Magnetic Energy of Force-Free Fields with Detached Field Lines

Using an axisymmetrical ideal MHD model in spherical coordinates, we present a numerical study of magnetic configurations characterized by a levitating flux rope embedded in a bipolar background field whose normal field at the solar surface is the same or very close to that of a central dipole. The characteristic plasma β (the ratio between gas pressure and magnetic pressure) is taken to be sosmall (β= 10^-4) that the magnetic field is close to being force-free. The system as a whole is then let evolve quasi-statically with a slow increase of either the annular magnetic flux or the axial magnetic flux of the rope, and the total magneticenergy of the system grows accordingly. It is found that there exists an energy threshold: the flux rope sticks to the solar surface in equilibrium if the magneticenergy of the system is below the threshold, whereas it loses equilibrium if the threshold is exceeded. The energy threshold is found to be larger than that of thecorresponding fully-open magnetic field by a factor of nearly 1.08 irrespective as towhether the background field is completely closed or partly open, or whether the magnetic energy is enhanced by an increase of annular or axial flux of the rope.This gives an example showing that a force-free magnetic field may have an energy larger than the corresponding open field energy if part of the field lines is allowed tobe detached from the solar surface. The implication of such a conclusion in coronal mass ejections is briefly discussed and some comments are made on the maximum energy of force-free magnetic fields.     

The Magnetic Topological Structure and Energy of the 2B/X2 Flare in NOAA 8100

In this paper, we reconstruct the finite energy force-free magnetic field of the active region NOAA 8100 on 4 November 1997 above the photosphere. In particular, the 3-D magnetic field structures before and after a 2B/X2 flare at 05:58 UT in this region are analyzed. The magnetic field lines were extrapolated in close coincidence with the Yohkoh soft X-ray (SXR) loops accordingly. It is found that the active region is composed of an emerging flux loop, a complex loop system with differential magnetic field shear, and large-scale, or open field lines. Similar magnetic connectivity has been obtained for both instants but apparent changes of the twisting situations of the calculated magnetic field lines can be observed that properly align with the corresponding SXR coronal loops. We conclude that this flare was triggered by the interaction of an emerging flux loop and a large loop system with differential magnetic field shear, as well as large-scale, or open field lines. The onset of the flare was at the common footpoints of several interacting magnetic loops and confined near the footpoints of the emerging flux loop. The sheared configuration remained even after the energetic flare, as demonstrated by calculated values of the twist for the loop system, which means that the active region was relaxed to a lower energy state but not completely to the minimum energy state (two days later another X-class flare occurred in this region).     

Differential rotation and the structure and energy content of coronal magnetic fields

It is argued that differential rotation of the photospheric magnetic fields will induce currents in the corona. The work done against surface magnetic stresses will increase the energy content of the coronal magnetic field. The electrical conductivities are high and the foot points of field lines move with the differential rotation. The force-free field equations are solved with this constraint to obtain a minimum estimate of the energy increase for a quadrupole field. During a solar rotation the magnetic energy increases by 25%. Local release of this energy in the corona would have a significant effect. The expansion of field lines as a result of the differential rotation should increase the amount of flux and the field strength in the solar wind region.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

灾变理论在太阳物理和天体物理其他研究领域中的应用

叙述和介绍了太阳爆发的磁通量绳灾变理论和模型的发展过程,强调了建立这样的模型所需要的观测基础。讨论了由模型所预言的爆发磁结构的几个重要特征以及观测结果对这种预言的证实。在此模型的基础上,讨论了一个典型的爆发过程中所出现的不同现象及它们之间的相互关系。最后,介绍了作者的一项最新尝试:将太阳爆发的灾变理论和模型应用到对黑洞吸积盘间歇性喷流的理论研究当中,以及研究所取得的初步结果。     

Catastrophe of coronal magnetic rope in partly open multipolar magnetic field

Catastrophe of coronal magnetic rope embedded in a partly open multipolar background magnetic field is studied by using a 2-dimensional, 3-component ideal MHD model in spherical coordinates. The background field is composed of three closed bipolar fields of a coronal streamer and an open field with an equatorial current sheet. The magnetic rope lies below the central bipolar field, and it is characterized by its annular and axial magnetic fluxes. For a given annual flux, there is a critical value of the axial flux, and for a given axial flux, there is a critical value of annual flux such that, below the critical value, the magnetic rope is attached to the solar surface and the system stays in equilibrium, but when the critical value is exceeded, the magnetic rope breaks free and erupts upward. This implies that catastrophe can occur in a coronal magnetic rope embedded in a partly open multipolar background magnetic field. Our computation gives a threshold value of magnetic energy that is about 15% greater than the energy of the partly open magnetic field (the central bipolar field open and the fields on either side closed). The excess energy may serve as source for solar explosions such as coronal mass ejections.     

The flare process in a topologically non-equilibrium magnetohydrodynamical system

The existing models for solar flares fail to treat in an appropriate manner the energy release mechanisms based on a step-like transformation of the magnetic field energy from magnetic field to energy of the hydrodynamical motion of the medium and dissipation of these motions through shock waves into heat.In considering an example of the relaxation process in a topologically non-equilibrium magnetohydrodynamical system resulting from the merging of two magnetic loops that possess balanced longitudinal currents, this paper suggests one such energy release mechanism. Due to a certain degree of universality for different topologically non-equilibrium systems, a variety of characteristics of the relaxation process obtained may form the basis for constructing a model of solar flares based on a step-like transformation of the magnetic field energy in topologically non-equilibrium magnetohydrodynamical systems.     

A Numerical Study of the Response of the Coronal Magnetic Field to Flux Emergence

Large-scale solar eruptions, known as coronal mass ejections (CMEs), are regarded as the main drivers of space weather. The exact trigger mechanism of these violent events is still not completely clear; however, the solar magnetic field indisputably plays a crucial role in the onset of CMEs. The strength and morphology of the solar magnetic field are expected to have a decisive effect on CME properties, such as size and speed. This study aims to investigate the evolution of a magnetic configuration when driven by the emergence of new magnetic flux in order to get a better insight into the onset of CMEs and their magnetic structure. The three-dimensional, time-dependent equations for ideal magnetohydrodynamics are numerically solved on a spherical mesh. New flux emergence in a bipolar active region causes destabilisation of the initial stationary structure, finally resulting in an eruption. The initial magnetic topology is suitable for the ??breakout?? CME scenario to work. Although no magnetic flux rope structure is present in the initial condition, highly twisted magnetic field lines are formed during the evolution of the system as a result of internal reconnection due to the interaction of the active region magnetic field with the ambient field. The magnetic energy built up in the system and the final speed of the CME depend on the strength of the overlying magnetic field, the flux emergence rate, and the total amount of emerged flux. The interaction with the global coronal field makes the eruption a large-scale event, involving distant parts of the solar surface.     

Thermodynamic study of non-linear electrodynamics in loop quantum cosmology

In this work, we have discussed the Maxwell’s electrodynamics in non-linear forms in FRW universe. The energy density and pressure for non-linear electrodynamics have been written in the electro-magnetic universe. The Einstein’s field equations for flat FRW model in loop quantum cosmology have been considered if the universe is filled with the matter and electro-magnetic field. We separately assumed the magnetic universe and electric universe. The interaction between matter and magnetic field have been considered in one section and for some particular form of interaction term, we have found the solutions of magnetic field and the energy density of matter. We have also considered the interaction between the matter and electric field and another form of interaction term has been chosen to solve the field equations. The validity of generalized second law of thermodynamics has been investigated on apparent and event horizons using Gibb’s law and the first law of thermodynamics for magnetic and electric universe separately.     

Compton scattering of electromagnetic radiation in pulsar magnetospheres

We have considered the spontaneous Compton scattering of radiation in the magnetic field by both a single ultra-relativistic electron and a system of electrons with the power-law energy distribution. The degree of radiation anisotropy was assumed arbitrary. Parameters of the scattering-generated radiation for the entire range of post-scattering photon energies are given in the paper for all possible scattering modes.     

太阳宏观电场测量进展

太阳耀斑爆发时,日冕中磁自由能通过磁重联在短时间内转换成其他形式的能量,并伴随等离子体的加速和加热,以及带电粒子的加速。在这些过程中,宏观电场的出现起到关键的作用。但是到目前为止,由于太阳上宏观电场的探测比较困难,对电场的研究较少。近几年来随着一系列空间探测卫星被投入使用,加深了人们对日地空间事件发生、发展的物理过程的认识。但是太阳爆发和日冕加热机制等磁活动现象没有得到本质上的认识。太阳宏观电场的探测对突破这一瓶颈具有重要作用。综述了国内外在太阳宏观电场测量上的进展,并提出中国巨型望远镜(ChineseGiant Solar Telescope)在宏观电场观测上可能的科学目标。     

The first magnetic maps of a pre-main-sequence binary star system – HD 155555

We present the first maps of the surface magnetic fields of a pre-main-sequence binary system. Spectropolarimetric observations of the young, 18 Myr, HD 155555 (V824 Ara, G5IV+K0IV) system were obtained at the Anglo-Australian Telescope in 2004 and 2007. Both data sets are analysed using a new binary Zeeman–Doppler imaging (ZDI) code. This allows us to simultaneously model the contribution of each component to the observed circularly polarized spectra. Stellar brightness maps are also produced for HD 155555 and compared to previous Doppler images.
Our radial magnetic maps reveal a complex surface magnetic topology with mixed polarities at all latitudes. We find rings of azimuthal field on both stars, most of which are found to be non-axisymmetric with the stellar rotational axis. We also examine the field strength and the relative fraction of magnetic energy stored in the radial and azimuthal field components at both epochs. A marked weakening of the field strength of the secondary star is observed between the 2004 and 2007 epochs. This is accompanied by an apparent shift in the location of magnetic energy from the azimuthal to radial field. We suggest that this could be indicative of a magnetic activity cycle. We use the radial magnetic maps to extrapolate the coronal field (by assuming a potential field) for each star individually – at present ignoring any possible interaction. The secondary star is found to exhibit an extreme tilt (≈75°) of its large-scale magnetic field to that of its rotation axis for both epochs. The field complexity that is apparent in the surface maps persists out to a significant fraction of the binary separation. Any interaction between the fields of the two stars is therefore likely to be complex also. Modelling this would require a full binary field extrapolation.     

Variations of Photospheric Magnetic Field Associated with Flares and CMEs

Using high-cadence magnetograms from the SOHO/MDI we have investigated variations of the photospheric magnetic field during solar flares and CMEs. In the case of a strong X-class flare of May 2, 1998, we have detected variations of magnetic field in a form of a rapidly propagating magnetic wave. During the impulsive phase of the flare we have observed a sudden decrease of the magnetic energy in the flare region. This provides direct evidence of magnetic energy release in solar flares. We discuss the physics of the magnetic field variations, and their relations to the Moreton Hα waves and the coronal waves observed by the EIT.     

Coronal Flux Rope Catastrophe in Octapole Magnetic Fields

As demonstrated by many previous studies, a system consisting of an isolated coronal flux rope and a surrounding background magnetic field exhibits a catastrophic behavior. In particular, if the magnetic field of the system is force-free and axisymmetric in spherical geometry, the magnetic energy at the catastrophic point, referred to as the catastrophic energy threshold, is found to be larger than the corresponding partly or fully open field energy. This paper takes an octapole field as the background and introduces a flux rope within the central arcade of the octapole field. A relaxation method based on time-dependent ideal magnetohydrodynamic (MHD) simulations is used to find axisymmetric force-free field solutions in spherical geometry associated with the flux rope system. With respect to an increase of either the annular flux Φ_p or the axial flux Φ_ϕ of the rope, the system exhibits a catastrophic behavior as expected, and the catastrophic energy threshold is larger than that of the corresponding partly open field, in which the central arcade is opened up, but the remainder remains closed. For a given octapole field, the energy threshold depends on either Φ_p or Φ_ϕ at the catastrophic point, and it increases with increasing Φ_p or decreasing Φ_ϕ. On the other hand, the extent to which the central bipolar component of the octapole field is open also affects the energy threshold. These results differ from those for the bipolar background field case, in which the catastrophic energy threshold is almost independent of the magnetic properties of the flux rope at the catastrophic points and the extent to which the background field is open. The reason for such a difference is briefly discussed.     

Self-similar propagation of axisymmetric radiative magnetogasdynamic shocks with increasing energy,II

In this paper self-similar solutions have been investigated for the propagation of axisymmetric radiative gasdynamic shocks caused by an explosion into an inhomogeneous ideal gas permeated by a current free azimuthal magnetic field. The effects of radiation flux and magnetic field together have been seen in the region of interest on the other flow variables. The total energy of the flow between the inner expanding surface and the shock is taken to be dependent on shock radius obeying a power law. The radiative pressure and energy have been neglected.     

Implosions in Coronal Transients

Coronal events such as flares or coronal mass ejections derive their energy from the energy stored locally in the magnetic field. This leads to the conjecture that a magnetic implosion must occur simultaneously with the energy release. The site of the implosion would show the location of preflare energy storage, and its detection should have a high priority. The Transition Region and Coronal Explorer EUV observations, for example, have sufficient resolution to show the geometry of a flare implosion by following the motions of tracers in the images.     

Physical conditions in the corona for a bipolar magnetic region

We have used the S-056 X-ray data from Skylab to determine quantitative values for the coronal conditions characterizing a new bipolar magnetic region (BMR). In particular, we include: (a) the time variation of the total soft X-ray flux from the BMR as a function of time; (b) the temporal and spatial variation of the temperature and emission measure; (c) the variation with time of thermal energy density; (d) the (calculated) magnetic field configuration and magnetic flux density in the corona; and (e) the temporal variation of the magnetic field energy in the corona. Detailed comparisons are made between the configuration of X-ray features and the magnetic field topology.     

Polarization of the Crab Nebula with disordered magnetic components

In this paper, we present an expanding disc model to derive the polarization properties of the Crab nebula. The distribution function of the plasma and the energy density of the magnetic field are prescribed as functions of the distance from the pulsar using the model derived by Kennel and Coroniti with  σ= 0.003  , where σ is the ratio of the Poynting flux to the kinetic energy flux in the bulk motion just before the termination shock. Unlike the case for previous models, we introduce a disordered magnetic field, which is parametrized by the fractional energy density of the disordered component. The flow dynamics are not solved, and the mean field is toroidal.
The averaged degree of polarization over the disc is obtained as a function of the inclination angle and fractional energy density of the disordered magnetic field. It is found for the Crab Nebula that the disordered component contains about 60 per cent of the magnetic field energy. This value is supported by the facts that the disc appears not as 'lip-shaped' but as 'rings' in the observed intensity map, and that the highest degree of polarization of ∼40 per cent is reproduced for rings, which is consistent with the observations.
We suggest that, because the disordered field contributes to the pressure rather than to the tension, the pinch force may have been overestimated in previous relativistic magnetohydrodynamic simulations. The disruption of the oppositely directed magnetic fields, which is proposed by Lyuvarsky, may actually take place. The relativistic flow speed, which is indicated by the front–back contrast, can be detected in the asymmetry of distributions of the position angle and depolarization.     

A model of magnetically induced disc–corona for black hole binaries

We propose a model of magnetic connection (MC) of a black hole with its surrounding accretion disc based on large-scale magnetic field. The MC gives rise to transport of energy and angular momentum between the black hole and the disc, and the closed field lines pipe the hot matter evaporated from the disc, and shape it in the corona above the disc to form a magnetically induced disc–corona system, in which the corona has the same configuration as the large-scale magnetic field. We numerically solve the dynamic equations in the context of the Kerr metric, in which the large-scale magnetic field is determined by dynamo process and equipartition between magnetic pressure and gas pressure. Thus we can obtain a global solution rather than assuming the distribution of large-scale magnetic field beforehand. The main MC effects lie in three aspects. (1) The rotational energy of a fast-spinning black hole can be extracted, enhancing the dissipation in the accretion disc, (2) the closed field lines provide a natural channel for corona matter escaping from disc and finally falling into black hole and (3) the scope of the corona can be bounded by the conservation of magnetic flux. We simulate the high-energy spectra of this system by using Monte Carlo method, and find that the relative hardness of the spectra decreases as accretion rate or black hole spin a _* increases. We fit the typical X-ray spectra of three black hole binaries  (GRO J1655−40, XTE 1118+480 and GX 339−4)  in the low/hard or very high state.     

Plasma heating in a sheared magnetic field

The mechanism of spatial resonance of Alfven waves for heating a collisionless plasma is studied in the presence of a twisted magnetic field. In addition to modifying the equilibrium condition for a cylindrical plasma, the azimuthal component of the magnetic field gives extra contribution to the energy deposition rate of the Alfven waves. This new term clearly brings out the effects associated with the finite lifetime of the Alfven waves. The theoretical system considered here conforms to the solar coronal regions.     

Anisotropic stellar structure equations for magnetized strange stars

The fact that a fermion system in an external magnetic field breaks the spherical symmetry suggests that its intrinsic geometry is axisymmetric rather than spherical. In this work we analyze the impact of anisotropic pressures, due to the presence of a magnetic field, in the structure equations of a magnetized quark star.We assume a cylindrical metric and an anisotropic energy momentum tensor for the source. We found that there is a maximum magnetic field that a strange star can sustain, closely related to the violation of the virial relations.