Wolfgang Dobler

Simulations of nonhelical hydromagnetic turbulence

Nonhelical hydromagnetic forced turbulence is investigated using large scale simulations on up to 256 processors and 1024(3) mesh points. The magnetic Prandtl number is varied between 1/8 and 30, although in most cases it is unity. When the magnetic Reynolds number is based on the inverse forcing wave number, the critical value for dynamo action is shown to be around 35 for magnetic Prandtl number of unity. For small magnetic Prandtl numbers we find the critical magnetic Reynolds number to increase with decreasing magnetic Prandtl number. The Kazantsev k(3/2) spectrum for magnetic energy is confirmed for the kinematic regime, i.e., when nonlinear effects are still unimportant and when the magnetic Prandtl number is unity. In the nonlinear regime, the energy budget converges for large Reynolds numbers (around 1000) such that for our parameters about 70% is in kinetic energy and about 30% is in magnetic energy. The energy dissipation rates are converged to 30% viscous dissipation and 70% resistive dissipation. Second-order structure functions of the Elsasser variables give evidence for a k(-5/3) spectrum. Nevertheless, the three-dimensional spectrum is close to k(-3/2), but we argue that this is due to the bottleneck effect. The bottleneck effect is shown to be equally strong both for magnetic and nonmagnetic turbulence, but it is far weaker in one-dimensional spectra that are normally studied in laboratory turbulence. Structure function exponents for other orders are well described by the She-Leveque formula, but the velocity field is significantly less intermittent and the magnetic field is more intermittent than the Elsasser variables.

Magnetic Field Generation in Fully Convective Rotating Spheres

Magnetohydrodynamic simulations of fully convective, rotating spheres with volume heating near the center and cooling at the surface are presented. The dynamo-generated magnetic field saturates at equipartition field strength near the surface. In the interior, the field is dominated by small-scale structures, but outside the sphere, by the global scale. Azimuthal averages of the field reveal a large-scale field of smaller amplitude also inside the star. The internal angular velocity shows some tendency to be constant along cylinders and is antisolar (fastest at the poles and slowest at the equator).

Hydromagnetic turbulence in computer simulations

The usefulness of high-order schemes in astrophysical MHD turbulence simulations is discussed. Simple advection tests of hat profiles are used to compare schemes of different order. Higher order schemes generally need less explicit diffusion. In the case of a standing Burgers shock it is shown that the overall accuracy improves as the order of the scheme is increased. A memory efficient 3-step 2N-RK scheme is used. For cache efficiency, the entire set of equations is solved along pencils in the yz-plane. The advantage of solving for the magnetic vector potential is highlighted. Finally, results from a simulation of helical turbulence exhibiting large scale dynamo action are discussed.

Is Nonhelical Hydromagnetic Turbulence Peaked at Small Scales

Nonhelical hydromagnetic turbulence without an imposed magnetic field is considered in the case where the magnetic Prandtl number is unity. The magnetic field is entirely due to dynamo action. The magnetic energy spectrum peaks at a wavenumber of about 5 times the minimum wavenumber in the domain, and not at the resistive scale, as has previously been argued. Throughout the inertial range, the spectral magnetic energy exceeds the kinetic energy by a factor of about 2.5, and both spectra are approximately parallel. At first glance, the total energy spectrum seems to be close to k-3/2, but there is a strong bottleneck effect and it is suggested that the asymptotic spectrum is k-5/3. This is supported by the value of the second-order structure function exponent that is found to be ζ2 = 0.70, suggesting a k-1.70 spectrum.

Structured outflow from a dynamo active accretion disc

We present an axisymmetric numerical model of a dynamo active accretion disc. If the dynamo-generated magnetic field in the disc is sufficiently strong (close to equipartition with thermal energ ...

Magnetic helicity in stellar dynamos: new numerical experiments

The theory of large scale dynamos is reviewed with particular emphasis on the magnetic helicity constraint in the presence of closed and open boundaries. In the presence of closed or periodic boundaries, helical dynamos respond to the helicity constraint by developing small scale separation in the kinematic regime, and by showing long time scales in the nonlinear regime where the scale separation has grown to the maximum possible value. A resistively limited evolution towards saturation is also found at intermediate scales before the largest scale of the system is reached. Larger aspect ratios can give rise to different structures of the mean field which are obtained at early times, but the final saturation field strength is still decreasing with decreasing resistivity. In the presence of shear, cyclic magnetic fields are found whose period is increasing with decreasing resistivity, but the saturation energy of the mean field is in strong super-equipartition with the turbulent energy. It is shown that artificially induced losses of small scale field of opposite sign of magnetic helicity as the large scale field can, at least in principle, accelerate the production of large scale (poloidal) field. Based on mean field models with an outer potential field boundary condition in spherical geometry, we verify that the sign of the magnetic helicity flux from the large scale field agrees with the sign of alpha. For solar parameters, typical magnetic helicity fluxes lie around 10^{47} Mx^2 per cycle.

Radiative transfer in decomposed domains

Aims. An efficient algorithm for calculating radiative transfer on massively parallel computers using domain decomposition is presented. Methods. The integral formulation of the transfer equation is used to divide the problem into a local but compute-intensive part for calculating the intensity and optical depth integrals, and a nonlocal part for communicating the intensity between adjacent processors. Results. The waiting time of idle processors during the nonlocal communication part does not have a severe impact on the scaling. The wall clock time thus scales nearly linearly with the inverse number of processors.

Three-dimensional simulations of the reorganization of a quark star's magnetic field as induced by the meissner effect

In a previous paper (Ouyed et al. 2004) we presented a new model for soft gamma-ray repeaters (SGR), based on the onset of colour superconductivity in quark stars. In this model, the bursts result from the reorganization of the exterior magnetic field following the formation of vortices that confine the internal magnetic field (the Meissner effect). Here we extend the model by presenting full 3-dimensional simulations of the evolution of the inclined exterior magnetic field immediately following vortex formation. The simulations capture the violent reconnection events in the entangled surface magnetic field as it evolves into a smooth, more stable, configuration which consists of a dipole field aligned with the star’s rotation axis. The total magnetic energy dissipated in this process is found to be of the order of 10 44 erg and, if it is emitted as synchrotron radiation, peaks typically at 280keV. The intensity decays temporally in a way resembling SGRs and AXPs (anomalous X-ray pulsars), with a tail lasting from a few to a few hundred times the rotation period of the star, depending on the initial inclination between the rotation and dipole axis. One of the obvious consequences of our model’s final state (aligned rotator) is the suppression of radio-emission in SGRs and AXPs following their bursting era. We suggest that magnetar-like magnetic field strength alone cannot be responsible for the properties of SGRs and AXPs, while a quark star entering the “Meissner phase” is compatible with the observational facts. We compare our model to observations and highlight our predictions.

The effects of vertical outflows on disk dynamos

We consider the effect of vertical outflows on the mean-field dynamo in a thin disk. These outflows could be due to winds or magnetic buoyancy. We analyse both two-dimensional finite-difference numerical solutions of the axisymmetric dynamo equations and a free-decay mode expansion using the thin-disk approximation. Contrary to expectations, a vertical velocity can enhance dynamo action, provided the velocity is not too strong. In the nonlinear regime this can lead to super-exponential growth of the magnetic field. vide a study of the effects of vertical velocities. We show how vertical velocities can enhance the dynamo, allow- ing a larger growth rate and leading to super-exponential growth of the magnetic field in the nonlinear regime.

Nonlinear states of the screw dynamo

The self-excitation of magnetic field by a spiral Couette flow between two coaxial cylinders is considered. We solve numerically the fully nonlinear, three-dimensional magnetohydrodynamic (MHD) equations for magnetic Prandtl numbers P(m) (ratio of kinematic viscosity to magnetic diffusivity) between 0.14 and 10 and kinematic and magnetic Reynolds numbers up to about 2000. In the initial stage of exponential field growth (kinematic dynamo regime), we find that the dynamo switches from one distinct regime to another as the radial width delta(r)(B) of the magnetic field distribution becomes smaller than the separation of the field maximum from the flow boundary. The saturation of magnetic field growth is due to a reduction in the velocity shear resulting mainly from the azimuthally and axially averaged part of the Lorentz force, which agrees with an asymptotic result for the limit of P(m)<<1. In the parameter regime considered, the magnetic energy decreases with kinematic Reynolds number as Re-0.84, which is approximately as predicted by the nonlinear asymptotic theory (approximately Re(-1)). However, when the velocity field is maintained by a volume force (rather than by viscous stress) the dependence of magnetic energy on the kinematic Reynolds number is much weaker.