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 so small (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 magnetic energy 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 magnetic energy 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 the corresponding fully-open magnetic field by a factor of nearly 1.08 irrespective as to whether 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 to be 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.

Preprocessing photospheric vector magnetograms for nonlinear force-free field extrapolation of the global corona

Nonlinear force-free magnetic field （NLFFF） extrapolation based on the observed photo- spheric magnetic field is the most important method to obtain the coronal magnetic field nowadays. However, raw photospheric magnetograms contain magnetic forces and small-scale noises, and fail to be consistent with the force-free assumption of NLFFF models. The procedure for removing the forces and noises in observed data is called preprocessing. In this paper, we extend the preprocessing code of Jiang ＆ Feng to spherical coordinates for a full sphere. We first smooth the observed data with Gaussian smoothing, and then split the smoothed magnetic field into a potential field and a non-potential field. The potential part is computed by a numerical potential field model, and the non-potential part is prepro- cessed using an optimization method to minimize the magnetic forces and magnetic torques. Applying the code to synoptic charts of the vector magnetic field from SDO/HMI, we find it can effectively reduce the noises and forces, and improve the quality of data for a better input which will be used for NLFFF extrapolations applied to the global corona.

A magnetic bald-patch flare in solar active region 11117

With SDO observations and a data-constrained magnetohydrodynamics （MHD） model, we identify a confined multi-ribbon flare that occurred on 2010 October 25 in solar active region 11117 as a magnetic bald patch （BP） flare with strong evidence. From the photospheric magnetic field observed by SDO/HMI, we find there are indeed magnetic BPs on the polarity inversion lines （PILs） which match parts of the flare ribbons. From the 3D coronal magnetic field derived from an MHD relaxation model constrained by the vector magnetograms, we find strikingly good agreement of the BP separatrix surface （BPSS） footpoints with the flare ribbons, and the BPSS itself with the hot flaring loop system. Moreover, the triggering of the BP flare can be attributed to a small flux emergence under the lobe of the BPSS, and the relevant change of coronal magnetic field through the flare is reproduced well by the pre-flare and post-flare MHD solutions, which match the corresponding pre- and post-flare AIA observations, respectively. Our work contributes to the study of non-typical flares that constitute the majority of solar flares but which cannot be explained by the standard flare model.

A Fluid Dynamics Approach for the Computation of Nonlinear 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.

Linear Correlations between Peak Frequency of Gyrosynchrotron Spectrum and Photosphere Magnetic Fields

The gyrosynchrotron spectra are computed in a nonuniform magnetic field case, taking into account the self- and gyroresonance absorption. It is found that the peak frequency νp of the gyrosynchrotron spectrum systematically increases with the increasing photosphere magnetic field strength B0 and increasing viewing angle θ. It is also found for the first time that there are good positive linear correlations between νp and B0, and between log νp and log θ, with linear correlation coefficient 0.99 between νp and B0 and 0.95 between log νp and log θ. We apply the correlations to analyze two burst events observed with OVSA and find that the evolution tendencies of the photosphere magnetic field strength B0 estimated from the above expression are comparable with the observational results of SOHO/MDI. We also give a comparison of the diagnostic results of coronal magnetic field strength in both uniform and nonuniform source models.

A comparison between magnetic shear and flare shear in a well-observed M-class flare

We give an extensive multi-wavelength analysis of an eruptive M1.0/1N class solar flare, which occurred in the active region NOAA 10044 on 2002 July 26. Our emphasis is on the relationship between magnetic shear and flare shear. Flare shear is defined as the angle formed between the line connecting the centroids of the two ribbons of the flare and the line perpendicular to the magnetic neutral line. The magnetic shear is computed from vector magnetograms observed at Big Bear Solar Observatory （BBSO）, while the flare shear is computed from Transition Region and Coronal Explorer （TRACE） 1700A images. By a detailed comparison, we find that; 1） The magnetic shear and the flare shear of this event are basically consistent, as judged from the directions of the transverse magnetic field and the line connecting the two ribbons＇ centroids. 2） During the period of the enhancement of magnetic shear, flare shear had a fast increase followed by a fluctuated decrease. 3） When the magnetic shear stopped its enhancement, the fluctuated decreasing behavior of the flare shear became very smooth. 4） Hard X-ray （HXR） spikes are well correlated with the unshearing peaks on the time profile of the rate of change of the flare shear. We give a discussion of the above phenomena.

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

Employing the Poincar6 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 nullpoint 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.

Calibration of Vector Magnetogram with the Nonlinear Least-squares Fitting Technique

To acquire Stokes profiles from observations of a simple sunspot with the Video Vector Magnetograph at Huairou Solar Observing Station (HSOS), we scanned the FeI λ5324.19 A line over the wavelength interval from 150mA redward of the line center to 150mA blueward, in steps of 10mA. With the technique of analytic inversion of Stokes profiles via nonlinear least-squares, we present the calibration coefficients for the HSOS vector magnetic magnetogram. We obtained the theoretical calibration error with linear expressions derived from the Unno-Becker equation under weak-field approximation.

Magnetic Field Strengths and Structures from Radio Observations of Solar Active Regions

Radio observations of some active regions (ARs) obtained with the Nobeyama radioheliograph at λ=1.76 cm are used for estimating the magnetic field strength in the upper chromosphere, based on thermal bremsstrahlung. The results are compared with the magnetic field strength in the photosphere from observations with the Solar Magnetic Field Telescope (SMFT) at Huairou Solar Observing Station of Beijing Astronomical Observatory. The difference in the magnetic field strength between the two layers seems reasonable. The solar radio maps of active regions obtained with the Nobeyama radioheliograph, both in total intensity (I-map) and in circular polarizations (V-map), are compared with the optical magnetograms obtained with the SMFT. The comparison between the radio map in circular polarization and the longitudinal photospheric magnetogram of a plage region suggests that the radio map in circular polarization is a kind of magnetogram of the upper chromosphere. The comparison of the radio map in total intensity with the photo-spheric vector magnetogram of an AR shows that the radio map in total intensity gives indications of magnetic loops in the corona, thus we have a method of defining the coronal magnetic structure from the radio I-maps at λ=1.76 cm. Analysing the I-maps, we identified three components: (a) a compact bright source; (b) a narrow elongated structure connecting two main magnetic islands of opposite polarities (observed in both the optical and radio magnetograms); (c) a wide, diffuse, weak component that corresponds to a wide structure in the solar active region which shows in most cases an S or a reversed S contour, which is probably due to the differential rotation of the Sun. The last two components suggest coronal loops on different spatial scales above the neutral line of the longitudinal photospheric magnetic field.

Short-term solar flare prediction using multi-model integration method

A multi-model integration method is proposed to develop a multi-source and heterogeneous model for short-term solar flare prediction. Different prediction models are constructed on the basis of extracted predictors from a pool of observation databases. The outputs of the base models are normal- ized first because these established models extract predictors from many data resources using different prediction methods. Then weighted integration of the base models is used to develop a multi-model integrated model （MIM）. The weight set that single models assign is optimized by a genetic algorithm. Seven base models and data from Solar and Heliospheric Observatory/Michelson Doppler Imager lon- gitudinal magnetograms are used to construct the MIM, and then its performance is evaluated by cross validation. Experimental results showed that the MIM outperforms any individual model in nearly every data group, and the richer the diversity of the base models, the better the performance of the MIM. Thus, integrating more diversified models, such as an expert system, a statistical model and a physical model, will greatly improve the performance of the MIM.

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.

Synthetic analysis of a two-ribbon microflare

High-resolution Stokes spectral data of Hα, Ca Ⅱ 8542A, and Fe 16302.5A lines for a two-ribbon microflare （TRMF） were simultaneously obtained by the THEMIS telescope on 2002 September 5. We derive the intensity, velocity, and longitudinal magnetic field maps. The hard X-ray emission observed by RHESSI provides evidence of nonthermal particle acceleration in the TRMF. Using Ha and Ca Ⅱ 8542A line profiles and a non-LTE calculation, we obtain semi-empirical atmospheric models for the two brightest kernels of the TRME Our result indicates that the temperature enhancement in the chromosphere is more than 2500 K. The kinetic and radiative energies at the kernels are also estimated, resulting in an estimate of the total energy of the TRMF of about 2.4×10^29 erg. Observations indicate that the TRMF results from the low coronal magnetic reconnection following the eruption of a small fila- ment. However, the local temperature ＂bump＂ in the chromosphere presents a puzzle for such a standard flare model. A possible solution to this is discussed.

The causality between the rapid rotation of a sunspot and an X3.4 flare

Using multi-wavelength data of Hinode, the rapid rotation of a sunspot in active region NOAA 10930 is studied in detail. We found extraordinary counterclockwise rotation of the sunspot with positive polarity before an X3.4 flare. From a series of vector magnetograms, it is found that magnetic force lines are highly sheared along the neutral line accompanying the sunspot rotation. Furthermore, it is also found that sheared loops and an inverse S-shaped magnetic loop in the corona formed gradually after the sunspot rotation. The X3.4 flare can be reasonably regarded as a result of this movement. A detailed analysis provides evidence that sunspot rotation leads to magnetic field lines twisting in the photosphere. The twist is then transported into the corona and triggers flares.

Solar Magnetism and the Activity Telescope at HSOS

A new solar telescope system is described, which has been operating at Huairou Solar Observing Station （HSOS）, National Astronomical Observatories, Chinese Academy of Sciences （CAS）, since the end of 2005. This instrument, the Solar Magnetism and Activity Telescope （SMAT）, comprises two telescopes which respectively make measurements of full solar disk vector magnetic field and Ha observation. The core of the full solar disk video vector magnetograph is a birefringent filter with 0.1A bandpass, installed in the tele-centric optical system of the telescope. We present some preliminary observational results of the full solar disk vector magnetograms and Ha filtergrams obtained with this telescope system.

Design and calibration of a high-sensitivity and high-accuracy polarimeter based on liquid crystal variable retarders

Polarimetry plays an important role in the measurement of solar magnetic fields. We devel- oped a high-sensitivity and high-accuracy polarimeter （HHP） based on nematic liquid crystal variable retarders （LCVRs）, which has a compact setup and no mechanical moving parts. The system design and calibration methods are discussed in detail. The azimuth error of the transmission axis of the polarizer as well as the fast axes of the two LCVRs and the quarter-wave plate were determined using dedicated procedures. Linearly and circularly polarized light were employed to evaluate the performance of the HHP. The experimental results indicate that a polarimetric sensitivity of better than 5.7 × 10-3 can be achieved by using a single short-exposure image, while an accuracy on the order of 10-5 can be reached by using a large number of short-exposure images. This makes the HHP a high-performance system that can be used with a ground-based solar telescope for high-precision solar magnetic field investigations.

Are Homologous Radio Bursts Driven by Solar Post-Flare Loops?

Three particularly complex radio bursts （2001 October 19, 2001 April 10 and 2003 October 26） obtained with the spectrometers （0.65-7.6GHz） at the National Astronomical Observatories, Chinese Academy of Sciences （NAOC, Beijing and Yunnan） and other instruments （NoRH, TRACE and SXT） are presented. They each have two groups of peaks occurring in different frequency ranges （broad-band microwave and narrow-band decimeter wavelengths）. We stress that the second group of burst peaks that occurred in the late phase of the flares and associated with post-flare loops may be homologous radio bursts. We think that they are driven by the post-flare loops. In contrast to the time profiles of the radio bursts and the images of coronal magnetic polarities, we are able to find that the three events are caused by the active regions including main single-bipole magnetic structures, which are associated with multipole magnetic structures during the flare evolutions. In particular, we point out that the later decimetric radio bursts are possibly the radio counterparts of the homologous flares （called ＂homologous radio bursts＂ by us）, which are also driven by the single-bipole mag- netic structures. By examining the evolutions of the magnetic polarities of sources （17 GHz）, we could presume that the drivers of the homologous radio bursts are new and/or recurring appearances/disappearances of the magnetic polarities of radio sources, and that the triggers are the magnetic reconnections of single-bipole configurations.

A quantity characterizing variation of observed magnetic twist in solar active regions

An alternative parameter RJz is introduced as the ratio of one of two kinds of opposite-sign current to the total current and is used to investigate the relationship between this quantity and the hemispheric helicity sign rule（HSR） that has been established by a series of previous statistical studies. The classification of current in each hemisphere obeys the following rule： if the product of the current and the corresponding longitudinal field component contributes a consistent sign with respect to the HSR,it is called ＂HSR-compliant＂ current,otherwise it is called ＂HSR-noncompliant＂ current. Firstly,consistency between the butterfly diagram of RJz and current helicity was obtained in a statistical study.Active regions with RJzsmaller than 0.5 tend to obey the HSR whereas those with RJz greater than 0.5 tend to disobey it. The ＂HSR-compliant＂ current systems have a 60% probability of realization compared to 40% for ＂HSR-noncompliant＂ current systems. Overall,the HSR is violated for active regions in which the ＂HSR-noncompliant＂ current is greater than the ＂HSR-compliant＂ current. Secondly,the parameter RJz was subsequently used to study the evolution of current systems in the case analyses of flare-productive active regions NOAA AR 11158 and AR 11283. It is found that there is a ＂RJz-quasistationary＂ phase that is relatively flare quiescent and ＂RJz-dynamic＂ phase that is characterized by the occurrence of large flares.

Study of temporal and spectral characteristics of the X-ray emission from solar flares

Temporal and spectral characteristics of X-ray emission from 60 flares of intensity ≥C class observed by the Solar X-ray Spectrometer （SOXS） during 2003-2011 are presented. We analyze the X-ray emission observed in four and three energy bands by the Si and Cadmium-Zinc-Telluride （CZT） detectors, respectively. The number of peaks in the intensity profile of the flares varies between 1 and 3. We find moderate correlation （R ~=0.2） between the rise time and the peak flux of the first peak of the flare irrespective of energy band, which is indicative of its energy-independent nature. Moreover, the magnetic field complexity of the flaring region is found to be highly anti-correlated （R = 0.61） with the rise time of the flares while positively correlated （R = 0.28） with the peak flux of the flare. The time delay between the peak of the X-ray emission in a given energy band and that in 25-30keV decreases with increasing energy, suggesting conduction cooling is dominant in the lower energies. Analysis of 340 spectra from 14 flares reveals that the peak of differential emission measure （DEM） evolution is delayed by 60-360 s relative to that of the temperature, and this time delay is inversely proportional to the peak flux of the flare. We conclude that temporal and intensity characteristics of flares are dependent on energy as well as the magnetic field configuration of the active region.

Study of white-light flares observed by Hinode

White-light flares are considered to be the most energetic flaring events that are observable in the optical broad-band continuum of the solar spectrum. They have not been commonly observed. Observations of white-light flares with sub-arcsecond resolution have been very rare. The continuous high resolution observations of Hinode provide a unique opportunity to systematically study the white-light flares with a spatial resolution around 0.2 arcsec. We surveyed all the flares above GOES magnitude C5.0 since the launch of Hinode in 2006 October. 13 of these kinds of flares were covered by the Hinode G-band observations. We analyzed the peak contrasts and equivalent areas （calculated via integrated excess emission contrast） of these flares as a function of the GOES X-ray flux, and found that the cut-off visibility is likely around M1 flares under the observing limit of Hinode. Many other observational and physical factors should affect the visibility of white-light flares; as the observing conditions are improved, smaller flares are likely to have detectable white-light emissions. We are cautious that this limiting visibility is an overestimate, because G-band observations contain emissions from the upper atmosphere. Among the 13 events analyzed, only the M8.7 flare of 2007 June 4 had near-simultaneous observations in both the G-band and the blue continuum. The blue continuum had a peak contrast of 94% vs. 175% in G-band for this event. The equivalent area in the blue continuum is an order of magnitude lower than that in the G-band. Very recently, Jess et al. studied a C2.0 flare with a peak contrast of 300% in the blue continuum. Compared to the events presented in this letter, that event is probably an unusual white-light flare： a very small kernel with a large contrast that can be detected in high resolution observations.

Flare-induced signals in polarization measurements during the X2.6 flare on 2005 January 15

Flare-induced signals in polarization measurements which were manifested as apparent polarity reversal in magnetograms have been reported since 1981. We are motivated to further quantify the phenomenon by asking two questions： can we distinguish the flare-induced signals from real magnetic changes during flares, and what we can learn about flare energy release from the flare-induced signals？ We select the X2.6 flare that occurred on 2005 January 15, for further study. The flare took place in NOAA active region （AR） 10720 at approximately the central meridian, which makes the interpretation of the vector magnetograms less ambiguous. We have identified that flare-induced signals during this flare appeared in six zones. The zones are located within an average distance of 5 Mm from their weight center to the main magnetic neutral line, have an average size of （0.6±0.4） ×10^17 cm^2, duration of 13±4 min, and flux density change of 181±125 G in the area of reversed polarity. The following new facts have been revealed by this study： （1） the flare-induced signal is also seen in the transverse magnetograms but with smaller magnitude, e.g., about 50 G; （2） the flare-induced signal mainly manifests itself as apparent polarity reversal, but the signal starts and ends as a weakening of flux density; （3） The flare-induced signals appear in phase with the peaks of hard X-ray emission as observed by the Ramaty High Energy Solar Spectroscopic Imager （RHESSI）, and mostly trace the position of RHESSI hard X-ray footpoint sources. （4） in four zones, it takes place cotemporally with real magnetic changes which persist after the flare. Only for the other two zones does the flux density recover to the pre-flare level immediately after the flare. The physical implications of the flare-induced signal are discussed in view of its relevance to the non-thermal electron precipitation and primary energy release in the flare.