that the contribution of density stratification might be even less important than suggested by the analytic theory.