Magnetic flux in an active solar region and its correlation with flares

The correlation between the magnetic flux in an active solar region and associated powerful solar flares is studied. The behavior of the active regions AR 10486 and AR 10365 is considered. These regions produced a series of class X flares as they crossed the solar disk. The flares appeared when the magnetic flux exceeded 10²² Mx. The magnetic flux remained constant during all the flares except for one. During this flare, the flux decreased by about 10%; this impulsive decrease of the flux was also recorded in the absence of flares. No energy flux from the photosphere to the corona at the time of the flare was observed. The behavior of the photospheric field in AR 10486 and AR 10365 is consistent with a slow accumulation of energy in the corona and the explosive release of energy stored in the magnetic field of a current sheet above an active region during the flare.     

Numerical simulation of a solar flare produced by the emergence of new magnetic flux

A scenario for the production of a current sheet above an active region during the emergence of new magnetic flux is considered. The formation of a current sheet is demonstrated via a numerical solution of a system of MHD equations with dissipative terms. The flare energy is stored in the magnetic field of the current sheet. The decay of the current sheet can account for a number of solar-flare phenomena, including the observed divergence of H _α ribbons.     

Formation of several current sheets preceding a series of flares above the active region AR 0365

We have carried out 3D MHD modeling of the solar corona above the active region AR 0365 before a series of flares observed on May 26–27, 2003. Maps of the evolving photospheric magnetic fields preceding the flares were used as boundary conditions. An emergence of new flux equal to ～1.5 × 10²² Maxwell preceded the observed series of X-ray flares. Modeling a large region 4 × 10¹⁰ cm in size demonstrates the formation of several current sheets in the vicinities of coronal Xlines, both already existing in the initial potential field and arising due to the emergence of the new magnetic flux. Each current sheet could be responsible for an elementary flare.     

The generation of hard X-rays and relativistic protons observed during solar flares

The flare source of thermal X-rays above a magnetic arch in the corona arises from the dissipation of the magnetic energy of the current sheet formed at the reconnection of magnetic-field lines. The sources of hard X-rays emitted from the footpoints of the magnetic arch are beams of electrons accelerated in field-aligned currents induced by the Hall electric field generated in the current sheet. Both the hard X-rays detected above the active region and the type III radio emission are radiated by electrons accelerated in the field-aligned currents induced by Alfven waves. The solar cosmic rays are emitted promptly at the instant of the flare. It is important that the Lorentz electric field accelerates protons along the singular magnetic X line. The relativistic protons propagate along the interplanetary magnetic field. These protons have exponential spectra, typical for acceleration occurring in current sheets. A mechanism that is relevant for the generation of delayed cosmic rays, which demonstrate significant anisotropy and a power-law spectrum with γ ∼5, is also discussed.     

A model of a solar flare: Comparisons with observations of high-energy processes

New data for the energy and location of the hard-emission centers of a solar flare agree with an electrodynamic model of a solar flare based on the idea of the accumulation of free magnetic energy in the field of a current sheet. Three-dimensional MHD simulations are used to show that the energy stored in the preflare magnetic field of the current sheet is sufficient for the development of a flare and a coronal mass ejection. The flare and coronal mass ejection result from the explosive decay of the current sheet. The position of the brightness-temperature maximum of the radio emission during the flare coincides with the maximum of the current in the current sheet. The exponential spectrum of relativistic protons generated during the flare is consistent with acceleration by the electric field during the current-sheet decay.     

Evidence for a relationship between emerging magnetic fields,electric currents,and solar flares observed on May 10, 2012

Multi-wavelength observations and magnetic-field data for the solar flare of May 10, 2012 (04: 18 UT) are analyzed. A sign change in the line-of-sight magnetic field in the umbra of a small spot has been detected. This is at least partly associated with the emergence of a new magnetic field. A hard X-ray flare was recorded at almost the same time, and a “sunquake” was generated by the impact of the disturbance in the range of energy release on the photosphere. A sigmoid flare was recorded at the beginning of the event, but did not spread, as it usually does, along the polarity inversion (neutral) line. SDO/HMI full vectormagnetic-fieldmeasurements are used to extrapolate the magnetic field of AR 11476 into the corona, and to derive the distribution of vertical currents jz in the photosphere. The relationship between the distribution of currents in the active region and the occurrence of flares is quite complex. The expected “ideal” behavior of the current system before and after the flare (e.g., described by Sharykin and Kosovichev) is observed only in the sigmoid region. The results obtained are compared with observations of two other flares recorded in this active region on the same day, one similar to the discussed flare and the other different. The results confirm that the formation and eruption of large-scale magnetic flux ropes in sigmoid flares is associated with shear motions in the photosphere, the emergence of twisted magnetic tubes, and the subsequent development of the torus instability.     

Topological model for the large solar flare of July 14, 2000

Using observational data obtained with the Yohkoh, SOHO, and TRACE satellites, it is shown that the three-dimensional structure of the large solar flare of July 14, 2000 was determined by the topology of the large-scale magnetic field of the active region giving rise to the flare. The locations and shapes of chromospheric ribbons and brightness centers on these ribbons are explained. The observed behavior of the flare is attributed to rapid magnetic reconnection in the corona. The electric field accelerating particles in the reconnecting current sheets is estimated.     

Propagation of a fast magnetoacoustic shock wave in the magnetosphere of an active region

The propagation of a fast magnetoacoustic shock wave the magnetosphere of a solar active region is considered the nonlinear geometrical acoustics approximation. The magnetic field is modeled as a subphotospheric magnetic dipole embedded in the radial field of the quiet corona. The initial parameters of the wave are specified at a spherical surface in the depths of the active region. The wave propagates asymmetrically and is reflected from regions of the strong magnetic field, which results in the radiation of the wave energy predominantly upwards. Substantial gradients in the Alfvén speed facilitate appreciable growth in the wave intensity. Non-linear damping of the wave and divergence of the wave front lead to the opposite effect. Analysis of the joint action of these factors shows that a fast magnetoacoustic perturbation outgoing from an active region can correspond to a shock wave of moderate intensity. This supports the scenario in which the primary source of the coronal wave is an eruptive filament that impulsively expands in the magnetosphere of an active region.     

Diagnostic of a Solar Flare via Analyses of Emission in Spectral Lines of Highly Ionized Iron

An analysis of the dynamics of the electron temperature of the solar atmosphere in regions where solar flares appear is presented. The temperatures are estimated from the emission in spectral lines of ions with various degrees of ionization. The emission of ionized helium and highly ionized iron was used. Images of preflare states and of flares from the archive of the American SDO spacecraft are analyzed. A solar flare is usually preceded by the registration of a bright glowing structure above the action region, with a temperature exceeding that of the corona. This preflare structure (~10¹⁰ cm) is identified with the development of a system of currents, which, according to numerical simulations, is responsible for the accumulation of energy above the active region before the flare. After several tens of hours of a slow increase in the brightness of the preflare glow in the 94 Å iron (FeXVIII) line, the emission in the 193 Å line of FeXXIV increases sharply, indicating a flare-like growth of the temperature up to at least 20 MK. This growth of the emission coincides with the onset of the solar flare. The observed dynamics of the emission in spectral lines of highly ionized ions is consistent with an electrodynamic model of a solar flare based on the accumulation of magnetic energy in a current sheet above the active region and the explosive release of the stored energy. Studies of mechanisms for solar flares are of special importance in connection with the discovery of solar cosmic rays. Information from the worldwide network of neutron monitors and from the GOES spacecraft has made it possible to firmly state that the source of solar rays is solar flares, not shocks generated by such flares. It cannot be ruled out that a similar mechanism, not shocks, is also responsible for the acceleration of cosmic rays in the Galaxy.     

地球等离子体片中爆震流的理论研究

地球等离子体片中持续时间很短的快速流动事件最近受到很多关注，这些事件被Angelopoulos等称为爆震流，简要回顾了爆震流的理论研究。当前理论认为，爆震流是磁泡（含较少等离子体的磁流通管）在交换不稳定性的作用下在等离子体片中的流动，磁泡图像很自然地解释了等离子体片中观测到的爆震流。理论预期的快速流在横穿磁尾方向的尺度，它的速度伴随着磁场松驰，压力和密度的降低以及电离层和地面特征都已被观测证实。     

An MHD model for a heliospheric current sheet

A numerical solution of the full set of MHD equations shows the generation of a heliospheric current sheet during the thermal expansion of the corona. Calculations were performed for a compressible plasma taking into account dissipative terms and anisotropy of the thermal conductivity of the magnetized plasma. It is shown that the current sheet is not magnetically neutral. The sheet contains a normal component of the magnetic field, which plays a fundamental role during the formation of the sheet and in the stationary state. The sheet is stable against MHD perturbations, which are apparently carried away by the plasma flow. For the numerical scheme chosen, the minimum sheet thickness is determined by the length of the spatial integration step. The PERESVET code was used for the calculations.     

Pre-flare changes in the turbulence regime for the photospheric magnetic field in a solar active region

Observations of the total magnetic field in the active region NOAA 6757 have been used to study the turbulence regime from 2.5 h before the onset of a 2B/X1.5 flare until two minutes after its maximum. The curvature of the exponent ζ(q) for the structure functions of the B _z field increases monotonically before the flare (i.e., the multifractal character of the B _z field becomes more complex) but straightens at the flare maximum and coincides with a linear Kolmogorov dependence (implying a monofractal structure for the B _z field). The observed deviations of ζ(q) from a Kolmogorov line can be used for short-term forecasting of strong flares. Analysis of the power spectra of the B _z field and the dissipation of magnetic-energy fluctuations shows that the beginning of the flare is associated with the onset of a new turbulence regime, which is closer to a classical Kolmogorov regime. The scaling parameter (cancellation index) of the current helicity of the magnetic field, k _h , remains at a high level right up until the last recording of the field just before the flare but decreases considerably at the flare maximum. The variations detected in the statistical characteristics of the turbulence can be explained by the formation and amplification of small-scale flux tubes with strong fields before the flare. The dissipation of magnetic energy before the flare is primarily due to reconnection at tangential discontinuities of the field, while the dissipation after the flare maximum is due to the anomalous plasma resistance. Thus, the flare represents an avalanche dissipation of tangential discontinuities.     

A Green’s function method for calculating the potential magnetic field in solar active regions in a spherical geometry

A Green’s function solution of Laplace’s equation for the potential magnetic field in an external spherical region is found using the derivative of the potential along a selected direction as a boundary condition. A set of programs applying this solution to construct the potential magnetic-field lines in solar active regions based on the photospheric line-of-sight field component has been developed. The method is tested using some model fields, and the optimal step size is found for realistic conditions. The developed software is applied to four real solar active regions, adopting HMI/SDO magnetograms as the boundary conditions. The potential magnetic field in the chromosphere and corona have been reconstructed for the selected regions. The calculated field lines are compared with flux tubes observed by AIA/SDO in the EUV. This comparison is used as a basis to discuss the applicability of a potential field approximation to the magnetic fields in solar active regions.     

The structure of solar filaments. Prominences in the corona free from external magnetic field

The new approach to the modeling of quiescent solar prominences is proposed. We solve the inverse magnetohydrostatic problem, when the pressure, density and temperature of plasma in the filament are calculated from the equilibrium equations using the given magnetic structure (magnetic flux function is proposed to be known). The new exact nonlinear solutions for dense (n ≈ (2?3) × 10¹¹ cm^?3) and cold (T ≈ (5?10) × 10³ K) filaments, embedded in the plan, vertically stratified atmosphere (hot solar corona) free of magnetic field, are derived. The filaments are stretched along the horizontal axisy(the translational symmetry is assumed: ?/?y = 0) and located parallel to and above a photospheric, magnetic polarity reversal line. The magnetic field lines have a structure of magnetic flux rope with helical field lines in three-dimensional space; the strength of magnetic field falls rapidly with distance from a rope axis. No external longitudinal magnetic field is needed to equilibrate the prominence. The net electric current along the filament is equal to zero. The model of magnetic arcade with the deflection (sag) on the top, proposed by Pikelner (1971) as a basic form of normal prominence, is calculated also using the method proposed. It is shown that such magnetic arcade, having the magnetic field strength of few gauss only, can effectively maintain the equilibrium of cool dense filament at the heights about 50–60 Mm.     

Acceleration of charged particles in collapsing magnetic traps during solar flares

This paper examines the mechanisms for the acceleration of electrons, protons, and ions during solar flares. The acceleration is assumed to occur in two steps. The particles are first pre-accelerated by the electric field of a high-temperature current sheet undergoing magnetic reconnection. A collapsing magnetic trap in the solar corona provides further acceleration. It is shown that the Fermi mechanism accelerates trapped protons and ions even more efficiently than it does electrons. The particles escaping from the trap have energies reaching several GeV. The energy distribution of the accelerated ions is essentially independent of their mass and degree of ionization.     

Magnetohydrostatic model for a coronal hole

A model treating a solar coronal hole as an axially symmetrical magnetic formation that is in equilibrium with the surrounding medium is proposed. The model is applicable in the lower corona (to heights of the order of several hundreds of Mm), where the influence of the solar-wind outflow on the state of the system can still be neglected. The magnetic field of the coronal hole is comprised of a relatively weak open flux that varies with height, which extends into interplanetary space, and a closed field, whose flux closes at the chromosphere near the coronal hole. Simple analytical formulas are obtained, which demonstrate for a given equilibrium configuration of the plasma and field the main effect of interest—the lowering of the temperature and density of the gas in the coronal hole compared to their values in the corona at the same geometric height. In particular, it is shown that, at heights of several tens of Mm, the temperature and density of the plasma in the coronal hole are roughly half the corresponding values at the same height in the corona, if the cross-sectional radius of the hole exceeds the scale height in the corona by roughly a factor of 1.5: R _h ≈ 1.5H(T ₀). In the special case when R _h ≈ H(T ₀), the plasma temperature in the hole is equal to the coronal temperature, and the darkening of the coronal hole is due only to an appreciable reduction of the plasma density in the hole, compared to the coronal density. An analogy of the properties of coronal holes and sunspots is discussed, based on the similarity of the magnetic structures of these formations. In spite of the fundamental difference in the mechanisms for energy transport in coronal holes and sunspots, the equilibrium distributions of the plasma parameters in these formations are determined only by the magnetic and gravitational forces, giving rise to a number of common properties, due to their similar magnetic structures.     

Origin of prolonged X-ray flares on active late-type stars

Soft X-ray data for prolonged flares in subgiants in RS CVn binary systems and some other active late-type stars (AB Dor, Algol) are analyzed. During these nonstationary events, a large amount of hot plasma with temperatures exceeding 10⁸ K exists for many hours. Numerical simulations of gas-dynamical processes in the X-ray source—giant loops—can yield reliable estimates of the plasma parameters and flare-source size. This confirms that such phenomena exist while considerable energy is supplied to the top part of a giant loop or system of loops. Refined estimates of the flare energy (up to 10³⁷ erg) and scales contradict the widely accepted idea that prolonged X-ray flares are associated with the evolution of local magnetic fields. The energy of the current component of the large-scale magnetic field arising during the ejection of magnetic field by plasma jets or stellar wind is estimated. Two cases are considered: a global stellar field and fields connecting regions with oppositely directed unipolar magnetic fields. The inferred energy of the current component of the magnetic field associated with distortion of the initial MHD configuration is close to the total flare energy, suggesting that large-scale magnetic fields play an important role in prolonged flares. The flare process encompasses some portion of a streamer belt and may propagate along the entire magnetic equator of the star during the most powerful prolonged events.     

The generation of magnetic field via convective motions in the photosphere,Alvén waves,and the origin of chromospheric spicules

The basis is laid out for a theory relating various phenomena in the solar atmosphere, including localized concentrations of magnetic field at the bases of coronal magnetic arches, chromospheric spicules, twisted coronal magnetic flux tubes, and flows of energy carried by Alfvén waves propagating upward into the corona. The structure of photospheric currents localized in the vicinity of supergranule boundaries and excited by convective motions is studied. These currents exist primarily in a “dynamo layer” of sharply enhanced transverse conductivity, which forms in the weakly ionized thermal photospheric plasma located in the solar gravitational field. The motions of the electrons and ions in this layer have appreciably different characters: the ions are collisionly driven by the flows of neutral atoms, while the electrons drift in the crossed electric and magnetic fields. The electric field supporting the current arises due to the polarization of the electrons and ions. This field also gives rise to Alfvén perturbations that propagate upward into the corona, together with their associated longitudinal currents. The character of this “loading” makes the system of fields and currents uniquely defined. Moreover, the momentum flux carried by these Alfvén waves should be transferred to the cool chromospheric gas, facilitating the vertical ejection of this gas in the form of spicules, as was first proposed in 1992 by Haerendel.     

Detection of new emerging magnetic flux from the topology of SOHO/MDI magnetograms

A topological method for detecting the new emergence of magnetic flux using SOHO/MDI magnetograms of the full solar disk is proposed. This method uses the number of pixels in the image that can be distinguished from a specified value to within a predetermined threshold (the number of disconnected components). We study more than ten very powerful active regions (ARs) with very high flare activity and show that the number of disconnected components increases directly before the development of a series of M and X flares, or accompanies this process. This behaviour is evident not only when there is an explicit emergence of a new flux and a series of fast flares, such as in AR 9236 (November 2000), but also in groups with many non-stationary processes developing along a neutral line of the large-scale magnetic field. We also discuss the possibility of using the obtained results for flare prediction.     

The spectrum of solar cosmic rays: Data of observations and numerical simulation

Analysis of the relativistic proton spectra of solar flares occurring in the 23rd solar activity cycle derived from data of a worldwide neutron monitor network and numerical modeling both provide evidence for the acceleration of charged particles by an electric field that arises in coronal current sheets during reconnection. The method used to obtain the spectra is based on simulating the response of a neutron monitor to an anisotropic flux of relativistic solar protons with specified parameters and determining the characteristics of the primary relativistic solar protons by fitting model responses to the observations. Studies of the dynamics of the energy spectra distinguish two populations of relativistic protons in solar cosmic-ray events: the so-called fast component, which arrives at the flux front of the solar cosmic rays, followed by the delayed slow component. The fast component is characterized by strong anisotropy and an exponential energy spectrum, in agreement with the spectrum yielded by mathematical modeling of particle acceleration by an electric field directed along the X line of the magnetic field. The slow component, whose propagation is probably diffusive, has a power-law spectrum.