Helicity In Solar Active Regions Research Articles

The Relationship between Kinetic and Magnetic Helicity in Solar Active Regions

Using Helioseismic and Magnetic Imager/Solar Dynamics Observatory data, we search for a relationship between kinetic helicity and magnetic helicity in solar active regions (ARs) using a sample of 62 ARs from 2010 May to 2015 May. The sample includes 32 mature ARs and 30 emerging ARs. We calculate kinetic helicity in the interior in the depth range from 0.6 to 11.6 Mm, magnetic helicity in the corona, helicity flux across the photosphere, and the magnetic twist and magnetic writhe of the ARs at the photosphere. From these data, relationships are found between magnetic helicity, helicity flux, and magnetic twist. However, magnetic writhe appears not to be related to the other magnetic quantities. No relationship is found between the kinetic helicity and any magnetic quantity. In particular, no relationship is found between the kinetic helicity and any of the following: magnetic helicity, magnetic helicity flux, magnetic twist, or magnetic writhe. These results suggest that (1) the magnetic helicity in the corona above ARs is mainly derived from the magnetic twist, and (2) the flow dynamics in the region from 0.6 to 11.6 Mm below the photosphere is not the primary source for the generation of magnetic helicity in ARs.

Changes of Magnetic Energy and Helicity in Solar Active Regions from Major Flares

Magnetic free energy powers solar flares and coronal mass ejections, 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 the Helioseismic and Magnetic Imager vector magnetic field observations from several hours before to several hours after each event, we employ (a) the Differential Affine Velocity Estimator for Vector Magnetograms to determine the photospheric fluxes of energy and helicity, and (b) nonlinear force-free field extrapolations to estimate the coronal content of energy and helicity in source-region fields. Using superposed epoch analysis, we find, on average, the following: (1) decreases in both magnetic energy and helicity, in both photospheric fluxes and coronal content, that persist for a few hours after eruptions, but no clear changes, notably in relative helicity, for confined events; (2) significant increases in the twist of photospheric fields in eruptive events, with twist uncertainties too large in confined events to constrain twist changes (and lower overall twist in confined events); and (3) on longer timescales (event time +12 hr), replenishment of free magnetic energy and helicity content to near preevent levels for eruptive events. For eruptive events, magnetic helicity and free energy in coronal models clearly decrease after flares, with the amounts of decrease proportional to each region’s pre-flare content.

Spectral Magnetic Helicity of Solar Active Regions between 2006 and 2017

Abstract We compute magnetic helicity and energy spectra from about 2485 patches of about 100 Mm side length on the solar surface using data from Hinode during 2006–2017. An extensive database is assembled where we list the magnetic energy and helicity, large- and small-scale magnetic helicity, mean current helicity density, fractional magnetic helicity, and correlation length along with the Hinode map identification number (MapID), as well as the Carrington latitude and longitude for each MapID. While there are departures from the hemispheric sign rule for magnetic and current helicities, the weak trend reported here is in agreement with the previous results. This is argued to be a physical effect associated with the dominance of individual active regions that contribute more strongly in the better-resolved Hinode maps. In comparison with earlier work, the typical correlation length is found to be 6– , while the length scale relating the magnetic and current helicities to each other is around .

Intermittency spectra of current helicity in solar active regions

We analyse the spatial distribution of current helicity in solar active regions. A comparison of current helicity maps derived from three different instruments (Helioseismic and Magnetc Imager on board the Solar Dynamics Observatory, SDO/HMI, Spectro-Polarimeter on board the Hinode, and Solar Magnetic Field Telescope at the Huairou Solar Observing Station, China, HSOS/SMFT) is carried out. The comparison showed an excellent correlation between the maps derived from the spaceborne instruments and moderate correlation between the maps derived from SDO/HMI and HSOS/SMFT vector magnetograms. The results suggest that the obtained maps characterize real spatial distribution of current helicity over an active region. To analyse intermittency of current helicity, we traditionally use the high-order structure functions and flatness function approach. The slope of a flatness function within some range of scales - the flatness exponent - is a measure of the degree of intermittency. SDO/HMI vector magnetograms for 3 ARs (NOAA 11158, 12494, and 12673) were used to calculate the flatness exponent time variations. All three ARs exhibited emergence of a new magnetic flux during the observational interval. The flatness exponent indicated the increase of intermittency 12-20 hours before the emergence of a new flux. We suppose that this behaviour can indicate subphotospheric fragmentation or distortion of the pre-existed electric current system by emerging magnetic flux.

Studying the Transfer of Magnetic Helicity in Solar Active Regions with the Connectivity-based Helicity Flux Density Method

Abstract 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 the photospheric flux of magnetic helicity. Because the magnetic field is not measured in the solar corona, modeled 3D solutions obtained from force-free magnetic field extrapolations must be used to derive the magnetic connectivity. Different extrapolation methods can lead to markedly different 3D magnetic field connectivities, thus questioning the reliability of the connectivity-based approach in observational applications. We address these concerns by applying this method to the isolated and internally complex AR 11158 with different magnetic field extrapolation models. We show that the connectivity-based calculations are robust to different extrapolation methods, in particular with regard to identifying regions of opposite magnetic helicity flux. We conclude that the connectivity-based approach can be reliably used in observational analyses and is a promising tool for studying the transfer of magnetic helicity in ARs and relating it to their flaring activity.

A statistical analysis of current helicity and twist in solar active regions over the phases of the solar cycle using the spectro-polarimeter data of Hinode

Abstract Current helicity and twist of solar magnetic fields are important in characterizing the dynamo mechanism working in the convection zone of the Sun. We have carried out a statistical study on the current helicity of solar active regions observed with the spectro-polarimeter (SP) of the Hinode Solar Optical Telescope (SOT). We used SOT-SP data of 558 vector magnetograms of a total of 80 active regions obtained during the period from 2006 to 2012. We have applied spatial smoothing and division of data points into weak and strong field ranges to compare the contributions from different scales and field strengths. We found that the current helicity follows the “hemispheric sign rule” when weak magnetic fields (absolute field strength < 300 gauss) are considered and no smoothing is applied. On the other hand, the pattern of current helicity fluctuates and violates the hemispheric sign rule when stronger magnetic fields are considered and smoothing of 2${^{\prime\prime}_{.}}$0 (modeled on ground-based observations) is applied. Furthermore, we found a tendency that weak and inclined fields conform to the hemispheric sign rule and strong and vertical fields violate it. These different properties of helicity through the strong and weak magnetic field components give important clues in understanding the solar dynamo as well as the mechanism of formation and evolution of solar active regions.

MAGNETIC HELICITY OF THE GLOBAL FIELD IN SOLAR CYCLES 23 AND 24

For the first time we reconstruct the magnetic helicity density of global axisymmetric field of the Sun using method proposed by Brandenburg et al. (2003) and Pipin et al. (2013). To determine the components of the vector potential, we apply the gauge which is typically employed in mean-field dynamo models. This allows for a direct comparison of reconstructed helicity with the predictions from the mean-field dynamo models. We apply the method to two different data sets: the synoptic maps of line-of-sight (LOS) magnetic field from the Michelson Doppler Imager (MDI) on board of Solar and Heliospheric Observatory (SOHO) and vector magnetic field measurements from Vector Spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) system. Based on the analysis of MDI/SOHO data, we find that in solar cycle 23 the global magnetic field had positive (negative) magnetic helicity in the northern (southern) hemisphere. This hemispheric sign asymmetry is opposite to helicity of solar active regions, but it is in agreement with the predictions of mean-field dynamo models. The data also suggest that the hemispheric helicity rule may have reversed its sign in early and late phases of cycle 23. Furthermore, the data indicate an imbalance in magnetic helicity between the northern and southern hemispheres. This imbalance seem to correlate with the total level of activity in each hemisphere in cycle 23. Magnetic helicity for rising phase of cycle 24 is derived from SOLIS/VSM data, and qualitatively, its latitudinal pattern is similar to the pattern derived from SOHO/MDI data for cycle 23.

INTERPRETING ERUPTIVE BEHAVIOR IN NOAA AR 11158 VIA THE REGION'S MAGNETIC ENERGY AND RELATIVE-HELICITY BUDGETS

In previous works we introduced a nonlinear force-free method that self-consistently calculates the instantaneous budgets of free magnetic energy and relative magnetic helicity in solar active regions (ARs). Calculation is expedient and practical, using only a single vector magnetogram per computation. We apply this method to a timeseries of 600 high-cadence vector magnetograms of the eruptive NOAA AR 11158 acquired by the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory over a five-day observing interval. Besides testing our method extensively, we use it to interpret the dynamical evolution in the AR, including eruptions. We find that the AR builds large budgets of both free magnetic energy and relative magnetic helicity, sufficient to power many more eruptions than the ones it gave within the interval of interest. For each of these major eruptions, we find eruption-related decreases and subsequent free-energy and helicity budgets that are consistent with the observed eruption (flare and coronal-mass-ejection [CME]) sizes. In addition, we find that (1) evolution in the AR is consistent with the recently proposed (free) energy - (relative) helicity diagram of solar ARs, (2) eruption-related decreases occur {\it before} the flare and the projected CME-launch times, suggesting that CME progenitors precede flares, and (3) self-terms of free energy and relative helicity most likely originate from respective mutual-terms, following a progressive mutual-to-self conversion pattern that most likely stems from magnetic reconnection. This results in the non-ideal formation of increasingly helical pre-eruption structures and instigates further research on the triggering of solar eruptions with magnetic helicity firmly placed in the eruption cadre.

Statistical distribution of current helicity in solar active regions over the magnetic cycle

The current helicity in solar active regions derived from vector magnetograph observations for more than 20 years indicates the so-called hemispheric sign rule; the helicity is predominantly negative in the northern hemisphere and positive in the southern hemisphere. In this paper we revisit this property and compare the statistical distribution of current helicity with Gaussian distribution using the method of normal probability paper. The data sample comprises 6630 independent magnetograms obtained at Huairou Solar Observing Station, China, over 1988-2005 which correspond to 983 solar active regions. We found the following. (1) For the most of cases in time-hemisphere domains the distribution of helicity is close to Gaussian. (2) At some domains (some years and hemispheres) we can clearly observe significant departure of the distribution from a single Gaussian, in the form of two- or multi-component distribution. (3) For the most non-single-Gaussian parts of the dataset we see co-existence of two or more components, one of which (often predominant) has a mean value very close to zero, which does not contribute much to the hemispheric sign rule. The other component has relatively large value of helicity that often determines agreement or disagreement with the hemispheric sign rule in accord with the global structure of helicity reported by Zhang et al. (2010).

Observations of magnetic and kinetic helicity proxies

AbstractThe helicity is important to present the basic topological configuration of magnetic field in solar atmosphere. The distribution of magnetic helicity in solar atmosphere is presented by means of the observational (vector) magnetograms. As the kinetic helicity in the solar subatmosphere can be inferred from the velocity field based on the technique of the helioseismology and used to compare with the magnetic helicity in the solar atmosphere, the observational helicities provide the important chance for the confirmation on the generation of magnetic fields in the subatmosphere and solar dynamo models also. In this paper, we present the observational magnetic and kinetic helicity in solar active regions and corresponding questions, except the relationship with solar eruptive phenomena.

Magnetic Helicity of Solar Active Regions as Revealed by Vector Magnetograms and Coronal X-Ray Images

Abstract We have used photospheric vector magnetograms of 15 different solar active regions to calculate the current helicity parameter, $ \alpha _{\rm av}$ , and the linear force-free field (LFFF) parameter, $ \alpha _{\rm best}$ , that fits best the observed transverse field. The data were obtained with the Solar Magnetic Field Telescope at the Huairou Solar Observing Station, the National Astronomical Observatories of China, the Solar Flare Telescope of the National Astronomical Observatory of Japan, and the Haleakala Stokes Polarimeter at the Mees Solar Observatory, University of Hawaii, from 1997 to 2000. The agreement in sign of $ \alpha _{\rm av}$ between three vector magnetographs is better than 90%. For $ \alpha _{\rm best}$ , the agreement is 80%–90%. The line-of-sight magnetograms observed with the Michelson–Doppler Imager (MDI) on SOHO and coronal X-ray images observed with the Soft X-ray Telescope (SXT) on Yohkoh have been used to determine the constant $ \alpha _{\rm c}$ of the LFFF in the corona. The value of $ \alpha _{\rm c}$ corresponds to the extrapolated coronal field whose field lines best match, by visual inspection, the structure of coronal loops in X-ray images. It is found that the sign agreement between photospheric $ \alpha _{\rm av}$ or $ \alpha _{\rm best}$ and coronal $ \alpha _{\rm c}$ is lower (60%–85%). We consider the differences in measurements, observing conditions, data reduction methods, and limitation in LFFF extrapolation, and discuss their contributions to the dispersions in the hemispheric sign rule of helicity.

Helicity of Solar Active Regions with Solar Cycles

The helicity is an important quantity to present the basic topological configuration of magnetic field in the solar atmosphere. In this paper, we present the observational magnetic helicity in solar active regions with solar cycles and the corresponding possible model.

Comparison of photospheric current helicity and subsurface kinetic helicity

Abstract We make a comparison between photospheric current helicity and subsurface kinetic helicity in solar active regions. Four parameters are employed: average value of vertical component of current helicity density 〈Bz· (∇×B)z〉 (〈Hc〉), average force-free field factor and mean subsurface kinetic helicity 〈v· (∇×v)/|v|2〉 (αv), which is denoted as two different parameters, 〈αv1〉 and 〈αv2〉, according to different depths beneath the solar surface. A total of 38 active regions are investigated. The results show that the signs of 〈Hc〉 and αave have a typical hemispheric distribution feature. In contrast, the sign of 〈αv1〉 presents the opposite feature to the above two parameters. For 〈αv2〉, there is no obvious preponderance of the sign in each hemisphere as with the other three parameters. Although there is an opposite hemispheric preponderance between the signs of current helicity and that of kinetic helicity at 0–3 Mm beneath the solar surface, the uncertain correlations between 〈Hc〉 and 〈αv1〉, αave and 〈αv1〉, 〈Hc〉 and 〈αv2〉, and αave and 〈αv2〉 (the correlation coefficients are -0.095, 0.118, -0.102 and -0.179, respectively) do not support that the photospheric current helicity has a cause and effect relation with the kinetic helicity at 0–12 Mm beneath the solar surface.

Magnetic helicity of solar active regions

AbstractMagnetic helicity is a quantity that describes the linkage and twistedness/shear in the magnetic field. It has the unique feature that it is probably the only physical quantity which is approximately conserved even in resistive MHD. This makes magnetic helicity an ideal tool for the exploration of the physics of eruptive events. The concept of magnetic helicity can be used to monitor the whole history of a CME event from the emergence of twisted magnetic flux from the convective zone to the eruption and propagation of the CME into interplanetary space. In this article, I discuss the sources of the magnetic helicity injected into active regions and the role of magnetic helicity in the initiation of solar eruptions.

A theoretical model for the magnetic helicity of solar active regions

Active regions on the solar surface are known to possess magnetic helicity, which is predominantly negative in the northern hemisphere and positive in the southern hemisphere. Choudhuri et al. [Choudhuri, A.R. On the connection between mean field dynamo theory and flux tubes. Solar Phys. 215, 31–55, 2003] proposed that the magnetic helicity arises due to the wrapping up of the poloidal field of the convection zone around rising flux tubes which form active regions. Choudhuri [Choudhuri, A.R., Chatterjee, P., Nandy, D. Helicity of solar active regions from a dynamo model. ApJ 615, L57–L60, 2004] used this idea to calculate magnetic helicity from their solar dynamo model. Apart from getting broad agreements with observational data, they also predict that the hemispheric helicity rule may be violated at the beginning of a solar cycle. Chatterjee et al. [Chatterjee, P., Choudhuri, A.R., Petrovay, K. Development of twist in an emerging magnetic flux tube by poloidal field accretion. A&A 449, 781–789, 2006] study the penetration of the wrapped poloidal field into the rising flux tube due to turbulent diffusion using a simple 1-d model. They find that the extent of penetration of the wrapped field will depend on how weak the magnetic field inside the rising flux tube becomes before its emergence. They conclude that more detailed observational data will throw light on the physical conditions of flux tubes just before their emergence to the photosphere.

Observational study of magnetic chirality of solar active regions

We present the evolution of magnetic field and relationship with the magnetic (current) helicity in solar active regions from a series of photospheric vector magnetograms obtained at Huairou Solar Observing Station near Beijing, and also longitudinal magnetograms by MDI of SOHO, white light and 171 Å images by TRACE and soft X-ray images by Yohkoh. The conclusions in the analysis of the formation process of complex and delta magnetic configuration in some super active regions are the following: (1) The magnetic shear and gradient provide the non-potentiality of the magnetic field of active regions reflecting the existence of electric current. (2) Some of large-scale delta active regions could be due to the emergence of highly sheared non-potential magnetic flux bundles from the subatmosphere with amount of magnetic helicity, in addition to the emergence of twisted magnetic ropes. (3) We also present some results on the study of the magnetic (current) helicity in solar active regions.

Loading of Magnetic Helicity in Solar Active Regions

Loading of Magnetic Helicity in Solar Active Regions

Helicity of solar active regions from a dynamo model

We calculate helicities of solar active regions based on the idea that poloidal flux lines get wrapped around a toroidal flux tube rising through the convection zone, thereby giving rise to the helicity. We use our solar dynamo model based on the Babcock-Leighton α-effect to study how helicity varies with latitude and time.

Magnetic Helicity Injection in Solar Active Regions

We present the evolution of magnetic field and its relationship with magnetic (current) helicity in solar active regions from a series of photospheric vector magnetograms obtained by Huairou Solar Observing Station, longitudinal magnetograms 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 current 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 density 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 magnetic 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.

A METHOD FOR DETERMINING MAGNETIC HELICITY OF SOLAR ACTIVE REGIONS FROM SOHO/MDI MAGNETO GRAMS

Recently a big progress has been made on the measurements of magnetic helicity of solar active regions based on photospheric magnetograms . In this paper, we present the details of Chae`s method of determining the rate of helicity transfer using line-of-sight magnetograms such as taken by SORO /MDI. The method is specifically applied to full-disk magnetograms that are routinely taken at 96-minute cadence.