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.     

A magnetic confinement nuclear fusion mechanism for solar flares

We propose a magnetic confinement nuclear fusion mechanism for the evolution of a solar flare in the solar atmosphere.The mechanism agrees with two observed characteristics of explosive flares and coronal mass ejections(CMEs) that have proved to be very difficult to explain with previous mechanisms:the huge enrichments of3 He and the high energy gamma ray radiation.The twisted magnetic flux rope is a typical structure during the solar flares,which is closely related to the solar active region that magnetic fields have almost complete control over the plasma.Consequently,the plasma inside the flux rope is heated to more than 1.0×107 K by an adiabatic compression process,and then the thermonuclear fusion can take place in the flux rope accompanied with high energy gamma rays.We utilize the time-dependent ideal 2.5-dimensional magnetohydrodynamic(MHD) simulation to demonstrate the physical mechanism for producing flares,which reveals three stages of flare development with the process of magnetic energy conversion and intense release during the solar flares and CMEs in the solar atmosphere.Furthermore,we discuss the relationship between magnetic reconnection and solar eruptions.     

The Filament Eruption of 1999 March 21 and Its Associated Coronal Dimmings and CME

We report a filament eruption near the center of the solar disk on 1999 March 21, in multi-wavelength observations by the Yohkoh Soft X-Ray Telescope (SXT), the Extreme-ultraviolet Images Telescope (EIT) and the Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO). The eruption involved in the disappearance of an Ha filament can be clearly identified in EIT 195 A difference images. Two flare-like EUV ribbons and two obvious coronal dimming regions were formed. The two dimming regions had a similar appearance in lines formed in temperature range 6×104 K to several 106 K. They were located in regions of opposite magnetic polarities near the two ends of the eruptive filament. No significant X-ray or Ha flare was recorded associated with the eruption and no obvious photospheric magnetic activity was detected around the eruptive region, and particularly below the coronal dimming regions. The above surface activities were closely associated with a partial halo-type coronal mass ejection (CME) observed by the Large Angle and Spectrometric Coronagraphs (LASCO) on the SOHO. In terms of the magnetic flux rope model of CMEs, we explained these multiple observations as an integral process of large-scale rearrangement of coronal magnetic field initiated by the filament eruption, in which the dimming regions marked the evacuated feet of the flux rope.     

Numerical experiments on the evolution in coronal magnetic configurations including a filament in response to the change in the photosphere

We investigate equilibrium height of a flux rope, and its internal equilibrium in a realistic plasma environment by carrying out numerical simulations of the evolution of systems including a current-carrying flux rope. We find that the equilibrium height of a flux rope is approximately described by a power-law function of the relative strength of the background field. Our simulations indicate that the flux rope can escape more easily from a weaker background field. This further confirms that a catastrophe in the magnetic configuration of interest can be triggered by a decrease in strength of the background field. Our results show that it takes some time to reach internal equilibrium depending on the initial state of the flux rope. The plasma flow inside the flux rope due to the adjustment for the internal equilibrium of the flux rope remains small and does not last very long when the initial state of the flux rope commences from the stable branch of the theoretical equilibrium curve. This work also confirms the influence of the initial radius of the flux rope in its evolution; the results indicate that a flux rope with a larger initial radius erupts more easily. In addition, by using a realistic plasma environment and a much higher resolution in our simulations,we notice some different characteristics compared to previous studies in Forbes.     

Numerical simulations of three-dimensional magnetic swirls in a solar flux-tube

We aim to numerically study evolution of Alfv′en waves that accompany short-lasting swirl events in a solar magnetic flux-tube that can be a simple model of a magnetic pore or a sunspot. With the use of the FLASH code we numerically solve three-dimensional ideal magnetohydrodynamic equations to simulate twists which are implemented at the top of the photosphere in magnetic field lines of the flux-tube. Our numerical results exhibit swirl events and Alfv′en waves with associated clockwise and counterclockwise rotation of magnetic lines, with the largest values of vorticity at the bottom of the chromosphere, and a certain amount of energy flux.     

Coronal Flux Rope Equilibria in Closed Magnetic Fields

Using a 2.5-dimensional ideal MHD model in Cartesian coordinates,we investigate the equilibrium properties of coronal magnetic flux ropes in background magnetic fields that are completely closed.The background fields are produced by a dipole,a quadrupole,and an octapole,respectively,located below the photosphere at the same depth.A magnetic flux rope is then launched from below the photo-sphere,and its magnetic properties,i.e,the annular magnetic fluxφp and the axial magnetic fluxφz,are controlled by a single emergence parameter.The whole sys-tem eventually evolves into equilibrium,and the resultant flux rope is characterized by three geometrical parameters:the height of the rope axis,the half-width of the rope,and the length of the vertical current sheet below the rope.It is found that the geometrical parameters increase monotonically and continuously with increasing φp and φz:no catastrophe occurs.Moreover,there exists a steep segment in the profiles of the geometrical parameters versus either φp or φz,and the faster the background field decays with height,the larger both the gradient and the growth amplitude within the steep segment will be.     

Energy Buildup,Flux Confinement and Helicity Accumulation in the Solar Corona

Starting from a dipole field and a given distribution of footpoint displace- ment of field lines on the photosphere,we find axisymmetric,force-free field solutions in spherical coordinates that have the same distribution of normal field on the photo- sphere and magnetic topology as the dipole field.A photospheric shear is introduced in the azimuthal direction in a region that strides across the equator and ends at latitude γ_s.The footpoint displacement has a sine distribution in latitude and a peak amplitude of (?)_m.The magnetic energy E,azimuthal flux F_(?),and magnetic helicity H_T in the solar corona are then calculated for each force-free field solution.It is found that for a given shear region range γ_s,all of the three quantities increase monotoni- cally with increasing (?)_m.In particular,both F_(?) and H_T have a linear dependence on (?)m.When (?)_m reaches a certain critical value (?)_(mc),the force-free field loses equilib- rium,leading to a partial opening of the field and the appearance of a current sheet in the equatorial plane.At this point,E,F_(?)and H_T reach their maximum values, E_c,F_((?)c) and H_(Tc).E_c increases,and F_((?)c) and H_(Tc)decrease with decreasing λ_s.It is found that E_c is always smaller than the open field energy,in agreement with the Aly conjecture.Of the three critical parameters,E_c has the weakest dependence on λ_s.Therefore,if one is interested in the transition of a magnetic configuration from a stable state to a dynamic one,the magnetic energy is probably the most appropriate marker of the transition.     

A comparison study of a solar active-region eruptive filament and a neighboring non-eruptive filament

Solar active region(AR) 11283 is a very magnetically complex region and it has produced many eruptions. However, there exists a non-eruptive filament in the plage region just next to an eruptive one in the AR, which gives us an opportunity to perform a comparison analysis of these two filaments. The coronal magnetic field extrapolated using our CESE–MHD–NLFFF code reveals that two magnetic flux ropes(MFRs) exist in the same extrapolation box supporting these two filaments, respectively. Analysis of the magnetic field shows that the eruptive MFR contains a bald-patch separatrix surface(BPSS) cospatial very well with a pre-eruptive EUV sigmoid, which is consistent with the BPSS model for coronal sigmoids. The magnetic dips of the non-eruptive MFRs match Hα observation of the non-eruptive filament strikingly well, which strongly supports the MFR-dip model for filaments. Compared with the non-eruptive MFR/filament(with a length of about 200 Mm), the eruptive MFR/filament is much smaller(with a length of about 20 Mm), but it contains most of the magnetic free energy in the extrapolation box and holds a much higher free energy density than the non-eruptive one. Both the MFRs are weakly twisted and cannot trigger kink instability. The AR eruptive MFR is unstable because its axis reaches above a critical height for torus instability, at which the overlying closed arcades can no longer confine the MFR stably. On the contrary, the quiescent MFR is very firmly held by its overlying field, as its axis apex is far below the torus-instability threshold height. Overall, this comparison investigation supports that an MFR can exist prior to eruption and the ideal MHD instability can trigger an MFR eruption.     

Formation of Transient Coronal Holes during the Eruption of a Quiescent Filament and its Overlying Sigmoid

By using Hα, He I 10830, EUV and soft X-ray (SXR) data, we examined a filament eruption that occurred on a quiet-sun region near the center of the solar disk on 2006 January 12, which disturbed a sigmoid overlying the filament channel observed by the GOES-12 SXR Imager (SXI), and led to the eruption of the sigmoid. The event was associated with a partial halo coronal mass ejection (CME) observed by the Large Angle and Spectrometric Coronagraphs (LASCO) on board the Solar and Heliospheric Observatory (SOHO), and resulted in the formation of two flare-like ribbons, post-eruption coronal loops, and two transient coronal holes (TCHs), but there were no significantly recorded GOES or Hα flares corresponding to the eruption. The two TCHs were dominated by opposite magnetic polarities and were located on the two ends of the eruptive sigmoid. They showed similar locations and shapes in He Ⅰ 10830, EUV and SXR observations. During the early eruption phase, brightenings first appeared on the locations of the two subsequent TCHs, which could be clearly identified on He Ⅰ 10830, EUV and SXR images. This eruption could be explained by the magnetic flux rope model, and the two TCHs were likely to be the feet of the flux rope.     

A disk-corona model for the low/hard state of black hole X-ray binaries

A disk-corona model for fitting the low/hard（LH）state of the associated steady jet in black hole X-ray binaries（BHXBs）is proposed based on the large-scale magnetic field configuration that arises from the coexistence of the Blandford-Znajek（BZ）and Blandford-Payne（BP）processes,where the magnetic field configuration for the BP process is determined by the requirement of energy conversion from Poynting energy flux into kinetic energy flux in the jet.It is found that corona current is crucial to guarantee the consistency of the jet launching from the accretion disk.The relative importance of the BZ and BP processes in powering jets from black hole accretion disks is discussed,and the LH state of several BHXBs is fitted based on our model.In addition,we suggest that magnetic field configuration can be regarded as the second parameter for governing the state transition of BHXBs.     

Polarization Position Angle Swings caused by Relativistic Effects

Polarization position angle swings of - 180 ° observed in extragalactic radio sources are a regular behavior of variability in polarization. They should be due to some kind of physically regular process. We consider relativistic shocks which propagate through and 'illuminate' regular configurations of magnetic field, producing polarization angle swing events. Two magnetic field configurations (force-free field and homogeneous helical field) are considered to demonstrate the results. It is shown that the properties of polarization angle swings and the relationship between the swings and variations in total and polarized flux density are critically dependent on the configuration of magnetic field and the dynamical behavior of the shock. In particular, we find that in some cases polarization angle swings can occur when the total and polarized flux densities only vary by a very small amount. These results may be useful for understanding the polarization variability with both long and short timescales obser     

Magnetic Helicity Injection in Solar Active Regions

We present the evolution of magnetic field and its relationship with mag- netic(current)helicity in solar active regions from a series of photospheric vector magnetograms obtained by Huairou Solar Observing Station,longitudinal magne- tograms by MDI of SOHO and white light images of TRACE.The photospheric current helicity density is a quantity reflecting the local twisted magnetic field and is related to the remaining magnetic helicity in the photosphere,even if the mean current helicity density brings the general chiral property in a layer of solar active regions.As new magnetic flux emerges in active regions,changes of photospheric cur- rent helicity density with the injection of magnetic helicity into the corona from the subatmosphere can be detected,including changes in sign caused by the injection of magnetic helicity of opposite sign.Because the injection rate of magnetic helicity and photospheric current helicity density have different means in the solar atmosphere, the injected magnetic helicity is probably not proportional to the current helicity den- sity remaining in the photosphere.The evidence is that rotation of sunspots does not synchronize exactly with the twist of photospheric transverse magnetic field in some active regions(such as,delta active regions).They represent different aspects of mag- netic chirality.A combined analysis of the observational magnetic helicity parameters actually provides a relative complete picture of magnetic helicity and its transfer in the solar atmosphere.     

A New Method of Identifying 3D Null Points in Solar Vector Magnetic Fields

Employing the Poincare index of isolated null-points in a vector field, we worked out a mathematical method of searching for 3D null-points in coronal magnetic fields. After introducing the relevant differential topology, we test the method by using the analytical model of Brown & Priest. The location of null-point identified by our method coincides precisely with the analytical solution. Finally we apply the method to the 3D coronal magnetic fields reconstructed from an observed MDI magnetogram of a super-active region (NOAA 10488). We find that the 3D null-point seems to be a key element in the magnetic topology associated with flare occurrence.     

Structure and evolution of magnetic fields associated with solar eruptions

This paper reviews the studies of solar photospheric magnetic field evolution in active regions and its relationship to solar flares. It is divided into two topics, the magnetic structure and evolution leading to solar eruptions and rapid changes in the photospheric magnetic field associated with eruptions. For the first topic, we describe the magnetic complexity, new flux emergence, flux cancelation, shear motions, sunspot rotation and magnetic helicity injection, which may all contribute to the storage and buildup of energy that trigger solar eruptions. For the second topic, we concentrate on the observations of rapid and irreversible changes of the photospheric magnetic field associated with flares, and the implication on the restructuring of the three-dimensional magnetic field. In particular, we emphasize the recent advances in observations of the photospheric magnetic field, as state-of-the-art observing facilities(such as Hinode and Solar Dynamics Observatory) have become available. The linkages between observations, theories and future prospectives in this research area are also discussed.     

Energetics and Propagation of Coronal Mass Ejections in Different Plasma Environments

Based on previous work, we investigate the propagation of CMEs in a more realistic plasma environment than the isothermal atmosphere, and find that it is a slightly faster reconnection for flux ropes to break free. The average Alfven Mach number MA for the inflow into the reconnection site has to be at least 0.013 in order to give a plausible eruption (compared to MA = 0.005 for the isothermal atmosphere). Taking MA = 0.1, we find that the energy output and the electric field induced inside the current sheet match the temporal behavior inferred from the energetic, long duration, CME-associated X-ray events. The results indicate that catastrophic loss of equilibrium in the coronal magnetic field provides the most promising mechanism for major solar eruptions, and that the more energetic the eruption is, the earlier the associated flare peaks. The variation of the output power with the background field strength revealed by our calculations implies the poor correlation between slow CMEs and solar flares. Th     

A brief report on the statistical study of net electric current in solar active regions with longitudinal fields of opposite polarity

Dynamic processes occurring in solar active regions are dominated by the solar magnetic field. As of now, observations using a solar magnetograph have supplied us with the vector components of a solar photospheric magnetic field. The two transverse components of a photospheric magnetic field allow us to compute the amount of electric current. We found that the electric current in areas with positive (negative) polarity due to the longitudinal magnetic field have both positive and negative signs in an active region, however, the net current is found to be an order-of-magnitude less than the mean absolute magnitude and has a preferred sign. In particular, we have statistically found that there is a systematic net electric current from areas with negative (positive) polarity to areas with positive (negative) polarity in solar active regions in the northern (southern) hemisphere, but during the solar minimum this tendency is reversed over time at some latitudes. The result indicates that there is weak net electric current in areas of solar active regions with opposite polarity, thus providing further details about the hemispheric helicity rule found in a series of previous studies.     

A Fluid Dynamics Approach for the Computation of Non—linear Force—Free Magnetic Field

Inspired by the analogy between the magnetic field and velocity field of incompressible fluid flow, we propose a fluid dynamics approach for computing nonlinear force-free magnetic fields. This method has the advantage that the divergence-free condition is automatically satisfied, which is a sticky issue for many other algorithms, and we can take advantage of modern high resolution algorithms to process the force-free magnetic field. Several tests have been made based on the well-known analytic solution proposed by Low & Lou. The numerical results are in satisfactory agreement with the analytic ones. It is suggested that the newly proposed method is promising in extrapolating the active region or the whole sun magnetic fields in the solar atmosphere based on the observed vector magnetic field on the photosphere.     

Formation of the CME Leading Edge Observed in the 2003 February 18 Event

This work investigates a typical coronal mass ejection (CME) observed on 2003 February 18, by various space and ground instruments, in white light, Ha, EUV and X-ray. The Ha and EUV images indicate that the CME started with the eruption of a long filament located near the solar northwest limb. The white light coronal images show that the CME initiated with the rarefaction of a region above the solar limb and followed by the formation of a bright arcade at the boundary of the rarefying region at height 0.46 R(?) above the solar surface. The rarefying process synchronized with the slow rising phase of the eruptive filament, and the CME leading edge was observed to form as the latter started to accelerate. The lower part of the filament brightened in Ha as the filament rose to a certain height and parts of the filament was visible in the GOES X-ray images during the rise. These brightenings imply that the filament may be heated by the magnetic reconnection below the filament in the early stage of the eruption. We suggest that a possible mechanism which leads to the formation of the CME leading edge and cavity is the magnetic reconnection which takes place below the filament after the filament has reached a certain height.     

Multi-wavelength fibril dynamics and oscillations above sunspot– I. morphological signature

In this work we selected one particular fibril from a high resolution observation of the solar chromosphere with the Dutch Open Telescope, and tried to obtain a broad picture of the intricate mechanism that might be operating in the multiple layers of the solar atmosphere visible in high cadence multi-wavelength observations. We analyzed the changing fibril pattern using multi-wavelength tomography, which consists of both the Hα line center and the blue wing, Doppler signal, Ca II H, and the G-band. We have found that the intermittent ejected material through the fibril from Doppler images has clearly shown an oscillation mode, as seen in the Hα blue wing.The oscillations in the umbrae and penumbrae magnetic field lines that are above the sunspot cause a broadening and the area forms a ring shape from 3 to 15 minute oscillations as a function of height. These made a distinct boundary between the umbrae and penumbrae which suggests a comb structure, and indicates that the oscillations could propagate along the inclined magnetic flux tubes from below. The 3 minute oscillations strongly appeared in the broadly inclined penumbrae magnetic field lines and showed a clear light bridge. The well known 5 minute oscillations were dominant in the umbrae-penumbrae region boundary. The long 7 minute oscillations were transparent in the Hα blue wing, as well as the 10 and 15 minute oscillations. They were concentrated in the inner-penumbrae, as seen in the Hα line center. From these findings we propose that the fibril acts as a fabric for interaction between the layers,as well as related activities around the active region under investigation.     

Support Vector Machine combined with K-Nearest Neighbors for Solar Flare Forecasting

A method combining the support vector machine (SVM) the K-Nearest Neighbors (KNN), labelled the SVM-KNN method, is used to construct a solar flare forecasting model. Based on a proven relationship between SVM and KNN, the SVM-KNN method improves the SVM algorithm of classification by taking advantage of the KNN algorithm according to the distribution of test samples in a feature space. In our flare forecast study, sunspots and 10cm radio flux data observed during Solar Cycle 23 are taken as predictors, and whether an M class flare will occur for each active region within two days will be predicted. The SVM- KNN method is compared with the SVM and Neural networks-based method. The test results indicate that the rate of correct predictions from the SVM-KNN method is higher than that from the other two methods. This method shows promise as a practicable future forecasting model.