Active Regions with Superpenumbral Whirls and Their Subsurface Kinetic Helicity

We search for a signature of helicity flow from the solar interior to the photosphere and chromosphere. For this purpose, we study two active regions, NOAA 11084 and 11092, that show a regular pattern of superpenumbral whirls in chromospheric and coronal images. These two regions are good candidates for comparing magnetic/current helicity with subsurface kinetic helicity because the patterns persist throughout the disk passage of both regions. We use photospheric vector magnetograms from SOLIS/VSM and SDO/HMI to determine a magnetic helicity proxy, the spatially averaged signed shear angle (SASSA). The SASSA parameter produces consistent results leading to positive values for NOAA 11084 and negative ones for NOAA 11092 consistent with the clockwise and counter-clockwise orientation of the whirls. We then derive the properties of the subsurface flows associated with these active regions. We measure subsurface flows using a ring-diagram analysis of GONG high-resolution Doppler data and derive their kinetic helicity, h _z . Since the patterns persist throughout the disk passage, we analyze synoptic maps of the subsurface kinetic helicity density. The sign of the subsurface kinetic helicity is negative for NOAA 11084 and positive for NOAA 11092; the sign of the kinetic helicity is thus anticorrelated with that of the SASSA parameter. As a control experiment, we study the subsurface flows of six active regions without a persistent whirl pattern. Four of the six regions show a mixture of positive and negative kinetic helicity resulting in small average values, while two regions are clearly dominated by kinetic helicity of one sign or the other, as in the case of regions with whirls. The regions without whirls follow overall the same hemispheric rule in their kinetic helicity as in their current helicity with positive values in the southern and negative values in the northern hemisphere.     

Solar-Cycle Variation of Subsurface-Flow Divergence: A Proxy of Magnetic Activity?

We study the solar-cycle variation of subsurface flows from the surface to a depth of 16 Mm. We have analyzed Global Oscillation Network Group (GONG) Dopplergrams with a ring-diagram analysis covering about 15 years and Helioseismic and Magnetic Imager (HMI) Dopplergrams covering more than 6 years. After subtracting the average rotation rate and meridional flow, we have calculated the divergence of the horizontal residual flows from the maximum of Solar Cycle 23 through the declining phase of Cycle 24. The subsurface flows are mainly divergent at quiet regions and convergent at locations of high magnetic activity. The relationship is essentially linear between divergence and magnetic activity at all activity levels at depths shallower than about 10 Mm. At greater depths, the relationship changes sign at locations of high activity; the flows are increasingly divergent at locations with a magnetic activity index (MAI) greater than about 24 G. The flows are more convergent by about a factor of two during the rising phase of Cycle 24 than during the declining phase of Cycle 23 at locations of medium and high activity (about 10 to 40 G MAI) from the surface to at least 10 Mm. The subsurface divergence pattern of Solar Cycle 24 first appears during the declining phase of Cycle 23 and is present during the extended minimum. It appears several years before the magnetic pattern of the new cycle is noticeable in synoptic maps. Using linear regression, we estimate the amount of magnetic activity that would be required to generate the precursor pattern and find that it should be almost twice the amount of activity that is observed.     

The Global Context of Solar Activity During the Whole Heliosphere Interval Campaign

The Whole Heliosphere Interval (WHI) was an international observing and modeling effort to characterize the 3-D interconnected ??heliophysical?? system during this solar minimum, centered on Carrington Rotation 2068, March 20??C?April 16, 2008. During the latter half of the WHI period, the Sun presented a sunspot-free, deep solar minimum type face. But during the first half of CR 2068 three solar active regions flanked by two opposite-polarity, low-latitude coronal holes were present. These departures from the quiet Sun led to both eruptive activity and solar wind structure. Most of the eruptive activity, i.e., flares, filament eruptions and coronal mass ejections (CMEs), occurred during this first, active half of the interval. We determined the source locations of the CMEs and the type of associated region, such as active region, or quiet sun or active region prominence. To analyze the evolution of the events in the context of the global solar magnetic field and its evolution during the three rotations centered on CR 2068, we plotted the CME source locations onto synoptic maps of the photospheric magnetic field, of the magnetic and chromospheric structure, of the white light corona, and of helioseismological subsurface flows. Most of the CME sources were associated with the three dominant active regions on CR 2068, particularly AR 10989. Most of the other sources on all three CRs appear to have been associated with either isolated filaments or filaments in the north polar crown filament channel. Although calculations of the flux balance and helicity of the surface magnetic features did not clearly identify a dominance of one region over the others, helioseismological subsurface flows beneath these active regions did reveal a pronounced difference among them. These preliminary results suggest that the ??twistedness?? (i.e., vorticity and helicity) of subsurface flows and its temporal variation might be related to the CME productivity of active regions, similar to the relationship between flares and subsurface flows.     

Solar Cycle Variation of Magnetic Flux Ropes in a Quasi-Static Coronal Evolution Model

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 magnetic structure predicted by this model – in particular the flux ropes – varies over the solar activity cycle, based on photospheric input data from six periods of cycle 23. The number of flux ropes doubles from minimum to maximum, following the total length of photospheric polarity inversion lines. However, the number of flux rope ejections increases by a factor of eight, following the emergence rate of active regions. This is broadly consistent with the observed cycle modulation of coronal mass ejections, although the actual rate of ejections in the simulation is about a fifth of the rate of observed events. The model predicts that, even at minimum, differential rotation will produce sheared, non-potential, magnetic structure at all latitudes.     

Solar-Cycle Variation of Subsurface Zonal Flow

We study the solar-cycle variation of the zonal flow in the near-surface layers of the solar convection zone from the surface to a depth of 16 Mm covering the period from mid-2001 to mid-2013 or from the maximum of Cycle 23 through the rising phase of Cycle 24. We have analyzed Global Oscillation Network Group (GONG) and Helioseismic and Magnetic Imager (HMI) Dopplergrams with a ring-diagram analysis. The zonal flow varies with the solar cycle showing bands of faster-than-average flows equatorward of the mean latitude of activity and slower-than-average flows on the poleward side. The fast band of the zonal flow and the magnetic activity appear first in the northern hemisphere during the beginning of Cycle 24. The bands of fast zonal flow appear at mid-latitudes about three years in the southern and four years in the northern hemisphere before magnetic activity of Cycle 24 is present. This implies that the flow pattern is a direct precursor of magnetic activity. The solar-cycle variation of the zonal flow also has a poleward branch, which is visible as bands of faster-than-average zonal flow near 50° latitude. This band appears first in the southern hemisphere during the rising phase of the Cycle 24 and migrates slowly poleward. These results are in good agreement with corresponding results from global helioseismology.     

A Study of Connections Between Solar Flares and Subsurface Flow Fields of Active Regions

We investigate the connections between the occurrence of major solar flares and subsurface dynamic properties of active regions. For this analysis, we select five active regions that produced a total of 11 flares with peak X-ray flux intensity higher than M5.0. The subsurface velocity fields are obtained from time–distance helioseismology analysis using SDO/HMI (Solar Dynamics Observatory/Helioseismic and Magnetic Imager) Doppler observations, and the X-ray flux intensity is taken from GOES (Geostationary Operational Environmental Satellites). It is found that among the eight amplitude bumps in the evolutionary curves of subsurface kinetic helicity, five (62.5%) of them had a flare stronger than M5.0 occurring within 8 hours, either before or after the bumps. Another subsurface parameter is the Normalized Helicity Gradient Variance (NHGV), reflecting kinetic helicity spread in different depth layers; it also shows bumps near the occurrence of these solar flares. Although there is no one-to-one correspondence between the flare and the subsurface properties, these observational phenomena are worth further studies to better understand the flares’ subsurface roots, and to investigate whether the subsurface properties can be used for major flare forecasts.     

Subsurface Vorticity of Flaring <Emphasis Type="Italic">versus</Emphasis> Flare-Quiet Active Regions

We apply discriminant analysis to 1023 active regions and their subsurface-flow parameters, such as vorticity and kinetic helicity density, with the goal of distinguishing between flaring and non-flaring active regions. We derive synoptic subsurface flows by analyzing GONG high-resolution Doppler data with ring-diagram analysis. We include magnetic-flux values in the discriminant analysis derived from NSO Kitt Peak and SOLIS synoptic maps binned to the same spatial scale as the helioseismic analysis. For each active region, we determine the flare information from GOES and include all flares within 60° central meridian distance to match the coverage of the ring-diagram analysis. The subsurface-flow characteristics improve the ability to distinguish between flaring and non-flaring active regions. For the C- and M-class flare category, the most important subsurface parameter is the so-called structure vorticity, which estimates the horizontal gradient of the horizontal-vorticity components. The no-event skill score, which measures the improvement over predicting that no events occur, reaches 0.48 for C-class flares and 0.32 for M-class flares, when the structure vorticity at three depths combined with total magnetic flux are used. The contributions come mainly from shallow layers within about 2 Mm of the surface and layers deeper than about 7 Mm.     

What helicity can tell us about solar magnetic fields

Concept of magnetic/current helicity was introduced to solar physics about 15 years ago. Earlier studies led to discovery of such fundamental properties as hemispheric helicity rule, and role of helicity in magnetic reconnection and solar eruptions. Later, the concept was successfully applied in studies of different solar processes from solar dynamo to flare and CME phenomena. Although no silver bullet, helicity has proven to be a very useful “tool” in answering many still-puzzling questions about origin and evolution of solar magnetic fields. I present an overview of some helicity studies and briefly analyze their findings.     

Subsurface Zonal and Meridional Flow During Cycles 23 and 24

We study the solar-cycle variation of subsurface flows from the surface to a depth of 16 Mm. We have used ring-diagram analysis to analyze Dopplergrams obtained with the Michelson Doppler Imager (MDI) Dynamics Program, the Global Oscillation Network Group (GONG), and the Helioseismic and Magnetic Imager (HMI) instrument. We combined the zonal and meridional flows from the three data sources and scaled the flows derived from MDI and GONG to match those from HMI observations. In this way, we derived their temporal variation in a consistent manner for Solar Cycles 23 and 24. We have corrected the measured flows for systematic effects that vary with disk positions. Using time-depth slices of the corrected subsurface flows, we derived the amplitudes and times of the extrema of the fast and slow zonal and meridional flows during Cycles 23 and 24 at every depth and latitude. We find an average difference between maximum and minimum amplitudes of \(8.6 \pm0.4~\mbox{m}\,\mbox{s}^{-1}\) for the zonal flows and \(7.9 \pm0.3~\mbox{m}\,\mbox{s}^{-1}\) for the meridional flows associated with Cycle 24 averaged over a depth range from 2 to 12 Mm. The corresponding values derived from GONG data alone are \(10.5 \pm0.3~\mbox{m}\,\mbox{s}^{-1}\) for the zonal and \(10.8 \pm0.3~\mbox{m}\,\mbox{s}^{-1}\) for the meridional flow. For Cycle 24, the flow patterns are precursors of the magnetic activity. The timing difference between the occurrence of the flow pattern and the magnetic one increases almost linearly with increasing latitude. For example, the fast zonal and meridional flow appear \(2.1 \pm 0.6\) years and \(2.5\pm 0.6\) years, respectively, before the magnetic pattern at \(30^{\circ}\) latitude in the northern hemisphere, while in the southern hemisphere, the differences are \(3.2 \pm 1.2\) years and \(2.6 \pm 0.6\) years. The flow patterns of Cycle 25 are present and have reached \(30^{\circ}\) latitude. The amplitude differences of Cycle 25 are about 22% smaller than those of Cycle 24, but are comparable to those of Cycle 23. Moreover, polynomial fits of meridional flows suggest that equatorward meridional flows (counter-cells) might exist at about \(80^{\circ}\) latitude except during the declining phase of the solar cycle.     

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.     

Relation of CME Speed and Magnetic Helicity in CME Source Regions on the Sun during the Early Phase of Solar Cycles 23 and 24

To investigate the relations between coronal mass ejection (CME) speed and magnetic field properties measured in the photospheric surface of CME source regions, we selected 22 disk CMEs in the rising and early maximum phases of the current Solar Cycle 24. For the CME speed, we used two-dimensional (2D) projected speed observed by the Large Angle and Spectroscopic Coronagraph onboard the Solar and Heliospheric Observatory (SOHO/LASCO), as well as a 3D speed calculated from the triangulation method using multi-point observations. Two magnetic parameters of CME source regions were considered: the average of magnetic helicity injection rate and the total unsigned magnetic flux. We then classified the selected CMEs into two groups, showing: i) a monotonically increasing pattern with one sign of helicity (group A: 16 CMEs) and ii) a pattern of significant helicity injection followed by its sign reversal (group B: 6 CMEs). We found that: 1) 3D speed generally shows better correlations with the magnetic parameters than the 2D speed for 22 CME events in Solar Cycle 24; 2) 2D speed and the magnetic parameters of 22 CME events in this solar cycle have lower values than those of 47 CME events in Solar Cycle 23; 3) all events of group B in Solar Cycle 24 occur only after the beginning of the maximum phase, a trend well consistent with that shown in Solar Cycle 23; 4) the 2D speed and the helicity parameter of group B events continue to increase in the declining phase of Solar Cycle 23, while those of group A events abruptly decrease in the same period. Our results indicate that the two CME groups have a different tendency in the solar cycle variations of CME speed and the helicity parameters. Active regions that show a complex helicity evolution pattern tend to appear in the maximum and declining phases, while active regions with a relatively simple helicity evolution pattern appear throughout the whole solar cycle.     

Vorticity of Subsurface Flows of Emerging and Decaying Active Regions

We study the temporal variation of the vorticity of subsurface flows of 828 active regions and 977 quiet regions. The vorticity of these flows is derived from measured subsurface velocities. The horizontal flows are determined by analyzing high-resolution Global Oscillation Network Group Doppler data with ring-diagram analysis covering a range of depths from the surface to about 16 Mm. The vertical velocity component is derived from the divergence of the measured horizontal flows using mass conservation. We determine the change in unsigned magnetic flux density during the disk passage of each active region using Michelson Doppler Imager (MDI) magnetograms binned to the ring-diagram grid with centers spaced by 7.5° ranging ± 52.5° in latitude and central meridian distance with an effective diameter of 15° after apodization. We then sort the data by their flux change from decaying to emerging flux and divide the data into five subsets of equal size. We find that the vorticity of subsurface flows increases during flux emergence and decreases when active regions decay. For flux emergence, the absolute values of the zonal and meridional vorticity components show the most coherent variation with activity, while for flux decrease the strongest signature is in the absolute values of the meridional and vertical vorticity components. The temporal variation of the enstrophy (residual vorticity squared) is thus a good indicator for either flux increase or decrease. There are some indications that the increase in vorticity during flux emergence happens about a day later at depths below about 8 Mm compared to layers shallower than about 4 Mm. This timing difference might imply that the vorticity signal analyzed here is caused by the interaction between magnetic flux and turbulent flows near the solar surface. There are also hints that the vorticity decrease during flux decay begins about a day earlier at layers deeper than about 8 Mm compared to shallower ones. However, the timing difference between the change at different depths is comparable to the time step of the analysis.     

Emerging and Decaying Magnetic Flux and Subsurface Flows

We study the temporal variation of subsurface flows of 788 active regions and 978 quiet regions. The vertical-velocity component used in this study is derived from the divergence of the measured horizontal flows using mass conservation. The horizontal flows cover a range of depths from the surface to about 16 Mm and are determined by analyzing about five years of GONG high-resolution Doppler data with ring-diagram analysis. We determine the change in unsigned magnetic flux during the disk passage of each active region using MDI magnetograms binned to the ring-diagram grid. We then sort the data by their flux change from decaying to emerging flux and divide the data into five subsets of equal size. The average vertical flows of the emerging-flux subset are systematically shifted toward upflows compared to the grand average values of the complete data set, whereas the average flows of the decaying-flux subset show comparably more pronounced downflows especially near 8 Mm. For flux emergence, upflows become stronger with time with increasing flux at depths greater than about 10 Mm. At layers shallower than about 4 Mm, the flows might start to change from downflows to upflows, when flux emerges, and then back to downflows after the active regions are established. The flows in the layers between these two depth ranges show no response to the emerging flux. In the case of decaying flux, the flows change from strong upflows to downflows at depths greater than about 10 Mm, whereas the flows do not change systematically at other depths. A cross-correlation analysis shows that the flows in the near-surface and the deeper layers might change about one day before flux emerges. The flows associated with the quiet regions fluctuate with time but do not show any systematic variation.     

Subsurface Meridional Flow from HMI Using the Ring-Diagram Pipeline

We have determined the meridional flows in subsurface layers for 18 Carrington rotations (CR 2097 to 2114) analyzing high-resolution Dopplergrams obtained with the Helioseismic and Magnetic Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO). We are especially interested in flows at high latitudes up to 75^° in order to address the question whether the meridional flow remains poleward or reverses direction (so-called counter cells). The flows have been determined in depth from near-surface layers to about 16 Mm using the HMI ring-diagram pipeline. The measured meridional flows show systematic effects, such as a variation with the B ₀-angle and a variation with central meridian distance (CMD). These variations have been taken into account to lead to more reliable flow estimates at high latitudes. The corrected average meridional flow is poleward at most depths and latitudes with a maximum amplitude of about $20~\mathrm{m\,s}^{-1}$ near 37.5^° latitude. The flows are more poleward on the equatorward side of the mean latitude of magnetic activity at 22^° and less poleward on the poleward side, which can be interpreted as convergent flows near the mean latitude of activity. The corrected meridional flow is poleward at all depths within ±?67.5^° latitude. The corrected flow is equatorward only at 75^° latitude in the southern hemisphere at depths between about 4 and 8 Mm and at 75^° latitude in the northern hemisphere only when the B ₀ angle is barely large enough to measure flows at this latitude. These counter cells are most likely the remains of an insufficiently corrected B ₀-angle variation and not of solar origin. Flow measurements and B ₀-angle corrections are difficult at the highest latitude because these flows are only determined during limited periods when the B ₀ angle is sufficiently large.     

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)     

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.     

Solar activity during first six years of solar cycle 24 and 23: a comparative study

Attempt to look into the nature of solar activity and variability have increased importance in recent days because of their terrestrial relationships. In the present work we have attempted to compare the solar activity events during first six years (2008–2013) of the ongoing solar cycle 24 with first six years (1996–2001) of solar cycle 23. To that end, we have considered sunspot numbers, F10.7 cm solar flux, halo CMEs and geomagnetic storms as comparison parameters. Sunspot number during the year 2008–2013 varied from 0 to 96.7 while during the year 1996 to 2001 it was observed from 0.9 to 170.1. Solar radio flux (F10.7 cm index) varied from 65 to 190 during the years 2008–2013 while it was observed from 65 to 283 during the years 1996–2001. 197 cases of halo CMEs (width=360^°) in solar cycle 23 (1996–2001) and 177 cases of halo CMEs (width=360^°) in solar cycle 24 (2008–2013) are investigated. 287 and 104 geomagnetic storm cases (Dst varies between ?50 and ?350 nT) are analysed during the half period of solar cycle 23 and 24 respectively. Comparative results indicate that solar cycle 23 was more pronounced in comparison of solar cycle 24.     

Determination of magnetic helicity content of solar active regions from SOHO/MDI magnetograms

Chae (2001) first proposed a method of self-consistently determining the rate of change of magnetic helicity using a time series of longitudinal magnetograms only, such as taken by SOHO/MDI. Assuming that magnetic fields in the photosphere are predominantly vertical, he determined the horizontal component of velocity by tracking the displacements of magnetic flux fragments using the technique of local correlation tracking (LCT). In the present paper, after briefly reviewing the recent advance in helicity rate measurement, we argue that the LCT method can be more generally applied even to regions of inclined magnetic fields. We also present some results obtained by applying the LCT method to the active region NOAA 10365 under emergence during the observable period, which are summarized as follows. (1) Strong shearing flows were found near the polarity inversion line that were very effective in helicity injection. (2) Both the magnetic flux and helicity of the active region steadily increased during the observing period, and reached 1.2 × 10²² Mx and 8 ×10⁴² Mx², respectively, 4.5 days after the birth of the active region. (3) The corresponding ratio of the helicity to the square of the magnetic flux, 0.05, is roughly compatible with the values determined by other studies using linear-force-free modeling. (4) A series of flares took place while the rate of helicity injection was high. (5) The choice of a smaller window size or a shorter time interval in the LCT method resulted in a bigger value of the LCT velocity and a bigger value of the temporal fluctuation of the helicity rate. (6) Nevertheless when averaged over a time period of about one hour or longer, the average rate of helicity became about the same within about 10%, almost irrespective of the chosen window size and time interval, indicating that short-lived, fluctuating flows may be insignificant in transferring magnetic helicity. Our results suggest that the LCT method may be applied to 96-minute cadence full-disk MDI magnetograms or other data of similar kind, to provide a practically useful, if not perfect, way of monitoring the magnetic helicity content of active regions as a function of time.     

Determination of magnetic helicity content of solar active regions from SOHO/MDI magnetograms

Chae (2001) first proposed a method of self-consistently determining the rate of change of magnetic helicity using a time series of longitudinal magnetograms only, such as taken by SOHO/MDI. Assuming that magnetic fields in the photosphere are predominantly vertical, he determined the horizontal component of velocity by tracking the displacements of magnetic flux fragments using the technique of local correlation tracking (LCT). In the present paper, after briefly reviewing the recent advance in helicity rate measurement, we argue that the LCT method can be more generally applied even to regions of inclined magnetic fields. We also present some results obtained by applying the LCT method to the active region NOAA 10365 under emergence during the observable period, which are summarized as follows. (1) Strong shearing flows were found near the polarity inversion line that were very effective in helicity injection. (2) Both the magnetic flux and helicity of the active region steadily increased during the observing period, and reached 1.2 × 10²² Mx and 8 ×10⁴² Mx², respectively, 4.5 days after the birth of the active region. (3) The corresponding ratio of the helicity to the square of the magnetic flux, 0.05, is roughly compatible with the values determined by other studies using linear-force-free modeling. (4) A series of flares took place while the rate of helicity injection was high. (5) The choice of a smaller window size or a shorter time interval in the LCT method resulted in a bigger value of the LCT velocity and a bigger value of the temporal fluctuation of the helicity rate. (6) Nevertheless when averaged over a time period of about one hour or longer, the average rate of helicity became about the same within about 10%, almost irrespective of the chosen window size and time interval, indicating that short-lived, fluctuating flows may be insignificant in transferring magnetic helicity. Our results suggest that the LCT method may be applied to 96-minute cadence full-disk MDI magnetograms or other data of similar kind, to provide a practically useful, if not perfect, way of monitoring the magnetic helicity content of active regions as a function of time.