Topological changes of the photospheric magnetic field inside active regions: A prelude to flares?

The detection of magnetic field variations as a signature of flaring activity is one of the main goals in solar physics. Past efforts gave apparently no unambiguous observations of systematic changes. In the present study, we discuss recent results from observations that scaling laws of turbulent current helicity inside a given flaring active region change in response to large flares in that active region. Such changes can be related to the evolution of current structures by a simple geometrical argument, which has been tested using high Reynolds number direct numerical simulations of the MHD equations. Interpretation of the observed data within this picture indicates that the change in scaling behavior of the current helicity seems to be associated with a topological reorganization of the footpoint of the magnetic field loops, namely with the dissipation of small scales structures in turbulent media.     

Galactic dynamo with helicity fluxes

We construct an approximation for the magnetic field of galaxies that takes into account the magnetic helicity conservation law. In our calculations, we use the fact that the galactic disk is fairly thin and, therefore, the magnetic field component perpendicular to the galactic disk can be neglected (the so-called no-z approximation). However, an averaging of the magnetic field over the entire galaxy, as was done in previous works, is not performed. Our results are compared both with the approximation that disregards the helicity flux and with the results obtained in models with helicity fluxes but without averaging. We show that, compared to the classical model, there are a number of new effects (for example, magnetic field oscillations) and, compared to the model with averaging, the behavior of the magnetic field “softens”: its stationary value is reached more slowly and the oscillation amplitude decreases. This is because the dissipative processes changing the magnetic field growth rate are taken into account in our model. In contrast to the model with averaging, here it becomes possible to construct the dependence of the magnetic field and helicity on the distance from the galactic center.     

Equatorial magnetic helicity flux in simulations with different gauges

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 alleviate catastrophic quenching at Reynolds numbers of more than several thousands. We further calculate the magnetic helicity density and its flux in the domain for three different gauges. We consider the Weyl gauge, in which the electrostatic potential vanishes, the pseudo‐Lorenz gauge, where the speed of light is replaced by the sound speed, and the ‘resistive gauge’ in which the Laplacian of the magnetic vector potential acts as a resistive term. We find that, in the statistically steady state, the time‐averaged magnetic helicity density and the magnetic helicity flux are the same in all three gauges (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Strong mean field dynamos require supercritical helicity fluxes

Several one and two dimensional mean field models are analyzed where the effects of current helicity fluxes and boundaries are included within the framework of the dynamical quenching model. In contrast to the case with periodic boundary conditions, the final saturation energy of the mean field decreases inversely proportional to the magnetic Reynolds number. If a nondimensional scaling factor in the current helicity flux exceeds a certain critical value, the dynamo can operate even without kinetic helicity, i.e. it is based only on shear and current helicity fluxes, as first suggested by Vishniac & Cho (2001, ApJ 550, 752). Only above this threshold is the current helicity flux also able to alleviate catastrophic quenching. The fact that certain turbulence simulations have now shown apparently non‐resistively limited mean field saturation amplitudes may be suggestive of the current helicity flux having exceeded this critical value. Even below this critical value the field still reaches appreciable strength at the end of the kinematic phase, which is in qualitative agreement with dynamos in periodic domains. However, for large magnetic Reynolds numbers the field undergoes subsequent variations on a resistive time scale when, for long periods, the field can be extremely weak. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

How Can a Negative Magnetic Helicity Active Region Generate a Positive Helicity Magnetic Cloud?

The geoeffective magnetic cloud (MC) of 20 November 2003 was associated with 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 did its solar source, active region (AR) NOAA 10501. In this article we show that the large-scale magnetic field of AR 10501 has a negative helicity sign. Since coronal mass ejections (CMEs) are one of the means by which the Sun ejects magnetic helicity excess into interplanetary space, the signs of magnetic helicity in the AR and MC must agree. Therefore, this finding contradicts what is expected from magnetic helicity conservation. However, using, for the first time, correct helicity density maps to determine the spatial distribution of magnetic helicity injections, we show the existence of a localized flux of positive helicity in the southern part of AR 10501. We conclude that positive helicity was ejected from this portion of the AR leading to the observed positive helicity MC.     

Magnetic Helicity Budget of Solar-Active Regions from the Photosphere to Magnetic Clouds

We have analyzed the long-term evolution of two active regions (ARs) from their emergence through their decay using observations from several instruments on board SoHO (MDI, EIT and LASCO) and Yohkoh/SXT. We have computed the evolution of the relative coronal magnetic helicity combining data from MDI and SXT with a linear force-free model of the coronal magnetic field. Next, we have computed the injection of helicity by surface differential rotation using MDI magnetic maps. To estimate the depletion of helicity we have counted all the CMEs of which these ARs have been the source, and we have evaluated their magnetic helicity assuming a one to one correspondence with magnetic clouds with an average helicity contain. When these three values (variation of coronal magnetic helicity, injection by differential rotation and ejection via CMEs) are compared, we find that surface differential rotation is a minor contributor to the helicity budget since CMEs carry away at least 10 times more helicity than the one differential rotation can provide. Therefore, the magnetic helicity flux needed in the global balance should come from localized photospheric motions that, at least partially, reflect the emergence of twisted flux tubes. We estimate that the total helicity carried away in CMEs can be provided by the end-to-end helicity of the flux tubes forming these ARs. Therefore, we conclude that most of the helicity ejected in CMEs is generated below the photosphere and emerges with the magnetic flux.     

Cross Helicity and Turbulent Magnetic Diffusivity in the Solar Convection Zone

In a density-stratified turbulent medium, the cross helicity 〈u′⋅B′〉 is considered as a result of the interaction of the velocity fluctuations and a large-scale magnetic field. By means of a quasilinear theory and by numerical simulations, we find the cross helicity and the mean vertical magnetic field to be anti-correlated. In the high-conductivity limit the ratio of the helicity and the mean magnetic field equals the ratio of the magnetic eddy diffusivity and the (known) density scale height. The result can be used to predict that the cross helicity at the solar surface will exceed the value of 1 gauss km s⁻¹. Its sign is anti-correlated to that of the radial mean magnetic field. Alternatively, we can use our result to determine the value of the turbulent magnetic diffusivity from observations of the cross helicity.     

Modelling the Global Solar Corona II: Coronal Evolution and Filament Chirality Comparison

This paper considers the hemispheric pattern of solar filaments using newly developed simulations of the real photospheric and 3D coronal magnetic fields over a six-month period, on a global scale. The magnetic field direction in the simulation is compared directly with the chirality of observed filaments, at their observed locations. In our model the coronal field evolves through a continuous sequence of nonlinear force-free equilibria, in response to the changing photospheric boundary conditions and the emergence of new magnetic flux. In total 119 magnetic bipoles with properties matching observed active regions are inserted. These bipoles emerge twisted and inject magnetic helicity into the solar atmosphere. When we choose the sign of this active-region helicity to match that observed in each hemisphere, the model produces the correct chirality for up to 96% of filaments, including exceptions to the hemispheric pattern. If the emerging bipoles have zero helicity, or helicity of the opposite sign, then this percentage is much reduced. In addition, the simulation produces a higher proportion of filaments with the correct chirality after longer times. This indicates that a key element in the evolution of the coronal field is its long-term memory, and the build-up and transport of helicity from low to high latitudes over many months. It highlights the importance of continuous evolution of the coronal field, rather than independent extrapolations at different times. This has significant consequences for future modelling such as that related to the origin and development of coronal mass ejections.     

Small-scale magnetic helicity losses from a mean-field dynamo

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 from advection by a mean flow, the turbulent mixing down the gradient of mean small-scale magnetic helicity density 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 for both large- and small-scale fields. In the presence of shear, there is also an additional magnetic helicity flux associated with the mean field, but this flux does not alleviate catastrophic quenching. Outside the dynamo-active region, there are neither sources nor sinks of magnetic helicity, so in a steady state this flux must be constant. It is shown that unphysical behaviour emerges if the small-scale magnetic helicity flux is forced to vanish within the computational domain.     

Comparison of Helicity Signs in Interplanetary CMEs and Their Solar Source Regions

If all coronal mass ejections (CMEs) have flux ropes, then the CMEs should keep their helicity signs from the Sun to the Earth according to the helicity conservation principle. This study presents an attempt to answer the question from the Coordinated Data Analysis Workshop (CDAW), “Do all CMEs have flux ropes?”, by using a qualitative helicity sign comparison between interplanetary CMEs (ICMEs) and their CME source regions. For this, we select 34 CME–ICME pairs whose source active regions (ARs) have continuous SOHO/MDI magnetogram data covering more than 24 hr without data gap during the passage of the ARs near the solar disk center. The helicity signs in the ARs are determined by estimation of cumulative magnetic helicity injected through the photosphere in the entire source ARs. The helicity signs in the ICMEs are estimated by applying the cylinder model developed by Marubashi (Adv. Space. Res., 26, 55, 2000) to 16 second resolution magnetic field data from the MAG instrument onboard the ACE spacecraft. It is found that 30 out of 34 events (88 %) are helicity sign-consistent events, while four events (12 %) are sign-inconsistent. Through a detailed investigation of the source ARs of the four sign-inconsistent events, we find that those events can be explained by the local helicity sign opposite to that of the entire AR helicity (28 July 2000 ICME), incorrectly reported solar source region in the CDAW list (20 May 2005 ICME), or the helicity sign of the pre-existing coronal magnetic field (13 October 2000 and 20 November 2003 ICMEs). We conclude that the helicity signs of the ICMEs are quite consistent with those of the injected helicities in the AR regions from where the CMEs erupted.     

Photospheric Injection of Magnetic Helicity: Connectivity-Based Flux Density Method

Magnetic helicity quantifies the degree to which the magnetic field in a volume is globally sheared and/or twisted. 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 derived a proxy to the helicity-flux density 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 that takes this connectivity into account. To use it for future observational studies, we tested the method and its precision on several types of models involving different patterns of helicity injection. We also tested it on more complex configurations – from magnetohydrodynamics (MHD) simulations – containing quasi-separatrix layers. We demonstrate that this connectivity-based proxy is best-suited to map the true distribution of photospheric helicity injection.     

Magnetic Helicity Injection in Solar Active Regions

We present the evolution of magnetic field and its relationship with mag- netic(current)helicity in solar active regions from a series of photospheric vector magnetograms obtained by Huairou Solar Observing Station,longitudinal magne- tograms by MDI of SOHO and white light images of TRACE.The photospheric current helicity density is a quantity reflecting the local twisted magnetic field and is related to the remaining magnetic helicity in the photosphere,even if the mean current helicity density brings the general chiral property in a layer of solar active regions.As new magnetic flux emerges in active regions,changes of photospheric cur- rent helicity density with the injection of magnetic helicity into the corona from the subatmosphere can be detected,including changes in sign caused by the injection of magnetic helicity of opposite sign.Because the injection rate of magnetic helicity and photospheric current helicity density have different means in the solar atmosphere, the injected magnetic helicity is probably not proportional to the current helicity den- sity remaining in the photosphere.The evidence is that rotation of sunspots does not synchronize exactly with the twist of photospheric transverse magnetic field in some active regions(such as,delta active regions).They represent different aspects of mag- netic chirality.A combined analysis of the observational magnetic helicity parameters actually provides a relative complete picture of magnetic helicity and its transfer in the solar atmosphere.     

Magnetic helicity in stellar dynamos: new numerical experiments

The theory of large scale dynamos is reviewed with particular emphasis on the magnetic helicity constraint in the presence of closed and open boundaries. In the presence of closed or periodic boundaries, helical dynamos respond to the helicity constraint by developing small scale separation in the kinematic regime, and by showing long time scales in the nonlinear regime where the scale separation has grown to the maximum possible value. A resistively limited evolution towards saturation is also found at intermediate scales before the largest scale of the system is reached. Larger aspect ratios can give rise to different structures of the mean field which are obtained at early times, but the final saturation field strength is still decreasing with decreasing resistivity. In the presence of shear, cyclic magnetic fields are found whose period is increasing with decreasing resistivity, but the saturation energy of the mean field is in strong super‐equipartition with the turbulent energy. It is shown that artificially induced losses of small scale field of opposite sign of magnetic helicity as the large scale field can, at least in principle, accelerate the production of large scale (poloidal) field. Based on mean field models with an outer potential field boundary condition in spherical geometry, we verify that the sign of the magnetic helicity flux from the large scale field agrees with the sign of α. For solar parameters, typical magnetic helicity fluxes lie around 10⁴⁷ Mx² per cycle.     

On the Shape of Force-Free Field Lines in the Solar Corona

This paper studies the shape parameters of looped field lines in a linear force-free magnetic field. Loop structures with a sufficient amount of kinking are generally seen to form S or inverse S (Z) shapes in the corona (as viewed in projection). For a single field line, we can ask how much the field line is kinked (as measured by the writhe), and how much neighbouring flux twists about the line (as measured by the twist number). The magnetic helicity of a flux element surrounding the field line can be decomposed into these two quantities. We find that the twist helicity contribution dominates the writhe helicity contribution, for field lines of significant aspect ratio, even when their structure is highly kinked. These calculations shed light on some popular assumptions of the field. First, we show that the writhe of field lines of significant aspect ratio (the apex height divided by the footpoint width) can sometimes be of opposite sign to the helicity. Secondly, we demonstrate the possibility of field line structures which could be interpreted as Z-shaped, but which have a helicity value sign expected of an S-shaped structure. These results suggest that caution should be exercised in using two-dimensional images to draw conclusions on the helicity value of field lines and flux tubes.     

The Magnetic Helicity Injected by Shearing Motions

Photospheric shearing motions are one of the possible ways to inject magnetic helicity into the corona. We explore their efficiency as a function of their particular properties and those of the magnetic field configuration. Based on the work of M. A. Berger, we separate the helicity injection into two terms: twist and writhe. For shearing motions concentrated between the centers of two magnetic polarities the helicity injected by twist and writhe add up, while for spatially more extended shearing motions, such as differential rotation, twist and writhe helicity have opposite signs and partially cancel. This implies that the amount of injected helicity can change in sign with time even if the shear velocity is time independent. We confirm the amount of helicity injected by differential rotation in a bipole in the two particular cases studied by DeVore (2000), and further explore the parameter space on which this injection depends. For a given latitude, tilt and magnetic flux, the generation of helicity is slightly more efficient in young active regions than in decayed ones (up to a factor 2). The helicity injection is mostly affected by the tilt of the AR with respect to the solar equator. The total helicity injected by shearing motions, with both spatial and temporal coherence, is at most equivalent to that of a twisted flux tube having the same magnetic flux and a number of turns of 0.3. In the solar case, where the motions have not such global coherence, the injection of helicity is expected to be much smaller, while for differential rotation this maximum value reduces to 0.2 turns. We conclude that shearing motions are a relatively inefficient way to bring magnetic helicity into the corona (compared to the helicity carried by a significantly twisted flux tube).     

Magnetic field, helicity and the 2000 July 14 flare in solar active region 9077

In this paper we analyse the non-potential magnetic field and the relationship with current (helicity) in the active region NOAA 9077 in 2000 July, using photospheric vector magnetograms obtained at different solar observatories and also coronal extreme-ultraviolet 171-Å images from the TRACE satellite.
We note that the shear and squeeze of magnetic field are two important indices for some flare-producing regions and can be confirmed by a sequence of photospheric vector magnetograms and EUV 171-Å features in the solar active region NOAA 9077. Evidence on the release of magnetic field near the photospheric magnetic neutral line is provided by the change of magnetic shear, electric current and current helicity in the lower solar atmosphere. It is found that the 'Bastille Day' 3B/5.7X flare on 2000 July 14 was triggered by the interaction of the different magnetic loop systems, which is relevant to the ejection of helical magnetic field from the lower solar atmosphere. The eruption of the large-scale coronal magnetic field occurs later than the decay of the highly sheared photospheric magnetic field and also current in the active region.     

太阳磁场观测研究

简要回顾了近几年国际上太阳磁场研究的一些重要进展，包括耀斑与磁切和电流的关系，电流螺度和磁螺度，磁场拓扑性，三维磁场外推，色球磁场研究，日冕磁场研究，内网络磁元，磁流和振荡，极区磁场观测以及色球磁元观测等方面内容，同时也介绍了怀柔太阳观测站最近所取得的主要成果，自20世纪90年代以来，YOHKOH高分辨率的太阳X射线数据，SOHO的多波段大尺度观测，TRACE的高分辨太阳过渡区资料，为研究太阳磁场从内部到距离几十太阳半径处的大范围演化提供了依据，高效的空间资料结合长期的地面资料，将是正派推动太阳磁场研究的重要手段和必然趋势。     

A study of the magnetic helicity during eight HELIOS-observed solar proton events

We have studied the influence of the magnetic helicity on solar particle propagation using the IMF data observed by the HELIOS spacecraft in the range 0.31–0.95 AU, during eight solar proton events. For this, we have derived power and helicity spectra of the turbulence of the magnetic field during the time of the events. These are used to compute the particle pitch-angle scattering coefficients according to the quasi-linear theory (QLT) treatment of particle propagation in turbulent magnetic fields. The results show that in all the cases the helicity effects are negligible and the particle's mean free paths deduced from the pitch-angle diffusion coefficients are the same regardless of whether or not helicity effects are included in the calculations. The computed mean free paths are quite different in each case.Deceased 10 April, 1995.     

Computation of Relative Magnetic Helicity in Spherical Coordinates

Magnetic helicity is a quantity of great importance in solar studies because it is conserved in ideal magnetohydrodynamics. While many methods for computing magnetic helicity in Cartesian finite volumes exist, in spherical coordinates, the natural coordinate system for solar applications, helicity is only treated approximately. We present here a method for properly computing the relative magnetic helicity in spherical geometry. The volumes considered are finite, of shell or wedge shape, and the three-dimensional magnetic field is considered to be fully known throughout the studied domain. Testing of the method with well-known, semi-analytic, force-free magnetic-field models reveals that it has excellent accuracy. Further application to a set of nonlinear force-free reconstructions of the magnetic field of solar active regions and comparison with an approximate method used in the past indicates that the proposed method can be significantly more accurate, thus making our method a promising tool in helicity studies that employ spherical geometry. Additionally, we determine and discuss the applicability range of the approximate method.     

Basic Properties of Mutual Magnetic Helicity

We derive the magnetic helicity for configurations formed by flux tubes contained fully or only partially in the spatial domain considered (called closed and open configurations, respectively). In both cases, magnetic helicity is computed as the sum of mutual helicity over all possible pairs of magnetic flux tubes weighted by their magnetic fluxes. We emphasize that these mutual helicities have properties which are not those of mutual inductances in classical circuit theory. For closed configurations, the mutual helicity of two closed flux tubes is their relative winding around each other (known as the Gauss linkage number). For open configurations, the magnetic helicity is derived directly from the geometry of the interlaced flux tubes so it can be computed without reference to a ground state (such as a potential field). We derive the explicit expression in the case of a planar and spherical boundary. The magnetic helicity has two parts. The first one is given only by the relative positions of the flux tubes on the boundary. It is the only part if all flux tubes are arch-shaped. The second part counts the integer number of turns each pair of flux tubes wind about each other. This provides a general method to compute the magnetic helicity with discrete or continuous distributions of magnetic field. The method sets closed and open configurations on an equal level within the same theoretical framework.