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 behaviors in the numerical simulations, which differ from one another by their imposed boundary-driving motions. Thus, we investigated the impact of different active regions surface flows on the development of the energy and helicity-related quantities. Despite general similarities in their overall behaviors, helicities and energies display different evolutions that cannot be explained in a unique framework. While the energy fluxes are similar in all simulations, the physical mechanisms that govern the evolution of the helicities are markedly distinct from one simulation to another: the evolution of volume-threading helicity can be governed by boundary fluxes or helicity transfer, depending on the simulation. The eruption takes place for the same value of the ratio of the current-carrying helicity to the total helicity in all simulations. However, our study highlights that this threshold can be reached in different ways, with different helicity-related processes dominating for different photospheric flows. This means that the details of the pre-eruptive dynamics do not influence the eruption-onset helicity-related threshold. Nevertheless, the helicity-flux dynamics may be more or less efficient in changing the time required to reach the onset of the eruption.
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…
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 compare the coronal magnetic energy and helicity of two solar active regions (ARs), prolific in major eruptive (AR~11158) and confined (AR~12192) flaring, and analyze the potential of deduced proxies to forecast upcoming flares. Based on nonlinear force-free (NLFF) coronal magnetic field models with a high degree of solenoidality, and applying three different computational methods to investigate the coronal magnetic helicity, we are able to draw conclusions with a high level of confidence. Based on real observations of two solar ARs we checked trends regarding the potential eruptivity of th…
Context. Magnetic helicity is a physical quantity of great importance in the study of astrophysical and natural plasmas. Although a density for helicity cannot be defined, a good proxy for it is field line helicity. The appropriate quantity for use in solar conditions is relative field line helicity (RFLH). Aims. This work aims to study in detail the behaviour of RFLH, for the first time, in a solar active region (AR). Methods. The target active region is the large, eruptive AR 11158. In order to compute RFLH and all other quantities of interest we use a non-linear force-free reconstruction of…
Solar flares fall into two types with eruptive ones associated with coronal mass ejection (CME) and confined ones without CME. To explore whether there are pre-flare conditions in terms of magnetic energy and helicity that can effectively determine the types of flares, here we analyzed a suite of related parameters of the reconstructed pre-flare coronal magnetic field of major solar flares, either eruptive or confined, from 2011 to 2017 near the solar disk center. The investigated parameters include the extensive-type quantities such as the total magnetic energy $E_T$, the potential energy $E_…
Using the photospheric magnetic and coronal observations of Solar Dynamics Observatory, we studied the build-up and eruption of coronal non-potential magnetic structure in emerging active region (AR) 12673. The velocity field derived from tracked vector-magnetograms indicates persistent shear and converging motions of flux regions about the polarity inversion line (PIL). A major helicity injection occurs during rapid flux emergence consistent with the very fast flux emergence phase. While this helicity flux builds-up the sigmoid by September 4, the helicity injection by the continued shear and…
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…
We investigate the coronal magnetic energy and helicity budgets of ten solar ARs, around the times of large flares. In particular, we are interested in a possible relation of the derived quantities to the particular type of the flares that the AR produces, i.e., whether they are associated with a CME or they are confined. Using an optimization approach, we employ time series of 3D nonlinear force-free magnetic field models of ten ARs, covering a time span of several hours around the time of occurrence of large solar flares (GOES class M1.0 and larger). We subsequently compute the 3D magnetic v…
We assess the validity of the free magnetic energy - relative magnetic helicity diagram for solar magnetic structures. We used two different methods of calculating the free magnetic energy and the relative magnetic helicity budgets: a classical, volume-calculation nonlinear force-free (NLFF) method applied to finite coronal magnetic structures and a surface-calculation NLFF derivation that relies on a single photospheric or chromospheric vector magnetogram. Both methods were applied to two different data sets, namely synthetic active-region cases obtained by three-dimensional magneto-hydrodyna…
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…
n order to better understand the solar genesis of interplanetary magnetic clouds (MCs) we model the magnetic and topological properties of four large eruptive solar flares and relate them to observations. We use the three-dimensional Minimum Current Corona model \cite{Longcope1996d} and observations of pre-flare photospheric magnetic field and flare ribbons to derive values of reconnected magnetic flux, flare energy, flux rope helicity and orientation of the flux rope poloidal field. We compare model predictions of those quantities to flare and MC observations and within the estimated uncertai…
Aims. We investigate the role of the accumulation of both magnetic helicity and magnetic energy in the generation of coronal mass ejections (CMEs) from emerging solar active regions (ARs). Methods. Using vector magnetic field data obtained by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, we calculate the magnetic helicity and magnetic energy injection rates as well as the resulting accumulated budgets in 52 emerging ARs from the start time of magnetic flux emergence until they reach heliographic longitude of 45$^{\circ}$ West (W45). Results. Seven of the ARs pro…
In this work we study how the input data cadence affects the photospheric energy and helicity injection estimates in eruptive NOAA active region 11158. We sample the novel 2.25-minute vector magnetogram and Dopplergram data from the \emph{Helioseismic and Magnetic Imager} (HMI) instrument onboard the \emph{Solar Dynamics Observatory} (SDO) spacecraft to create input datasets of variable cadences ranging from 2.25 minutes to 24 hours. We employ state-of-the-art data processing, velocity and electric field inversion methods for deriving estimates of the energy and helicity injections from these …
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…
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…
Expanding on an earlier work that relied on linear force-free magnetic fields, we self-consistently derive the instantaneous free magnetic energy and relative magnetic helicity budgets of an unknown three-dimensional nonlinear force-free magnetic structure extending above a single, known lower-boundary magnetic field vector. The proposed method does not rely on the detailed knowledge of the three-dimensional field configuration but is general enough to employ only a magnetic connectivity matrix on the lower boundary. The calculation yields a minimum free magnetic energy and a relative magnetic…
The orientation, chirality, and dynamics of solar eruptive filaments is a key to understanding the magnetic field of coronal mass ejections (CMEs) and therefore to predicting the geoeffectiveness of CMEs arriving at Earth. However, confusion and contention remain over the relationship between the filament chirality, magnetic helicity, and sense of rotation during eruption. To resolve the ambiguity in observations, in this paper, we used stereoscopic observations to determine the rotation direction of filament apex and the method proposed by Chen et al. (2014) to determine the filament chiralit…
We study the relative helicity of active region (AR) NOAA~12673 during a ten-hour time interval centered around a preceding X2.2 flare (SOL2017-09-06T08:57) and also including an eruptive X9.3 flare that occurred three hours later (SOL2017-09-06T11:53). In particular, we aim for a reliable estimate of the normalized self-helicity of the current-carrying magnetic field, the so-called helicity ratio $|H_{\mathrm{J}}|/|H_{\mathcal{V}}|$, a promising candidate to quantity the eruptive potential of solar ARs. Using SDO/HMI vector magnetic field data as an input, we employ nonlinear force-free (NLFF…
We analyze the complete chain of effects caused by a solar eruptive event in order to better understand the dynamic evolution of magnetic-field related quantities in interplanetary space, in particular that of magnetic flux and helicity. We study a series of connected events (a confined C4.5 flare, a flare-less filament eruption and a double-peak M-class flare) that originated in NOAA active region (AR) 12891 on 2021 November 1 and November 2. We deduce the magnetic structure of AR 12891 using stereoscopy and nonlinear force-free (NLFF) magnetic field modeling, allowing us to identify a corona…
For axisymmetric models for coronal loops the relationship between the bifurcation points of magnetohydrodynamic (MHD) equilibrium sequences and the points of linear ideal MHD instability is investigated imposing line-tied boundary conditions. Using a well-studied example based on the Gold-Hoyle equilibrium, it is demonstrated that if the equilibrium sequence is calculated using the Grad-Shafranov equation, the instability corresponds to the second bifurcation point and not the first bifurcation point because the equilibrium boundary conditions allow for modes which are excluded from the linea…
The underlying origin of solar eruptive events (SEEs), ranging from giant coronal mass ejections to small coronal-hole jets, is that the lowest-lying magnetic flux in the Sun's corona undergoes the continual buildup of stress and free energy. This magnetic stress has long been observed as the phenomenon of "filament channels:" strongly sheared magnetic field localized around photospheric polarity inversion lines. However, the mechanism for the stress buildup - the formation of filament channels - is still debated. We present magnetohydrodynamic simulations of a coronal volume that is driven by…
Plasma relaxation in the presence of an initially braided magnetic field can lead to self-organization into relaxed states that retain non-trivial magnetic structure. These relaxed states may be in conflict with the linear force-free fields predicted by the classical Taylor theory, and remain to be fully understood. Here, we study how the individual field line helicities evolve during such a relaxation, and show that they provide new insights into the relaxation process. The line helicities are computed for numerical resistive-magnetohydrodynamic simulations of a relaxing braided magnetic fiel…
The solar corona routinely exhibits explosive activity, in particular coronal mass ejections and their accompanying eruptive flares, that have global-scale consequences. These events and their smaller counterparts, coronal jets, originate in narrow, sinuous filament channels. The key processes that form and evolve the channels operate on still smaller spatial scales and much longer time scales, culminating in a vast separation of characteristic lengths and times that govern these explosive phenomena. In this article, we describe implementation and tests of an efficient subgrid-scale model for …
Morphology of Solar Filaments During the Solar Maximum of Cycle 24: A Study of 35 Filaments Focusing on Chirality, Barb Orientation, Skewness, and Eruptive Behavior
National Institute of Technology Calicut（国立卡尔卡提理工学院）；Indian Institute of Astrophysics（印度天体物理研究所）
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）
While free/non-potential magnetic energy is a necessary element of any active phenomenon in the solar corona, its role as a marker of the trigger of eruptive process remains elusive. Based on the unique decomposition of the magnetic field into potential and non-potential components, magnetic energy and helicity can also both be uniquely decomposed into two quantities. Using two 3D MHD parametric simulations of a configuration that can produce coronal jets, we compare the dynamics of the magnetic energies and of the relative magnetic helicities. Both simulations share the same initial set-up an…
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…
Context: Relaxation theory offers a straightforward method for estimating the energy that is released when a magnetic field becomes unstable, as a result of continual convective driving. Aims: We present new results obtained from nonlinear magnetohydrodynamic (MHD) simulations of idealised coronal loops. The purpose of this work is to determine whether or not the simulation results agree with Taylor relaxation, which will require a modified version of relaxation theory applicable to unbounded field configurations. Methods: A three-dimensional (3D) MHD Lagrangian-remap code is used to simulate …
