Aims. The main aim of this work is to study the evolution of the recently introduced relative helicity of the magnetic polarity inversion line (PIL) in a magnetohydrodynamics simulation. Methods. The simulation used is a typical flux emergence simulation in which there is additionally an oblique, pre-existing magnetic field. The interaction of the emerging and ambient fields produces intense coronal activity, with four jets standing out. The 3D magnetic field allows us to compute various energies and helicities, and to study their evolution during the simulation, especially around the identified jets. We examine the evolution of all quantities in three different regions: in the whole volume, in three separate subvolumes of the whole volume, and in a 2D region around the PIL on the photosphere. Results. We find that the helicities are in general more responsive to the jets, followed by the free energy. The eruptivity index, the ratio of the current-carrying helicity to the relative helicity, does not show the typical behaviour it has in other cases, as its variations do not follow the production of the jets. By considering the subvolumes we find that the magnetic field gets more potential and less helical with height. The PIL relative helicity confirms the recent results it showed in observed active regions, exhibiting stronger variations during the jets compared to the standard relative helicity. Moreover, the current-carrying helicity around the PIL has a similar behaviour to the PIL relative helicity, and so this quantity could be equally useful in solar eruptivity studies.
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…
We present a new methodology which can determine magnetic helicity transport by the passage of helical magnetic field lines from sub-photosphere and the shuffling motions of foot-points of preexisting coronal field lines separately. It is well known that only the velocity component which is perpendicular to the magnetic field ($\upsilon_{\perp B}$) has contribution to the helicity accumulation. Here, we demonstrate that $\upsilon_{\perp B}$ can be deduced from horizontal motion and vector magnetograms, under a simple relation of $\upsilon_t = μ_t + \frac{\upsilon_n}{B_n} B_t$ as suggested by D…
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…
Magnetic helicity flux gives information about the topology of a magnetic field passing through a boundary. In solar physics applications, this boundary is the photosphere and magnetic helicity flux has become an important quantity in analysing magnetic fields emerging into the solar atmosphere. In this work we investigate the evolution of magnetic helicity flux in magnetohydrodynamic (MHD) simulations of solar flux emergence. We consider emerging magnetic fields with different topologies and investigate how the magnetic helicity flux patterns corresponds to the dynamics of emergence. To inves…
Combined action of helical motions of plasma (the $α$ effect) and non-uniform (differential) rotation is a key dynamo mechanism of solar and galactic large-scale magnetic fields. Dynamics of magnetic helicity of small-scale fields is a crucial mechanism in a nonlinear dynamo saturation where turbulent magnetic helicity fluxes allow to avoid catastrophic quenching of the $α$ effect. The convective zone of the Sun and solar-like stars as well as galactic discs are the source for production of turbulent magnetic helicity fluxes. In the framework of the mean-field approach and the spectral $τ$ app…
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…
Magnetic helicity has risen to be a major player in dynamo theory, with the helicity of the small-scale field being linked to the dynamo saturation process for the large-scale field. It is a nearly conserved quantity, which allows its evolution equation to be written in terms of production and flux terms. The flux term can be decomposed in a variety of fashions. One particular contribution that has been expected to play a significant role in dynamos in the presence of mean shear was isolated by Vishniac & Cho (2001, ApJ 550, 752). Magnetic helicity fluxes are explicitly gauge dependent however…
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…
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…
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…
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…
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…
Magnetic clouds (MCs) are formed by flux ropes (FRs) launched from the Sun as part of coronal mass ejections (CMEs). They carry away an important amount of magnetic flux and helicity. The main aim of this study is to quantify these quantities from insitu measurements of MCs at 1 AU. The fit of these data by a local FR model provides the axial magnetic field strength, the radius, the magnetic flux and the helicity per unit length along the FR axis. We show that these quantities are statistically independent of the position along the FR axis. We then derive the generic shape and length of the FR…
Using mean-field models with a dynamical quenching formalism we show that in finite domains magnetic helicity fluxes associated with small-scale magnetic fields are able to alleviate catastrophic quenching. We consider fluxes that result either from advection by a mean flow, the turbulent mixing down the gradient of mean small-scale magnetic helicity concentration, or the explicit removal which may be associated with the effects of coronal mass ejections in the Sun. In the absence of shear, all the small-scale magnetic helicity fluxes are found to be equally strong both for large-scale and sma…
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）
In turbulent dynamos the production of large-scale magnetic fields is accompanied by a separation of magnetic helicity in scale. The large- and small-scale parts increase in magnitude. The small-scale part can eventually work against the dynamo and quench it, especially at high magnetic Reynolds numbers. A one-dimensional mean-field model of a dynamo is presented where diffusive magnetic helicity fluxes within the domain are important. It turns out that this effect helps to alleviate the quenching. Here we show that internal magnetic helicity fluxes, even within one hemisphere, can be importan…
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…
We present the results of simulations of forced turbulence in a slab where the mean kinetic helicity has a maximum near the mid-plane, generating gradients of magnetic helicity of both large and small-scale fields. We also study systems that have poorly conducting buffer zones away from the midplane in order to assess the effects of boundaries. The dynamical alpha quenching phenomenology requires that the magnetic helicity in the small-scale fields approaches a nearly static, gauge independent state. To stress-test this steady state condition we choose a system with a uniform sign of kinetic h…
We compare the magnetic helicity in the 17-18 March 2013 interplanetary coronal mass ejection (ICME) flux-rope at 1 AU and in its solar counterpart. The progenitor coronal mass ejection (CME) erupted on 15 March 2013 from NOAA active region 11692 and associated with an M1.1 flare. We derive the source region reconnection flux using post-eruption arcade (PEA) method (Gopalswamy et al. 2017a) that uses the photospheric magnetogram and the area under the PEA. The geometrical properties of the near-Sun flux rope is obtained by forward-modeling of white-light CME observations. Combining the geometr…
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…
In this paper we propose that additive self helicity, introduced by Longcope and Malanushenko (2008), plays a role in the kink instability for complex equilibria, similar to twist helicity for thin flux tubes (Hood and Priest (1979), Berger and Field (1984)). We support this hypothesis by a calculation of additive self helicity of a twisted flux tube from the simulation of Fan and Gibson (2003). As more twist gets introduced, the additive self helicity increases, and the kink instability of the tube coincides with the drop of additive self helicity, after the latter reaches the value of $H_A/Φ…
Dynamos in the Sun and other bodies tend to produce magnetic fields that possess magnetic helicity of opposite sign at large and small scales, respectively. The build-up of magnetic helicity at small scales provides an important saturation mechanism. In order to understand the nature of the solar dynamo we need to understand the details of the saturation mechanism in spherical geometry. In particular, we want to understand the effects of magnetic helicity fluxes from turbulence and meridional circulation. We consider a model with just radial shear confined to a thin layer (tachocline) at the b…
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…
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…
The aim of this paper is to look at the magnetic helicity structure of an emerging active region and show that both emergence and flaring signatures are consistent with a same sign for magnetic helicity. We present a multi-wavelength analysis of an M1.6 flare occurring in the active region NOAA 10365 on 27 May, 2003, in which a large new bipole emerges in a decaying active region. The diverging flow pattern and the "tongue" shape of the magnetic field in the photosphere with elongated polarities are highly suggestive of the emergence of a twisted flux tube. The orientation of these tongues ind…
We present nonlinear mean-field alpha-Omega dynamo simulations in spherical geometry with simplified profiles of kinematic alpha effect and shear. We take magnetic helicity evolution into account by solving a dynamical equation for the magnetic alpha effect. This gives a consistent description of the quenching mechanism in mean-field dynamo models. The main goal of this work is to explore the effects of this quenching mechanism in solar-like geometry, and in particular to investigate the role of magnetic helicity fluxes, specifically diffusive and Vishniac-Cho (VC) fluxes, at large magnetic Re…
Evidence for the emergence of twisted flux tubes into the solar atmosphere has, so far, come from indirect signatures. In this work, we investigate the topological input of twisted flux tube emergence directly by studying helicity and winding fluxes. In magnetohydrodynamic simulations with domains spanning from the top of the convection zone to the lower corona, we simulate the emergence of twisted flux tubes with a range of different initial field strengths. One important feature of this work is the inclusion of a convectively-unstable layer beneath the photosphere. We find approximately self…
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…
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 …
In this paper we study the effects of hemispheric imbalance of magnetic helicity density on breaking the equatorial reflection symmetry of the dynamo generated large-scale magnetic field. Our study employs the axisymmetric dynamo model which takes into account the nonlinear effect of magnetic helicity conservation. We find that the evolution of the net magnetic helicity density, in other words, the magnetic helicity imbalance, on the surface follows the evolution of the parity of the large-scale magnetic field. Random fluctuations of the $α$-effect and the helicity fluxes can inverse the causa…
The role of magnetic helicity in astrophysical large-scale dynamos is reviewed and compared with cases where there is no energy supply and an initial magnetic field can only decay. In both cases magnetic energy tends to get redistributed to larger scales. Depending on the efficiency of magnetic helicity fluxes, the decay of a helical field can speed up. Likewise, the saturation of a helical dynamo can speed up through magnetic helicity fluxes. The astrophysical importance of these processes is reviewed in the context of the solar dynamo and an estimated upper limit for the magnetic helicity fl…
We study the writhe, twist and magnetic helicity of different magnetic flux ropes, based on models of the solar coronal magnetic field structure. These include an analytical force-free Titov--Démoulin equilibrium solution, non force-free magnetohydrodynamic simulations, and nonlinear force-free magnetic field models. The geometrical boundary of the magnetic flux rope is determined by the quasi-separatrix layer and the bottom surface, and the axis curve of the flux rope is determined by its overall orientation. The twist is computed by the Berger--Prior formula that is suitable for arbitrary ge…
It has been suggested that coronal mass ejections (CMEs) remove the magnetic helicity of their coronal source region from the Sun. Such removal is often regarded to be necessary due to the hemispheric sign preference of the helicity, which inhibits a simple annihilation by reconnection between volumes of opposite chirality. Here we monitor the relative magnetic helicity contained in the coronal volume of a simulated flux rope CME, as well as the upward flux of relative helicity through horizontal planes in the simulation box. The unstable and erupting flux rope carries away only a minor part o…
In this ISSI-supported series of studies on magnetic helicity in the Sun, we systematically implement different magnetic helicity calculation methods on high-quality solar magnetogram observations. We apply finite-volume, discrete flux tube (in particular, connectivity-based) and flux-integration methods to data from Hinode's Solar Optical Telescope. The target is NOAA active region 10930 during a ~1.5 day interval in December 2006 that included a major eruptive flare (SOL2006-12-13T02:14X3.4). Finite-volume and connectivity-based methods yield instantaneous budgets of the coronal magnetic hel…
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…
We quantitatively address the conjecture that magnetic helicity must be shed from the Sun by eruptions launching coronal mass ejections in order to limit its accumulation in each hemisphere. By varying the ratio of guide and strapping field and the flux rope twist in a parametric simulation study of flux rope ejection from approximately marginally stable force-free equilibria, different ratios of self- and mutual helicity are set and the onset of the torus or helical kink instability is obtained. The helicity shed is found to vary over a broad range from a minor to a major part of the initial …
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…
Selected topics in solar dynamo theory are being highlighted. The possible relevance of the near-surface shear layer is discussed. The role of turbulent downward pumping is mentioned in connection with earlier concerns that a dynamo-generated magnetic field would be rapidly lost from the convection zone by magnetic buoyancy. It is argued that shear-mediated small-scale magnetic helicity fluxes are responsible for the success of some of the recent large-scale dynamo simulations. These fluxes help in disposing of excess small-scale magnetic helicity. This small-scale magnetic helicity, in turn, …
The emergence of dipolar magnetic features on the solar surface is an idealization. Most of the magnetic flux emergence occurs in complex multipolar regions. Here, we show that the surface pattern of magnetic structures alone can reveal the sign of the underlying magnetic helicity in the nearly force-free coronal regions above. The sign of the magnetic helicity can be predicted to good accuracy by considering the three-dimensional position vectors of three spots on the sphere ordered by their relative strengths at the surface and compute from them the skew product. This product, which is a pse…
In this paper we continue our theoretical studies on addressing what are the possible consequences of magnetic helicity accumulation in the solar corona. Our previous studies suggest that coronal mass ejections (CMEs) are natural products of coronal evolution as a consequence of magnetic helicity accumulation and the triggering of CMEs by surface processes such as flux emergence also have their origin in magnetic helicity accumulation. Here we use the same mathematical approach to study the magnetic helicity of axisymmetric power-law force-free fields, but focus on a family whose surface flux …
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…
In the paper we study the helicity density patterns which can result from the emerging bipolar regions. Using the relevant dynamo model and the magnetic helicity conservation law we find that the helicity density pattern around the bipolar regions depends on the configuration of the ambient large-scale magnetic field, and in general they show the quadrupole distribution. The position of this pattern relative to the equator can depend on the tilt of the bipolar region. We compute the time-latitude diagrams of the helicity density evolution. The longitudinally averaged effect of the bipolar regi…
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 study magnetic field evolution in AR12371 relating its successive eruptive nature. During the disk transit of seven days, the AR launched four sequential fast coronal mass ejections (CMEs) associated with long duration M-class flares. Morphological study delineates a pre-eruptive coronal sigmoid structure above the polarity inversion line (PIL) similar to Moore et al study. Velocity field derived from tracked magnetograms indicates persistent shear and converging motions of polarity regions about the PIL. While these shear motions continue, the crossed arms of two sigmoid elbows are being b…
{In order to understand the emergence of the active region, we investigate the emerging process and magnetic properties of a naked anti-Hale active region during the period between August 24 to 25, 2018.} {Using the data from Helioseismic and Magnetic Imager on board the Soar Dynamic Observatory and the New Vacuum Solar Telescope, we calculated different evolving parameters (such as pole separation, tilt angle) and magnetic parameters (such as vertical electric current, force-free parameter, relative magnetic helicity) during the emergence of the active region. With these calculated parameters…
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…
We use direct numerical simulations of forced MHD turbulence with a forcing function that produces two different signs of kinetic helicity in the upper and lower parts of the domain. We show that the mean flux of magnetic helicity from the small-scale field between the two parts of the domain can be described by a Fickian diffusion law with a diffusion coefficient that is approximately independent of the magnetic Reynolds number and about one third of the estimated turbulent magnetic diffusivity. The data suggest that the turbulent diffusive magnetic helicity flux can only be expected to allev…
Solar active regions and sunspots are believed to be formed by the emergence of strong toroidal magnetic flux from the solar interior. Modeling of such events has focused on the dynamics of compact magnetic entities, colloquially known as "flux tubes", often considered to be isolated magnetic structures embedded in an otherwise field-free environment. In this paper, we show that relaxing such idealized assumptions can lead to surprisingly different dynamics. We consider the rise of tube-like flux concentrations embedded in a large-scale volume-filling horizontal field in an initially quiescent…
The buoyant transport of magnetic fields from the solar interior towards the surface plays an important role in the emergence of active regions, the formation of sunspots and the overall solar dynamo. Observations suggest that toroidal flux concentrations often referred to as "flux tubes", rise from their region of initiation likely in the solar tachocline towards the solar surface due to magnetic buoyancy. Many studies have assumed the existence of such magnetic structures and studied the buoyant rise of an isolated flux tube in a quiescent, field-free environment. Here, motivated by their fo…
Much work on turbulent three-dimensional dynamos has been done using triply periodic domains, in which there are no magnetic helicity fluxes. Here we present simulations where the turbulent intensity is still nearly homogeneous, but now there is a perfect conductor boundary condition on one end and a vertical field or pseudo-vacuum condition on the other. This leads to migratory dynamo waves. Good agreement with a corresponding analytically solvable alpha^2 dynamo is found. Magnetic helicity fluxes are studied in both types of models. It is found that at moderate magnetic Reynolds numbers, mos…
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…
