Magnetic helicity quantifies how globally sheared and/or twisted is the magnetic field in a volume. This quantity is believed to play a key role in solar activity due to its conservation property. Helicity is continuously injected into the corona during the evolution of active regions (ARs). To better understand and quantify the role of magnetic helicity in solar activity, the distribution of magnetic helicity flux in ARs needs to be studied. The helicity distribution can be computed from the temporal evolution of photospheric magnetograms of ARs such as the ones provided by SDO/HMI and Hinode/SOT. Most recent analyses of photospheric helicity flux derive an helicity flux density proxy based on the relative rotation rate of photospheric magnetic footpoints. Although this proxy allows a good estimate of the photospheric helicity flux, it is still not a true helicity flux density because it does not take into account the connectivity of the magnetic field lines. For the first time, we implement a helicity density which takes into account such connectivity. In order to use it for future observational studies, we test the method and its precision on several types of models involving different patterns of helicity injection. We also test it on more complex configurations - from magnetohydrodynamics (MHD) simulations - containing quasi-separatrix layers. We demonstrate that this connectivity-based helicity flux density proxy is the best to map the true distribution of photospheric helicity injection.
An investigation on correlations between photospheric current helicity and subsur- face kinetic helicity is carried out by analyzing vector magnetograms and subsurface velocities for two rapidly developing active regions. The vector magnetograms are from the SDO/HMI (Solar Dynamics Observatory / Helioseismic and Magnetic Im- ager) observed Stokes parameters, and the subsurface velocity is from time-distance data-analysis pipeline using HMI Dopplergrams. Over a span of several days, the evo- lution of the weighted current helicity shows a tendency similar to that of the weighted subsurface kine…
We compare the average photospheric current helicity $H_c$, photospheric twist parameter $α$ (a well-known proxy for the full relative magnetic helicity), and subsurface kinetic helicity $H_k$ for 194 active regions observed between 2006-2013. We use 2440 Hinode photospheric vector magnetograms, and the corresponding subsurface fluid velocity data derived from GONG (2006-2012) and HMI (2010-2013) Dopplergrams. We find a significant hemispheric bias in all three parameters. The subsurface kinetic helicity is preferentially positive in the southern hemisphere and negative in the northern hemisph…
In the solar atmosphere the twist parameter $α$ has the same sign as magnetic helicity. It has been observed using photospheric vector magnetograms that negative/positive helicity is dominant in the northern/southern hemisphere of the Sun. Chromospheric features show dextral/sinistral dominance in the northern/southern hemisphere and sigmoids observed in X-rays also have a dominant sense of reverse-S/forward-S in the northern/southern hemisphere. It is of interest whether individual features have one-to-one correspondence in terms of helicity at different atmospheric heights. We use UBF \Halph…
The origin and evolution of the magnetic helicity in the solar corona are not well understood. For instance, the magnetic helicity of an active region is often about $10^{42}$ Mx$^2$ ($10^{26}$ Wb$^{2}$), but the observed processes whereby it is thought to be injected into the corona do not yet provide an accurate estimate of the resulting magnetic helicity budget or time evolution. The variation in magnetic helicity is important for understanding the physics of flares, coronal mass ejections, and their associated magnetic clouds. To shed light on this topic, we investigate here the changes in…
The flux-injection hypothesis for driving coronal mass ejections (CMEs) requires the transport of substantial magnetic energy and helicity flux through the photosphere concomitant with the eruption. Under the magnetohydrodynamics approximation, these fluxes are produced by twisting magnetic field and/or flux emergence in the photosphere. A CME trajectory, observed 2000 September 12 and fitted with a flux-rope model constrains energy and helicity budgets for testing the flux-injection hypothesis. Optimal velocity profiles for several driving scenarios are estimated by minimizing the photospheri…
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…
Towards a Robust Estimate of the Solar Photospheric Poynting Flux and Helicity Flux
Institute for Astronomy, University of Hawai ‘ i at Mānoa（夏威夷大学马诺阿分校天文研究所）；Heliophysics Science Division, NASA Goddard Space Flight Center（NASA戈达德太空飞行中心日球物理科学部）；The Catholic University of America（美国天主教大学）
Understanding the nature and evolution of the photospheric helicity flux transfer is a key to reveal the role of magnetic helicity in coronal dynamics of solar active regions. Using SDO/HMI photospheric vector magnetograms and the derived flow velocity field, we computed boundary driven helicity flux with a 12 minute cadence during the emergence of AR 11928. Accounting the foot point connectivity defined by non-linear force-free magnetic extrapolations, we derived and analyzed the corrected distribution of helicity flux maps. The photospheric helicity flux injection is found to changes sign du…
Measuring the magnetic helicity distribution in the solar corona can help in understanding the trigger of solar eruptive events because magnetic helicity is believed to play a key role in solar activity due to its conservation property. A new method for computing the photospheric distribution of the helicity flux was recently developed. This method takes into account the magnetic field connectivity whereas previous methods were based on photospheric signatures only. This novel method maps the true injection of magnetic helicity in active regions. We applied this method for the first time to an…
We use daily full-disk vector magnetograms from Vector Spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) system to synthesize the first Carrington maps of the photospheric vector magnetic field. We describe these maps and make a comparison of observed radial field with the radial field estimate from LOS magnetograms. Further, we employ these maps to study the hemispheric pattern of current helicity density, Hc, during the rising phase of the solar cycle 24. Longitudinal average over the 23 consecutive solar rotations shows a clear signature of the hemisp…
The main objective of this study is to better understand how magnetic helicity injection in an active region is related to the occurrence and intensity of solar flares. We therefore investigate magnetic helicity injection rate and unsigned magnetic flux, as a reference. In total, 378 active regions are analyzed using $SOHO$/MDI magnetograms. The 24-hour averaged helicity injection rate and unsigned magnetic flux are compared with the flare index and the flare-productive probability in next 24 hours following an measurement. In addition, we study the variation of helicity over a span of several…
We have studied the evolution of magnetic helicity and chirality in an active region over three consecutive solar rotations. The region when it first appeared was named NOAA10923 and in subsequent rotations it was numbered NOAA 10930, 10935 and 10941. We compare the chirality of these regions at photospheric, chromospheric and coronal heights. The observations used for photospheric and chromospheric heights are taken from Solar Vector Magnetograph (SVM) and H_alpha imaging telescope of Udaipur Solar Observatory (USO), respectively. We discuss the chirality of the sunspots and associated H_alph…
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…
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 …
An investigation of helicity injection by photospheric shear motions is carried out for two active regions(ARs), NOAA 11158 and 11166, using line-of-sight magnetic field observations obtained from the Helioseismic and Magnetic Imager on-board Solar Dynamics Observatory. We derived the horizontal velocities in the active regions from the Differential Affine Velocity Estimator(DAVE) technique. Persistent strong shear motions at the maximum velocities in the range of 0.6--0.9km/s along the magnetic polarity inversion line and outward flows from the peripheral regions of the sunspots were observed…
Magnetic helicity (MH) is a measure of twist and shear of magnetic field. MH is injected in the active region (AR) corona through photospheric footpoint motions causing twisted and sheared magnetic fields. From the conservation property of the helicity, it was conjectured that an already twisted flux rope (FR) with continuous injection of MH inevitably erupts to remove the excess accumulated coronal helicity. Therefore, understanding the nature and evolution of the photospheric helicity flux transfer is crucial to reveal the intensity of the flare/CME activity. Using the time-sequence vector-m…
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 sam…
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…
Using time-sequence vector magnetic field and coronal observations from \textit{Solar Dynamics Observatory}, we report the observations of the magnetic field evolution and coronal activity in four emerging active regions (ARs). The ARs emerge with leading polarity being the same as for the majority of ARs in a hemisphere of solar cycle 24. After emergence, the magnetic polarities separate each other without building a sheared polarity inversion line. In all four ARs, the magnetic fields are driven by foot point motions such that the sign of the helicity injection ($dH/dt$) in the first half of…
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…
Long-term (a few days) variation of magnetic helicity injection was calculated for 28 solar active regions which produced 47 CMEs to find its relationships with the CME occurrence and speed using SOHO/MDI line-of-sight magnetograms. As a result, we found that the 47 CMEs can be categorized into two different groups by two characteristic evolution patterns of helicity injection in their source active regions which appeared for about 0.5-4.5 days before their occurrence: (1) a monotonically increasing pattern with one sign of helicity (Group A; 30 CMEs in 23 active regions) and (2) a pattern of …
Estimates of the photospheric magnetic, electric and plasma velocity fields are essential for studying the dynamics of the solar atmosphere, for example through the derivative quantities of Poynting and relative helicity flux and by using of the fields to obtain the lower boundary condition for data-driven coronal simulations. In this paper we study the performance of a data processing and electric field inversion approach that requires only high-resolution and high-cadence line-of-sight or vector magnetograms -- which we obtain from Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamic…
To study the three-dimensional (3D) magnetic field topology and its long-term evolution associated with the X3.4 flare of 2006 December 13, we investigate the coronal relative magnetic helicity in the flaring active region (AR) NOAA 10930 during the time period of December 8-14. The coronal helicity is calculated based on the 3D nonlinear force-free magnetic fields reconstructed by the weighted optimization method of Wiegelmann, and is compared with the amount of helicity injected through the photospheric surface of the AR. The helicity injection is determined from the magnetic helicity flux d…
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…
A major unexplained feature of the solar atmosphere is the accumulation of magnetic shear, in the form of filament channels, at photospheric polarity inversion lines (PILs). In addition to free energy, this shear also represents magnetic helicity, which is conserved under reconnection. In this paper, we address the problem of filament channel formation and show how they acquire their shear and magnetic helicity. The results of 3D simulations using the Adaptively Refined Magnetohydrodynamics Solver (ARMS) are presented that support the model of filament channel formation by magnetic helicity co…
We analyse the topology of photospheric magnetic fields and sub-photospheric flows of several active regions (ARs) that are observed during the peak to descending phase of the solar cycle 23. Our analysis shows clear evidence of hemispheric preferences in all the topological parameters such as the magnetic, current and kinetic helicities, and the 'curl-divergence'. We found that 68\%(67\%) ARs in the northern (southern) hemisphere with negative (positive) magnetic helicities. Same hemispheric preference sign is found for the current helicities in 68\%(68\%) ARs. The hemispheric preferences are…
We employ the DAVE (differential affine velocity estimator, Schuck 2005; 2006) tracking technique on a time series of MDI/1m high spatial resolution line- of-sight magnetograms to measure the photospheric flow velocity for three newly emerging bipolar active regions. We separately calculate the magnetic helicity injection rate of the leading and following polarities to confirm or refute the magnetic helicity asymmetry, found by Tian & Alexander (2009) using MDI/96m low spatial resolution magnetograms. Our results demonstrate that the magnetic helicity asymmetry is robust being present in the t…
It is generally believed that the evolution of magnetic helicity has a close relationship with solar activity. Before the launch of SDO, earlier studies have mostly used MDI/SOHO line of sight magnetograms and assumed that magnetic fields are radial when calculating magnetic helicity injection rate from photospheric magnetograms. However, this assumption is not necessarily true. Here we use the vector magnetograms and line of sight magnetograms, both taken by HMI/SDO, to estimate the effects of non-radial magnetic field on measuring magnetic helicity injection rate. We find that: 1) The effect…
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…
To better understand a preferred magnetic field configuration and its evolution during Coronal Mass Ejection events, we investigated the spatial and temporal evolution of photospheric magnetic fields in the active region NOAA 9236 that produced eight flare-associated CMEs during the time period of 2000 November 23-26. The time variations of the total magnetic helicity injection rate and the total unsigned magnetic flux are determined and examined not only in the entire active region but also in some local regions such as the main sunspots and the CME-associated flaring regions using SOHO/MDI m…
Two of the most widely observed and yet most puzzling features of the Sun's magnetic field are coronal loops that are smooth and laminar and prominences/filaments that are strongly sheared. These two features would seem to be quite unrelated in that the loops are near their minimum-energy current-free state, whereas filaments are regions of high magnetic stress and intense electric currents. We argue that, in fact, these two features are inextricably linked in that both are due to a single process: the injection of magnetic helicity into the corona by photospheric motions and the subsequent ev…
The most important factors determining solar coronal activity are believed to be the availability of magnetic free energy and the constraint of magnetic helicity conservation. Direct measurements of the helicity and magnetic free energy in the coronal volume are difficult, but their values may be estimated from measurements of the helicity and free energy transport rates through the photosphere. We examine these transport rates for a topologically open system such as the corona, in which the magnetic fields have a nonzero normal component at the boundaries, and derive a new formula for the hel…
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 structure of electric current and magnetic helicity in the solar corona is closely linked to solar activity over the 11-year cycle, yet is poorly understood. As an alternative to traditional current-free "potential field" extrapolations, we investigate a model for the global coronal magnetic field which is non-potential and time-dependent, following the build-up and transport of magnetic helicity due to flux emergence and large-scale photospheric motions. This helicity concentrates into twisted magnetic flux ropes, which may lose equilibrium and be ejected. Here, we consider how the magnet…
Potential field extrapolations are widely used as minimum-energy models for the Sun's coronal magnetic field. As the reference to which other magnetic fields are compared, they have -- by any reasonable definition -- no global (signed) magnetic helicity. Here we investigate the internal topological structure that is not captured by the global helicity integral, by splitting it into individual field line helicities. These are computed using potential field extrapolations from magnetogram observations over Solar Cycle 24, as well as for a simple illustrative model of a single bipolar region in a…
Observation of solar-like stars show a clear relation between X-ray emission and their rotation. Higher stellar rotation can lead to a larger magnetic helicity production in stars. We aim to understand the relation between magnetic helicity on the surface of a star to their coronal X-ray emission. We use 3D MHD simulations to model the corona of the solar-like stars. We take an observed magnetogram as in photospheric activity input, and inject different values of magnetic helicity. We use synthesis emission to calculate the X-ray emission flux of each simulation and investigate how this scales…
The energy storage and trigger mechanisms of solar flares are important for understanding of solar activity. We analyzed multi-wavelength observations of a M1.5 flare on 1 August 2014, in active region NOAA 12127 (SOL2014-08-01T18:13). There are evident large scale sunspot rotations in positive magnetic field of the main energy release region before the eruption; the rotations contain both clockwise and counter-clockwise directions. Injection of magnetic helicity from the photosphere prior to the flare. The sign of the helicity injection is reversed after the flare. It is found that both persi…
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…
The electric current helicity density $\displaystyle χ=\langleε_{ijk}b_i\frac{\partial b_k}{\partial x_j}\rangle$ contains six terms, where $b_i$ are components of the magnetic field. Due to the observational limitations, only four of the above six terms can be inferred from solar photospheric vector magnetograms. By comparing the results for simulation we distinguished the statistical difference of above six terms for isotropic and anisotropic cases. We estimated the relative degree of anisotropy for three typical active regions and found that it is of order 0.8 which means the assumption of …
In the solar corona, magnetic helicity slowly and continuously accumulates in response to plasma flows tangential to the photosphere and magnetic flux emergence through it. Analyzing this transfer of magnetic helicity is key for identifying its role in the dynamics of active regions (ARs). The connectivity-based helicity flux density method was recently developed for studying the 2D and 3D transfer of magnetic helicity in ARs. The method takes into account the 3D nature of magnetic helicity by explicitly using knowledge of the magnetic field connectivity, which allows it to faithfully track th…
The helicity of a magnetic field is a fundamental property that is conserved in ideal MHD. It can be explored in the stellar context by mapping large-scale magnetic fields across stellar surfaces using Zeeman-Doppler imaging. A recent study of 51 stars in the mass range 0.1-1.34 M$_\odot$ showed that the photospheric magnetic helicity density follows a single power law when plotted against the toroidal field energy, but splits into two branches when plotted against the poloidal field energy. These two branches divide stars above and below $\sim$ 0.5 M$_\odot$. We present here a novel method of…
Context. Magnetic helicity is an important quantity in studies of magnetized plasmas as it provides a measure of the geometrical complexity of the magnetic field in a given volume. A more detailed description of the spatial distribution of magnetic helicity is given by the field line helicity that expresses the amount of helicity associated to individual field lines, rather than in the full analysed volume. Aims. Magnetic helicity is not a gauge-invariant quantity in general, unless it is computed with respect to a reference field, yielding the so called relative magnetic helicity. The field l…
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…
The geoeffective magnetic cloud (MC) of 20 November 2003, has been associated to the 18 November 2003, solar active events in previous studies. In some of these, it was estimated that the magnetic helicity carried by the MC had a positive sign, as well as its solar source, active region (AR) NOAA 10501. In this paper we show that the large-scale magnetic field of AR 10501 had a negative helicity sign. Since coronal mass ejections (CMEs) are one of the means by which the Sun ejects magnetic helicity excess into the interplanetary space, the signs of magnetic helicity in the AR and MC should agr…
One of the greatest challenges in solar physics is understanding the heating of the Sun's corona. Most theories for coronal heating postulate that free energy in the form of magnetic twist/stress is injected by the photosphere into the corona where the free energy is converted into heat either through reconnection or wave dissipation. The magnetic helicity associated with the twist/stress, however, is expected to be conserved and appear in the corona. In previous work we showed that helicity associated with the small-scale twists undergoes an inverse cascade via stochastic reconnection in the …
We compute for the first time magnetic helicity and energy spectra of the solar active region NOAA 11158 during 11-15 February 2011 at 20^o southern heliographic latitude using observational photospheric vector magnetograms. We adopt the isotropic representation of the Fourier-transformed two-point correlation tensor of the magnetic field. The sign of magnetic helicity turns out to be predominantly positive at all wavenumbers. This sign is consistent with what is theoretically expected for the southern hemisphere. The magnetic helicity normalized to its theoretical maximum value, here referred…
Sequences of line-of-sight (LOS) magnetograms recorded by the Michelson-Doppler Imager are used to quantitatively characterize photospheric magnetic structure and evolution in three active regions that rotated across the Sun's disk during the Whole Heliosphere Interval (WHI), in an attempt to relate the photospheric magnetic properties of these active regions to flares and coronal mass ejections (CMEs). Several approaches are used in our analysis, on scales ranging from whole active regions, to magnetic features, to supergranular scales, and, finally, to individual pixels. We calculated severa…
A hemispheric preference in the dominant sign of magnetic helicity has been observed in numerous features in the solar atmosphere: i.e., left-handed/right-handed helicity in the northern/southern hemisphere. The relative importance of different physical processes which may contribute to the observed hemispheric sign preference (HSP) of magnetic helicity is still under debate. Here, we estimate magnetic helicity flux ($dH/dt$) across the photospheric surface for 4,802 samples of 1,105 unique active regions (ARs) that appeared over an 8-year period from 2010 to 2017 during solar cycle 24, using …
Context. Observations of flux emergence indicate that rotational velocities may develop within sunspots. However, the dependence of this rotation on sub-photospheric field strength and twist remains largely unknown. Aims. We investigate the effects of varying the initial field strength and twist of an emerging sub-photospheric magnetic flux tube on the rotation of the sunspots at the photosphere. Methods. We consider a simple model of a stratified domain with a sub-photospheric interior layer and three overlying atmospheric layers. A twisted arched flux tube is inserted in the interior and is …
Relative magnetic helicity is conserved by magneto-hydrodynamic evolution even in the presence of moderate resistivity. For that reason, it is often invoked as the most relevant constraint to the dynamical evolution of plasmas in complex systems, such as solar and stellar dynamos, photospheric flux emergence, solar eruptions, and relaxation processes in laboratory plasmas. However, such studies often indirectly imply that relative magnetic helicity in a given spatial domain can be algebraically split into the helicity contributions of the composing subvolumes, i.e., that it is an additive quan…
We recently proposed a method to calculate the relative magnetic helicity in a finite volume for a given magnetic field which however required the flux to be balanced separately on all the sides of the considered volume. In order to allow finite magnetic fluxes through the boundaries, a Coulomb gauge is constructed that allows for global magnetic flux balance. We tested and verified our method in a theoretical fore-free magnetic field model. We apply the new method to the former calculation data and found a difference of less than 1.2\%. We also applied our method to the magnetic field above a…
Using the 135-second cadence of the photospheric vector data provided by the Helioseismic and Magnetic Imager telescope on board the Solar Dynamic Observatory, we examined the time-evolution of magnetic helicity fluxes across the photosphere during 16 flares with the energy class lower than M5.0. During the flare in 4 out of 16 events, we found impulsive changes in the helicity fluxes. This indicates that even the flare with less energy could be associated with anomalistic transportation of the magnetic helicity across the photosphere. Accompanying the impulsive helicity fluxes, the poynting f…
To study the build up of a magnetic flux rope before a major flare and coronal mass ejection (CME), we compute the magnetic helicity injection, twist accumulation, and the topology structure of the three dimensional magnetic field, which is derived by the nonlinear force-free field model. The Extreme-ultraviolet Imaging Telescope on board the Solar and Heliospheric Observatory observed a series of confined flares without any CME before a major flare with a CME at 23:02 UT on 2005 January 15 in active region NOAA 10720. We derive the vector velocity at eight time points from 18:27 UT to 22:20 U…
