Fig 2 - uploaded by Yihua Yan
Content may be subject to copyright.
Source publication
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 f...
Context in source publication
Context 1
... geometry for application of Green's second identity is as shown in Figure 2. A treatment of the integrals in equation (8) similar to that of Yan & Sakurai (2000), which follows that in classical exterior boundary value problems (e.g., Stratton 1941;Courant & Hilbert 1962), gives the following results. ...
Similar publications
Low-frequency (80 MHz) imaging and spectral (≈85-20 MHz) observations of moving type IV radio bursts associated with coronal mass ejections (CMEs) from the Sun on three different days are reported. The estimated drift speed of the bursts is in the range ≈150-500 km s–1. We find that all three bursts are most likely due to second harmonic plasma emi...
The Full-disk MagnetoGraph (FMG) onboard the Advanced Space based Solar Observatory has obtained a series of line-of-sight magnetic-field measurements since its launch in October 2022. It is important to compare its observational data with other existing solar telescopes. In this paper, we make a detailed comparison of four active regions and a por...
We examine the turbulent relaxation of solar coronal loops containing non-trivial field line braiding. Such field line tangling in the corona has long been postulated in the context of coronal heating models. We focus on the observational signatures of energy release in such braided magnetic structures using MHD simulations and forward modeling too...
Unraveling the intricate interplay between the solar photosphere's magnetic field and the dynamics of the upper solar atmosphere is paramount to understanding the organization of solar magnetic fields and their influence on space weather events. This study delves into the organization of photospheric magnetic fields particularly in the context of C...
In the present article, we analyze long-term changes in the intensity of galactic cosmic rays (GCRs) in different polarity epochs of the solar magnetic cycles from 1959 to 2014. Our purpose is to carry out a study of the delay time (DT) between the changes of the GCR intensity and various parameters characterizing the conditions in the heliosphere....
Citations
... For this reason, we performed the nonlinear force-free field (NLFF) extrapolation using a method proposed by He et al. (2011). This method is based on the formulation of the direct boundary integral equation (Yan & Li 2006). For our goal we used as boundary conditions the Space-weather Active Region Patches (SHARPs) version (Hoeksema et al. 2014) of the vector magnetograms taken by SDO/HMI on October 22 at 14:00 UT, i.e., some minutes before the flare onset. ...
We report on observations acquired by the Interferometric Bidimensional Spectropolarimeter (IBIS) during SOL2014-10-22T14:02, an X1.6 flare that occurred in active region NOAA 12192, taken in the Fe i 617.30 nm and Ca ii 854.2 nm line profiles. We analyze polarization signatures in the Stokes profiles of the two lines across one of the flare ribbons. Focusing our attention on the chromospheric signals and using the weak-field approximation (WFA), we study the temporal variation of the line-of-sight (LOS) magnetic field. We find variations of the magnetic field or the opacity along the flare ribbon, in most cases within the first 3 minutes of the observation just after the flare peak, during the tail of the flare impulsive phase. This result was validated by the STiC inversion of the pixels used for the WFA analysis. The analysis of the photospheric magnetic field shows that in this layer, the LOS magnetic field does not show the same changes observed in the chromosphere in the selected pixels, nor clear evidence of changes along the polarity inversion line around a magnetic polarity intrusion. In this respect, we also find that the temporal observing window is not suitable for assessing the presence of stepwise changes. The nonlinear force-free field extrapolations, together with the analysis of the ribbons’ isophotes obtained from Interface Region Imaging Spectrograph data, suggest that the region corresponding to the magnetic intrusion observed by IBIS is characterized by a complex magnetic connectivity and is almost cospatial with the area affected by the initial energy release.
... In addition to the two classes of methods above, the boundary integral method, also called boundary element method, has also been used for practical purposes (He & Wang 2008;Guo et al. 2019;He et al. 2020). This method is quite similar to the Green function method for partial differential equations, and a surface integral involving a reference function over the photospheric boundary needs to be evaluated to obtain B at each coronal point at every iteration step (Yan & Sakurai 2000;Yan & Li 2006). It is a merit of the boundary integral method that a finite computational domain does not need to be set up, nor any artificial boundary conditions at the outer boundary, because it assumes a semiinfinite domain and a finite total magnetic energy in it. ...
A new method for reconstruction of coronal magnetic fields as force-free fields (FFFs) is presented. Our method employs poloidal and toroidal functions to describe divergence-free magnetic fields. This magnetic field representation naturally enables us to implement the boundary conditions at the photospheric boundary, i.e., the normal magnetic field and the normal current density there, in a straightforward manner. At the upper boundary of the corona, a source surface condition can be employed, which accommodates magnetic flux imbalance at the bottom boundary. Although our iteration algorithm is inspired by extant variational methods, it is nonvariational and requires far fewer iteration steps than most others. The computational code based on our new method is tested against the analytical FFF solutions by Titov & Démoulin. It is found to excel in reproducing a tightly wound flux rope, a bald patch, and quasi-separatrix layers with a hyperbolic flux tube.
... Besides the two classes of methods above, the boundary integral method, also called boundary element method, has also been used for practical purposes (He & Wang 2008;He et al. 2020;Guo et al. 2019). This method is quite similar to the Green function method for partial differential equations, and a surface integral involving a reference function over the photospheric boundary needs to be evaluated to obtain B at each coronal point at every iteration step (Yan & Sakurai 2000;Yan & Li 2006). It is a merit of the boundary integral method that a finite computational domain does not need to be set up, nor any artificial boundary conditions at the outer boundary, because it assumes a semiinfinite domain and a finite total magnetic energy in it. ...
A new method for reconstruction of coronal magnetic fields as force-free fields (FFFs) is presented. Our method employs poloidal and toroidal functions to describe divergence-free magnetic fields. This magnetic field representation naturally enables us to implement the boundary conditions at the photospheric boundary, i.e., the normal magnetic field and the normal current density there, in a straightforward manner. At the upper boundary of the corona, a source-surface condition can be employed, which accommodates magnetic flux imbalance at the bottom boundary. Although our iteration algorithm is inspired by extant variational methods, it is non-variational and requires much less iteration steps than most of them. The computational code based on our new method is tested against the analytical FFF solutions by Titov & D\'{e}moulin (1999). It is found to excel in reproducing a tightly wound flux rope, a bald patch and quasi-separatrix layers with a hyperbolic flux tube.
... Another method is to compare the diagnosing result with MHD modeling and extrapolations (such as Yan & Sakurai 2000;Yan & Li 2006;Wiegelmann 2008;Metcalf et al. 2008;Jiang & Feng 2013;Chifu et al. 2015;Zhu & Wiegelmann 2018, etc.) from direct measurements in the photosphere and, to a lesser degree, in the chromosphere, which are based mainly on the Zeeman effect. Such comparison can not only verify the reliability of the diagnosis results, but also optimize and improve the modeling extrapolation methods. ...
In solar physics, it is a big challenge to measure the magnetic fields directly from observations in the upper solar atmosphere, including the chromosphere and corona. Radio observations are regarded as the most feasible approach to diagnose the magnetic field in solar chromosphere and corona. However, because of the complexity and diversity of the emission mechanisms, the previous studies have only presented the implicit diagnostic functions of the magnetic field for specific mechanism from solar radio observations. This work collected and sorted out all methods for diagnosing coronal magnetic field from solar radio observations, which are expressed as a set of explicit diagnostic functions. In particular, this work supplemented some important diagnostic methods missed in other reviews. This set of diagnostic functions can completely cover all regions of the solar chromosphere and corona, including the quiet region, active region and flaring source regions. At the same time, it also includes incoherent radiation such as bremsstrahlung emission of thermal plasma above the quiet region, cyclotron and gyro-synchrotron emissions of magnetized hot plasma and mildly relativistic nonthermal electrons above the active regions, as well as coherently plasma emission around flaring source regions. Using this set of diagnostic functions and the related broadband spectral solar radio imaging observations, we can derive the magnetic fields of almost all regions in the solar atmosphere,which may help us to make full use of the spectral imaging observations of the new generation solar radio telescopes (such as MUSER, EVOSA and the future FASR, etc.) to study the solar activities, and provide a reliable basis for the prediction of disastrous space weather events.
... The time evolution of the photospheric vector magnetic fields can be traced continuously for nearly all active regions appearing on the solar disk except for the marginal area near the solar limb. By numerical modeling of the coronal magnetic fields with the sophisticated nonlinear force-free field (NLFFF) model from the observed photospheric vector magnetograms [80,81], the time series data of the coronal magnetic fields corresponding to the time series photospheric vector magnetograms can also be obtained. Then the numerical analysis can be performed on the coronal magnetic field data, and the time evolution of the internal coronal structures as well as the evolution of the non-potentiality in active regions can be revealed [82,83]. ...
The Advanced Space-based Solar Observatory (ASO-S) is a mission aiming at exploring solar flares, coronal mass ejections (CMEs), solar magnetic field and their relationships. To fulfill its major scientific objectives, ASO-S has three elaborately-designed payloads onboard: the Full-disk vector MagnetoGraph (FMG), the Lyman-alpha Solar Telescope (LST), and the Hard X-ray Imager (HXI) dedicated to observe vector magnetic fields, CMEs, and flares, respectively. Beside the scientific objectives, we have an operational objective to observe solar eruptions and magnetic field for making related space weather forecasts. More specifically, we have set a priority for the downlink of CME data observed by LST, and will distribute those data to different space weather prediction centers in China within 2 h once the Science Operation and Data Center (SODC) of ASO-S receive the data. After data downlink and archiving, different automatic detection, tracking, and cataloging procedures are planned to run for the most critical solar eruptive features. On the other hand, based on the distributed and downloaded data, different space weather prediction centers are to activate their forecast systems for the ASO-S observed solar eruption events. Our particular interests are currently focused on nowcast of different eruption events, prediction of CME arrivals, forecast of solar flares and the onset of solar eruptions. We are also working on further forecast potentials using the ASO-S data to make contributions to other possible important issues of space weather.
... There are several methods for numerically computing NLFFFs, such as the magnetofrictional (MF) method (van Ballegooijen 2004;Valori et al. 2005Valori et al. , 2007Mackay et al. 2011;Cheung & DeRosa 2012;Gibb et al. 2014), the Grad-Rubin method (Grad & Rubin 1958;Sakurai 1981;Amari et al. 1999Amari et al. , 2006Wheatland 2004Wheatland , 2006Malanushenko et al. 2012), the optimization approach (Wheatland et al. 2000;Wiegelmann 2004;Wiegelmann et al. 2007), the MHD relaxation method (Chodura & Schlueter 1981;Yang et al. 1986;Mikic & McClymont 1994;Roumeliotis 1996;Inoue et al. 2011Inoue et al. , 2012Jiang et al. 2011;Jiang & Feng 2012), or the boundary-element method (Yan & Sakurai 2000;Yan & Li 2006;He & Wang 2008;He et al. 2011). We use the van Ballegooijen (2004) flux-rope insertion method to perform the NLFFF modeling here. ...
In this paper, we present an analysis of a pseudostreamer embedding a filament cavity, observed on 2015 April 18 on the solar southwest limb. We use the flux-rope insertion method to construct nonlinear force-free field (NLFFF) models constrained by observed Solar Dynamics Observatory ( SDO )/AIA coronal structures and the SDO /Helioseismic Magnetic Imager photospheric magnetogram. The resulting magnetic field models are forward-modeled to produce synthetic data directly comparable to Mauna Loa Solar Observatory/Coronal Multichannel Polarimeter (CoMP) observations of the intensity and linear polarization of the Fe xiii 1074.7 nm infrared coronal emission line using FORWARD. In addition, we determine the location of quasi-separatrix layers in the magnetic models, producing a Q-map from which the signatures of magnetic null points and separatrices can be identified. An apparent magnetic null observed in linear polarization by CoMP is reproduced by the model and appears in the region of the 2D-projected magnetic null in the Q-map. Further, we find that the height of the CoMP null is better reproduced by our NLFFF model than by the synthetic data we produce with potential-field source-surface models, implying the presence of a flux rope in the northern lobe of the pseudostreamer.
... In particular we highlight the various peculiarities of the two events, addressing the point of identifying the 3D null points as a key ingredient in understanding the magnetic topology associated to the WLF episode. In order to reconstruct the 3D coronal magnetic field configuration we adopted the non-linear force-free (NLFF) extrapolation method proposed by He, Wang, and Yan (2011) and based on the direct boundary integral equation (DBIE) formulation (Yan and Li, 2006). We used as boundary conditions for the NLFF field extrapolations the vector magnetograms taken by HMI (Schmidt et al., 2012) onboard the Solar Dynamic Observatory (SDO; Pesnell, Thompson, and Chamberlin (2012)) in the Fe I line at 617.3 nm and pixel size of 0. ′′ 51. ...
Recently, two strong homologous white light flares of X-GOES class occurred on the Sun on Sept. 06, 2017, providing a rare exceptional opportunity to study the mechanisms responsible for the formation of the magnetic field configurations suitable for the manifestation of such yet enigmatic eruptive events and their effects in the lower layers of the solar atmosphere. Using photospheric vector magnetograms, taken before the beginning of the two X-class events, as boundary conditions to reconstruct the non$-$linear coronal magnetic field configuration, we identified two related 3D null points located at low heights above the photosphere (i.e. in very low corona). These null points are most likely responsible for the triggering of the two strong X-GOES class flares. We deduced that their formation at such low altitudes may plausibly be ascribed to the peculiar photospheric horizontal motions of the main magnetic structures of the hosting Active Region NOAA 12673. These events can be adopted as a hint for a possible interpretation of the activity of young G-type stars, recently reported by the Kepler mission. We argued that a possible explanation of the acceleration of huge numbers of particles producing white light emission, during the Sept. 6 events as well as during white light flares in young Sun-like stars, might be attributed to the special accompanying conditions of the occurrence of magnetic reconnection at low altitudes of their atmospheres.
... In particular we highlight the various peculiarities of the two events, addressing the point of identifying the 3D null points as a key ingredient in understanding the magnetic topology associated to the WLF episode. In order to reconstruct the 3D coronal magnetic field configuration we adopted the non-linear force-free (NLFF) extrapolation method proposed by He, Wang, and Yan (2011) and based on the direct boundary integral equation (DBIE) formulation (Yan and Li, 2006). We used as boundary conditions for the NLFF field extrapolations the vector magnetograms taken by HMI (Schmidt et al., 2012) onboard the Solar Dynamic Observatory (SDO; Pesnell, Thompson, and Chamberlin (2012)) in the Fe I line at 617.3 nm and pixel size of 0. ′′ 51. ...
Recently, two strong homologous white light flares of X-GOES class occurred on the Sun on Sept. 06, 2017, providing a rare exceptional opportunity to study the mechanisms responsible for the formation of the magnetic field configurations suitable for the manifestation of such yet enigmatic eruptive events and their effects in the lower layers of the solar atmosphere. Using photospheric vector magnetograms, taken before the beginning of the two X-class events, as boundary conditions to reconstruct the non−linear coronal magnetic field configuration, we identified two related 3D null points located at low heights above the photosphere (i.e. in very low corona). These null points are most likely responsible for the triggering of the two strong X-GOES class flares. We deduced that their formation at such low altitudes may plausibly be ascribed to the peculiar photospheric horizontal motions of the main magnetic structures of the hosting Active Region NOAA 12673. These events can be adopted as a hint for a possible interpretation of the activity of young G-type stars, recently reported by the Kepler mission. We argued that a possible explanation of the acceleration of huge numbers of particles producing white light emission, during the Sept. 6 events as well as during white light flares in young Sun-like stars, might be attributed to the special accompanying conditions of the occurrence of magnetic reconnection at low altitudes of their atmospheres. SOLA: WLFs_Null3D_SOLA_PHYS.tex; 12 December 2018; 1:32; p. 1 P. Romano et al. et al.
... To analyze and compare the magnetic structures associated with the two flare events in AR 10930 and AR 11158, for each flare source AR, we selected one photospheric vector magnetogram before the flare and one magnetogram after the flare eruption, and calculated the corresponding coronal magnetic field distributions from the photospheric vector magnetograms based on the NLFFF model. The algorithm of the NLFFF modeling is an improvement to the direct boundary integral equation (DBIE) approach suggested by Yan and Li (2006). (DBIE, in turn, is an advancement to the original BIE method proposed by Yan and Sakurai (2000), see also Wang et al., 2000;Wang et al., 2001;He and Wang, 2006;He et al., 2011.) ...
Magnetic configuration of flare-bearing active regions (ARs) is one key aspect for understanding the initiation mechanism of solar flares. In this paper, we perform a comparative analysis between the magnetic configurations of two X-class two-ribbon flares happened in AR 10930 (on 2006 December 13) and AR 11158 (on 2011 February 15), whose photospheric magnetic fields were observed by Hinode and SDO satellites, respectively, and coronal magnetic fields were calculated based on nonlinear force-free field model. The analysis shows that both the flares initiated in local areas with extremely strong current density intensity, and the magnetic field chirality (indicated by sign of force-free factor {\alpha}) along the main polarity inversion line (PIL) is opposite for the two ARs, that is, left-hand ({\alpha}<0) for AR 10930 and right-hand ({\alpha}>0) for AR 11158. Our previous study (He et al. 2014) showed that, for the flare of AR 10930, a prominent magnetic connectivity was formed above the main PIL before the flare and was totally broken after the flare eruption, and the two branches of broken magnetic connectivity combined with the isolated electric current at the magnetic connectivity breaking site compose a Z-shaped configuration. In this work, we find similar result for the flare of AR 11158 except that its magnetic configuration is inverse Z-shaped, which corresponds to the right-hand chirality of AR 11158 in contrast to the left-hand chirality of AR 10930. We speculate that two-ribbon flares can be generally classified to these two magnetic configurations by chirality ({\alpha} signs) of ARs.
... where c=1/2 on the boundary S and c=1 in the volume above S, and Y is a reference function of a diagonal matrix that can be determined by a volume integration. This method has been improved and applied to observations in Yan et al. (2001), Yan and Li (2006), and Wang (2006, 2008). And recently, it has also been implemented with the acceleration of the graphics processor unit (GPU; Wang et al., 2013). ...
The topology and dynamics of the three-dimensional magnetic field in the solar atmosphere govern various solar eruptive phenomena and activities, such as flares, coronal mass ejections, and filaments/prominences. We have to observe and model the vector magnetic field to understand the structures and physical mechanisms of these solar activities. Vector magnetic fields on the photosphere are routinely observed via the polarized light, and inferred with the inversion of Stokes profiles. To analyze these vector magnetic fields, we need first to remove the 180° ambiguity of the transverse components and correct the projection effect. Then, the vector magnetic field can be served as the boundary conditions for a force-free field modeling after a proper preprocessing. The photospheric velocity field can also be derived from a time sequence of vector magnetic fields. Three-dimensional magnetic field could be derived and studied with theoretical force-free field models, numerical nonlinear force-free field models, magnetohydrostatic models, and magnetohydrodynamic models. Magnetic energy can be computed with three-dimensional magnetic field models or a time series of vector magnetic field. The magnetic topology is analyzed by pinpointing the positions of magnetic null points, bald patches, and quasi-separatrix layers. As a well conserved physical quantity, magnetic helicity can be computed with various methods, such as the finite volume method, discrete flux tube method, and helicity flux integration method. This quantity serves as a promising parameter characterizing the activity level of solar active regions.
