arXiv subjects
Publications and source records attributed to Axel Brandenburg.
Some basic properties of the solar convection zone are considered and the use of helioseismology as an observational tool to determine its depth and internal angular velocity is discussed. Aspects of solar magnetism are described and explained in the framework of dynamo theory. The main focus is on mean field theories for the Sun's magnetic field and its differential rotation.
The backreaction of the Lorentz force on the alpha-effect is studied in the limit of small magnetic and fluid Reynolds numbers, using the first order smoothing approximation (FOSA) to solve both the induction and momentum equations. Both steady and time dependent forcings are considered. In the low Reynolds number limit, the velocity and magnetic fields can be expressed explicitly in terms of the forcing function. The nonlinear alpha-effect is then shown to be expressible in several equivalent forms in agreement with formalisms that are used in various closure schemes. On the one hand, one can express alpha completely in terms of the helical properties of the velocity field as in traditional FOSA, or, alternatively, as the sum of two terms, a so-called kinetic alpha-effect and an oppositely signed term proportional to the helical part of the small scale magnetic field. These results hold for both steady and time dependent forcing at arbitary strength of the mean field (abridged).
The thermal instability with a piecewise power law cooling function is investigated using one- and three-dimensional simulations with periodic and shearing-periodic boundary conditions in the presence of constant thermal diffusion and kinematic viscosity coefficients. Consistent with earlier findings, the flow behavior depends on the average density, . When $\braρ$ is in the range 1-5 x 10^{-24} g cm^{-3} the system is unstable and segregates into cool and warm phases with temperatures of roughly 100 and 10^4 K, respectively. However, in all cases the resulting average pressure is independent of and just a little above the minimum value. For a constant heating rate of 0.015 erg g^{-1} s^{-1}, the mean pressure is around 24 x 10^{-14} dyn (corresponding to p/k_B ~ K cm^{-3}). Cool patches tend to coalesce into bigger ones. In all cases investigated there is no sustained turbulence, which is in agreement with earlier results. Simulations in which turbulence is driven by a body force show that when rms velocities of between 10 and 30 km/s are obtained, the resulting dissipation rates rates are comparable to the thermal energy input rate. The resulting mean pressures are then about 30 x 10^{-14} dyn, corresponding to p/k_B ~ 2170 K cm^{-3}. This is comparable to the value expected for the Galaxy. Differential rotation tends to make the flow two-dimensional, that is, uniform in the streamwise direction, but this does not lead to instability.
The outer surface layers of the sun show a clear deceleration at low latitudes. This is generally thought to be the result of a strong dominance of vertical turbulent motions associated with strong downdrafts. This strong negative radial shear should not only contribute to amplifying the toroidal field locally and to expelling magnetic helicity, but it may also be responsible for producing a strong prograde pattern speed in the supergranulation layer. Using simulations of rotating stratified convection in cartesian boxes located at low latitudes around the equator it is shown that in the surface layers patterns move in the prograde direction on top of a retrograde mean background flow. These patterns may also be associated with magnetic tracers and even sunspot proper motions that are known to be prograde relative to the much slower surface plasma.
Large scale dynamo-generated fields are a combination of interlocked poloidal and toroidal fields. Such fields possess magnetic helicity that needs to be regenerated and destroyed during each cycle. A number of numerical experiments now suggests that stars may do this by shedding magnetic helicity. In addition to plain bulk motions, a favorite mechanism involves magnetic helicity flux along lines of constant rotation. We also know that the sun does shed the required amount of magnetic helicity mostly in the form of coronal mass ejections. Solar-like stars without cycles do not face such strong constraints imposed by magnetic helicity evolution and may not display coronal activity to that same extent. I discuss the evidence leading to this line of argument. In particular, I discuss simulations showing the generation of strong mean toroidal fields provided the outer boundary condition is left open so as to allow magnetic helicity to escape. Control experiments with closed boundaries do not produce strong mean fields.
A recently proposed model of non-autocatalytic reactions in dipeptide reactions leading to spontaneous symmetry breaking and homochirality is examined. The model is governed by activation, polymerization, epimerization and depolymerization of amino acids. Symmetry breaking is primarily a consequence of the fact that the rates of reactions involving homodimers and heterodimers are different, i.e., stereoselective, and on the fact that epimerization can only occur on the N-terminal residue and not on the Cterminal residue. This corresponds to an auto-inductive cyclic process that works only in one sense. It is argued that epimerization mimics both autocatalytic behavior as well as mutual antagonism - both of which were known to be crucial for producing full homochirality.
The macroscopic behaviour of cosmic rays in turbulent magnetic fields is discussed. An implementation of anisotropic diffusion of cosmic rays with respect to the magnetic field in a non-conservative, high-order, finite-difference magnetohydrodynamic code is discussed. It is shown that the standard implementation fails near singular X-points of the magnetic field, which are common if the field is random. A modification to the diffusion model for cosmic rays is described and the resulting telegraph equation (implemented by solving a dynamic equation for the diffusive flux of cosmic rays) is used; it is argued that this modification may better describe the physics of cosmic ray diffusion. The present model reproduces several processes important for the propagation and local confinement of cosmic rays, including spreading perpendicular to the local large-scale magnetic field, controlled by the random-to-total magnetic field ratio, and the balance between cosmic ray pressure and magnetic tension. Cosmic ray diffusion is discussed in the context of a random magnetic field produced by turbulent dynamo action. It is argued that energy equipartition between cosmic rays and other constituents of the interstellar medium do not necessarily imply that cosmic rays play a significant role in the balance of forces.
In an attempt to determine the outer scale of turbulence driven by localized sources, such as supernova explosions in the interstellar medium, we consider a forcing function given by the gradient of gaussian profiles localized at random positions. Different coherence times of the forcing function are considered. In order to isolate the effects specific to the nature of the forcing function we consider the case of a polytropic equation of state and restrict ourselves to forcing amplitudes such that the flow remains subsonic. When the coherence time is short, the outer scale agrees with the half-width of the gaussian. Longer coherence times can cause extra power at large scales, but this would not yield power law behavior at scales larger than that of the expansion waves. At scales smaller than the scale of the expansion waves the spectrum is close to power law with a spectral exponent of -2. The resulting flow is virtually free of vorticity. Viscous driving of vorticity turns out to be weak and self-amplification through the nonlinear term is found to be insignificant. No evidence for small scale dynamo action is found in cases where the magnetic induction equation is solved simultaneously with the other equations.
A gauge invariant and hence physically meaningful definition of magnetic helicity density for random fields is proposed, using the Gauss linking formula, as the density of correlated field line linkages. This definition is applied to the random small scale field in weakly inhomogeneous turbulence, whose correlation length is small compared with the scale on which the turbulence varies. For inhomogeneous systems, with or without boundaries, our technique then allows one to study the local magnetic helicity density evolution in a gauge independent fashion, which was not possible earlier. This evolution equation is governed by local sources (owing to the mean field) and by the divergence of a magnetic helicity flux density. The role of magnetic helicity fluxes in alleviating catastrophic quenching of mean field dynamos is discussed.
We review advances in the theoretical and computational studies of disk winds, jets and outflows including: the connection between accretion and jets, the launch of jets from magnetized disks, the coupled evolution of jets and disks, the interaction of magnetized young stellar objects with their surrounding disks and the relevance to outflows, and finally, the link between jet formation and gravitational collapse. We also address the predictions that the theory makes about jet kinematics, collimation, and rotation, that have recently been confirmed by high spatial and spectral resolution observations. Disk winds have a universal character that may account for jets and outflows during the formation of massive stars as well as brown dwarfs.
Some common properties of helical magnetic fields in decaying and driven turbulence are discussed. These include mainly the inverse cascade that produces fields on progressively larger scales. Magnetic helicity also restricts the evolution of the large scale field: the field decays less rapidly than a non-helical field, but it also saturates more slowly, i.e. on a resistive time scale if there are no magnetic helicity fluxes. The former effect is utilized in primordial field scenarios, while the latter is important for successfully explaining astrophysical dynamos that saturate faster than resistively. Dynamo action is argued to be important not only in the galactic dynamo, but also in accretion discs in active galactic nuclei and around protostars, both of which contribute to producing a strong enough seed magnetic field. Although primordial magnetic fields may be too weak to compete with these astrophysical mechanisms, such fields could perhaps still be important in producing polarization effects in the cosmic background radiation.
Aims: To quantify the transient growth of nonaxisymmetric perturbations in unstratified magnetized and stratified non-magnetized rotating linear shear flows in the shearing sheet approximation of accretion disc flows. Method: The Rayleigh quotient in modal approaches for the linearized equations (with time-dependent wavenumber) and the amplitudes from direct shearing sheet simulations using a finite difference code are compared. Results: Both approaches agree in their predicted growth behavior. The magneto-rotational instability for axisymmetric and non-axisymmetric perturbations is shown to have the same dependence of the (instantaneous) growth rate on the wavenumber along the magnetic field, but in the nonaxisymmetric case the growth is only transient. However, a meaningful dependence of the Rayleigh quotient on the radial wavenumber is obtained. While in the magnetized case the total amplification factor can be several orders of magnitude, it is only of order ten or less in the nonmagnetic case. Stratification is shown to have a stabilizing effect. In the present case of shearing-periodic boundaries the (local) strato-rotational instability seems to be absent.
Nonlinear behaviour of galactic dynamos is studied, allowing for magnetic helicity removal by the galactic fountain flow. A suitable advection speed is estimated, and a one-dimensional mean-field dynamo model with dynamic alpha-effect is explored. It is shown that the galactic fountain flow is efficient in removing magnetic helicity from galactic discs. This alleviates the constraint on the galactic mean-field dynamo resulting from magnetic helicity conservation and thereby allows the mean magnetic field to saturate at a strength comparable to equipartition with the turbulent kinetic energy.
The location of the solar dynamo is discussed in the context of new insights into the theory of nonlinear turbulent dynamos. It is argued that, from a dynamo-theoretic point of view, the bottom of the convection zone is not a likely location and that the solar dynamo may be distributed over the convection zone. The near surface shear layer produces not only east-west field alignment, but it also helps the dynamo disposing of its excess small scale magnetic helicity.
Arguments are presented in favor of the idea that the solar dynamo may operate not just at the bottom of the convection zone, i.e. in the tachocline, but it may operate in a more distributed fashion in the entire convection zone. The near-surface shear layer is likely to play an important role in this scenario.
Star-disc coupling is considered in numerical models where the stellar field is not an imposed perfect dipole, but instead a more irregular self-adjusting dynamo-generated field. Using axisymmetric simulations of the hydromagnetic mean-field equations, it is shown that the resulting stellar field configuration is more complex, but significantly better suited for driving a stellar wind. In agreement with recent findings by a number of people, star-disc coupling is less efficient in braking the star than previously thought. Moreover, stellar wind braking becomes equally important. In contrast to a perfect stellar dipole field, dynamo-generated stellar fields favor field-aligned accretion with considerably higher velocity at low latitudes, where the field is weaker and originating in the disc. Accretion is no longer nearly periodic (as it is in the case of a stellar dipole), but it is more irregular and episodic.
Accretion disc turbulence is investigated in the framework of the shearing box approximation. The turbulence is either driven by the magneto-rotational instability or, in the non-magnetic case, by an explicit and artificial forcing term in the momentum equation. Unlike the magnetic case, where most of the dissipation occurs in the disc corona, in the forced hydrodynamic case most of the dissipation occurs near the midplane. In the hydrodynamic case evidence is presented for the stochastic excitation of epicycles. When the vertical and radial epicyclic frequencies are different (modeling the properties around rotating black holes), the beat frequency between these two frequencies appear to show up as a peak in the temporal power spectrum in some cases. Finally, the full turbulent resistivity tensor is determined and it is found that, if the turbulence is driven by a forcing term, the signs of its off-diagonal components are such that this effect would not be capable of dynamo action by the shear--current effect.
Several one and two dimensional mean field models are analyzed where the effects of current helicity fluxes and boundaries are included within the framework of the dynamical quenching model. In contrast to the case with periodic boundary conditions, the final saturation energy of the mean field decreases inversely proportional to the magnetic Reynolds number. If a nondimensional scaling factor in the current helicity flux exceeds a certain critical value, the dynamo can operate even without kinetic helicity, i.e. it is based only on shear and current helicity fluxes, as first suggested by Vishniac & Cho (2001, ApJ 550, 752). Only above this threshold is the current helicity flux also able to alleviate catastrophic quenching. The fact that certain turbulence simulations have now shown apparently non-resistively limited mean field saturation amplitudes may be suggestive of the current helicity flux having exceeded this critical value. Even below this critical value the field still reaches appreciable strength at the end of the kinematic phase, which is in qualitative agreement with dynamos in periodic domains. However, for large magnetic Reynolds numbers the field undergoes subsequent variations on a resistive time scale when, for long periods, the field can be extremely weak.