Plasma turbulence in solar flares as an explanation of some observed phenomena

It is suggested that, in Petschek's model of magnetic field annihilation, plasma which flows through the boundary layer where its magnetic energy is released is rendered highly turbulent by current driven electrostatic instability. This leads to a physical insight into the mechanism of dissipation, and, by analogy with laboratory experiments on turbulent plasma, can explain the observed X-ray and microwave emissions.When the microstructure is calculated using electrical conductivity appropriate to highly turbulent plasma, a field configuration exists in which protons can be accelerated to very high energies. The results of some numerical calculations of this process are presented.     

On discontinuous plasma flows in the vicinity of reconnecting current sheets in solar flares

The question about the interpretation of numerical experiments on magnetic reconnection in solar flares is considered. A correspondence between the standard classification of magnetohydrodynamic discontinuities and the parameters characterizing the mass flux through a discontinuity and the magnetic field configuration has been established within a classical formulation of the problem on discontinuous magnetohydrodynamic flows. A pictorial graphical representation of the relationship between the angles of the magnetic field vector relative to the normal to the discontinuity plane on both its sides has also been found. The relations between the parameters of a two-dimensional discontinuous flow have the simplest form in a frame of reference where the magnetic field lines (B) are parallel to the matter velocity (u)—the deHoffmann-Teller frame. The question about the transformation of the magnetic field configuration when passing to a “laboratory” frame of reference where (v · B) ≠ 0, i.e., an electric field is present, is considered in this connection. The result is applied to the analytical solution of the problem on the magnetic field structure in the vicinity of a reconnecting current sheet obtained previously by Bezrodnykh et al. The regions of nonevolutionary shocks are shown to appear near the endpoints of a current sheet with reverse currents.     

On the formation of coronal cavities

We present a theoretical study of the formation of a coronal cavity and its relation to a quiescent prominence. We argue that the formation of a coronal cavity is initiated by the condensation of plasma which is trapped by the coronal magnetic field in a closed streamer and which then flows down to the chromosphere along the field lines due to lack of stable magnetic support against gravity. The existence of a coronal cavity depends on the coronal magnetic field strength; with low strength, the plasma density is not high enough for condensation to occur. Furthermore, we suggest that prominence and cavity material is supplied from the chromospheric level. Whether a coronal cavity and a prominence coexist depends on the magnetic field configuration; a prominence requires stable magnetic support.We initiate the study by considering the stability of condensation modes of a plasma in the coronal streamer model obtained by Steinolfson et al. (1982) using a 2-D, time dependent, ideal MHD computer simulation; they calculated the dynamic interaction between outward flowing solar wind plasma and a global coronal magnetic field. In the final steady state, they found a density enhancement in the closed field region with the enhancement increasing with increasing strength of the magnetic field. Our stability calculation shows that if the density enhancement is higher than a critical value, the plasma is unstable to condensation modes. We describe how, depending on the magnetic field configuration, the condensation may produce a coronal cavity and/or initiate the formation of a prominence.NRC Research Associate.     

Two-dimensional,time-dependent MHD description of interplanetary disturbances: Simulation of high speed solar wind interactions

A two-dimensional, time-dependent, magnetohydrodynamic, numerical model is used to investigate multiple, transient solar wind flows which start close to the Sun and then extend into interplanetary space. The initial conditions are assumed to be appropriate for steady, homogeneous solar wind conditions with an average, spiral magnetic field configuration. Because both radial and azimuthal dimensions are included, it is possible to place two or more temporally-developing streams side-by-side at the same time. Thus, the evolution of the ensuing stream interaction is simulated by this numerical code. Advantages of the present method are as follows: (1) the development and decay of asymmetric MHD shocks and their interactions are clearly indicated; and (2) the model allows flexibility in the specification of evolutionary initial conditions in the azimuthal direction, thereby making it possible to gain insight concerning the interplanetary consequences of real physical situations more accurately than by use of the one-dimensional approach. Examples of such situations are the occurrence of near-simultaneous solar flares in adjacent active regions and the sudden appearance or enlargement of coronal holes as a result of a transient re-arrangement from a closed to an open magnetic field topology.     

Self-similar solution of hot accretion flows with ordered magnetic field and outflow

Observations and numerical magnetohydrodynamic (MHD) simulations indicate the existence of outflows and ordered large-scale magnetic fields in the inner region of hot accretion flows. In this paper, we present the self-similar solutions for advection-dominated accretion flows (ADAFs) with outflows and ordered magnetic fields. Stimulated by numerical simulations, we assume that the magnetic field has a strong toroidal component and a vertical component in addition to a stochastic component. We obtain the self-similar solutions to the equations describing the magnetized ADAFs, taking into account the dynamical effects of the outflow. We compare the results with the canonical ADAFs and find that the dynamical properties of ADAFs such as radial velocity, angular velocity and temperature can be significantly changed in the presence of ordered magnetic fields and outflows. The stronger the magnetic field is, the lower the temperature of the accretion flow will be and the faster the flow rotates. The relevance to observations is briefly discussed.     

An unconventional accretion disc dynamo

In the light of recent results from numerical simulations of accretion disc MHD turbulence, we revisit the problem of the configuration of large-scale magnetic fields resulting from an α Ω dynamo operating in a thin accretion disc. In particular, we analyse the consequences of the peculiar sign of the α -effect suggested by numerical simulations . We determine the symmetry of the fastest-growing modes in the kinematic dynamo approximation and, in the framework of an ' α -quenched' dynamo model, study the evolution of the magnetic field. We find that the resulting field for this negative polarity of the α -effect generally has dipole symmetry with respect to the disc midplane, although the existence of an equilibrium configuration depends on the properties of the turbulence. The role of magnetic field dragging is discussed and, finally, the presence of an external uniform magnetic field is included to address the issue of magneto centrifugal wind launching from accretion discs.     

Coronal disturbances

We have studied chromospheric mass injection into an overlying coronal dipole magnetic field using a 2-D ideal magnetohydrodynamic (MHD) numerical model. The results indicate that such injection can produce magnetic field deformation conducive to active region prominences - namely, Kippenhahn-Schlüter (K-S) type configurations for stable support of injected plasma. We show the optimum conditions for such dynamical formation of K-S-type field configurations.Observations show that an active region prominence formation is preceded by the accumulation of absorptive strands above a neutral line. We hypothesize that an absorptive strand is formed by a chromospheric asymmetric mass injection into the overlying coronal magnetic field and that a necessary condition for the accumulation of the strands is that the mass injection forms a K-S-type field configuration. The results of our numerical simulation of the injection dynamics support our hypothesis. To form a K-S-type magnetic field configuration, we find that a narrow range of injection density, velocity, and magnetic field strength must be used; spicule-like, asymmetric mass injection seems favorable.The limited parameter range that exists for the formation of K-S-type magnetic field configurations in asymmetric injections may explain why active region prominences do not form everywhere on every neutral line.     

一类偶发物质抛射事件的观测和数值模拟物理解释

研究了2000年紫金山天文台赣榆观测站观测到的在太阳上7个中小抛射事件，认为它们的特点是不伴随发亮现象，长1—2．5万公里，宽3—5千公里，寿命3—7分钟，产生在弱磁场处远离大黑子的地方，用一维沿磁弧流动的流体力学方程的数值模拟来解释这种抛射，结果显示，与Suematsu等和Shibata等模拟针状物和日浪不同，不是激波或反弹激波将光球色球密度量级的物质推向日冕，而是重联后的连续物质流动形成这类抛射的，大约5分钟的演化，即可达到流体力学稳定解。     

Generalized analytical models of Syrovatskii’s current sheet

Two-dimensional stationary magnetic reconnection models that include a thin Syrovatskii-type current sheet and four discontinuous magnetohydrodynamic flows of finite length attached to its endpoints are considered. The flow pattern is not specified but is determined from a self-consistent solution of the problem in the approximation of a strong magnetic field. Generalized analytical solutions that take into account the possibility of a current sheet discontinuity in the region of anomalous plasma resistivity have been found. The global structure of the magnetic field in the reconnection region and its local properties near the current sheet and attached discontinuities are studied. In the reconnection regime in which reverse currents are present in the current sheet, the attached discontinuities are trans-Alfvénic shock waves near the current sheet endpoints. Two types of transitions from nonevolutionary shocks to evolutionary ones along discontinuous flows are shown to be possible, depending on the geometrical model parameters. The relationship between the results obtained and numerical magnetic reconnection experiments is discussed.     

Non-ideal evolution of non-axisymmetric, force-free magnetic fields in a magnetar

Recent numerical magnetohydrodynamic calculations by Braithwaite and collaborators support the 'fossil field' hypothesis regarding the origin of magnetic fields in compact stars and suggest that the resistive evolution of the fossil field can explain the reorganization and decay of magnetar magnetic fields. Here, these findings are modelled analytically by allowing the stellar magnetic field to relax through a quasi-static sequence of non-axisymmetric, force-free states, by analogy with spheromak relaxation experiments, starting from a random field. Under the hypothesis that the force-free modes approach energy equipartition in the absence of resistivity, the output of the numerical calculations is semiquantitatively recovered: the field settles down to a linked poloidal–toroidal configuration, which inflates and becomes more toroidal as time passes. A qualitatively similar (but not identical) end state is reached if the magnetic field evolves by exchanging helicity between small and large scales according to an α-dynamo-like, mean-field mechanism, arising from the fluctuating electromotive force produced by the initial random field. The impossibility of matching a force-free internal field to a potential exterior field is discussed in the magnetar context.     

Mass upflows in ‘post’-flare loops

A self-consistent numerical model of a reconnecting magnetic field configuration similar to that occurring during the main-phase of two-ribbon flares is used to estimate the upflow caused by the fast-mode expansion of the magnetic field moving into the reconnection region. Such an expansion creates a field-aligned pressure gradient which accelerates plasma upward from the chromospheric base of magnetic field lines in the region external to the loops. The numerical results imply that the amount of mass sucked up in this way is even smaller than was previously estimated by Kopp and Pneuman who used a kinematic model. Therefore, some indirect mechanism (such as evaporation), which would probably derive its motive power from the thermal energy generated by the reconnection, is required to explain the large mass upflows inferred from observations.     

Experimental Studies of Magnetically Driven Plasma Jets

We present experimental results on the formation of supersonic, radiatively cooled jets driven by pressure due to the toroidal magnetic field generated by the 1.5 MA, 250 ns current from the MAGPIE generator. The morphology of the jet produced in the experiments is relevant to astrophysical jet scenarios in which a jet on the axis of a magnetic cavity is collimated by a toroidal magnetic field as it expands into the ambient medium. The jets in the experiments have similar Mach number, plasma beta and cooling parameter to those in protostellar jets. Additionally the Reynolds, magnetic Reynolds and Peclet numbers are much larger than unity, allowing the experiments to be scaled to astrophysical flows. The experimental configuration allows for the generation of episodic magnetic cavities, suggesting that periodic fluctuations near the source may be responsible for some of the variability observed in astrophysical jets. Preliminary measurements of kinetic, magnetic and Poynting energy of the jets in our experiments are presented and discussed, together with estimates of their temperature and trapped toroidal magnetic field.     

Magnetic Null Points due to Multiple Sources of Solar Photospheric Flux

How common are magnetic null points in the highly complex magnetic field of the solar atmosphere? In this work we seek to model the magnetic structure of quiet regions by placing magnetic sources and sinks on a hexagonal network of supergranule cells to represent the intense magnetic fields that occur at the boundaries of these cells. The resulting potential coronal magnetic field is then computed analytically and searched numerically for magnetic null points, which are classified according to their types and spine directions. Two relations from the theory of vector fields relate the numbers of null points to the numbers of sources and sinks and these are used to check the numerical results. Previous results relating these quantities for monopolar and dipolar magnetic fields are described and a new one for a particular class of quadrupolar fields arising in this study is derived. We model a three-cell configuration and study the effects of increasing the strength of a central sink and of moving the central sink. A twelve-cell configuration is studied in lesser detail.

     

Re-connexion of magnetic lines of force: Evolution in incompressible MHD fluids

Time-dependent incompressible MHD solutions in two dimensions are obtained numerically to study the evolutionary process involving a re-connexion of magnetic lines of force. Given an initial antiparallel magnetic field, or a current sheet, to which there is an injection of fluid in a transverse direction, we seek to see how the process of re-connexion builds up. In this numerical experiment, special considerations are given to the confirmation of reconnexion, the formation of X-type magnetic field, the speed of growth, conditions that control the evolution, acceleration of particles, the structure of the diffusion region and so forth. The findings are: magnetic lines of force can re-connect and grow to the X-type configuration in fluids of any finitely large hydromagnetic and hydrodynamic Reynolds numbers; the conditions local to the neutral point are less important than the boundary conditions that set up global flow patterns; acceleration of fluid in bulk only concerns whether the X-type configuration grows to the comparably large extent or not; the electric field at the neutral point due to the rapidly changing magnetic field is less efficient in accelerating charged particles.     

MHD Simulations of Relativistic Jets

In a series of time dependent numerical simulations we have performed a parameter study of magnetised relativistic jets. We have found that the impact of the magnetic field on the morphology of a jet depends strongly on the configuration of the field.     

Helical structures around quiescent solar prominences computed from observable magnetic fields

We analyse the magnetic support of solar prominences in two-dimensional linear force-free fields. A line current is added to model a helical configuration, well suited to trap dense plasma in its bottom part. The prominence is modeled as a vertical mass-loaded current sheet in equilibrium between gravity and magnetic forces.We use a finite difference numerical technique which incorporates both vertical photospheric and horizontal prominence magnetic field measurements. The solution of this mixed boundary problem generally presents singularities at both the bottom and top of the model prominence. The removal of the singularities is achieved by superposition of solutions. Together with the line current equilibrium, these three conditions determine the amplitude of the magnetic field in the prominence, the flux below the prominence and the current intensity, for a given height of the line current. A numerical check of accuracy in the removal of singularities, is done by using known analytical solutions in the potential limit.We have investigated both bipolar and quadrupolar photospheric regions. In this mixed boundary problem the polarity of the field component orthogonal to the prominence is mainly fixed by the imposed height of the line current. For bipolar regions above (respectively below) a critical height the configuration is inverse (respectively normal). For quadrupolar regions the polarity is reversed if we refer the prominence polarity to the closest photospheric polarities. We introduce the polarity of the component parallel to the prominence axis with reference to a sheared arcade. Increasing the shear with fixed boundary conditions can increase or decrease the mass supported depending on the configuration.     

Radiation Induced Dynamics of the Galactic Halo

We show results of numerical simulations of a three component plasma consisting of electrons, ions and dust with external gravitation and radiation fields. We perform simulation runs, starting from an analytic halo equilibrium, balancing pressure, gravitational, and radiative forces. Within these the equilibrium is perturbed by the radiation of a typical OB-star association. The perturbation has a total energy input of 10⁷ L _⊙ and a duration of 30 Myrs. After switching off the perturbation, the simulations are continued to further investigate the dynamics induced. We start with a self consistent one-fluid MHD model without background magnetic field and show for an asymmetric case that the system approaches a new equilibrium after switching on the perturbation. Later it relaxes into the starting configuration again, when the additional radiation is turned off. We then show, first by including a disk-parallel magnetic field and then by redoing the simulations with a full three-fluid code, the influence of magnetic fields and species separation on the plasma dynamics. With our computations we demonstrate that these features can be important for the explanation of the structures of galactic halos and large scale mass flows. This revised version was published online in July 2006 with corrections to the Cover Date.     

Self-consistent magnetohydrodynamic coronal hole flows

Magnetic fields are thought to play a crucial role in determining the dynamics and energetics of coronal hole flows. In this paper we investigate the possibility that the large scale structure of the magnetic field and plasma within a coronal hole may be determined from the effects of plasma-magnetic field interactions. The overall state is then governed by a complex balance of inertial, pressure gravitational and magnetic forces. Integration of the highly non-linear system of differential equations, which describe the plasma-magnetic field coupling, is made possible by employing a numerical iterative technique developed by Pneuman and Kopp (1971). The method of solution is modified and extended to describe thermally conductive plasma flow in coronal holes. We consider the features of a typical converged solution, representing the distribution of velocity, temperature, density and magnetic field strength within a coronal hole.     

Small-Scale Energy Release Driven by Supergranular Flows on the Quiet Sun

We present data and modelling for the quiet Sun that strongly suggest a ubiquitous small-scale atmospheric heating mechanism that is driven solely by converging supergranular flows. A possible energy source for such events is the power transfer to the plasma via the work done on the magnetic field by photospheric convective flows, which exert drag on the footpoints of magnetic structures. We present evidence of small-scale energy release events driven directly by the hydrodynamic forces that act on the magnetic elements in the photosphere, as a result of supergranular-scale flows. We show strong spatial and temporal correlation between quiet-Sun soft X-ray emission (from Yohkoh SXT) and SOHO MDI-derived flux removal events driven by deduced photospheric flows. We also present a simple model of heating generated by flux submergence, based on particle acceleration by converging magnetic mirrors. In the near future, high resolution soft X-ray images from XRT on the Hinode satellite will allow definitive, quantitative verification of our results. Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.     

Numerical simulations of rotating axisymmetric sunspots

A numerical model of axisymmetric convection in the presence of a vertical magnetic flux bundle and rotation about the axis is presented. The model contains a compressible plasma described by the non-linear MHD equations, with density and temperature gradients simulating the upper layer of the Sun's convection zone. The solutions exhibit a central magnetic flux tube in a cylindrical numerical domain, with convection cells forming collar flows around the tube. When the numerical domain is rotated with a constant angular velocity, the plasma forms a Rankine vortex, with the plasma rotating as a rigid body where the magnetic field is strong, as in the flux tube, while experiencing sheared azimuthal flow in the surrounding convection cells, forming a free vortex. As a result, the azimuthal velocity component has its maximum value close to the outer edge of the flux tube. The azimuthal flow inside the magnetic flux tube and the vortex flow is prograde relative to the rotating cylindrical reference frame. A retrograde flow appears at the outer wall. The most significant convection cell outside the flux tube is the location for the maximum value of the azimuthal magnetic field component. The azimuthal flow and magnetic structure are not generated spontaneously, but decay exponentially in the absence of any imposed rotation of the cylindrical domain.