The heating of the solar corona

The heating of the solar corona has been a fundamental astrophysical issue for over sixty years. Over the last decade in particular, space-based solar observatories (Yohkoh, SOHO and TRACE) have revealed the complex and often subtle magnetic-field and plasma interactions throughout the solar atmosphere in unprecedented detail. It is now established that any energy release mechanism is magnetic in origin - the challenge posed is to determine what specific heat input is dominating in a given coronal feature throughout the solar cycle. This review outlines a range of possible magnetohydrodynamic (MHD) coronal heating theories, including MHD wave dissipation and MHD reconnection as well as the accumulating observational evidence for quasi-periodic oscillations and small-scale energy bursts occurring in the corona. Also, we describe current attempts to interpret plasma temperature, density and velocity diagnostics in the light of specific localised energy release. The progress in these investigations expected from future solar missions (Solar-B, STEREO, SDO and Solar Orbiter) is also assessed.Received: 6 February 2003, Published online: 14 November 2003 Correspondence to: R. W. Walsh     

Effects of a kappa distribution function of electrons on incoherent scatter spectra

In usual incoherent scatter data analysis, the plasma distribution function is assumed to be Maxwellian. In space plasmas, however, distribution functions with a high energy tail which can be well modeled by a generalized Lorentzian distribution function with spectral index kappa (kappa distribution) have been observed. We have theoretically calculated incoherent scatter spectra for a plasma that consists of electrons with kappa distribution function and ions with Maxwellian neglecting the effects of the magnetic field and collisions. The ion line spectra have a double-humped shape similar to those from a Maxwellian plasma. The electron temperatures are underestimated, however, by up to 40% when interpreted assuming Maxwellian distribution. Ion temperatures and electron densities are affected little. Accordingly, actual electron temperatures might be underestimated when an energy input maintaining a high energy tail exists. We have also calculated plasma lines with the kappa distribution function. They are enhanced in total strength, and the peak frequencies appear to be slightly shifted to the transmitter frequency compared to the peak frequencies for a Maxwellian distribution. The damping rate depends on the electron temperature. For lower electron temperatures, plasma lines for electrons with a distribution function are more strongly damped than for a Maxwellian distribution. For higher electron temperatures, however, they have a relatively sharp peak.     

日冕物质抛射的理想MHD模型研究

概括了日冕物质抛射的一些观测结果和它们与其它太阳活动现象的相关性。简要回顾了较早期日冕物质抛射的理论研究,着重介绍了最近研究得较多的理论机制,即能量储存机制,以及其中的磁通量绳突变模型与其它理论模型的MHD数值和解析研究以及相应的重要应用．     

Evolution of Magnetic Fields in Galaxies with Spiral Structure

We present simulations of the 3D nonlinear induction equation in order to investigate the temporal evolution of large-scale magnetic fields in spiral galaxies. Our model includes differential rotation, ambipolar diffusion and, based on small-scale turbulence, eddy diffusivity and the tensorial -effect with magnetic feedback. The nonaxisymmetric spiral pattern and – if considered – the vertical stratification of the galaxy are represented in its density and turbulence profile. Neglecting vertical stratification the lifetime and geometry of an initial magnetic field depend on the correlation time of interstellar turbulence _corr . Short correlation times increase the lifetime of the initial magnetic field, but the field is rapidly wound up. Its pitch-angles develop to zero. The magnetic field has disappeared after at most 1 to 1.5 Gyr. A resonance like phenomenon is found by tuning the pattern velocity of the galactic spiral. The simulations then show an exceptional amplification of the magnetic field in the case that the pattern speed and a magnetic drift velocity have similar values. Considering a vertical stratification we achieve sufficiently long living grand-designed magnetic fields excited by dynamo action. The behaviour and geometry of the resulting field is again significantly influenced by the correlation time _corr . Small values of _corr lead to axisymmetric fields with small pitch-angles and field-concentration between the spiral arms. Increasing the correlation time the solutions show larger pitch-angles; and depending on very large correlation times the galactic dynamo rather generates fields clearly within the spiral arms and having a bisymmetric structure.     

Non-linear spherical Alfvén waves

We present a one-dimensional numerical study of Alfvén waves propagating along a radial magnetic field. Neglecting losses, any spherical Alfvén wave, no matter how small its initial amplitude is, becomes non-linear at sufficiently large radii. From previous simulations of Alfvén waves in plane-parallel atmospheres we expected the waves to steepen and produce current sheets in the non-linear regime, which was confirmed by our new calculations. On the other hand we found that even the least non-linear waves were damped out almost completely before 10 R_⊙. A damping of that kind is required by models of Alfvén wave driven winds from old low-mass stars as these winds are mainly accelerated within a few stellar radii.     

Modulation and symmetry changes in stellar dynamos

Stellar dynamos are governed by non-linear partial differential equations (PDEs) which admit solutions with dipole, quadrupole or mixed symmetry (i.e. with different parities). These PDEs possess periodic solutions that describe magnetic cycles, and numerical studies reveal two different types of modulation. For modulations of Type 1 there are parity changes without significant changes of amplitude, while for Type 2 there are amplitude changes without significant changes in parity. In stars like the Sun, cyclic magnetic activity is interrupted by grand minima that correspond to Type 2 modulation. Although the Sun's magnetic field has maintained dipole symmetry for almost 300 yr, there was a significant parity change at the end of the Maunder Minimum. We infer that the solar field may have flipped from dipole to quadrupole polarity (and back) after deep minima in the past and may do so again in the future. Other stars, with different masses or rotation rates, may exhibit cyclic activity with dipole, quadrupole or mixed parity. The origins of such behaviour can be understood by relating the PDE results to solutions of appropriate low-order systems of ordinary differential equations (ODEs). Type 1 modulation is reproduced in a fourth-order system while Type 2 modulation occurs in a third-order system. Here we construct a new sixth-order system that describes both types of modulation and clarifies the interactions between symmetry-breaking and modulation of activity. Solutions of these non-linear ODEs reproduce the qualitative behaviour found for the PDEs, including flipping of polarity after a prolonged grand minimum. Thus we can be confident that these patterns of behaviour are robust, and will apply to stars that are similar to the Sun.     

Superbubbles in magnetized interstellar media: blowout or confinement?

The importance of the interstellar magnetic field is studied in relation to the evolution of superbubbles with a three-dimensional (3D) numerical magnetohydrodynamical (MHD) simulation. A superbubble is a large supernova remnant driven by sequential supernova explosions in an OB association. Its evolution is affected by the density stratification in the galactic disc. After the superbubble size reaches 2–3 times the density scaleheight, it expands preferentially in the z -direction, until finally it can punch out a hole in the gas disc (blowout). On the other hand, the magnetic field running parallel to the galactic disc has the effect of preventing it from expanding in the direction perpendicular to the field. The density stratification and the magnetic fields have completely opposite effects on the evolution of the superbubble. We present results of a 3D MHD simulation in which both effects are included. As a result, it is concluded that when the magnetic field has a much larger scaleheight than the density, even for a model in which the bubble would blow out from the disc if the magnetic field were absent, a magnetic field with a strength of 5 μG can confine the bubble in | z |≲300 pc for ≃ 20 Myr (confinement). In a model in which the field strength decreases in the halo as B  ∝ ρ^1/2, the superbubble eventually blows out like a model with B  = 0 even if the magnetic field in the mid-plane is as strong as B  = 5 μG.     

A two-layer αω-dynamo model with dynamic feedback on the ω-effect

In an attempt to produce a simple representation of an interface dynamo, I examine a dynamo model composed of two one-dimensional (radially averaged) pseudo-spherical layers, one in the convection zone and possessing an α-effect, and the other in the tachocline and possessing an ω-effect. The two layers communicate by means of an analogue of Newton's law of cooling, and a dynamical back-reaction of the magnetic field on ω is provided. Extensive bifurcation diagrams are calculated for three separate values of η, the ratio of magnetic diffusivities of the two layers. I find recognizable similarities to, but also dramatic differences from, the comparable one-layer model examined by Roald &38; Thomas. In particular, the solar-like dynamo mode found previously is no longer stable in the two-layer version; in its place there is a sequence of periodic, quasi-periodic and chaotic modes probably created in a homoclinic bifurcation. These differences are important enough to provide support for the view that the solar dynamo cannot be meaningfully modelled in one dimension.     

On a Physically Realistic Fast Dynamo

As a step towards a physically realistic model of a fast dynamo, we study numerically a kinematic dynamo driven by convection in a rapidly rotating cylindrical annulus. Convection maintains the quasi-geostrophic balance whilst developing more complicated time-dependence as the Rayleigh number is increased. We incorporate the effects of Ekman suction and investigate dynamo action resulting from a chaotic flow obtained in this manner. We examine the growth rate as a function of magnetic Prandtl number Pm, which is proportional to the magnetic Reynolds number. Even for the largest value of Pm considered, a clearly identifiable asymptotic behaviour is not established. Nevertheless the available evidence strongly suggests a fast dynamo process.     

Bifurcations in Spherical MHD Models

A series of numerical studies on the behaviour of magnetic fields and motions in a spherical body of an electrically conducting incompressible fluid have been carried out. The magnetic field was assumed to be maintained by a given electromotive force inside the body and to continue as a potential field in outer space. In view of the motion an external forcing was taken into account, and boundary conditions were considered which correspond to a stress-free surface. The stability of several steady states has been studied as well as the evolutions starting from unstable states. In this paper a configuration with a poloidal magnetic field and a differential rotation, both symmetric about the same axis, is considered. This configuration is stable only for sufficiently small Hartmann numbers but evolves, if disturbed, in the case of larger Hartmann numbers toward a non-axisymmetric state. In this case the well-known symmetrization effect of differential rotation in magnetic fields is destroyed.