D. O. Gomez

DYNAMO ACTION IN MAGNETOHYDRODYNAMICS AND HALL-MAGNETOHYDRODYNAMICS

The first direct numerical simulations of turbulent Hall dynamos are presented. The evolution of an initially weak and small-scale magnetic field in a system maintained in a stationary regime of hydrodynamic turbulence (by a stirring force at a macroscopic scale) is studied to explore the conditions for exponential growth of the magnetic energy. The Hall current is shown to have a profound effect on turbulent dynamo action; it can strongly enhance or suppress the generation of the large-scale magnetic energy depending on the relative values of the length scales of the system.

MAGNETOHYDRODYNAMIC TURBULENCE OF CORONAL ACTIVE REGIONS AND THE DISTRIBUTION OF NANOFLARES

We present results from numerical simulations of an externally driven two-dimensional magnetohydrodynamic system over extended periods of time, used to model the dynamics of a transverse section of a solar coronal loop. A stationary forcing was imposed to model the photospheric motions at the loop footpoints. After several photospheric turnover times, a turbulent stationary regime is reached that has an energy dissipation rate consistent with the heating requirements of coronal loops. The turbulent velocities obtained in our simulations are consistent with those derived from the nonthermal broadening of coronal spectral lines. We also show the development of small scales in the spatial distribution of electric currents, which are responsible for most of the energy dissipation. The energy dissipation rate as a function of time displays an intermittent behavior, in the form of impulsive events, that is a direct consequence of the strong nonlinearity of the system. We associate these impulsive events of magnetic energy dissipation with the so-called nanoflares. A statistical analysis of these events yields a power-law distribution as a function of their energies with a negative slope of 1.5, consistent with those obtained for flare energy distributions reported from X-ray observations. A simple model of dissipative structures, based on Kraichnans theory for MHD turbulence, is also presented.

QUASI-SEPARATRIX LAYERS IN A REDUCED MAGNETOHYDRODYNAMIC MODEL OF A CORONAL LOOP

We run a pseudospectral magnetohydrodynamic code to simulate reconnection between two —ux tubes inside a solar coronal loop. We apply a stationary velocity —eld at one of the footpoints consisting of two vortices in such a way as to induce the development of a current layer and force the —eld lines to reconnect. During the process we —nd a remarkable coincidence between the location of the current layer and the location of quasi-separatrix layers, which are thin magnetic volumes where the —eld line connec- tivity changes abruptly. This result lends support to a scenario in which quasi-separatrix layers are the most likely locations for impulsive energy release in the solar corona. Another important result of this simulation is the observed transient of strong magnetohydrodynamic turbulence characterized by a k~3@2 energy spectrum. This transient reaches its peak activity in coincidence with a maximum in the energy dissipation rate, thus suggesting that the direct energy cascade associated with this turbulent transient plays a key role in enhancing energy dissipation in magnetic reconnection processes. Subject headings: MHDSun: coronaSun: —aresSun: magnetic —elds

Turbulent Coronal Heating and the Distribution of Nanoflares

We perform direct numerical simulations of an externally driven two-dimensional magnetohydrodynamic system over extended periods of time to simulate the dynamics of a transverse section of a solar coronal loop. A stationary and large-scale magnetic forcing was imposed, to model the photospheric motions at the magnetic loop footpoints. A turbulent stationary regime is reached, which corresponds to energy dissipation rates consistent with the heating requirements of coronal loops. The temporal behavior of quantities such as the energy dissipation rate shows clear indications of intermittency, which are exclusively due to the strong nonlinearity of the system. We tentatively associate these impulsive events of magnetic energy dissipation (from 5 × 1024 to 1026 ergs) to the so-called nanoflares. A statistical analysis of these events yields a power-law distribution as a function of their energies with a negative slope of 1.5, which is consistent with those obtained for flare energy distributions reported from X-ray observations.

Direct Simulations of Helical Hall-MHD Turbulence and Dynamo Action

Direct numerical simulations of turbulent Hall dynamos are presented. The evolution of an initially weak and small-scale magnetic field in a system maintained in a stationary turbulent regime by a stirring force at a macroscopic scale is studied to explore the conditions for exponential growth of the magnetic energy. Scaling of the dynamo efficiency with Reynolds numbers is studied, and the resulting total energy spectra are found to be compatible with a Kolmogorov-type law. A faster growth of large-scale magnetic fields is observed at intermediate intensities of the Hall effect.

Role of the Hall Current in Magnetohydrodynamic Dynamos

A theoretical mean field closure for Hall magnetohydrodynamics (Hall-MHD) is developed to investigate magnetic field generation through dynamo processes in low electron density astrophysical systems. We show that by modifying the dynamics of microscopic flows, the Hall currents could have a profound impact on the generation of macroscopic magnetic fields. As an illustrative example, we show how dynamo waves are modified by the inclusion of Hall currents. By dropping the usual assumption of a correlation time τ for the microscopic dynamics in the mean field dynamos, we find qualitative changes in the growth rate of dynamo modes.

Energy spectrum of turbulent fluctuations in boundary driven reduced magnetohydrodynamics

The nonlinear dynamics of a bundle of magnetic flux ropes driven by stationary fluid motions at their endpoints is studied, by performing numerical simulations of the magnetohydrodynamic (MHD) equations. The development of MHD turbulence is shown, where the system reaches a state that is characterized by the ratio between the Alfven time (the time for incompressible MHD waves to travel along the field lines) and the convective time scale of the driving motions. This ratio of time scales determines the energy spectra and the relaxation toward different regimes ranging from weak to strong turbulence. A connection is made with phenomenological theories for the energy spectra in MHD turbulence.

Ring current decay rates of magnetic storms: A statistical study from 1957 to 1998

[1] We perform a statistical study of the decay times for the recovery phase of the 300 most intense magnetic storms that occurred from 1 January 1957 to 31 December 1998. The Dst index in the decaying stage has been fitted by an exponential function, and a very good correlation has been obtained for most of the storms. Statistically representative values for the decay time (T) are obtained by averaging the most reliable T values, which resulted from applying a least squares method to the Dst index time series during every recovery phase. The mean value of T turned out to be ∼14 ± 4 hours. We have also found that for very intense storms (Dst min < -250 nT) the values of T tend to decrease as the intensity of the storm increases.

Dynamo Action in Hall Magnetohydrodynamics

We show that the generally neglected Hall term in the equations for two-fluid magnetohydrodynamics may have a profound effect on α-dynamo action. The new calculation, in addition to subsuming the standard results from the mean field approach, contains a contribution to the α-coefficient entirely due to the Hall current in the microscale.

Scaling Law for the Heating of Solar Coronal Loops

We report preliminary results from a series of numerical simulations of the reduced magnetohydrodynamic equations used to describe the dynamics of magnetic loops in active regions of the solar corona. A stationary velocity field is applied at the photospheric boundaries to imitate the driving action of granule motions. A turbulent stationary regime is reached, characterized by a broadband power spectrum Ek approximately k-3&solm0;2 and heating rate levels compatible with the energy requirements of active region loops. A dimensional analysis of the equations indicates that their solutions are determined by two dimensionless parameters: the Reynolds number and the ratio between the Alfvén time and the photospheric turnover time. From a series of simulations for different values of this ratio, we determine how the heating rate scales with the physical parameters of the problem, which might be useful for an observational test of this model.