Global Forces in Eruptive Solar Flares: The Lorentz Force Acting on the Solar Atmosphere and the Solar Interior

We compute the change in the Lorentz force integrated over the outer solar atmosphere implied by observed changes in vector magnetograms that occur during large, eruptive solar flares. This force perturbation should be balanced by an equal and opposite force perturbation acting on the solar photosphere and solar interior. The resulting expression for the estimated force change in the solar interior generalizes the earlier expression presented by Hudson, Fisher, and Welsch (Astron. Soc. Pac. CS-383, 221, 2008), providing horizontal as well as vertical force components, and provides a more accurate result for the vertical component of the perturbed force. We show that magnetic eruptions should result in the magnetic field at the photosphere becoming more horizontal, and hence should result in a downward (toward the solar interior) force change acting on the photosphere and solar interior, as recently argued from an analysis of magnetogram data by Wang and Liu (Astrophys. J. Lett. 716, L195, 2010). We suggest the existence of an observational relationship between the force change computed from changes in the vector magnetograms, the outward momentum carried by the ejecta from the flare, and the properties of the helioseismic disturbance driven by the downward force change. We use the impulse driven by the Lorentz-force change in the outer solar atmosphere to derive an upper limit to the mass of erupting plasma that can escape from the Sun. Finally, we compare the expected Lorentz-force change at the photosphere with simple estimates from flare-driven gasdynamic disturbances and from an estimate of the perturbed pressure from radiative backwarming of the photosphere in flaring conditions.     

Time-Dependent Stochastic Modeling of Solar Active Region Energy

A time-dependent model for the energy of a flaring solar active region is presented based on an existing stochastic jump-transition model (Wheatland and Glukhov in Astrophys. J. 494, 858, 1998; Wheatland in Astrophys. J. 679, 1621, 2008 and Solar Phys. 255, 211, 2009). The magnetic free energy of an active region is assumed to vary in time due to a prescribed (deterministic) rate of energy input and prescribed (random) jumps downwards in energy due to flares. The existing model reproduces observed flare statistics, in particular flare frequency – size and waiting-time distributions, but modeling presented to date has considered only the time-independent choices of constant energy input and constant flare-transition rates with a power-law distribution in energy. These choices may be appropriate for a solar active region producing a constant mean rate of flares. However, many solar active regions exhibit time variation in their flare productivity, as exemplified by NOAA active region (AR) 11029, observed during October – November 2009 (Wheatland in Astrophys. J. 710, 1324, 2010). Time variation is incorporated into the jump-transition model for two cases: (1) a step change in the rates of flare transitions, and (2) a step change in the rate of energy supply to the system. Analytic arguments are presented describing the qualitative behavior of the system in the two cases. In each case the system adjusts by shifting to a new stationary state over a relaxation time which is estimated analytically. The model exhibits flare-like event statistics. In each case the frequency – energy distribution is a power law for flare energies less than a time-dependent rollover set by the largest energy the system is likely to attain at a given time. The rollover is not observed if the mean free energy of the system is sufficiently large. For Case 1, the model exhibits a double exponential waiting-time distribution, corresponding to flaring at a constant mean rate during two intervals (before and after the step change), if the average energy of the system is large. For Case 2 the waiting-time distribution is a simple exponential, again provided the average energy of the system is large. Monte Carlo simulations of Case 1 are presented which confirm the estimate for the relaxation time and the expected forms of the frequency – energy and waiting-time distributions. The simulation results provide a qualitative model for observed flare statistics in AR 11029.     

The Free Energy of NOAA Solar Active Region AR 11029

The NOAA active region (AR) 11029 was a small but highly active sunspot region which produced 73 GOES soft X-ray flares during its transit of the disk in late October 2009. The flares appear to show a departure from the well-known power law frequency-size distribution. Specifically, too few GOES C-class and no M-class flares were observed by comparison with a power law distribution (Wheatland, Astrophys. J. 710, 1324, 2010). This was conjectured to be due to the region having insufficient magnetic energy to power the missing large events. We construct nonlinear force-free extrapolations of the coronal magnetic field of AR 11029 using data taken on 24 October by the SOLIS Vector SpectroMagnetograph (SOLIS/VSM) and data taken on 27 October by the Hinode Solar Optical Telescope SpectroPolarimeter (Hinode/SP). Force-free modeling with photospheric magnetogram data encounters problems, because the magnetogram data are inconsistent with a force-free model. We employ a recently developed “self-consistency” procedure which addresses this problem and accommodates uncertainties in the boundary data (Wheatland and Régnier, Astrophys. J. 700, L88, 2009). We calculate the total energy and free energy of the self-consistent solution, which provides a model for the coronal magnetic field of the active region. The free energy of the region was found to be ≈?4×10²⁹?erg on 24 October and ≈?7×10³¹?erg on 27 October. An order of magnitude scaling between RHESSI non-thermal energy and GOES peak X-ray flux is established from a sample of flares from the literature and is used to estimate flare energies from the observed GOES peak X-ray flux. Based on the scaling, we conclude that the estimated free energy of AR 11029 on 27 October when the flaring rate peaked was sufficient to power M-class or X-class flares; hence, the modeling does not appear to support the hypothesis that the absence of large flares is due to the region having limited energy.     

An Improved Approach to Non-Force-Free Coronal Magnetic Field Extrapolation

We develop an approach to deriving the three-dimensional non-force-free coronal magnetic field from vector magnetograms. Based on the principle of minimum dissipation rate, a general non-force-free magnetic field is expressed as the superposition of one potential field and two constant-α (linear) force-free fields. Each is extrapolated from its bottom boundary data, providing the normal component only. The constant-α parameters are distinct and determined by minimizing the deviations between the numerically computed and measured transverse magnetic field at the bottom boundary. The boundary conditions required are at least two layers of vector magnetograms, one at the photospheric level and the other at the chromospheric level, presumably. We apply our approach to a few analytic test cases, especially to two nonlinear force-free cases examined by Schrijver et al. (Solar Phys. 235, 161, 2006). We find that for one case with small α parameters, the quantitative measures of the quality of our result are better than the median values of those from a set of nonlinear force-free methods. The reconstructed magnetic-field configuration is valid up to a vertical height of the transverse scale. For the other cases, the results remain valid to a lower vertical height owing to the limitations of the linear force-free-field solver. Because our method is based on the fast-Fourier-transform algorithm, it is much faster and easy to implement. We discuss the potential usefulness of our method and its limitations.     

Quasi-periodic Oscillations of Solar Active Regions in Connection with Their Flare Activity – NoRH Observations

The sunspot-associated sources at the frequency of 17 GHz give information on plasma parameters in the regions of magnetic field about B=2000 G at the level of the chromosphere-corona transition region. The observations of short period (from one to ten minutes) oscillations in sunspots reflect propagation of magnetohydrodynamic (MHD) waves in the magnetic flux tubes of the sunspots. We investigate the oscillation parameters in active regions in connection with their flare activity. We confirm the existence of a link between the oscillation spectrum and flare activity. We find differences in the oscillations between pre-flare and post-flare phases. In particular, we demonstrate a case of powerful three-minute oscillations that start just before the burst. This event is similar to the cases of the precursors investigated by Sych et al. (Astron. Astrophys. 505, 791, 2009). We also found well-defined eight-minute oscillations of microwave emission from sunspot. We interpret our observations in terms of a relationship between MHD waves propagating from sunspots and flare processes.     

Study on Two Methods for Nonlinear Force-Free Extrapolation Based on Semi-Analytical Field

In this paper, two semi-analytical solutions of force-free fields (Low and Lou, Astrophys. J. 352, 343, 1990) have been used to test two nonlinear force-free extrapolation methods. One is the boundary integral equation (BIE) method developed by Yan and Sakurai (Solar Phys. 195, 89, 2000), and the other is the approximate vertical integration (AVI) method developed by Song et al. (Astrophys. J. 649, 1084, 2006). Some improvements have been made to the AVI method to avoid the singular points in the process of calculation. It is found that the correlation coefficients between the first semi-analytical field and extrapolated field using the BIE method, and also that obtained by the improved AVI method, are greater than 90% below a height 10 of the 64×64 lower boundary. For the second semi-analytical field, these correlation coefficients are greater than 80% below the same relative height. Although differences between the semi-analytical solutions and the extrapolated fields exist for both the BIE and AVI methods, these two methods can give reliable results for heights of about 15% of the extent of the lower boundary.     

On Signatures of Twisted Magnetic Flux Tube Emergence

Recent studies of NOAA active region 10953, by Okamoto et al. (Astrophys. J. Lett. 673, 215, 2008; Astrophys. J. 697, 913, 2009), have interpreted photospheric observations of changing widths of the polarities and reversal of the horizontal magnetic field component as signatures of the emergence of a twisted flux tube within the active region and along its internal polarity inversion line (PIL). A filament is observed along the PIL and the active region is assumed to have an arcade structure. To investigate this scenario, MacTaggart and Hood (Astrophys. J. Lett. 716, 219, 2010) constructed a dynamic flux emergence model of a twisted cylinder emerging into an overlying arcade. The photospheric signatures observed by Okamoto et al. (2008, 2009) are present in the model although their underlying physical mechanisms differ. The model also produces two additional signatures that can be verified by the observations. The first is an increase in the unsigned magnetic flux in the photosphere at either side of the PIL. The second is the behaviour of characteristic photospheric flow profiles associated with twisted flux tube emergence. We look for these two signatures in AR 10953 and find negative results for the emergence of a twisted flux tube along the PIL. Instead, we interpret the photospheric behaviour along the PIL to be indicative of photospheric magnetic cancellation driven by flows from the dominant sunspot. Although we argue against flux emergence within this particular region, the work demonstrates the important relationship between theory and observations for the successful discovery and interpretation of signatures of flux emergence.     

Vertical current and a 3B/X12 flare in a highly sheared active region (NOAA 6659) on June 9, 1991

NOAA active region 6659, during its June 1991 transit across the solar disk, showed highly sheared vector magnetic field structures and produced numerous powerful flares, including five white-light flares. Photospheric vector magnetograms of this active region were obtained at the Huairou Solar Observing Station of the Beijing Astronomical Observatory. After the resolution of the 180° ambiguity of the transverse magnetic field and transformation of off-center vector magnetograms to the heliographic plane, we have determined the photospheric vertical current density and discussed the relationship with powerful flares. The following results were obtained: (a) The powerful 3B/X12 flare on June 9, 1991 was triggered by the interaction between the large-scale electric current system and magnetic flux of opposite polarity. (b) The kernels of the powerful Hβ flare (sites of the white-light flare) were close to the peaks of the vertical electric current density. (c) Some small-scale structures of the vertical current relative to the magnetic islands of opposite polarity have not been found. This probably implies that the electric current is not always parallel to the magnetic field in solar active regions.     

Magnetofrictional Extrapolations of Low and Lou’s Force-Free Equilibria

We present a careful investigation of the magnetofrictional relaxation and extrapolation technique applied to the reconstruction of two test fields. These fields are taken from the family of nonlinear force-free magnetic equilibria constructed by Low and Lou (Astrophys. J. 352, 343, 1990), which have emerged as standard tests for extrapolation techniques in recent years. For the practically relevant case that only the field values in the bottom plane of the considered volume (vector magnetogram) are used as input information (i.e., not including the knowledge about the test field at the side and top boundaries), the test field is reconstructed to a higher accuracy than obtained previously. Detailed diagnostics of the reconstruction accuracy show that the implementation of fourth-order spatial discretization was essential to reach this accuracy for the given test fields and to achieve near machine precision in satisfying the solenoidal condition. Different variants of boundary conditions are tested, which all yield comparable accuracy. In its present implementation, the technique yields a scaling of computing time with total number of grid points only slightly below N ^5/3, which is too steep for applications to large (≥1024²) magnetograms, except on supercomputers. Directions for improvement are outlined.     

Short-Term Periodicities in Sunspot Activity and Flare Index Data during Solar Cycle 23

The short-term periodicities in sunspot numbers, sunspot areas, and flare index data are investigated in detail using the Date Compensated Discrete Fourier Transform (DCDFT) for the full disk of the Sun separately over the rising, the maximum, and the declining portions of solar cycle 23 (1996 – 2006). While sunspot numbers and areas show several significant periodicities in a wide range between 23.1 and 36.4 days, the flare index data do not exhibit any significant periodicity. The earlier conclusion of Pap, Tobiska, and Bouwer (1990, Solar Phys. 129, 165) and Kane (2003, J. Atmos. Solar-Terr. Phys. 65, 1169), that the 27-day periodicity is more pronounced in the declining portion of a solar cycle than in the rising and maximum ones, seems to be true for sunspot numbers and sunspot area data analyzed here during solar cycle 23.     

A Cross-Comparison of Cotemporal Magnetograms Obtained with MDI/SOHO and SP/<Emphasis Type="Italic">Hinode</Emphasis>

We compared a set of cotemporal magnetograms of active regions obtained with the Michelson Doppler Imager (MDI) aboard SOHO and the Spectro-Polarimeter (SP) of the Solar Optical Telescope (SOT) on board Hinode. The comparison shows that even with the recent calibration of level-1.8 data, the magnetic flux density derived from the MDI data is still lower than that obtained with SP. The average ratio between current version 2008 MDI level-1.8 data and SP magnetograms is 0.71, and is 0.82 for version 2007 MDI level-1.8 data. The comparison also shows that the most recent version 2008 calibration of MDI level-1.8 data has successfully removed the center-to-limb variation, while version 2007 level-1.8 data did not, as estimated by Ulrich et al. (Solar Phys. 255, 53, 2009).     

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.     

Structures of chromospheric magnetic field in the vicinity of the filament of active region 5669

In this paper, the chromospheric magnetic structures and their relation to the photospheric vector magnetic field in the vicinity of a dark filament in active region 5669 have been demonstrated. Structural variations are shown in chromospheric magnetograms after a solar flare. Filament-like structures in the chromospheric magnetograms occurred after a solar flare. They correspond to the reformation of the chromospheric dark filament, but there is no obvious variation of the photospheric magnetic field. We conclude that (a) some of the obvious changes of the chromospheric magnetic fields occurred after the flare, and (b) a part of these changes is perhaps due to flare brightening in the chromospheric H line.During the reforming process of the dark filament, a part of its chromospheric velocity field shows downward flow, and it later shows upward flow.     

Lorentz Force: A Possible Driving Force for Sunspot Rotation

Zhao and Kosovichev (Astrophys. J. 591, 446, 2003) found two opposite sub-photospheric vortical flows in the depth range of 0 – 12 Mm around a fast rotating sunspot. So far there is no theoretical model explaining such flow motions. In this paper, we try to explain this phenomenon from the point of view of magnetic flux tubes interacting with large-scale vortical motions of plasma. In the deeper zone under the photosphere, the magnetic force may be less than the nonmagnetic force of plasma. The vortical flow located there twists the flux tube and magnetic free energy is built up in the tube. In the shallower zone under the photosphere, the magnetic force may be greater than the nonmagnetic force. Thus, part of the stored magnetic free energy is released to drive the plasma to rotate in two opposite directions, e.g., in the depth ranges of 0 – 3(5) and 9 – 12 Mm. In addition, we also define a vector of nonpotential magnetic stress τ, which can be related to flare occurrence. It is calculated for the active region NOAA 10930 on 11 December 2006. We find that: i) the integral of its line-of-sight (LOS) stress successively increases around the magnetic neutral line (MNL) prior to and during the flare and decreases to a minimum after the flare; ii) the integral of its transverse stress exceeds the integral of its LOS component by one order of magnitude over the whole field of view; iii) the transverse stress first points toward the MNL, then along it, and finally it points away from it. We need other data to verify whether or not the magnetic energy is transported in the horizontal direction to the neutral line, and then partly changes into the energy in LOS direction before and during the flare.     

Coronal Magnetic Connectivity and EUV Dimmings

Coronal dimming can be considered to be a disk signature of front-side coronal mass ejections (CMEs) (Thompson et al.: 2000, Geophys. Res. Lett. 27, 1431). The study of the magnetic connectivity associated with coronal dimming can shed new light on the magnetic nature of CMEs. In this study, four major flare-CME events on 14 July 2000, 28 October 2003, 7 November 2004, and 15 January 2005 are analyzed. They were all halo CMEs associated with major flare activity in complex active regions (ARs) and produced severe space weather consequences. To explore the magnetic connectivity of these CMEs, global potential-field extrapolations based on the composite synoptic magnetograms from the Michelson Doppler Imager onboard the Solar and Heliospheric Observatory are constructed, and their association with coronal dimming is revealed by the Extreme ultraviolet Imaging Telescope. It is found that each flare-CME event involved interaction of more than ten sets of magnetic-loop systems. These loop systems occupied over 50% of all identified loop systems in the visible hemisphere and covered a wide range of solar longitudes and latitudes. We categorize the loop systems as active-region loops (ARLs), AR-interconnecting loops (ARILs) including transequatorial loops (TLs), and long arcades (LAs) straddling filament channels. A recurring pattern, the saddle-field configuration (SFC), consisting of ARILs, is found to be present in all four major flare-CME events. The magnetic connectivity revealed by this work implies that intercoupling and interaction of multiple flux-loop systems are required for a major CME. For comparison, a simple flare-CME event of 12 May 1997 with a relatively simple magnetic configuration is chosen. Even for this simple flare-CME event, we find that multiple flux-loop systems are also present.     

A Rate-Independent Test for Solar Flare Sympathy

Solar flare sympathy is the triggering of a flare in one active region by a flare in another. Statistical tests for flare sympathy have returned varying results. However, existing tests have relied on flaring rates in active regions being constant in time, or else have attempted to model the rate variation, which is a difficult task. A simple test is described which is independent of flaring rates. The test generalizes the approach of L. Fritzová-Švestkova, R.C. Chase, and Z. Švestka [Solar Phys. 48, 275, 1976], and examines the distribution of flare coincidences in pairs of active regions as a function of coincidence interval τ. The test is applied to available soft X-ray and Hα flare event listings. The soft X-ray events exhibit a deficit of flare coincidences for τ≤;20 min, which is most likely due to an event-selection effect whereby the increased soft X-ray emission due to one flare prevents a second flare being identified. The Hα events show an excess of flare coincidences for τ≤; 10 min, suggesting flare sympathy. The number of Hα event pairs occurring within 10 min of one another is higher than that expected on the basis of random coincidence by a fraction 0.12± 0.02. Nearby active regions (spatial separation <50˚) show a greater excess of coincidences for τ≤; 10 min than do active regions which are far apart (spatial separation ≥50˚). However, the active regions which are far apart still show some evidence for an excess of coincidences at very short coincidence intervals (τ≤; 2 min), which appears to exclude the possibility of a coronal disturbance propagating from one region to another.     

Physical State of the Photosphere at the Onset Phase of a Two-Ribbon Solar Flare

We study the physical state of the photosphere at about 30 minutes before and at the onset of a 2N/M2 two-ribbon solar flare. Semiempirical photospheric models are obtained for two Hα-kernels with the help of the SIR inversion code described by Ruiz Cobo and del Toro Iniesta (Astrophys. J. 398, 375, 1992). The models derived from the inversion reproduce spectral observations in seven Fraunhofer lines. The inferred models show variations in all photospheric parameters both before and at the onset of the flare relative to the quiet-Sun model. The temperature enhancement in the upper photospheric layers is found in the atmospheres in both kernels. The dynamical structure in the models reveals the variations at the onset of the flare relative to the preflaring ones. The inferred atmospheres show some difference in the thermodynamical parameters of two kernels.     

The Hinode X-Ray Telescope (XRT): Camera Design, Performance and Operations

The X-ray Telescope (XRT) aboard the Hinode satellite is a grazing incidence X-ray imager equipped with a 2048×2048 CCD. The XRT has 1 arcsec pixels with a wide field of view of 34×34 arcmin. It is sensitive to plasmas with a wide temperature range from < 1 to 30 MK, allowing us to obtain TRACE-like low-temperature images as well as Yohkoh/SXT-like high-temperature images. The spacecraft Mission Data Processor (MDP) controls the XRT through sequence tables with versatile autonomous functions such as exposure control, region-of-interest tracking, flare detection, and flare location identification. Data are compressed either with DPCM or JPEG, depending on the purpose. This results in higher cadence and/or wider field of view for a given telemetry bandwidth. With a focus adjust mechanism, a higher resolution of Gaussian focus may be available on-axis. This paper follows the first instrument paper for the XRT (Golub et al., Solar Phys. 243, 63, 2007) and discusses the design and measured performance of the X-ray CCD camera for the XRT and its control system with the MDP.     

Role of Sunspot and Sunspot-Group Rotation in Driving Sigmoidal Active Region Eruptions

We study active region NOAA 9684 (N06L285) which produced an X1.0/3B flare on November 4, 2001 associated with a fast CME (1810 km s⁻¹) and the largest proton event (31 700 pfu) in cycle 23. SOHO/MDI continuum image data show that a large leading sunspot rotated counter-clockwise around its umbral center for at least 4 days prior to the flare. Moreover, it is found from SOHO/MDI 96 m line-of-sight magnetograms that the systematic tilt angle of the bipolar active region, a proxy for writhe of magnetic fluxtubes, changed from a positive value to a negative one. This signifies a counter-clockwise rotation of the spot-group as a whole. Using vector magnetograms from Huairou Solar Observing Station (HSOS), we find that the twist of the active region magnetic fields is dominantly left handed (α_best = −0.03), and that the vertical current and current helicity are predominantly negative, and mostly distributed within the positive rotating sunspot. The active region exhibits a narrow inverse S-shaped H_α filament and soft X-ray sigmoid distributed along the magnetic neutral line. The portion of the filament which is most closely associated with the rotating sunspot disappeared on November 4, and the corresponding portion of the sigmoid was observed to erupt, producing the flare and initiating the fast CME and proton event. These results imply that the sunspot rotation is a primary driver of helicity production and injection into the corona. We suggest that the observed active region dynamics and subsequent filament and sigmoid eruption are driven by a kink instability which occurred due to a large amount of the helicity injection.