Differential Affine Velocity Estimator Research Articles

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.

Magnetic field evolution around a fast-moving pore emerging from the quiet Sun

Context. Solar pores are intense concentrations of magnetic fields on the solar surface and plasma flows have always played a key role in spurring the evolution of the pores. Aims. In this study, we present the evolution of the magnetic field and plasma velocity around a fast-moving pore. The target pore expands into the quiet Sun area with a sufficiently fast speed after its emergence, while the background magnetic fields around the pore are simple. These characteristics provide us with an excellent opportunity to study the interaction between plasma motions and ambient magnetic fields. Methods. We analyzed the Helioseismic and Magnetic Imager (HMI) vector magnetograms with a pixel size of 0.5″ and a temporal cadence of 12 min across a duration of 11 h. We also adopted he HMI dopplergrams present the line-of-sight velocities. The horizontal flow fields were obtained using the Differential Affine Velocity Estimator for Vector Magnetograms method. Results. Pure horizontal magnetic fields are generated in the moving frontwards when the pore is subject to fast movement. The generated magnetic fields occur outside the emerging site and thus can be ruled out as the emerging flux from the interior. Instead, they are highly correlated with the broader downflows and expanding horizontal plasma motions in front of the pore. A magnetic gap can be observed between the magnetic fields inside and outside the pore. The temporal evolution of the generated magnetic fields is related to the speed of the pore, which is also distinguished from the original fields within the pore. Conclusions. The observations suggest that the plasma flows driven by the fast proper motion of the pore compress and stretch the local magnetic field to a horizontal non-radial direction, ultimately leading to the magnetic field amplification in the front part of the moving pore.

Comparison of Two Methods for Calculating Magnetic Helicity in the Solar Corona

Duo to the large magnetic Reynolds number, the magnetic helicity originating from the solar interior can be carried away through the photosphere into the corona. However, the relationship between the accumulated magnetic helicity flux through the photosphere and the magnetic helicity in the corona is still unclear. By selecting 36 newly emerging active regions in the 23rd solar cycle, we apply optical flow methods to derive the accumulated magnetic helicity through the photosphere (H m p ) by using the sequential longitudinal magnetograms, we use nonlinear force-free field extrapolation to obtain the 3D coronal magnetic field, and we adopt finite volume methods to calculate the instantaneous relative magnetic helicity in the corona (H m c ) by using vector magnetograms. It is found that the local correlation tracking (LCT)–based H m p is larger than H m c in 1″, and that the Differential Affine Velocity Estimator–based H m p is more consistent with H m c than the LCT-based H m p . H m p is more consistent with H m c in evaluation from 2″ than from 1″. Moreover, systematically shows consistency with the Hemispheric Helicity Rule (over 55%), no matter which resolution and method are used. These estimations suggest that the consistency of H m c and H m p is partly dependent on the resolution of the magnetograms and the calculation methods.

Probing the Effect of Cadence on the Estimates of Photospheric Energy and Helicity Injections in Eruptive Active Region NOAA AR 11158

We study how the input-data cadence affects the photospheric energy and helicity injection estimates in eruptive NOAA Active Region 11158. We sample the novel 2.25-minute vector magnetogram and Dopplergram data from the Helioseismic and Magnetic Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO) spacecraft to create input datasets of variable cadences ranging from 2.25 minutes to 24 hours. We employ state-of-the-art data processing, velocity, and electric-field inversion methods for deriving estimates of the energy and helicity injections from these datasets. We find that the electric-field inversion methods that reproduce the observed magnetic-field evolution through the use of Faraday’s law are more stable against variable cadence: the PDFI (PTD-Doppler-FLCT-Ideal, where PTD refers to Poloidal–Toroidal Decomposition, and FLCT to Fourier Local Correlation Tracking) electric-field inversion method produces consistent injection estimates for cadences from 2.25 minutes up to two hours, implying that the photospheric processes acting on time scales below two hours contribute little to the injections, or that they are below the sensitivity of the input data and the PDFI method. On other hand, the electric-field estimate derived from the output of DAVE4VM (Differential Affine Velocity Estimator for Vector Magnetograms), which does not fulfill Faraday’s law exactly, produces significant variations in the energy and helicity injection estimates in the 2.25 minutes – two hours cadence range. We also present a third, novel DAVE4VM-based electric-field estimate, which corrects the poor inductivity of the raw DAVE4VM estimate. This method is less sensitive to the changes of cadence, but it still faces significant issues for the lowest of considered cadences (≥ two hours). We find several potential problems in both PDFI- and DAVE4VM-based injection estimates and conclude that the quality of both should be surveyed further in controlled environments.

Magnetohydrodynamic Simulations for Solar Active Regions using Time-series Data of Surface Plasma Flow and Electric Field Inferred from Helioseismic Magnetic Imager Vector Magnetic Field Measurements

Abstract Temporal evolution of magnetic structures of the solar active region (AR) NOAA AR 11158, is simulated with our magnetohydrodynamic (MHD) simulation models using time-dependent solar-surface electric field or plasma flow data. Using the Solar Dynamics Observatory/Helioseismic Magnetic Imager vector magnetogram data, the solar-surface boundary electric field maps are derived with our recently developed algorithm to reproduce the temporal evolution of solar-surface vector magnetic field as observed. The plasma motion velocity maps are calculated through the Differential Affine Velocity Estimator for Vector Magnetograms. In both data-driven models, the simulated evolutionary magnetic field structures at strong-field low-beta regions appear near force-free state, as the current helicity density ( ) are roughly constant along each field line. Although the magnetic energy simulated with the newly developed plasma-velocity-driven model is about 10% of that by the electric-field driven model, the plasma-velocity-driven model can maintain the frozen-in condition, and evolution of current and free energy generated by the solar-surface plasma motions can be spatially and temporally traced. The present MHD simulation models for AR system can be a step toward better, more realistic data-driven evolutionary modeling, in particular, establishing boundary treatments for introducing the time-dependent observation data in a physically and mathematically consistent manner.

Solar Magnetic Flux Rope Eruption Simulated by a Data-driven Magnetohydrodynamic Model

Abstract The combination of magnetohydrodynamic (MHD) simulation and multi-wavelength observations is an effective way to study the mechanisms of magnetic flux rope eruption. We develop a data-driven MHD model using the zero-β approximation. The initial condition is provided by a nonlinear force-free field derived from the magneto-frictional method based on vector magnetic field observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. The bottom boundary uses observed time series of the vector magnetic field and the vector velocity derived by the Differential Affine Velocity Estimator for Vector Magnetograms. We apply the data-driven model to active region 11123 observed from 06:00 UT on 2010 November 11 to about 2 hr later. The evolution of the magnetic field topology coincides with the flare ribbons observed in the 304 and 1600 Å wavebands by the Atmospheric Imaging Assembly. The morphology, propagation path, and propagation range of the flux rope are comparable with the observations in 304 Å. We also find that a data-constrained boundary condition, where the bottom boundary is fixed to the initial values, reproduces a similar simulation result. This model can reproduce the evolution of a magnetic flux rope in its dynamic eruptive phase.

Photospheric Shear Flows in Solar Active Regions and Their Relation to Flare Occurrence

Solar active regions (ARs) that produce major flares typically exhibit strong plasma shear flows around photospheric magnetic polarity inversion lines (MPILs). It is therefore important to quantitatively measure such photospheric shear flows in ARs for a better understanding of their relation to flare occurrence. Photospheric flow fields were determined by applying the Differential Affine Velocity Estimator for Vector Magnetograms (DAVE4VM) method to a large data set of 2,548 co-aligned pairs of AR vector magnetograms with 12-min separation over the period 2012-2016. From each AR flow-field map, three shear-flow parameters were derived corresponding to the mean (<S>), maximum (S_max) and integral (S_sum) shear-flow speeds along strong-gradient, strong-field MPIL segments. We calculated flaring rates within 24 hr as a function of each shear-flow parameter, and also investigated the relation between the parameters and the waiting time ({\tau}) until the next major flare (class M1.0 or above) after the parameter observation. In general, it is found that the larger S_sum an AR has, the more likely it is for the AR to produce flares within 24 hr. It is also found that among ARs which produce major flares, if one has a larger value of S_sum then {\tau} generally gets shorter. These results suggest that large ARs with widespread and/or strong shear flows along MPILs tend to not only be more flare productive, but also produce major flares within 24 hr or less.

On the extent of the moat flow in axisymmetric sunspots

Unipolar, axisymmetric sunspots are figuratively called "theoretician's sunspots" because their simplicity supposedly makes them more suitable for theoretical descriptions or numerical models. On 2013 November 18, a very large specimen (active region NOAA 11899) crossed the central meridian of the Sun. The moat flow associated with this very large spot is quantitatively compared to that of a medium and a small sunspot to determine the extend of the moat flow in different environments. We employ continuum images and magnetograms of the Helioseismic and Magnetic Imager (HMI) as well as extreme ultraviolet (EUV) images at $\lambda$160 nm of the Atmospheric Imaging Assembly (AIA), both on board the Solar Dynamics Observatory (SDO), to measure horizontal proper motions with Local Correlation Tracking (LCT) and flux transport velocities with the Differential Affine Velocity Estimator (DAVE). We compute time-averaged flow maps ($\pm$6 hours around meridian passage) and radial averages of photometric, magnetic and flow properties. Flow fields of a small- and a medium-sized axisymmetric sunspot provide the context for interpreting the results. All sunspots show the outward moat flow and the advection of moving magnetic features (MMFs). However, the extent of the moat flow varies from spot to spot but a correlation of flow properties with size is tenuous, if at all present. The moat flow is asymmetric and predominantly in the east-west direction, whereby deviations are related to the tilt angle of the sunspot group as well as to the topology and activity level of the trailing plage.

The origin of two X-class flares in active region NOAA 12673

Flare-prolific active region NOAA 12673 produced consecutive X2.2 and X9.3 flares on the 6 September 2017. To scrutinize the morphological, magnetic, and horizontal flow properties associated with these flares, a seven-hour time series was used consisting of continuum images, line-of-sight and vector magnetograms, and 1600 Å UV images. These data were acquired with the Helioseismic and Magnetic Imager (HMI) and the Atmospheric Imaging Assembly (AIA). The white-light flare emission differed for both flares, while the X2.2 flare displayed localized, confined flare kernels, the X9.3 flare exhibited a two-ribbon structure. In contrast, the excess UV emission exhibited a similar structure for both flares, but with larger areal extent for the X9.3 flare. These two flares represented a scenario in which the first confined flare acted as precursor, setting up the stage for the more extended flare. Difference maps for continuum and magnetograms revealed locations of significant changes, that is, penumbral decay and umbral strengthening. The curved magnetic polarity inversion line in the δ-spot was the fulcrum of most changes. Horizontal proper motions were computed using the differential affine velocity estimator for vector magnetograms (DAVE4VM). Persistent flow features included (1) strong shear flows along the polarity inversion line, where the negative, parasitic polarity tried to bypass the majority, positive-polarity part of the δ-spot in the north, (2) a group of positive-polarity spots, which moved around the δ-spot in the south, moving away from the δ-spot with significant horizontal flow speeds, and (3) intense moat flows partially surrounding the penumbra of several sunspots, which became weaker in regions with penumbral decay. The enhanced flare activity has its origin in the head-on collision of newly emerging flux with an already existing regular, α-spot. Umbral cores of emerging bipoles were incorporated in its penumbra, creating a δ-configuration with an extended polarity inversion line, as the parasitic umbral cores were stretched while circumventing the majority polarity.

Evolution of Photospheric Flow and Magnetic Fields Associated with the 2015 June 22 M6.5 Flare

Abstract The evolution of photospheric flow and magnetic fields before and after flares can provide important information regarding the flare triggering and back-reaction processes. However, such studies on the flow field are rare due to the paucity of high-resolution observations covering the entire flaring period. Here we study the structural evolution of penumbra and shear flows associated with the 2015 June 22 M6.5 flare in NOAA AR 12371, using high-resolution imaging observation in the TiO band taken by the 1.6 m Goode Solar Telescope at Big Bear Solar Observatory, with the aid of the differential affine velocity estimator method for flow tracking. The accompanied photospheric vector magnetic field changes are also analyzed using data from the Helioseismic and Magnetic Imager. As a result, we found, for a penumbral segment in the negative field adjacent to the magnetic polarity inversion line (PIL), an enhancement of penumbral flows (up to an unusually high value of ∼2 km s−1) and extension of penumbral fibrils after the first peak of the flare hard X-ray emission. We also found an area at the PIL, which is co-spatial with a precursor brightening kernel, that exhibits a gradual increase of shear flow velocity (up to ∼0.9 km s−1) after the flare. The enhancing penumbral and shear flow regions are also accompanied by an increase of horizontal field and decrease of magnetic inclination angle (measured from the solar surface). These results are discussed in the context of the theory of back-reaction of coronal restructuring on the photosphere as a result of flare energy release.

Horizontal flow fields in and around a small active region

Aims. Combining high-resolution and synoptic observations aims to provide a comprehensive description of flux emergence at photospheric level and of the growth process that eventually leads to a mature active region. Methods. Small active region NOAA 12118 was observed on 2014 July 18 with the 1.5-meter GREGOR solar telescope on 2014 July 18. High-resolution time-series of blue continuum and G-band images acquired in the blue imaging channel (BIC) of the GREGOR Fabry-P\'erot Interferometer (GFPI) were complemented by LOS magnetograms and continuum images obtained with the HMI onboard the SDO. Horizontal proper motions and horizontal plasma velocities were computed with local correlation tracking (LCT) and the differential affine velocity estimator, respectively. Morphological image processing was employed to measure the photometric/magnetic area, magnetic flux, and the separation profile of the EFR during its evolution. Results. The computed growth rates for photometric area, magnetic area, and magnetic flux are about twice as high as the respective decay rates. The space-time diagram using HMI magnetograms of five days traces a leaf-like structure, which is determined by the initial separation of the two polarities, a rapid expansion phase, a time when the spread stalls, and a period when the region slowly shrinks again. The separation rate of 0.26 km\s is highest in the initial stage, and it decreases when the separation comes to a halt. Horizontal plasma velocities computed at four evolutionary stages indicate a changing pattern of inflows. In LCT maps we find persistent flow patterns such as outward motions in the outer part of the two major pores, a diverging feature near the trailing pore marking the site of upwelling plasma and flux emergence, and low velocities in the interior of pores. We detected many elongated rapidly expanding granules between the two major polarities.

Relationship Between Sunspot Rotation and a Major Solar Eruption on 12 July 2012

We present an analysis of Solar Dynamics Observatory (SDO) observations of an X1.4 class flare on 12 July 2012 (SOL2012-07-12T15:37L082C105), which was associated with a pronounced sunspot rotation in the associated active region. Based on the magnetograms taken with the Helioseismic and Magnetic Imager (HMI) on the SDO, we measured the rotational speed of the sunspot. We also used a technique, called the differential affine velocity estimator for vector magnetograms (DAVE4VM), to determine the horizontal velocities and the magnetic helicity flux transport. The helicity flux rate due to shearing motion changed sign after the onset of the eruption. A high correlation between the sunspot rotation speed and the change in the total accumulated helicity was found. We also calculated the net fluxes of the respective magnetic polarities and the net vertical currents. The net current in the region of interest showed a synchronous change with the sunspot rotation rate. The magnetic configurations of the sigmoid filament in the active region and the associated possible interaction between different structures were further investigated by means of a nonlinear force-free field extrapolation. We identified a possible magnetic reconnection region from the three-dimensional magnetic fields and its association with EUV structures. These results suggest that the major eruption of this active region was connected with the sunspot rotation.

INVESTIGATION OF HELICITY AND ENERGY FLUX TRANSPORT IN THREE EMERGING SOLAR ACTIVE REGIONS

We report the results of an investigation of helicity and energy flux transport from three emerging solar active regions (ARs). Using time sequence vector magnetic field observations obtained from the Helioseismic Magnetic Imager, the velocity field of plasma flows is derived by the differential affine velocity estimator for vector magnetograms. In three cases, the magnetic fluxes evolve to pump net positive, negative, and mixed-sign helicity flux into the corona. The coronal helicity flux is dominantly coming from the shear term that is related to horizontal flux motions, whereas energy flux is dominantly contributed by the emergence term. The shear helicity flux has a phase delay of 5–14 hr with respect to absolute magnetic flux. The nonlinear curve of coronal energy versus relative helicity identifies the configuration of coronal magnetic fields, which is approximated by a fit of linear force-free fields. The nature of coronal helicity related to the particular pattern of evolving magnetic fluxes at the photosphere has implications for the generation mechanism of two kinds of observed activity in the ARs.

ASYMMETRY OF MAGNETIC HELICITY FLUX IN EMERGING BIPOLAR ACTIVE REGIONS

We apply differential affine velocity estimator (DAVE) to the Solar Dynamics Observatory (SDO)/Helioseismic and Magnetic Imager (HMI) 12-min line-of-sight magnetograms, and separately calculate the injected magnetic helicity for the leading and the following polarities of nine emerging bipolar active regions (ARs). Comparing magnetic helicity flux of the leading polarity with the following polarity, we find that six ARs studied in this paper have the following polarity that injected more magnetic helicity flux than that of the leading polarity. We also measure the mean area of each polarity in all the nine ARs, and find that the compact polarity tend to possess more magnetic helicity flux than the fragmented one. Our results confirm the previous studies on asymmetry of magnetic helicity that emerging bipolar ARs have a polarity preference in injecting magnetic helicity. Based on the changes of unsigned magnetic flux, we divide the emergence process into two evolutionary stages: (1) an increasing stage before the peak flux and (2) a constant or decreasing stage after the peak flux. Obvious changes on magnetic helicity flux can be seen during transition from one stage to another. Seven ARs have one or both polarity that changed the sign of magnetic helicity flux. Additionally, the prevailing polarity of the two ARs, which injects more magnetic helicity, changes form the following polarity to the leading one.

SUDDEN PHOTOSPHERIC MOTION AND SUNSPOT ROTATION ASSOCIATED WITH THE X2.2 FLARE ON 2011 FEBRUARY 15

The Helioseismic and Magnetic Imager provides 45 s cadence intensity images and 720 s cadence vector magnetograms. These unprecedented high-cadence and high-resolution data give us a unique opportunity to study the change of photospheric flows and sunspot rotations associated with flares. By using the differential affine velocity estimator method and the Fourier local correlation tracking method separately, we calculate velocity and vorticity of photospheric flows in the flaring NOAA AR 11158, and investigate their temporal evolution around the X2.2 flare on 2011 February 15. It is found that the shear flow around the flaring magnetic polarity inversion line exhibits a sudden decrease, and both of the two main sunspots undergo a sudden change in rotational motion during the impulsive phase of the flare. These results are discussed in the context of the Lorentz-force change that was proposed by Hudson et al. (2008) and Fisher et al. (2012). This mechanism can explain the connections between the rapid and irreversible photospheric vector magnetic field change and the observed short-term motions associated with the flare. In particular, the torque provided by the horizontal Lorentz force change agrees with what is required for the measured angular acceleration.

TWIST ACCUMULATION AND TOPOLOGY STRUCTURE OF A SOLAR MAGNETIC FLUX ROPE

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 UT with the differential affine velocity estimator for vector magnetic fields, which were observed by the Digital Vector Magnetograph at Big Bear Solar Observatory. The injected magnetic helicity is computed with the vector magnetic and velocity fields. The helicity injection rate was (-16.47 \pm 3.52) \times 10^{40} Mx^2/hr. We find that only about 1.8% of the injected magnetic helicity became finally the internal helicity of the magnetic flux rope, whose twist increasing rate was -0.18 \pm 0.08 Turns/hr. The quasi-separatrix layers (QSLs) of the three dimensional magnetic field are computed by evaluating the squashing degree, Q. We find that the flux rope was wrapped by QSLs with large Q values, where the magnetic reconnection induced by the continuously injected magnetic helicity further produced the confined flares. We suggest that the flux rope was built up and heated by the magnetic reconnection in the QSLs.

ON THE INJECTION OF HELICITY BY THE SHEARING MOTION OF FLUXES IN RELATION TO FLARES AND CORONAL MASS EJECTIONS

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 in the two active regions. The helicities injected in NOAA 11158 and 11166 during their six days' evolution period were estimated as $14.16\times10^{42}$Mx$^2$ and $9.5\times10^{42}$Mx$^2$, respectively. The estimated injection rates decreased up to 13% by increasing the time interval between the magnetograms from 12 min to 36 min, and increased up to 9% by decreasing the DAVE window size from $21\times18$ to $9\times6$ pixel$^2$, resulting in 10% variation in the accumulated helicity. In both ARs, the flare prone regions (R2) had inhomogeneous helicity flux distribution with mixed helicities of both signs and that of CME prone regions had almost homogeneous distribution of helicity flux dominated by single sign. The temporal profiles of helicity injection showed impulsive variations during some flares/CMEs due to negative helicity injection into the dominant region of positive helicity flux. A quantitative analysis reveals a marginally significant association of helicity flux with CMEs but not flares in AR 11158, while for the AR 11166, we found marginally significant association of helicity flux with flares but not CMEs, providing evidences of the role of helicity injection at localized sites of the events.

Horizontal Flows in the Photosphere and Subphotosphere of Two Active Regions

We compare horizontal flow fields in the photosphere and in the subphotosphere (a layer 0.5 Mm below the photosphere) in two solar active regions: AR 11084 and AR 11158. AR 11084 is a mature, simple active region without significant flaring activity, and AR 11158 is a multipolar, complex active region with magnetic flux emerging during the period studied. Flows in the photosphere are derived by applying the Differential Affine Velocity Estimator for Vector Magnetograms (DAVE4VM) on HMI-observed vector magnetic fields, and the subphotospheric flows are inferred by time–distance helioseismology using HMI-observed Dopplergrams. Similar flow patterns are found for both layers for AR 11084: inward flows in the sunspot umbra and outward flows surrounding the sunspot. The boundary between the inward and outward flows, which is slightly different in the photosphere and the subphotosphere, is within the sunspot penumbra. The area having inward flows in the subphotosphere is larger than that in the photosphere. For AR 11158, flows in these two layers show great similarities in some areas and significant differences in other areas. Both layers exhibit consistent outward flows in the areas surrounding sunspots. On the other hand, most well-documented flux-emergence-related flow features seen in the photosphere do not have counterparts in the subphotosphere. This implies that the horizontal flows caused by flux emergence do not extend deeply into the subsurface.

Velocity Characteristics of Rotating Sunspots

A statistical study is carried out to investigate the detailed relationship between rotating sunspots and the emergence of magnetic flux tubes. This paper presents the velocity characteristics of 132 sunspots in 95 solar active regions. The rotational characteristics of the sunspots are calculated from successive SOHO/MDI magnetograms by applying the Differential Affine Velocity Estimator (DAVE) technique (Schuck, 2006, Astrophys. J.646, 1358). Among 82 sunspots in active regions exhibiting strong flux emergence, 63 showed rotation with rotational angular velocity larger than 0.4° h−1. Among 50 sunspots in active regions without well-defined flux emergence, 14 showed rotation, and the rotation velocities tend to be slower, compared to those in emerging regions. In addition, we investigated 11 rotating sunspot groups in which both polarities show evidence for co-temporary rotation. In seven of these cases the two polarities co-rotate, while the other four are found to be counter-rotating. Plausible reasons for the observed characteristics of the rotating sunspots are discussed.

ON ASYMMETRY OF MAGNETIC HELICITY IN EMERGING ACTIVE REGIONS: HIGH-RESOLUTION OBSERVATIONS

We employ the DAVE (differential affine velocity estimator, Schuck 2005; 2006) tracking technique on a time series of MDI/1m high spatial resolution line- of-sight magnetograms to measure the photospheric flow velocity for three newly emerging bipolar active regions. We separately calculate the magnetic helicity injection rate of the leading and following polarities to confirm or refute the magnetic helicity asymmetry, found by Tian & Alexander (2009) using MDI/96m low spatial resolution magnetograms. Our results demonstrate that the magnetic helicity asymmetry is robust being present in the three active regions studied, two of which have an observed balance of the magnetic flux. The magnetic helicity injection rate measured is found to depend little on the window size selected, but does depend on the time interval used between the two successive magnetograms tracked. It is found that the measurement of the magnetic helicity injection rate performs well for a window size between 12x10 and 18x15 pixels, and at a time interval {\Delta}t=10 minutes. Moreover, the short-lived magnetic structures, 10-60 minutes, are found to contribute 30-50% of the magnetic helicity injection rate. Comparing with the results calculated by MDI/96m data, we find that the MDI/96m data, in general, can outline the main trend of the magnetic properties, but they significantly underestimate the magnetic flux in strong field region and are not appropriate for quantitative tracking studies, so provide a poor estimate of the amount of magnetic helicity injected into the corona.