S. B. F. Dorch

Waves in the Magnetized Solar Atmosphere. I. Basic Processes and Internetwork Oscillations

We have modeled numerically the propagation of waves through magnetic structures in a stratified atmosphere. We first simulate the propagation of waves through a number of simple, exemplary field geometries in order to obtain a better insight into the effect of differing field structures on the wave speeds, amplitudes, polarizations, direction of propagation, etc., with a view to understanding the wide variety of wavelike and oscillatory processes observed in the solar atmosphere. As a particular example, we then apply the method to oscillations in the chromospheric network and internetwork. We find that in regions where the field is significantly inclined to the vertical, refraction by the rapidly increasing phase speed of the fast modes results in total internal reflection of the waves at a surface whose altitude is highly variable. We conjecture a relationship between this phenomenon and the observed spatiotemporal intermittancy of the oscillations. By contrast, in regions where the field is close to vertical, the waves continue to propagate upward, channeled along the field lines but otherwise largely unaffected by the field.

On the transport of magnetic fields by solar-like stratified convection

The interaction of magnetic elds and stratied convection was studied in the context of the solar and late type stellar dynamos by using numerical 3D MHD simulations. The topology of stratied asymmetric and over-turning convection enables a pumping mechanism that may render the magnetic flux storage problem obsolete. The inclusion of open boundary conditions leads to a considerable flux loss unless the open boundary is placed close to the physical boundary. Simulations including solar-like latitudinal shear indicates that a toroidal eld of several tens of kilo-Gauss may be held down by the pumping mechanism.

Numerical simulations of kinematic dynamo action

Numerical simulations of kinematic dynamo action in steady and three-dimensional ABC flows are presented with special focus on the difference in growth rates between cases with single and multiple periods of the prescribed velocity field. It is found that the difference in growth rate (apart from a trivial factor stemming from a scaling of the rate of strain with the wavenumber of the velocity field) is due to differences in the recycling of the weakest part of the magnetic field. The single wavelength classical ABC-flow experiments impose stronger symmetry requirements, which results in a suppression of the growth rate. The experiments with larger wave number achieve growth rates that are more compatible with the turn-over time scale by breaking the symmetry of the resulting dynamo-generated magnetic field. Differences in topology in cases with and without stagnation points in the imposed velocity field are also investigated, and it is found that the cigar-like structures that develop in the classical A = B = C dynamos are replaced by ribbon structures in cases where the flow is without stagnation points.

On the Saturation of Astrophysical Dynamos: Numerical Experiments with the No-Cosines Flow

In the context of astrophysical dynamos we illustrate that the no-cosines flow, with zero mean helicity, can drive fast dynamo action and we study the dynamo’s mode of operation during both the linear and non-linear saturation regimes. It turns out that in addition to a high growth rate in the linear regime, the dynamo saturates at a level significantly higher than normal turbulent dynamos, namely at exact equipartition when the magnetic Prandtl number Prm∼ 1. Visualization of the magnetic and velocity fields at saturation will help us to understand some of the aspects of the non-linear dynamo problem.

Nonlinear MHD dynamo operating at equipartition

Context. We present results from non linear MHD dynamo experiments with a three-dimensional steady and smooth flow that drives fast dynamo action in the kinematic regime. In the saturation regime, the system yields strong magnetic fields, which undergo transitions between an energy-equipartition and a turbulent state. The generation and evolution of such strong magnetic fields is relevant for the understanding of dynamo action that occurs in stars and other astrophysical objects. Aims. We study the mode of operation of this dynamo, in the linear and non-linear saturation regimes. We also consider the effect of varying the magnetic and fluid Reymolds number on the non-linear behaviour of the system. Methods. We perform three-dimensional non-linear MHD simulations and visualization using a high resolution numerical scheme. Results. We find that this dynamo has a high growth rate in the linear regime, and that it can saturate at a level significantly higher than intermittent turbulent dynamos, namely at energy equipartition, for high values of the magnetic and fluid Reynolds numbers. The equipartition solution however does not remain time-independent during the simulation but exhibits a much more intricate behaviour than previously thought. There are periods in time where the solution is smooth and close to energy-equipartition and others where it becomes turbulent. Similarities and differences in the way the magnetic field is amplified and sustained for experiments with varying Reynolds numbers are discussed. Conclusions. Strong magnetic fields, in near equipartition, can be generated also by a non-turbulent dynamo. A striking result is that the saturation state of this dynamo reveals interesting transitions between turbulent and laminar states.

Flux-loss of buoyant ropes interacting with convective flows

We present 3-d numerical magneto-hydrodynamic simulations of a buoyant, twisted magnetic flux rope embedded in a stratied, solar-like model convection zone. The flux rope is given an initial twist such that it neither kinks nor fragments during its ascent. Moreover, its magnetic energy content with respect to convection is chosen so that the flux rope retains its basic geometry while being deflected from a purely vertical ascent by convective flows. The simulations show that magnetic flux is advected away from the core of the flux rope as it interacts with the convection. The results thus support the idea that the amount of toroidal flux stored at or near the bottom of the solar convection zone may currently be underestimated.

Small-scale magnetic fields on late-type M-dwarfs

We performed kinematic studies of the evolution of small-scale magneticfields in the surface layers of M-dwarfs. We solved the inductionequation for a prescribed velocity field, magnetic Reynolds number ReM,and boundary conditions in a Cartesian box, representing a volumecomprising the optically thin stellar atmosphere and the uppermost partof the optically thick convective envelope. The velocity field isspatially and temporally variable, and stems from detailedradiation-hydrodynamics simulations of convective flows in aproto-typical late-type M-dwarf (Teff =2800pun {K}, logg =5.0, solarchemical composition, spectral type ~M6). We find dynamo action for ReM>= 400. Growth time scales of the magnetic field are comparable tothe convective turn-over time scale (~ 150pun {sec}). The convectivevelocity field concentrates the magnetic field in sheets and tubularstructures in the inter-granular downflows. Scaling from solarconditions suggests that field strengths as high as 20pun{kG} might bereached locally. Perhaps surprisingly, ReM is of order unity in thesurface layers of cooler M-dwarfs, rendering the dynamo inoperative. Inall studied cases we find a rather low spatial filling factor of themagnetic field.

Magnetoconvection and the Solar Dynamo

We review current understanding of the interaction of magnetic fields with convective motions in stellar convection zones. Among the most exciting recent results is the discovery that magnetic fields need not primarily be confined to the stable layer below the convection zone; numerical simulations have shown that surprisingly, strong magnetic fields can be maintained in the interior of the convection zone.

A Non-Helical Dynamo — MHD Simulations of Dynamo Action by a Non-Helical Flow

We illustrate that helicity is not a necessary ingredient for fast dynamo action; we use the stagger-grid method of Galsgaard, Nordlund and others (e.g. Galsgaard & Nordlund 1997, and applied to dynamos by e.g. Dorch 2000): we solve the full MHD equations including a forcing term that keeps the kinetic energy at an approximately constant level. A 3-d flow with no mean helicity (an ABC-like flow without cosines, cf. Galloway & Proctor 1992) is implemented and it turns out that apart from the high growth rate in the linear regime (compared to kinematic dynamo action, cf. Archontis & Dorch 2003a), the dynamo saturates at a level significantly higher that the intermittent turbulent dynamos (cf. Archontis & Dorch 2003b); namely at exact energy equipartition. During the linear regime, several kinematic modes are present, e.g. a sheet/vortex-mode and a mode that resembles the ABC ”double cigar” mode (e.g. Dorch 2000). In the non-linear regime, the magnetic topology is not symmetric, but the initial structure of the velocity field is retained. The presence of helicity is not a requirement for dynamo action but it is rather the stretching ability of the flow that amplifies the magnetic energy in an exponential manner (Archontis & Dorch, in preparation).

A Magnetic Betelgeuse? Numerical Simulations of Non-Linear Dynamo Action

Betelgeuse is an example of a cool super-giant displaying brightness fluctuations and irregular surface structures. Simulations by Freytag et al. (2002) of the convective envelope of the star have shown that the fluctuations in the stars luminosity may be caused by giant cell convection. A related question regarding the nature of Betelgeuse and supergiants in general is whether these stars may be magnetically active. If so, that may in turn also contribute to their variability. By performing detailed numerical simulations, I find that both linear kinematic and non-linear dynamo action are possible and that the non-linear magnetic field saturates at a value somewhat below equipartition: in the linear regime there are two modes of dynamo action.