The relative magnetic helicity is a quantity that is often used to describe the level of entanglement of non-isolated magnetic fields, such as the magnetic field of solar active regions.The aim of this paper is to investigate how different kinds of photospheric boundary flows accumulate relative magnetic helicity in the corona and if and how-well magnetic helicity related quantities identify the onset of an eruption. We use a series of three-dimensional, parametric magnetohydrodynamic simulations of the formation and eruption of magnetic flux ropes. All the simulations are performed on the same grid, using the same parameters, but they are characterized by different driving photospheric flows, i.e., shearing, convergence, stretching, peripheral- and central- dispersion flows. For each of the simulations, the instant of the onset of the eruption is carefully identified by using a series of relaxation runs. We find that magnetic energy and total relative helicity are mostly injected when shearing flows are applied at the boundary, while the magnetic energy and helicity associated with the coronal electric currents increase regardless of the kind of photospheric flows. We also find that, at the onset of the eruptions, the ratio between the non-potential magnetic helicity and the total relative magnetic helicity has the same value for all the simulations, suggesting the existence of a threshold in this quantity. Such threshold is not observed for other quantities as, for example, those related to the magnetic energy.
In previous works we introduced a nonlinear force-free method that self-consistently calculates the instantaneous budgets of free magnetic energy and relative magnetic helicity in solar active regions (ARs). Calculation is expedient and practical, using only a single vector magnetogram per computation. We apply this method to a timeseries of 600 high-cadence vector magnetograms of the eruptive NOAA AR 11158 acquired by the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory over a five-day observing interval. Besides testing our method extensively, we use it to interpret th…
Using vector magnetograms from the HMI/SDO and a magnetic connectivity-based method, we calculate the instantaneous relative magnetic helicity and free magnetic energy budgets for several days in two solar active regions (ARs), AR11890 and AR11618, both with complex photospheric magnetic field configurations. The ARs produced several major eruptive flares while their photospheric magnetic field exhibited primarily flux decay in AR11890 and primarily flux emergence in AR11618. Throughout much of their evolution both ARs featured substantial budgets of free magnetic energy and of both positive a…
The active region magnetic field surrounding the filament plays an important role in filament formation, their evolution and disruption. We investigated a filament eruption that occurred in southern hemisphere of the Sun on July 08, 2011 using AIA and HMI data. The filament was located in a region close to the active region NOAA 11247 with its West-most footpoint anchored in the negative polarity plage region and the East-most in the positive polarity plage region. During observations, the magnetic flux was emerging in the active region and also in the plage regions. The flux emergence was sto…
We aim at investigating the morphology, kinematic and helicity evolution of a loop-like prominence during its eruption. We use multi-instrument observations from AIA/SDO, EUVI/STEREO and LASCO/SoHO. The kinematic, morphological, geometrical, and helicity evolution of a loop-like eruptive prominence are studied in the context of the magnetic flux rope model of solar prominences. The prominence eruption evolved as a height expanding twisted loop with both legs anchored in the chromosphere of a plage area. The eruption process consists of a prominence activation, acceleration, and a phase of cons…
We study the magnetic field evolution in the active region (AR) 12673 that produced the largest solar flare in the past decade on 2017 September 6. Fast flux emergence is one of the most prominent features of this AR. We calculate the magnetic helicity from photospheric tangential flows that shear and braid field lines (shear-helicity), and from normal flows that advect twisted magnetic flux into the corona (emergence-helicity), respectively. Our results show that the emergence-helicity accumulated in the corona is $-1.6\times10^{43}~Mx^2$ before the major eruption, while the shear-helicity ac…
Based on a decomposition of the magnetic field into potential and nonpotential components, magnetic energy and relative helicity can both also be decomposed into two quantities: potential and free energies, and volume-threading and current-carrying helicities. In this study, we perform a coupled analysis of their behaviors in a set of parametric 3D magnetohydrodynamic (MHD) simulations of solar-like eruptions. We present the general formulations for the time-varying components of energy and helicity in resistive MHD. We calculated them numerically with a specific gauge, and compared their beha…
In this paper, we study the onset process of a solar eruption on 21 February 2015, focusing on its unambiguous precursor phase. With multi-wavelength imaging observations from the Atmospheric Imaging Assembly (AIA), definitive tether-cutting (TC) reconnection signatures, i.e., flux convergence and cancellation, bidirectional jets, as well as topology change of hot loops, were clearly observed below the pre-eruption filament. As TC reconnection progressed between the sheared arcades that enveloped the filament, a channel-like magnetic flux rope (MFR) arose in multi-wavelength AIA passbands wrap…
We examine two successive flare eruptions (X5.4 and X1.3) on 2012 March 7 in the NOAA active region 11429 and investigate the magnetic field reconfiguration associated with the two eruptions. Using an advanced non-linear force-free field (NLFFF) extrapolation method based on the SDO/HMI vector magnetograms, we obtain a stepwise decrease in the magnetic free energy during the eruptions, which is roughly 20%-30% of the energy of the pre-flare phase. We also calculate the magnetic helicity, and suggest that the changes of the sign of the helicity injection rate might be associated with the erupti…
An investigation of magnetic energy and helicity thresholds at the onset of solar eruptions based on numerical simulations
State Key Laboratory of Solar Activity and Space Weather, School of Aerospace, Harbin Institute of Technology（哈尔滨工业大学航天学院太阳活动与空间天气国家重点实验室）；School of Science, Harbin Institute of Technology, Shenzhen（深圳清华大学研究院（注：此处为Harbin Institute of Technology, Shenzhen，即哈尔滨工业大学（深圳）理学院））；School of Opto-electronic Engineering, Zaozhuang University（枣庄大学光电工程学院）
Volume Dependence of Helicity-based Eruption Diagnostics in Recurrent Coronal Jets
School of Astronomy and Space Science and Key Laboratory of Modern Astronomy and Astrophysics, Nanjing University（南京大学天文与空间科学学院与现代天文学和天体物理学重点实验室）；National Key Laboratory of Deep Space Exploration/School of Earth and Space Sciences, University of Science and Technology of China（中国科学技术大学深空探测全国重点实验室/地球与空间科学学院）；Institute for Space-Earth Environmental Research, Nagoya University（名古屋大学宇宙地球环境研究所）；School of Earth and Space Sciences, Peking University（北京大学地球与空间科学学院）
Using the observations from the Optical and Near-infrared Solar Eruption Tracer and the Solar Dynamics Observatory, we study an M5.7 flare in AR 11476 on 2012 May 10 and a micro-flare in the quiet Sun on 2017 March 23. Before the onset of each flare, there is a reverse S-shaped filament above the polarity inversion line. Then the filaments become unstable and begin to rise. The rising filaments gain the upper hand over the tension force of the dome-like overlying loops and thus successfully erupt outward. The footpoints of the reconnecting overlying loops successively brighten and are observed…
A new multi-wavelength solar telescope, Optical and Near-infrared Solar Eruption Tracer (ONSET) of Nanjing University, was constructed, being fabricated by Nanjing Institute of Astronomical Optics & Technology and run in cooperation with Yunnan Astronomical Observatory. ONSET is able to observe the Sun in three wavelength windows: He {\small I} 10830 Å, H$α$, and white-light at 3600 Åand 4250 Å, which are selected in order to obtain the dynamics in the corona, chromosphere, and the photosphere simultaneously. Full-disk or partial-disk solar images with a field of 10 arcmin at three wavelengths…
We examine the initiation of 10 coronal jet eruptions in quiet regions on the central disk, thereby avoiding near-limb spicule-forest obscuration of the slow-rise onset of the minifilament eruption. From the SDO/AIA 171A 12-second-cadence movie of each eruption, we (1) find and compare the start times of the minifilament's slow rise, the jet-base bright point, the jet-base interior brightening, and the jet spire, and (2) measure the minifilament's speed at the start and end of its slow rise. From (a) these data, (b) prior observations showing that each eruption was triggered by magnetic flux c…
Magnetic flux ropes are topological structures consisting of twisted magnetic field lines that globally wrap around an axis. The torus instability model predicts that a magnetic flux rope of major radius $R$ undergoes an eruption when its axis reaches a location where the decay index $-d(\ln B_{ex})/d(\ln R)$ of the ambient magnetic field $B_{ex}$ is larger than a critical value. In the current-wire model, the critical value depends on the thickness and time-evolution of the current channel. We use magneto-hydrodynamic (MHD) simulations to investigate if the critical value of the decay index a…
We present a combined analysis of the applications of the weighted horizontal magnetic gradient (denoted as WG_M in Korsos et al., ApJ, 802, L21, 2015) method and the magnetic helicity tool (Berger & Field, JFM, 147, 133, 1984) employed for three active regions (ARs), namely NOAA AR11261, AR11283 and AR11429. All three active regions produced series flares and CMEs. We followed the evolution of the components of the WG_M and the magnetic helicity before the flare and CME occurrences. We found an unique and mutually shared behavior, called the U-shaped pattern, of the weighted distance componen…
Utilizing multiwavelength observations and magnetic field data from SDO/AIA, SDO/HMI, GOES and RHESSI, we investigate a large-scale ejective solar eruption of 2014 December 18 from active region NOAA 12241. This event produced a distinctive three-ribbon flare, having two parallel ribbons corresponding to the ribbons of a standard two-ribbon flare, and a larger-scale third quasi-circular ribbon offset from the other two ribbons. There are two components to this eruptive event. First, a flux rope forms above a strong-field polarity-inversion line and erupts and grows as the parallel ribbons turn…
Context: Using unique quadrature observations with the two STEREO spacecraft, we investigate coronal dimmings at the onset of small-scale eruptions. In CMEs they are believed to indicate the opening up of the coronal magnetic fields at the start of the eruption. Aims: It is to determine whether coronal dimming seen in small-scale eruptions starts before or after chromospheric plasma ejection. Methods: One STEREO spacecraft obtained high cadence, 75 s, images in the He II 304A channel, and the other simultaneous images in the Fe IX/FeX 171A channel. We concentrate on two well-positioned chromos…
During eruptive solar flares and coronal mass ejections, a non-pot{\-}ential magnetic arcade with much excess magnetic energy goes unstable and reconnects. It produces a twisted erupting flux rope and leaves behind a sheared arcade of hot coronal loops. We suggest that: the twist of the erupting flux rope can be determined from conservation of magnetic flux and magnetic helicity and equipartition of magnetic helicity. It depends on the geometry of the initial pre-eruptive structure. Two cases are considered, in the first of which a flux rope is not present initially but is created during the e…
An isolated and fast decayed active region (NOAA 9729) was observed when passing through solar disk. There is only one CME related with it that give us a good opportunity to investigate the whole process of the CME. Filament in this active region rises up rapidly and then hesitates and disintegrates into flare loops. The rising filament from EIT images separates into two parts just before eruption. A new filament reforms several hours later after CME and the axis of this new one rotates clockwise about 22 degrees comparing with that of the former one. We also observed a bright transient J-shap…
Solar atmosphere is a single system unified by the presence of large-scale magnetic fields. Topological changes in magnetic fields that occur in one place may have consequences for coronal heating and eruptions for other, even remote locations. Coronal magnetic fields also play role in transport of magnetic helicity from Sun's subphotosphere/upper convection zone to the interplanetary space. We discuss observational evidence pertinent to some aspects of the solar corona being a global interconnected system, i.e., large-scale coronal heating due to new flux emergence, eruption of chromospheric …
The eruption of the filament with the kink fashion is often regarded as a signature of the kink instability. However, the kink instability threshold for the filament magnetic structure has been not widely understood. Using the H-alpha observation from the New Vacuum Solar Telescope (NVST), we present a partial eruptive filament. In the eruption, a filament thread appeared to split from the middle portion of the filament and to break out in a kinklike fashion. During this period, the left filament material remained below, which erupted without the kinking motion later on. The coronal magnetic f…
To better understand the structures of active-region filaments and the eruption process, we study an active-region filament eruption in active region NOAA 11082 in detail on June 22, 2010. Before the filament eruption, the opposite unidirectional material flows appeared in succession along the spine of the filament. The rising of the filament triggered two B-class flares at the upper part of the filament. As the bright material was injected into the filament from the sites of the flares, the filament exhibited a rapid uplift accompanying the counterclockwise rotation of the filament body. From…
We analyze multi-wavelength and multi-viewpoint observations of a helically twisted plasma jet formed during a confined filament eruption on 10-11 April 2013. Given a rather large scale event with its high spatial and temporal resolution observations, it allows us to clearly understand some new physical details about the formation and triggering mechanism of twisting jet. We identify a pre-existing flux rope associated with a sinistral filament, which was observed several days before the event. The confined eruption of the filament within a null point topology, also known as an Eiffel tower (o…
The onset of a solar eruption is formulated here as either a magnetic catastrophe or as an instability. Both start with the same equation of force balance governing the underlying equilibria. Using a toroidal flux rope in an external bipolar or quadrupolar field as a model for the current-carrying flux, we demonstrate the occurrence of a fold catastrophe by loss of equilibrium for several representative evolutionary sequences in the stable domain of parameter space. We verify that this catastrophe and the torus instability occur at the same point; they are thus equivalent descriptions for the …
Solar eruptive events such as coronal mass ejections and eruptive flares are frequently associated with the emergence of magnetic flux from the convection zone into the corona. We use three dimensional magnetohydrodynamic numerical simulations to study the interaction of coronal magnetic fields with emerging flux and determine the conditions that lead to eruptive activity. A simple parameter study is performed, varying the relative angle between emerging magnetic flux and a pre-existing coronal dipole field. We find that in all cases, the emergence results in a sheared magnetic arcade that tra…
The discovery of clear criteria that can deterministically describe the eruptive state of a solar active region would lead to major improvements on space weather predictions. Using series of numerical simulations of the emergence of a magnetic flux rope in a magnetized coronal, leading either to eruptions or to stable configurations, we test several global scalar quantities for the ability to discriminate between the eruptive and the non-eruptive simulations. From the magnetic field generated by the three-dimensional magnetohydrodynamical simulations, we compute and analyse the evolution of th…
We follow up on the Sterling et al (2015) discovery that nearly all polar coronal X-ray jets are made by an explosive eruption of closed magnetic field carrying a miniature filament in its core. In the same X-ray and EUV movies used by Sterling et al (2015), we examine the onset and growth of the driving magnetic explosion in 15 of the 20 jets that they studied. We find evidence that: (1) in a large majority of polar X-ray jets, the runaway internal/tether-cutting reconnection under the erupting minifilament flux rope starts after both the minifilaments rise and the spire-producing external/br…
Solar filaments/prominences exhibit rotational motion during different phases of their evolution from their formation to eruption. We have observed the rotational/vortical motion in the photosphere near the ends of ten filaments during their initial phase of eruption, at the onset of the fast rise phase. All the filaments were associated with active regions. The photospheric vortical motions we observed lasted for 4--20 minutes. In the vicinity of the conjugate ends of the filament the direction of rotation was opposite, except for two cases, where rotational motion was observed at only one en…
Two-ribbon brightenings are one of the most remarkable characteristics of an eruptive solar flare and are often used for predicting the occurrence of coronal mass ejections (CMEs). Nevertheless, it was called in question recently whether all two-ribbon flares are eruptive. In this paper, we investigate a two ribbon-like white-light (WL) flare that is associated with a failed magnetic flux rope (MFR) eruption on 2015 January 13, which has no accompanying CME in the WL coronagraph. Observations by \textit{Optical and Near-infrared Solar Eruption Tracer} and \textit{Solar Dynamics Observatory} re…
Helicity is a fundamental property of magnetic fields, conserved in ideal MHD. In flux rope topology, it consists of twist and writhe helicity. Despite the common occurrence of helical structures in the solar atmosphere, little is known about how their shape relates to the writhe, which fraction of helicity is contained in writhe, and how much helicity is exchanged between twist and writhe when they erupt. Here we perform a quantitative investigation of these questions relevant for coronal flux ropes. The decomposition of the writhe of a curve into local and nonlocal components greatly facilit…
Magnetic free energy powers solar flares and coronal mass ejections (CMEs), 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 HMI vector magnetic field observations from several hours before to several hours after e…
Using a recently proposed nonlinear force-free method designed for single vector magnetograms of solar active regions we calculate the instantaneous free magnetic energy and relative magnetic helicity budgets in 162 vector magnetograms corresponding to 42 different active regions. We find a statistically robust, monotonic correlation between the free magnetic energy and the relative magnetic helicity in the studied regions. This correlation implies that magnetic helicity, besides free magnetic energy, may be an essential ingredient for major solar eruptions. Eruptive active regions appear well…
Relative magnetic helicity is a gauge invariant quantity suitable for the study of the magnetic helicity content of heliospheric plasmas. Relative magnetic helicity can be decomposed uniquely into two gauge invariant quantities, the magnetic helicity of the non-potential component of the field, and a complementary volume-threading helicity. Recent analysis of numerical experiments simulating the generation of solar eruptions have shown that the ratio of the non-potential helicity to the total relative helicity is a clear marker of the eruptivity of the magnetic system, and that the high value …
It is widely believed that magnetic flux ropes are the key structure of solar eruptions; however, their observable counterparts are not clear yet. We study a flare associated with flux rope eruption in a comprehensive radiative magnetohydrodynamic simulation of flare-productive active regions, especially focusing on the thermodynamic properties of the plasma involved in the eruption and their relation to the magnetic flux rope. The pre-existing flux rope, which carries cold and dense plasma, rises quasi-statically before the eruption onsets. During this stage, the flux rope does not show obvio…
Magneto-hydrodynamic (MHD) simulations of the emergence of twisted magnetic flux tubes from the solar interior into the corona are discussed to illustrate how twisted and sheared coronal magnetic structures (with free magnetic energy), capable of driving filament eruptions, can form in the corona in emerging active regions. Several basic mechanisms that can disrupt the quasi-equilibrium coronal structures and trigger the release of the stored free magnetic energy are discussed. These include both ideal processes such as the onset of the helical kink instability and the torus instability of a t…
We propose a new ``helicity-pumping'' method for energizing coronal equilibria that contain a magnetic flux rope (MFR) toward an eruption. We achieve this in a sequence of magnetohydrodynamics relaxations of small line-tied pulses of magnetic helicity, each of which is simulated by a suitable rescaling of the current-carrying part of the field. The whole procedure is ``magnetogram-matching'' because it involves no changes to the normal component of the field at the photospheric boundary. The method is illustrated by applying it to an observed force-free configuration whose MFR is modeled with …
This paper reviews the studies of solar photospheric magnetic field evolution in active regions and its relationship to solar flares. It is divided into two topics, the magnetic structure and evolution leading to solar eruptions and the rapid changes of photospheric magnetic field associated with eruptions. For the first topic, we describe the magnetic complexity, new flux emergence, flux cancellation, shear motions, sunspot rotation, and magnetic helicity injection, which may all contribute to the storage and buildup of energy and triggering of solar eruptions. For the second topic, we concen…
Data-driven simulation is becoming an important approach for realistically characterizing the configuration and evolution of solar active regions, revealing the onset mechanism of solar eruption events and hopefully achieving the goal of accurate space weather forecast, which is beyond the scope of any existing theoretical modelling. Here we performed a full 3D MHD simulation using the data-driven approach and followed the whole evolution process from quasi-static phase to eruption successfully for solar active region NOAA 11429. The MHD system was driven at the bottom boundary by photospheric…
Coronal mass ejections (CMEs) are one of the primary manifestations of solar activity and can drive severe space weather effects. Therefore, it is vital to work towards being able to predict their occurrence. However, many aspects of CME formation and eruption remain unclear, including whether magnetic flux ropes are present before the onset of eruption and the key mechanisms that cause CMEs to occur. In this work, the pre-eruptive coronal configuration of an active region that produced an interplanetary CME with a clear magnetic flux rope structure at 1 AU is studied. A forward-S sigmoid appe…
The evolution of magnetic helicity has a close relationship with solar eruptions and is of interest as a predictive diagnostic. In this case study, we analyse the evolution of the normalised emergence, shearing and total magnetic helicity components in the case of three flaring and three non-flaring active regions (ARs) using SHARPs (Spaceweather Helioseismic Magnetic Imager Active Region Patches) vector magnetic field data. The evolution of the three magnetic helicity components is analysed with wavelet transforms, revealing significant common periodicities of the normalised emergence, sheari…
We present the first IRIS Mg II slit-raster spectra that fully capture the genesis and coronal-jet-generating eruption of a central-disk solar minifilament. The minifilament arose in a negative-magnetic-polarity coronal hole. The Mg II spectroheliograms verify that the minifilament plasma temperature is chromospheric. The Mg II spectra show that the erupting minifilament's plasma has blueshifted upflow in the jet spire's onset and simultaneous redshifted downflow at the location of the compact jet bright point (JBP). From the Mg II spectra together with AIA EUV images and HMI magnetograms, we …
Coronal mass ejections (CMEs) and eruptive flares (EFs) are the most energetic explosions in the solar system. Their underlying origin is the free energy that builds up slowly in the sheared magnetic field of a filament channel. We report the first end-to-end numerical simulation of a CME/EF, from zero-free-energy initial state through filament-channel formation to violent eruption, driven solely by the magnetic-helicity condensation process. Helicity is the topological measure of linkages between magnetic flux systems, and is conserved in the corona, building up inexorably until it is ejected…
Coronal mass ejections (CMEs) play a decisive role in driving space weather, especially, the fast ones (e.g., with speeds above $800$~km~s$^{-1}$). Understanding the trigger mechanisms of fast CMEs can help us gaining important information in forecasting them. The filament eruptions accompanied with CMEs provide a good tracer in studying the early evolution of CMEs. Here we surveyed 66 filament-accompanied fast CMEs to analyse the correlation between the trigger mechanisms, namely either magnetic reconnection or ideal MHD process, associated flares, and CME speeds. Based on the data gathering …
The structure of the coronal magnetic field prior to eruptive processes and the conditions for the onset of eruption are important issues that can be addressed through studying the magnetohydrodynamic stability and evolution of nonlinear force-free field (NLFFF) models. This paper uses data-constrained NLFFF models of a solar active region that erupted on 2010 April 8 as initial condition in MHD simulations. These models, constructed with the techniques of flux rope insertion and magnetofrictional relaxation, include a stable, an approximately marginally stable, and an unstable configuration. …
Most of the commonly discussed solar coronal jets are of the type consisting of a single spire extending approximately vertically from near the solar surface into the corona. Recent research supports that eruption of a miniature filament (minifilament) drives many such single-spire jets, and concurrently generates a miniflare at the eruption site. A different type of coronal jet, identified in X-ray images during the Yohkoh era, are two-sided-loop jets, which extend from a central excitation location in opposite directions, along low-lying coronal loops more-or-less horizontal to the surface. …
Using high-resolution images from 1.6 m New Solar Telescope (NST) at Big Bear Solar Observatory (BBSO), we report the direct evidence of chromospheric reconnection at the polarity inversion line (PIL) between two small opposite polarity sunspots. Small jet-like structures (with velocities of ~20-55 km/s) were observed at the reconnection site before the onset of the first M1.0 flare. The slow rise of untwisting jets was followed by the onset of cool plasma inflow (~10 km/s) at the reconnection site, causing the onset of a two-ribbon flare. The reconnection between two sheared J-shaped cool H$α…
