M. J. Korpi

A Supernova-regulated Interstellar Medium: Simulations of the Turbulent Multiphase Medium

The dynamic state of the interstellar medium, heated and stirred by supernovae (SNe), is simulated using a three-dimensional, nonideal MHD model in a domain extended 0.5×0.5 kpc horizontally and 2 kpc vertically, with the gravitational field symmetric about the midplane of the domain, z=0. We include both Type I and Type II SNe, allowing the latter to cluster in regions with enhanced gas density. The system segregates into two main phases: a warm, denser phase and a hot, dilute gas in global pressure equilibrium; there is also dense, cool gas compressed into filaments, shells, and clumps by expanding SN remnants. The filling factor of the hot phase grows with height, so it dominates at |z| 0.5 kpc. The multicomponent structure persists throughout the simulation, and its statistical parameters show little time variation. The warm gas is in hydrostatic equilibrium, which is supported by thermal and turbulent pressures. The multiphase gas is in a state of developed turbulence. The rms random velocity is different in the warm and hot phases, 10 and 40 km s-1, respectively, at |z| 1 kpc; the turbulent cell size (twice the velocity correlation scale) is about 60 pc in the warm phase.

Large-scale dynamos in turbulent convection with shear

Aims. To study the existence of large-scale convective dynamos under the influence of shear and rotation. Methods. Three-dimensional numerical simulations of penetrative compressible convection with uniform horizontal shear are used to study dynamo action and the generation of large-scale magnetic fields. We consider cases where the magnetic Reynolds number is either marginal or moderately supercritical with respect to small-scale dynamo action in the absence of shear and rotation. Our magnetic Reynolds number is based on the wavenumber of the depth of the convectively unstable layer. The effects of magnetic helicity fluxes are studied by comparing results for the magnetic field with open and closed boundaries. Results. Without shear no large-scale dynamos are found even if the ingredients necessary for the α-effect (rotation and stratification) are present in the system. When uniform horizontal shear is added, a large-scale magnetic field develops, provided the boundaries are open. In this case the mean magnetic field contains a significant fraction of the total field. For those runs where the magnetic Reynolds number is between 60 and 250, an additional small-scale dynamo is expected to be excited, but the field distribution is found to be similar to cases with smaller magnetic Reynolds number where the small-scale dynamo is not excited. In the case of closed (perfectly conducting) boundaries, magnetic helicity fluxes are suppressed and no large-scale fields are found. Similarly, poor large-scale field development is seen when vertical shear is used in combination with periodic boundary conditions in the horizontal directions. If, however, open (normal-field) boundary conditions are used in the x-direction, a large-scale field develops. These results support the notion that shear not only helps to generate the field, but it also plays a crucial role in driving magnetic helicity fluxes out of the system along the isocontours of shear, thereby allowing efficient dynamo action.

Alpha effect and turbulent diffusion from convection

Aims. We study turbulent transport coefficients that describe the evolution of large-scale magnetic fields in turbulent convection. Methods. We use the test field method, together with three-dimensional numerical simulations of turbulent convection with shear and rotation, to compute turbulent transport coefficients describing the evolution of large-scale magnetic fields in mean-field theory in the kinematic regime. We employ one-dimensional mean-field models with the derived turbulent transport coefficients to examine whether they give results that are compatible with direct simulations. Results. The results for the α-effect as a function of rotation rate are consistent with earlier numerical studies, i.e. increasing magnitude as rotation increases and approximately cos θ latitude profile for moderate rotation. Turbulent diffusivity, ηt, is proportional to the square of the turbulent vertical velocity in all cases. Whereas ηt decreases approximately inversely proportional to the wavenumber of the field, the α-effect and turbulent pumping show a more complex behaviour with partial or full sign changes and the magnitude staying roughly constant. In the presence of shear and no rotation, a weak α-effect is induced which does not seem to show any consistent trend as a function of shear rate. Provided that the shear is large enough, this small α-effect is able to excite a dynamo in the mean-field model. The coefficient responsible for driving the shear-current effect shows several sign changes as a function of depth but is also able to contribute to dynamo action in the mean-field model. The growth rates in these cases are, however, well below those in direct simulations, suggesting that an incoherent α-shear dynamo may also act in the simulations. If both rotation and shear are present, the α-effect is more pronounced. At the same time, the combination of the shear-current and Ω × J-effects is also stronger than in the case of shear alone, but subdominant to the α-shear dynamo. The results of direct simulations are consistent with mean-field models where all of these effects are taken into account without the need to invoke incoherent effects.

Convective dynamos in spherical wedge geometry

Astronomy Unit, School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E14NS, United KingdomReceived 2009 Sep 9, accepted 2009 Nov 16Published online 2009 Dec 30Key words Sun: magnetic fields – magnetohydrodynamics (MHD)Self-consistent convective dynamo simulations in wedge-shaped spherical shells are presented. Differential rotation isgenerated by the interaction of convection with rotation. Equatorward acceleration and dynamo action are obtained onlyfor sufficiently rapid rotation. The angular velocity tends to be constant along cylinders. Oscillatory large-scale fields arefound to migrate in the poleward direction. Comparison with earlier simulations in full spherical shells and Cartesiandomains is made.

LARGE-SCALE DYNAMOS IN RIGIDLY ROTATING TURBULENT CONVECTION

The existence of large-scale dynamos in rigidly rotating turbulent convection without shear is studied using threedimensional numerical simulations of penetrative rotating compressible convection. We demonstrate that rotating convection in a Cartesian domain can drive a large-scale dynamo even in the absence of shear. The large-scale field contains a significant fraction of the total field in the saturated state. The simulation results are compared with one-dimensional mean-field dynamo models where turbulent transport coefficients, as determined using the test field method, are used. The reason for the absence of large-scale dynamo action in earlier studies is shown to be due to the rotation being too slow: whereas the α-effect can change sign, its magnitude stays approximately constant as a function of rotation, and the turbulent diffusivity decreases monotonically with increasing rotation. Only when rotation is rapid enough a large-scale dynamo can be excited. The one-dimensional mean-field model with dynamo coefficients from the test-field results predicts reasonably well the dynamo excitation in the direct simulations. This result further validates the test field procedure and reinforces the interpretation that the observed dynamo is driven by a turbulent α-effect. This result demonstrates the existence of an α-effect and an α 2 -dynamo with natural forcing.

Magnetoconvection and dynamo coefficients - III. α-effect and magnetic pumping in the rapid rotation regime

Aims. The α -a ndγ-effects, which are responsible for the generation and turbulent pumping of large scale magnetic fields, respectively, due to passive advection by convection are determined in the rapid rotation regime corresponding to the deep layers of the solar convection zone. Methods. A 3D rectangular local model is used for solving the full set of MHD equations in order to compute the electromotive force (emf), E = u × b, generated by the interaction of imposed weak gradient-free magnetic fields and turbulent convection with varying rotational influence and latitude. By expanding the emf in terms of the mean magnetic field, Ei = aijBj, all nine components of aij are computed. The diagonal elements of aij describe the α-effect, whereas the off-diagonals represent magnetic pumping. The latter is essentially the advection of magnetic fields by means other than the underlying large-scale velocity field. Comparisons are made to analytical expressions of the coefficients derived under the first-order smoothing approximation (FOSA). Results. In the rapid rotation regime the latitudinal dependence of the α-components responsible for the generation of the azimuthal and radial fields does not exhibit a peak at the poles, as is the case for slow rotation, but at a latitude of about 30 ◦ . The magnetic pumping is predominantly radially down- and latitudinally equatorward as in earlier studies. The numerical results compare surprisingly well with analytical expressions derived under first-order smoothing, although the present calculations are expected to lie near the limits of the validity range of FOSA.

A 3D MHD model of astrophysical flows: Algorithms, tests and parallelisation

In this paper we describe a numerical method designed for modelling dierent kinds of astrophysical flows in three dimensions. Our method is a standard explicit nite dierence method employing the local shearing- box technique. To model the features of astrophysical systems, which are usually compressible, magnetised and turbulent, it is desirable to have high spatial resolution and large domain size to model as many features as possible, on various scales, within a particular system. In addition, the time-scales involved are usually wide- ranging also requiring signicant amounts of CPU time. These two limits (resolution and time-scales) enforce huge limits on computational capabilities. The model we have developed therefore uses parallel algorithms to increase the performance of standard serial methods. The aim of this paper is to report the numerical methods we use and the techniques invoked for parallelising the code. The justication of these methods is given by the extensive tests presented herein.

Local models of stellar convection: Reynolds stresses and turbulent heat transport

We study stellar convection using a local three-dimensional MHD model, with which we investigate the influence of rotation and large-scale magnetic fields on the turbulent momentum and heat transport and their role in generating large-scale flows in stellar convection zones. The former is studied by computing the turbulent velocity correlations, known as Reynolds stresses, the latter by calculating the correlation of velocity and temperature fluctuations, both as functions of rotation and latitude. We find that the horizontal correlation, Qθφ, capable of generating horizontal differential rotation, attains significant values and is mostly negative in the southern hemisphere for Coriolis numbers exceeding unity, corresponding to equatorward flux of angular momentum. This result is also in accordance with solar observations. The radial component Qrφ is negative for slow and intermediate rotation indicating inward transport of angular momentum, while for rapid rotation, the transport occurs outwards. Parametrisation in terms of the mean-field Λ-effect shows qualitative agreement with the turbulence model of Kichatinov & Rudiger (1993) for the horizontal part H ∝ Q θφ cos θ , whereas for the vertical Λ-effect, V ∝ Qrφ sin θ , agreement only for intermediate rotation exists. The Λ-coefficients become suppressed in the limit of rapid rotation, this rotational quenching being stronger and occurring with slower rotation for the V component than for H. We have also studied the behaviour of the Reynolds stresses under the influence of a large-scale azimuthal magnetic field of varying strength. We find that the stresses are enhanced by the presence of the magnetic field for field strengths up to and above the equipartition value, without significant quenching. Concerning the turbulent heat transport, our calculations show that the transport in the radial direction is most efficient at the equatorial regions, obtains a minimum at midlatitudes, and shows a slight increase towards the poles. The latitudinal heat transport does not show a systematic trend as a function of latitude or rotation.

Solar dynamo models with α -effect and turbulent pumping from local 3D convection calculations

Results from kinematic solar dynamo models employing α -effect and turbulent pumping from local convection calculations are presented. We estimate the magnitude of these effects to be around 2–3 m s–1, having scaled the local quantities with the convective velocity at the bottom of the convection zone from a solar mixing-length model. Rotation profile of the Sun as obtained from helioseismology is applied in the models; we also investigate the effects of the observed surface shear layer on the dynamo solutions. With these choices of the small- and large-scale velocity fields, we obtain estimate of the ratio of the two induction effects, Cα/CΩ ≈ 10–3, which we keep fixed in all models. We also include a one-cell meridional circulation pattern having a magnitude of 10–20 m s–1 near the surface and 1–2 m s–1 at the bottom of the convection zone. The model essentially represents a distributed turbulent dynamo, as the α -effect is nonzero throughout the convection zone, although it concentrates near the bottom of the convection zone obtaining a maximum around 30° of latitude. Turbulent pumping of the mean fields is predominantly down- and equatorward. The anisotropies in the turbulent diffusivity are neglected apart from the fact that the diffusivity is significantly reduced in the overshoot region. We find that, when all these effects are included in the model, it is possible to correctly reproduce many features of the solar activity cycle, namely the correct equatorward migration at low latitudes and the polar branch at high latitudes, and the observed negative sign of BrBϕ. Although the activity clearly shifts towards the equator in comparison to previous models due to the combined action of the α -effect peaking at midlatitudes, meridional circulation and latitudinal pumping, most of the activity still occurs at too high latitudes (between 5° … 60°). Other problems include the relatively narrow parameter space within which the preferred solution is dipolar (A0), and the somewhat too short cycle lengths of the solar-type solutions. The role of the surface shear layer is found to be important only in the case where the α -effect has an appreciable magnitude near the surface. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Magnetorotational instability driven dynamos at low magnetic Prandtl numbers

Numerical simulations of the magnetorotational instabili ty (MRI) with zero initial net flux in a non-stratified isothermal cubic domain are used to demonst rate the importance of magnetic boundary conditions.In fully periodic systems the level of turbulence generated by the MRI strongly decreases as the magnetic Prandtl number ( Pm), which is the ratio of kinematic viscosity and magnetic diffusion, is decreased. No MRI or dy namo action belowPm = 1 is found, agreeing with earlier investigations. Using vertic al field conditions, which allow the generation of a net toroidal flux and magnetic helicity fluxes out of the system, the MRI is found to be excited in the range 0.1 ≤ Pm ≤ 10, and that the saturation level is independent of Pm. In the vertical field runs strong mean-field dynamo develops and helps to sustain the MRI.