Yihua Yan

New Boundary Integral Equation Representation for Finite Energy Force-Free Magnetic Fields in Open Space above the Sun

A boundary integral equation to describe a force-free magnetic field with finite energy content in the open space above the solar surface is found. This is a new representation for a 3-D nonlinear force-free field in terms of the boundary field and its normal gradient at the boundary. Therefore the magnetic field observed on the solar surface can be incorporated into the formulation directly and a standard numerical technique, the boundary element method, can be applied to solve the field. A numerical test case demonstrates the power of the method by recovering the analytical solution to the desired accuracy and its application to practical solar magnetic field problems is straightforward and promising.

The Magnetic Rope Structure and Associated Energetic Processes in the 2000 July 14 Solar Flare

In the reconstructed nonlinear force-free magnetic field of NOAA Active Region 9077 before the X5.7/3B (10:24 UT) flare on 2000 July 14, we reveal for the first time the presence of a magnetic rope from the extrapolation of the three-dimensional magnetic field structure. This magnetic rope is located in a space above the magnetic neutral lines of the filament. The calculated field lines of the rope rotate around its axis for more than three turns. Overlying the rope are multilayer magnetic arcades with different orientations. These arcades are in agreement with the Transition Region and Coronal Explorer observations. The estimated free magnetic energy in this rope system is about 1.6 × 1032 ergs. Such magnetic field structure provides a favorable model for the interpretation of the energetic flare processes as revealed by Hα, EUV, and radio observations. In particular, the intermittent cospatial brightening of the rope in EUV 1600 A image leading to the onset of the flare suggests that the rope instability may have triggered the flare event, and the drifting pulsation structure in the decimetric frequency range is considered to manifest the initial phase of the coronal mass ejection.

The large-scale coronal field structure and source region features for a halo coronal mass ejection

On 1998 May 2 a class X1/3B flare occurred at 13:42 UT in NOAA Active Region 8210 near disk center, which was followed by a halo coronal mass ejection (CME) at 15:03 UT observed by SOHO/LASCO. Using the boundary element method (BEM) on a global potential model, we reconstruct the large-scale coronal field structure from a composite boundary by SOHO/MDI and Kitt Peak magnetograms. The extrapolated large field lines well model a transequatorial interconnecting loop (TIL) seen in the soft X-ray (SXR) between AR 8210 and AR 8214, which disappeared after the CME. The EUV Imaging Telescope (EIT) observed the widely extending dimmings, which noticeably deviate from the SXR TIL in position. We find that the major dimmings are magnetically linked to the flaring active region but some dimmings are not. The spatial relationships of these features suggest that the CME may be led by a global restructuring of multipolar magnetic systems due to flare disturbances. Mass, magnetic energy, and flux of the ejected material estimated from the dimming regions are comparable to the output of large CMEs, derived from the limb events. At the CME source region, Huairou vector magnetograms show that a strong shear was rapidly developed in a newly emerging flux region (EFR) near the main spot before the flare. Magnetic field extrapolations reveal the presence of a bald patch (defined as the locations where the magnetic field is tangent to the photosphere) at the edge of the EFR. The preflare features such as EUV loop brightenings and SXR jets appearing at the bald patch suggest a slow reconnection between the TIL field system and a preexisting overlying field above the sheared EFR flux system. High-cadence Yohkoh/SXT images reveal a fast expanding motion of loops above a bright core just several minutes before the hard X-ray onset. This may be a precursor for the eruption of the sheared EFR flux to produce the flare. We propose a scenario, similar to the breakout model in principle, that can interpret many observed features.

Direct Boundary Integral Formulation for Solar Non-constant-α Force-free Magnetic Fields

A direct boundary integral formulation for a force-free magnetic field with finite energy content in the semispace above the Sun is presented. This is a new formulation for a three-dimensional nonlinear force-free field in which the boundary data can easily be incorporated. We have proposed an optimal method to numerically find the non-constant-α force-free field solution at any position in semispace. Therefore, the present computational procedure for the new representation is actually a pointwise method, so that no volume integration is needed. A test case study has been carried out to demonstrate the convergence, accuracy, and efficiency of the numerical procedures. The computational procedure is quite robust. The agreement between numerical and exact results validates the correctness and merits of the new formulation and computational procedure proposed. The application of the new direct boundary integral formulation to practical solar magnetic field problems is straightforward and prospective.

The Microwave Pulsations and the Tearing Modes in the Current-Carrying Flare Loops

Solar microwave observations of the X3.4 Flare/CME event observed in Chinese solar broadband radiospectrometer (SBRS/Huairou) on 2006 December 13 show a series of very short period pulsations (VSP) with the period of <1.0 s in the frequency range of 2.60-3.80 GHz. Many pulsating events have the period of only several tens of milliseconds. These pulsations are quasi-periodic, broad bandwidth, and ubiquitous during all the phases of the flare/CME event. Based on theoretical analysis of the temporal behavior of the resistive tearing mode in the electric current-carrying flare loops, we propose that microwave pulsations are a result of the modulation of the tearing-mode oscillations in the current-carrying flare loops. Our calculation of the period of the tearing-mode oscillations are in good agreement with the observations.

On the Zebra Structure in the Frequency Range near 3 GHz

We present 19 cases of zebra pattern structure (ZPS) and fiber bursts (FB) in radio bursts in frequency range around 3 GHz, and one such case in the range 5.2–7.6 GHz, using the new microwave spectrometer of NAOC between 2.6–3.8 and 5.2–7.6 GHz (China, Huairou station) with high resolution (10 MHz and 8 ms). The FB and ZPS have about the same spectral parameters: the frequency bandwidth of emission stripes Δf ~ 20 MHz, the frequency separation between the emission and the neighboring low frequency absorption -Δfea ~ 30 MHz and the frequency separation between emission stripes (when a periodic structure persists) Δfs ~ 60-70 MHz. Therefore we consider both these fine structures to be whistler manifestations, i.e., interactions of plasma electrostatic waves with whistler waves (generated by the same fast particles with loss-cone anisotropy) l + w → t. The duration of the fiber bursts of about 2s corresponds to whistler waves propagating undamped at about 2s, which requires a whistler increment < 0.5 s−1. In the frequency range 3–7 GHz the relation between the ratios of plasma to cyclotron frequencies and whistler to cyclotron frequencies is almost independent of the decrement of whistler electron damping. This finding is used to obtain the magnetic field strength in the region of generation. For a reasonable value of electron temperature (2–20 MK), we find B = 125–190 G when the electron density is (8-18) × 1010 cm-3 and B = 520–610 G when the electron density is (35–60) × 1010 cm-3. In two remarkable events, 1998-04-15 and 2000-10-29, the right-hand polarization is strong for all the fine structures and corresponds to ordinary wave.

ANALYSIS OF it YOHKOH SXT CORONAL LOOPS AND CALCULATED FORCE-FREE MAGNETIC FIELD LINES FROM VECTOR MAGNETOGRAMS

In this paper some soft X-ray loops observed by Yohkoh/SXT and extrapolated magnetic fields from the vector magnetogram data observed at the Mitaka Flare Telescope are compared and analyzed. The computed field lines generally agree with Yohkoh/SXT coronal loops. Typical examples of the magnetic field intensities, loop widths, and loop heights along field lines are presented.

OSCILLATIONS IN A SUNSPOT WITH LIGHT BRIDGES

The Solar Optical Telescope on board Hinode observed a sunspot (AR 11836) with two light bridges (LBs) on 2013 August 31. We analyzed a two-hour Ca II H emission intensity data set and detected strong five-minute oscillation power on both LBs and in the inner penumbra. The time-distance plot reveals that the five-minute oscillation phase does not vary significantly along the thin bridge, indicating that the oscillations are likely to originate from underneath it. The slit taken along the central axis of the wide LB exhibits a standing wave feature. However, at the center of the wide bridge, the five-minute oscillation power is found to be stronger than at its sides. Moreover, the time-distance plot across the wide bridge exhibits a herringbone pattern that indicates a counter-stream of two running waves, which originated at the bridges sides. Thus, the five-minute oscillations on the wide bridge also resemble the properties of running penumbral waves. The five-minute oscillations are suppressed in the umbra, while the three-minute oscillations occupy all three cores of the sunspots umbra, separated by the LBs. The three-minute oscillations were found to be in phase at both sides of the LBs. This may indicate that either LBs do not affect umbral oscillations, or that umbral oscillations at different umbral cores share the same source. It also indicates that LBs are rather shallow objects situated in the upper part of the umbra. We found that umbral flashes (UFs) follow the life cycles of umbral oscillations with much larger amplitudes. They cannot propagate across LBs. UFs dominate the three-minute oscillation power within each core; however, they do not disrupt the phase of umbral oscillation.

EVIDENCE OF CHROMOSPHERIC EVAPORATION IN THE 2004 DECEMBER 1 SOLAR FLARE

In this paper, we present the radio and hard X-ray evidence of chromospheric evaporation during an M1.0 flare which occurred on 2004 December 1. The radio emission was observed by the Solar Broadband Radio Dynamic Spectrometer in China, which yielded dynamic spectra of decimetric emission. The hard X-ray emission was observed by RHESSI. In the radio spectra, the burst is characterized by two groups of parallel-drifting structures, some of which change their drifting rates from positive to negative. Based on the standard flare model, we may explain these decimetric bursts in terms of chromospheric evaporation. On the other hand, RHESSI observations show that the hard X-ray emission in the energy range of 10-15 keV tends to rise from two footpoints to the looptop and eventually merges into a single looptop source, which is accepted as evidence of hard X-ray chromospheric evaporation. Such processes happened twice in this event. The drifting radio structures occurred between them, at the same time as the third hard X-ray peak was observed at 25-50 keV.

TOPOLOGY OF MAGNETIC FIELD AND CORONAL HEATING IN SOLAR ACTIVE REGIONS II. The Role of Quasi-Separatrix Layers

The photospheric vector magnetic fields, Hα and soft X-ray images of AR 7321 were simultaneously observed with the Solar Flare Telescope at Mitaka and the Soft X-ray Telescope of Yohkoh on October 26, 1992, when there was no important activity in this region. Taking the observed photospheric vector magnetic fields as the boundary condition, 3D magnetic fields above the photosphere were computed with a new numerical technique. Then quasi-separatrix layers (QSLs), i.e., regions where 3D magnetic reconnection takes place, were determined in the computed 3D magnetic fields. Since Yohkoh data and Mitaka data were obtained in well-arranged time sequences during the day, the evolution of 3D fields, Hα features and soft X-ray features in this region can be studied in detail. Through a comparison among the 3D magnetic fields, Hα features and soft X-ray features, the following results have been obtained: (a) Hα plages are associated with the portions of QSLs in the chromosphere; (b) diffuse coronal features (DCFs) and bright coronal features (BCFs) are morphologically confined by the coronal linkage of the field lines related to the QSLs; (c) BCFs are associated with a part of the magnetic field lines related to the QSLs. These results suggest that as the likely places where energy release may occur by 3D magnetic reconnection, QSLs play an important role in the chromospheric and coronal heating in this active region.