Small-scale dynamos in simulations of stratified turbulent convection

Small-scale dynamo action is often held responsible for the generation of quiet-Sun magnetic fields. We aim to determine the excitation conditions and saturation level of small-scale dynamos in non-rotating turbulent convection at low magnetic Prandtl numbers. We use high resolution direct numerical simulations of weakly stratified turbulent convection. We find that the critical magnetic Reynolds number for dynamo excitation increases as the magnetic Prandtl number is decreased, which might suggest that small-scale dynamo action is not automatically evident in bodies with small magnetic Prandtl numbers as the Sun. As a function of the magnetic Reynolds number (${\rm Rm}$), the growth rate of the dynamo is consistent with an ${\rm Rm}^{1/2}$ scaling. No evidence for a logarithmic increase of the growth rate with ${\rm Rm}$ is found.Comment: 6 pages, 5 figures, submitted to Astron. Nach

Testing turbulent closure models with convection simulations

We compare simple analytical closure models of homogeneous turbulent Boussinesq convection for stellar applications with three-dimensional simulations. We use simple analytical closure models to compute the fluxes of angular momentum and heat as a function of rotation rate measured by the Taylor number. We also investigate cases with varying angles between the angular velocity and gravity vectors, corresponding to locating the computational domain at different latitudes ranging from the pole to the equator of the star. We perform three-dimensional numerical simulations in the same parameter regimes for comparison. The free parameters appearing in the closure models are calibrated by two fitting methods using simulation data. Unique determination of the closure parameters is possible only in the non-rotating case or when the system is placed at the pole. In the other cases the fit procedures yield somewhat differing results. The quality of the closure is tested by substituting the resulting coefficients back into the closure model and comparing with the simulation results. To eliminate the possibilities that the results obtained depend on the aspect ratio of the simulation domain or suffer from too small Rayleigh numbers we performed runs varying these parameters. The simulation data for the Reynolds stress and heat fluxes broadly agree with previous compressible simulations. The closure works fairly well with slow and fast rotation but its quality degrades for intermediate rotation rates. We find that the closure parameters depend not only on rotation rate but also on latitude. The weak dependence on Rayleigh number and the aspect ratio of the domain indicates that our results are generally validComment: 21 pages, 9 figures, submitted to Astron. Nach

From convective to stellar dynamos

Volume: 6 Host publication title: Astrophysical Dynamics Host publication sub-title: From Stars to GalaxiesNon peer reviewe

Helical coronal ejections and their role in the solar cycle

The standard theory of the solar cycle in terms of an alpha-Omega dynamo hinges on a proper understanding of the nonlinear alpha effect. Boundary conditions play a surprisingly important role in determining the magnitude of alpha. For closed boundaries, the total magnetic helicity is conserved, and since the alpha effect produces magnetic helicity of one sign in the large scale field, it must simultaneously produce magnetic helicity of the opposite sign. It is this secondary magnetic helicity that suppresses the dynamo in a potentially catastrophic fashion. Open boundaries allow magnetic helicity to be lost. Simulations are presented that allow an estimate of alpha in the presence of open or closed boundaries, either with or without solar-like differential rotation. In all cases the sign of the magnetic helicity agrees with that observed at the solar surface (negative in the north, positive in the south), where significant amounts of magnetic helicity can be ejected via coronal mass ejections. It is shown that open boundaries tend to alleviate catastrophic alpha quenching. The importance of looking at current helicity instead of magnetic helicity is emphasized and the conceptual advantages are discussed.Comment: 8 pages, 7 figs, IAU Symp. 223, In: Multi-Wavelength Investigations of Solar Activity. Eds: A.V. Stepanov, E.E. Benevolenskaya & A.G. Kosoviche

Lambda-effect from forced turbulence simulations

Aims: We determine the components of the $\Lambda$-effect tensor that quantifies the contributions to the turbulent momentum transport even for uniform rotation. Methods: Three-dimensional numerical simulations are used to study turbulent transport in triply periodic cubes under the influence of rotation and anisotropic forcing. Comparison is made with analytical results obtained via the so-called minimal tau-approximation. Results: In the case where the turbulence intensity in the vertical direction dominates, the vertical stress is always negative. This situation is expected to occur in stellar convection zones. The horizontal component of the stress is weaker and exhibits a maximum at latitude 30 degrees - regardless of how rapid the rotation is. The minimal tau-approximation captures many of the qualitative features of the numerical results, provided the relaxation time tau is close to the turnover time, i.e. the Strouhal number is of order unity.Comment: 20 pages, 14 figures, accepted for publication in Astronomy & Astrophysic

Long-term variations of turbulent transport coefficients in a solar-like convective dynamo simulation

The Sun, aside from its eleven year sunspot cycle is additionally subject to long term variation in its activity. In this work we analyse a solar-like convective dynamo simulation, containing approximately 60 magnetic cycles, exhibiting equatorward propagation of the magnetic field, multiple frequencies, and irregular variability, including a missed cycle and complex parity transitions between dipolar and quadrupolar modes. We compute the turbulent transport coefficients, describing the effects of the turbulent velocity field on the mean magnetic field, using the test-field method. The test-field analysis provides a plausible explanation of the missing cycle in terms of the reduction of $\alpha_{\phi\phi}$ in advance of the reduced surface activity, and enhanced downward turbulent pumping during the event to confine some of the magnetic field at the bottom of the convection zone, where local maximum of magnetic energy is observed during the event. At the same time, however, a quenching of the turbulent magnetic diffusivities is observed, albeit differently distributed in depth compared to the other transport coefficients. Therefore, dedicated mean-field modelling is required for verification.Comment: 11 pages, 12 figures, accepted by AN for 14th Potsdam Thinksho

Star-in-a-box simulations of fully convective stars

(abridged) Context: Main-sequence late-type stars with masses less than $0.35 M_\odot$ 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, where a spherical star is immersed inside of a Cartesian cube, are used. The model corresponds to a $0.2M_\odot$ M5 dwarf. Rotation periods ($P_{\rm rot}$) between 4.3 and 430 days are explored. Results: The slowly rotating model with $P_{\rm rot}=430$ 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 ($P_{\rm rot}=144$ and $43$ days) differential rotation is solar-like (fast equator, slow poles) and 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 comparable $P_{\rm rot}$. 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.Comment: 17 pages, 11 figures, submitted to Astron. Astrophys, revised as per referee repor

Effects of Rotation and Input Energy Flux on Convective Overshooting

We study convective overshooting by means of local 3D convection calculations. Using a mixing length model of the solar convection zone (CZ) as a guide, we determine the Coriolis number (Co), which is the inverse of the Rossby number, to be of the order of ten or larger at the base of the solar CZ. Therefore we perform convection calculations in the range Co = 0...10 and interpret the value of Co realised in the calculation to represent a depth in the solar CZ. In order to study the dependence on rotation, we compute the mixing length parameters alpha_T and alpha_u relating the temperature and velocity fluctuations, respectively, to the mean thermal stratification. We find that the mixing length parameters for the rapid rotation case, corresponding to the base of the solar CZ, are 3-5 times smaller than in the nonrotating case. Introducing such depth-dependent alpha into a solar structure model employing a non-local mixing length formalism results in overshooting which is approximately proportional to alpha at the base of the CZ. Although overshooting is reduced due to the reduced alpha, a discrepancy with helioseismology remains due to the steep transition to the radiative temperature gradient. In comparison to the mixing length models the transition at the base of the CZ is much gentler in the 3D models. It was suggested recently (Rempel 2004) that this discrepancy is due to the significantly larger (up to seven orders of magnitude) input energy flux in the 3D models in comparison to the Sun and solar models, and that the 3D calculations should be able to approach the mixing length regime if the input energy flux is decreased by a moderate amount. We present results from local convection calculations which support this conjecture.Comment: 6 pages, 3 figures, to appear in Convection in Astrophysics, Proc. IAUS 239, edited by F. Kupka, I.W. Roxburgh, K.L. Cha