Nonlinear Force-free Field Extrapolation Research Articles

Evidence for Plasmoid-mediated Magnetic Reconnection during a Small-scale Flare in the Partially Ionized Low Solar Atmosphere

Magnetic reconnection plays a crucial role in the energy release process for different kinds of solar eruptions and activities. The rapid solar eruption requires a fast reconnection model. Plasmoid instability in the reconnecting current sheets is one of the most acceptable fast reconnection mechanisms for explaining the explosive events in the magnetohydrodynamics (MHD) scale, which is also a potential bridge between the macroscopic MHD reconnection process and microscale dissipations. Plenty of high-resolution observations indicate that the plasmoid-like structures exist in the high-temperature solar corona, but such evidences are very rare in the lower solar atmosphere with partially ionized plasmas. Utilizing joint observations from the Goode Solar Telescope and the Solar Dynamics Observatory, we discovered a small-scale eruptive phenomenon in NOAA Active Region 13085, characterized by clear reconnection cusp structures, supported by nonlinear force-free field extrapolation results. The plasmoid-like structures with a size of about 150 km were observed to be ejected downward from the current sheet at a maximum velocity of 24 km s−1 in the Hα line wing images, followed by enhanced emissions at around the postflare loop region in multiple wavelengths. Our 2.5D high-resolution MHD simulations further reproduced such a phenomenon and revealed reconnection fine structures. These results provide comprehensive evidences for the plasmoid-mediated reconnection in partially ionized plasmas, and suggest a unified reconnection model for solar flares with different length scales from the lower chromosphere to the corona.

3D Magnetic Free Energy and Flaring Activity Using 83 Major Solar Flares

In this Letter, we examine the relationship between 3D magnetic free energy (MFE) and flaring activity using 83 major solar flares (M-class and X-class) in nine solar active regions (ARs). For this, we use 998 nonlinear force-free field extrapolations compiled by the “Institute for Space-Earth Environmental Research Database” at Nagoya University. These ARs produced at least three major flares with distinct rising and peak phases of 3D MFE. For each phase, the solar flare occurrence rate (FOR) is calculated as a ratio of the number of flares to the duration. The major results from this study are summarized as follows. First, there is no clear linear correlation (CC = 0.15) between 3D MFE and flare peak flux. Second, the FOR (3.4 day−1) of the rising phase is a little higher than that (3.1 day−1) of the peak phase, depending on AR. Third, for several flares, there are noticeable decreases in 3D MFE, which correspond to the typical energy of a major flare (about 1032 erg). Fourth, it is interesting to note that there are noticeable enhancements in FORs at several local maxima of 3D MFE, which may be associated with flux emergence and/or shearing motions. Fifth, the flare index rates, which are defined as the summation of flaring activity divided by the duration, of rising and peak phases are 151 day−1 and 314 day−1, respectively. Our results imply that the traditional and simple “storage and release” model does not apply to flare activities, and the random perturbation may be important for triggering flares.

Rotation and Confined Eruption of a Double Flux-rope System

We perform a data-constrained simulation with the zero-β assumption to study the mechanisms of strong rotation and failed eruption of a filament in active region 11474 on 2012 May 5 observed by Solar Dynamics Observatory and Solar Terrestrial Relations Observatory. The initial magnetic field is provided by nonlinear force-free field extrapolation, which is reconstructed by the regularized Biot–Savart laws and magnetofrictional method. Our simulation reproduces most observational features very well, e.g., the filament large-angle rotation of about 130°, the confined eruption, and the flare ribbons, allowing us to analyze the underlying physical processes behind observations. We discover two flux ropes in the sigmoid system, an upper flux rope (MFR1) and a lower flux rope (MFR2), which correspond to the filament and hot channel in observations, respectively. Both flux ropes undergo confined eruptions. MFR2 grows by tether-cutting reconnection during the eruption. The rotation of MFR1 is related to the shear-field component along the axis. The toroidal field tension force and the nonaxisymmetry forces confine the eruption of MFR1. We also suggest that the mutual interaction between MFR1 and MFR2 contributes to the large-angle rotation and the eruption failure. In addition, we calculate the temporal evolution of the twist and writhe of MFR1, which is a hint of probable reversal rotation.

The Link between Nonthermal Velocity and Free Magnetic Energy in Solar Flares

The cause of excess spectral line broadening (nonthermal velocity) is not definitively known, but given its rise before and during flaring, the causal processes hold clues to understanding the triggers for the onset of reconnection and the release of free magnetic energy from the coronal magnetic field. A comparison of data during a 9 hr period from the extreme ultraviolet Imaging Spectrometer on the Hinode spacecraft—at a 3 minute cadence—and nonlinear force-free field extrapolations performed on Helioseismic and Magnetic Imager magnetograms—at a 12 minute cadence—shows an inverse relationship between nonthermal velocity and free magnetic energy on short timescales during two X-class solar flares on 2017 September 6. Analysis of these results supports suggestions that unresolved Doppler flows do not solely cause nonthermal broadening, and instead other mechanisms like Alfvén wave propagation and isotropic turbulence have a greater influence.

Are Electric-field-driven Magnetohydrodynamic Simulations of the Solar Corona Sensitive to the Initial Condition?

Magnetohydrodynamic (MHD) simulations of the solar corona are often started from a potential field initial condition, which may be far from the true state of the coronal magnetic field. To test the sensitivity of the simulations to the initial condition, an electric-field-driven MHD code was initiated from three different initial conditions: the commonly used potential field, a nonlinear force-free field (NLFFF) extrapolation, which is believed to be a better representation of the true coronal magnetic field, and a purely vertical field. After relaxation, the magnetic field in the MHD simulations was compared. It was found that there is a tendency for all of the initial conditions to converge to a similar connectivity, particularly in areas of strong fields that are not close to the boundary, suggesting that the final state of the simulation is not particularly sensitive to the initial condition. The relaxed solution more closely resembles the NLFFF initial condition than the other initial conditions, but still exhibits substantial differences from it.

Coronal Magnetic Field Extrapolation and Topological Analysis of Fine-scale Structures during Solar Flare Precursors

Magnetic field plays an important role in various solar eruption phenomena. The formation and evolution of the characteristic magnetic field topology in solar eruptions are critical problems that will ultimately help us understand the origin of these eruptions in the solar source regions. With the development of advanced techniques and instruments, observations with higher resolutions in different wavelengths and fields of view have provided more quantitative information for finer structures. It is therefore essential to improve the method with which we study the magnetic field topology in the solar source regions by taking advantage of high-resolution observations. In this study, we employ a nonlinear force-free field extrapolation method based on a nonuniform grid setting for an M-class flare eruption event (SOL2015-06-22T17:39) with embedded vector magnetograms from the Solar Dynamics Observatory (SDO) and the Goode Solar Telescope (GST). The extrapolation results for which the nonuniform embedded magnetogram for the bottom boundary was employed are obtained by maintaining the native resolutions of the corresponding GST and SDO magnetograms. We compare the field line connectivity with the simultaneous GST/Hα and SDO/Atmospheric Imaging Assembly observations for these fine-scale structures, which are associated with precursor brightenings. Then we perform a topological analysis of the field line connectivity corresponding to fine-scale magnetic field structures based on the extrapolation results. The analysis results indicate that when we combine the high-resolution GST magnetogram with a larger magnetogram from the SDO, the derived magnetic field topology is consistent with a scenario of magnetic reconnection among sheared field lines across the main polarity inversion line during solar flare precursors.

Photospheric and Chromospheric Magnetic Field Evolution during the X1.6 Flare in Active Region NOAA 12192

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.

The Formation of a U-shaped Filament Due to the Successive Magnetic Reconnection between a Filament and Its Nearby Chromospheric Fibrils

Although magnetic reconnection plays a key role in the formation of a solar filament, the detailed formation process is still ambiguous. Combining the observational data from the New Vacuum Solar Telescope and the Solar Dynamics Observatory, we analyzed the formation of a U-shaped filament via successive magnetic reconnection in the AR NOAA 11598 on 2012 October 25. The successive reconnection occurred between a filament (F) and its nearby chromospheric fibrils (CF). The associated brightening and magnetic cancellation were observed. The changes in appearance of the CF at the reconnection site were accompanied by the formation and accumulation of some new magnetic loops, as well as plasmas propagated along the formed magnetic loops from the reconnection site, indicating the changes in the topology of the F and CF. These can provide comprehensive observational evidence for successive reconnection. After the reconnection, a longer U-shaped filament was formed. During the formation of the U-shaped filament, two major magnetic energy releases took place. While in the two energy release processes, the injected plasma from the reconnection site can provide part of the material for the formation of the U-shaped filament. Therefore, we conclude that the successive reconnection results in both the dynamical evolution and the subsequent formation associated with the U-shaped filament. And the results of nonlinear force-free field extrapolation demonstrated that the magnetic topology of the F was changed significantly; this is consistent with the observational results and further confirms the formation of the U-shaped filament.

Data-constrained Solar Modeling with GX Simulator

To facilitate the study of solar flares and active regions, we have created a modeling framework, the freely distributed GX Simulator IDL package, that combines 3D magnetic and plasma structures with thermal and nonthermal models of the chromosphere, transition region, and corona. Its object-based modular architecture, which runs on Windows, Mac, and Unix/Linux platforms, offers the ability to either import 3D density and temperature distribution models, or to assign numerically defined coronal or chromospheric temperatures and densities, or their distributions, to each individual voxel. GX Simulator can apply parametric heating models involving average properties of the magnetic field lines crossing a given voxel, as well as compute and investigate the spatial and spectral properties of radio, (sub)millimeter, EUV, and X-ray emissions calculated from the model, and quantitatively compare them with observations. The package includes a fully automatic model production pipeline that, based on minimal users input, downloads the required SDO/HMI vector magnetic field data, performs potential or nonlinear force-free field extrapolations, populates the magnetic field skeleton with parameterized heated plasma coronal models that assume either steady-state or impulsive plasma heating, and generates non-LTE density and temperature distribution models of the chromosphere that are constrained by photospheric measurements. The standardized models produced by this pipeline may be further customized through specialized IDL scripts, or a set of interactive tools provided by the graphical user interface. Here, we describe the GX Simulator framework and its applications.

A comparative study of data-driven MHD simulations of solar coronal evolution with photospheric flows derived from two different approaches

Data-driven simulation proves to be a powerful tool in revealing the dynamic process of the solar corona, but it remains challenging to implement the driving boundary conditions in a self-consistent way and match the observables at the photosphere. Here, we test two different photospheric velocity-driven MHD simulations in studying the quasi-static evolution of solar active region NOAA 11158. The two simulations were identically initialized with an MHD equilibrium as relaxed from a non-linear force-free field extrapolation from a vector magnetogram. Then, we energized the MHD system by applying the time series of photospheric velocity at the bottom boundary as derived by two different codes, the DAVE4VM and PDFI, from the observed vector magnetograms. To mimic the small-scale flux cancellation on the photosphere, the magnetic diffusion at the bottom boundary was set to be inversely proportional to the local scale length of the magnetic field. The result shows the evolution curves of the total magnetic energy and unsigned magnetic flux generated by the PDFI velocity match the corresponding curves from the observations much better than those by the DAVE4VM one. The structure of the current layer and synthetic image in PDFI simulation also has a more reasonable consistency with SDO/AIA 131 Å observation. The only shortage of the PDFI velocity is its capability in reproducing the morphology of sunspots, as characterized by a slightly lower correlation coefficient for the bottom magnetic field in simulations and magnetograms. Overall, this study suggests the superiority of each method in the models driven by the bottom velocity, which represents a further step toward the goal of reproducing more realistically the evolution of coronal magnetic fields using data-driven modeling.

A Large-Scale Dataset of Three-Dimensional Solar Magnetic Fields Extrapolated by Nonlinear Force-Free Method

It has been widely accepted that solar magnetic field manipulates all solar activities, especially violent solar bursts in solar corona. Thus, it is extremely important to reconstruct three-dimentional (3D) magnetic field of solar corona from really observed photospheric magnetogram. In this paper, a large-scale dataset of 3D solar magnetic fields of active regions is built by using the nonlinear force-free magnetic field (NLFFF) extrapolation from vector magnetograms of Helioseismic and Magnetic Imager (HMI) on Solar Dynamics Observatory (SDO). In this dataset, all space-weather HMI active region patches (SHARPs) with the corresponding serial numbers of national oceanic and atmospheric administration (NOAA) are included. They are downloaded from the SHARP 720 s series of JSOC every 96 minutes. In addition, each sample is labelled with a finer grained label for solar flare forecast. This paper is with the purpose of open availability of data resource and source code to the peers for refraining from repeated labor of data preparation. Meanwhile, with such a large-scale, high spatio-temporal resolution and high quality scientific data, we anticipate a wide attention and interest from artificial intelligence (AI) and computer vision communities, for exploring AI for astronomy over such a large-scale dataset.

Evolution of coronal magnetic field parameters during X5.4 solar flare

The coronal magnetic field over NOAA Active Region 11,429 during a X5.4 solar flare on 7 March 2012 is modeled using optimization based Non-Linear Force-Free Field extrapolation. Specifically, 3D magnetic fields were modeled for 11 timesteps using the 12-min cadence Solar Dynamics Observatory (SDO) Helioseismic and Magnetic Imager photospheric vector magnetic field data, spanning a time period of 1 hour before through 1 hour after the start of the flare. Using the modeled coronal magnetic field data, seven different magnetic field parameters were calculated for 3 separate regions: areas with surface |Bz|≥ 300 G, areas of flare brightening seen in SDO Atmospheric Imaging Assembly imagery, and areas with surface |B| ≥ 1000 G and high twist. Time series of the magnetic field parameters were analyzed to investigate the evolution of the coronal field during the solar flare event and discern pre-eruptive signatures. The data shows that areas with |B| ≥ 1000 G and |Tw|≥ 1.5 align well with areas of initial flare brightening during the pre-flare phase and at the beginning of the eruptive phase of the flare, suggesting that measurements of the photospheric magnetic field strength and twist can be used to predict the flare location within an active region if triggered. Additionally, the evolution of seven investigated magnetic field parameters indicated a destabilizing magnetic field structure that could likely erupt.

Data-constrained MHD Simulation of a Multi-ribbon Flare Corresponding to a Successful and a Confined Eruption

The formation and eruption mechanisms of multi-ribbon flares are extremely complicated, especially when the flare is associated with homologous eruptions in the same region. In this paper, we investigate such an event, corresponding to a successful eruption and a confined eruption. This is an M7.1 flare, starting at 12:33 UT on 2011 September 24 in active region NOAA 11302. We obtain the coronal magnetic configuration for this region, using a nonlinear force-free field extrapolation based on the photospheric magnetogram at 12:00 UT. Taking this as the initial condition, we perform a data-constrained MHD simulation to study the evolution of the magnetic topology for this region. We analyze the magnetic null points and the 3D squashing degree for this region, indicating the existence of three flux ropes and two spine–fan structures. The model reproduces the rising processes of the two flux ropes, which form two homologous eruptions consistent with the observations as shown in 94 Å: a large-scale successful eruption that is followed by a small-scale confined eruption. By analyzing the magnetic configuration, the Lorentz force, and the decay index, we find that the torus instability plays an important role in driving the successful eruption of the large flux rope. The magnetic reconnection above the medium flux rope changes the direction of the overlying magnetic field, which provides a downward component of the Lorentz force to confine the eruption of the medium flux rope.

Sympathetic Partial Filament Eruptions Caused by the Interaction between Two Nearby Filaments

To better understand the physical connections in sympathetic solar eruptions, we investigated the interaction between two nearby filaments and their successive partial eruptions in the active region (AR) NOAA 12866 on 2021 September 9 by using data from the Solar Dynamics Observatory and the New Vacuum Solar Telescope. Based on Hα and extreme ultraviolet observations, we found that the right part of one filament (F1) became active first and experienced an obvious rolling motion. Then the whole body of the filament became wider and expanded toward another filament (F2). They collided with each other, and the interaction between them was accompanied by the brightening and bidirectional flows that appeared between them. This implies that magnetic reconnection occurred between the threads of two filaments. The interaction resulted in a rightward motion of F2 at first, and then its activation, and finally part of it erupted. Furthermore, when the erupted F2 deflected rapidly toward the middle part of F1, the left part of F1 erupted with its overlying magnetic fields pushed by F2. These observational results imply that these successive eruptions within a short time are physically linked, and this was caused by the interaction of the filaments. Nonlinear force-free field extrapolation reveals that the magnetic structure of the filament F1 was composed of several magnetic flux ropes with different twists. These results further advance our understanding of partial filament eruptions and sympathetic solar eruptions.

Changes of Magnetic Energy and Helicity in Solar Active Regions from Major Flares

Magnetic free energy powers solar flares and coronal mass ejections, and the buildup of magnetic helicity might play a role in the development of unstable structures that subsequently erupt. To better understand the roles of energy and helicity in large flares and eruptions, we have characterized the evolution of magnetic energy and helicity associated with 21 X-class flares from 2010 to 2017. Our sample includes both confined and eruptive events, with 6 and 15 in each category, respectively. Using the Helioseismic and Magnetic Imager vector magnetic field observations from several hours before to several hours after each event, we employ (a) the Differential Affine Velocity Estimator for Vector Magnetograms to determine the photospheric fluxes of energy and helicity, and (b) nonlinear force-free field extrapolations to estimate the coronal content of energy and helicity in source-region fields. Using superposed epoch analysis, we find, on average, the following: (1) decreases in both magnetic energy and helicity, in both photospheric fluxes and coronal content, that persist for a few hours after eruptions, but no clear changes, notably in relative helicity, for confined events; (2) significant increases in the twist of photospheric fields in eruptive events, with twist uncertainties too large in confined events to constrain twist changes (and lower overall twist in confined events); and (3) on longer timescales (event time +12 hr), replenishment of free magnetic energy and helicity content to near preevent levels for eruptive events. For eruptive events, magnetic helicity and free energy in coronal models clearly decrease after flares, with the amounts of decrease proportional to each region’s pre-flare content.

Magnetic Helicity Evolution and Eruptive Activity in NOAA Active Region 11158

Coronal mass ejections are among the Sun’s most energetic activity events yet the physical mechanisms that lead to their occurrence are not yet fully understood. They can drive major space weather impacts at Earth, so knowing why and when these ejections will occur is required for accurate space weather forecasts. In this study we use a 4 day time series of a quantity known as the helicity ratio, ∣H J ∣/∣H V ∣ (helicity of the current-carrying part of the active region field to the total relative magnetic helicity within the volume), which has been computed from nonlinear force-free field extrapolations of NOAA active region 11158. We compare the evolution of ∣H J ∣/∣H V ∣ with the activity produced in the corona of the active region and show this ratio can be used to indicate when the active region is prone to eruption. This occurs when ∣H J ∣/∣H V ∣ exceeds a value of 0.1, as suggested by previous studies. We find the helicity ratio variations to be more pronounced during times of strong flux emergence, collision and reconnection between fields of different bipoles, shearing motions, and reconfiguration of the corona through failed and successful eruptions. When flux emergence, collision, and shearing motions have lessened, the changes in helicity ratio are somewhat subtle despite the occurrence of significant eruptive activity during this time.

Quantitative Characterization of Magnetic Flux Rope Properties for Two Solar Eruption Events

In order to bridge the gap between heliospheric and solar observations of coronal mass ejections (CMEs), one of the key steps is to improve the understanding of their corresponding magnetic structures like the magnetic flux ropes (MFRs). But it remains a challenge to confirm the existence of a coherent MFR before or upon the CME eruption on the Sun and to quantitatively characterize the CME-MFR due to the lack of direct magnetic field measurements in the corona. In this study, we investigate MFR structures originating from two active regions (ARs), AR 11719 and AR 12158, and estimate their magnetic properties quantitatively. We perform nonlinear force-free field extrapolations with preprocessed photospheric vector magnetograms. In addition, remote-sensing observations are employed to find indirect evidence of MFRs on the Sun and to analyze the time evolution of magnetic reconnection flux associated with the flare ribbons during the eruption. A coherent “preexisting” MFR structure prior to the flare eruption is identified quantitatively for one event from the combined analysis of the extrapolation and observation. Then the characteristics of MFRs for two events on the Sun before and during the eruption forming the CME-MFR, including the axial magnetic flux, field line twist, and reconnection flux, are estimated and compared with the corresponding in situ modeling results. We find that the magnetic reconnection associated with the accompanying flares for both events injects a significant amount of flux into the erupted CME-MFRs.

A Double-decker Filament Formation Driven by Sunspot Rotation and Magnetic Reconnection

In this paper, through analyzing data from the Solar Dynamics Observatory (SDO) and the Global Oscillation Network Group (GONG), we present a study on the formation of a double-decker filament in NOAA Active Region 12665 from 2017 July 8 to 14. We find that magnetic reconnection occurs between two smaller filaments to form a longer filament. According to the evolution of the leading sunspot, it is obvious that the sunspot experiences a continuous rotation around its umbra. During the period from 03:00 UT on July 11 to 10:00 UT on July 14, the average speed of sunspot rotation is about 3.°7 hr–1. The continuous rotation of sunspot stretches the filament and results in the formation of a reversed S-shaped filament. Due to the motion of the magnetic field and internal magnetic reconnection, the filament splits into two branches and forms a double-decker filament structure. In the process of filament separation, internal magnetic reconnection can also accelerate the filament separation. Nonlinear force-free field extrapolation indicates that there are two magnetic flux ropes, which are consistent with the observed results. Eventually, the upper filament erupts and produces an M-class flare and a halo coronal mass ejection.

Homologous Compact Major Blowout-eruption Solar Flares and their Production of Broad CMEs

We analyze the formation mechanism of three homologous broad coronal mass ejections (CMEs) resulting from a series of solar blowout-eruption flares with successively increasing intensities (M2.0, M2.6, and X1.0). The flares originated from NOAA Active Region 12017 during 2014 March 28–29 within an interval of ≈24 hr. Coronal magnetic field modeling based on nonlinear force-free field extrapolation helps to identify low-lying closed bipolar loops within the flaring region enclosing magnetic flux ropes. We obtain a double flux rope system under closed bipolar fields for all the events. The sequential eruption of the flux ropes led to homologous flares, each followed by a CME. Each of the three CMEs formed from the eruptions gradually attained a large angular width, after expanding from the compact eruption-source site. We find these eruptions and CMEs to be consistent with the “magnetic-arch-blowout” scenario: each compact-flare blowout eruption was seated in one foot of a far-reaching magnetic arch, exploded up the encasing leg of the arch, and blew out the arch to make a broad CME.

Apparent Footpoint Rotation and Writhe of Double Hot Channels in a Solar Flare

We investigate the M6.5 class flare (SOL2015-06-22T18:23) occurring in NOAA Active Region 12371 on 2015 June 22. This eruptive flare is associated with a halo coronal mass ejection with a speed of 1200 km s−1. The 94 Å observations by Atmospheric Image Assembly onboard Solar Dynamics Observatory show that one hot channel first rises up, then forms a kinking structure with negative crossing and erupts, which is followed by the eruption of another kinking hot channel with negative crossing at a similar location between the start and peak times of the flare. Consistent with the standard flare model, footpoint drifting of the two hot channels is observed during the eruption. More interestingly, the two footpoints of the first hot channel continue to drift and display an apparent clockwise rotation after leaving the area of the hook-shaped flare ribbons. This apparent rotation is along the high-Q region of the log Q map derived from the nonlinear force-free field extrapolation. Our analysis suggests that the apparent rotational motion is likely caused by magnetic reconnection between the first hot channel and the surrounding magnetic fields at the high-Q region during the unwrithing process. The unwrithing of the second hot channel is accompanied by a significant slipping motion of its right footpoint.