Investigation of Quasi-periodic Variations in Hard X-Rays of Solar Flares. II. Further Investigation of Oscillating Magnetic Traps

In our recent paper (Jakimiec and Tomczak, Solar Physics 261, 233, 2010) we investigated quasi-periodic oscillations of hard X-rays during the impulsive phase of solar flares. We have come to the conclusion that they are caused by magnetosonic oscillations of magnetic traps within the volume of hard-X-ray (HXR) loop-top sources. In the present paper we investigate four flares that show clear quasi-periodic sequences of the HXR pulses. We also describe our phenomenological model of oscillating magnetic traps to show that it can explain the observed properties of the HXR oscillations. The main results are the following: i) Low-amplitude quasi-periodic oscillations occur before the impulsive phase of some flares. ii) The quasi-periodicity of the oscillations can change in some flares. We interpret this as being due to changes of the length of oscillating magnetic traps. iii) During the impulsive phase a significant part of the energy of accelerated (non-thermal) electrons is deposited within a HXR loop-top source. iv) The quick development of the impulsive phase is due to feedback between the pressure pulses by accelerated electrons and the amplitude of the magnetic-trap oscillation. v) The electron number density and magnetic field strength values obtained for the HXR loop-top sources in several flares fall within the limits of N≈(2 – 15)×10¹⁰ cm⁻³, B≈(45 – 130) gauss. These results show that the HXR quasi-periodic oscillations contain important information about the energy release in solar flares.     

Observations of Double-Periodic X-Ray Emission in Interacting Systems of Solar Flare Loops

We investigate the M1.8 solar flare of 20 October 2002. The flare was accompanied by quasi-periodic pulsations (QPP) of both thermal and nonthermal hard X-ray emissions (HXR) observed by RHESSI in the 3?–?50 keV energy range. Analysis of the HXR time profiles in different energy channels made with the Lomb periodogram has indicated two statistically significant time periods of about 16 and 36 s. The 36 s QPP were observed only in the nonthermal HXR emission in the impulsive phase of the flare. The 16 s QPP were found in thermal and nonthermal HXR emission both in the impulsive and in the decay phases of the flare. Imaging analysis of the flare region, the determined time periods of the QPP, and the estimated physical parameters of the flare loops allowed us to interpret the observed QPP in terms of MHD oscillations excited in two spatially separated, but interacting systems of flaring loops.     

An Extreme Solar Event of 20 January 2005: Properties of the Flare and the Origin of Energetic Particles

The famous extreme solar and particle event of 20 January 2005 is analyzed from two perspectives. Firstly, using multi-spectral data, we study temporal, spectral, and spatial features of the main phase of the flare, when the strongest emissions from microwaves up to 200 MeV gamma-rays were observed. Secondly, we relate our results to a long-standing controversy on the origin of solar energetic particles (SEP) arriving at Earth, i.e., acceleration in flares, or shocks ahead of coronal mass ejections (CMEs). Our analysis shows that all electromagnetic emissions from microwaves up to 2.22 MeV line gamma-rays during the main flare phase originated within a compact structure located just above sunspot umbrae. In particular, a huge (≈ 10⁵ sfu) radio burst with a high frequency maximum at 30 GHz was observed, indicating the presence of a large number of energetic electrons in very strong magnetic fields. Thus, protons and electrons responsible for various flare emissions during its main phase were accelerated within the magnetic field of the active region. The leading, impulsive parts of the ground-level enhancement (GLE), and highest-energy gamma-rays identified with π ⁰-decay emission, are similar and closely correspond in time. The origin of the π ⁰-decay gamma-rays is argued to be the same as that of lower-energy emissions, although this is not proven. On the other hand, we estimate the sky-plane speed of the CME to be 2 000 – 2 600 km s⁻¹, i.e., high, but of the same order as preceding non-GLE-related CMEs from the same active region. Hence, the flare itself rather than the CME appears to determine the extreme nature of this event. We therefore conclude that the acceleration, at least, to sub-relativistic energies, of electrons and protons, responsible for both the major flare emissions and the leading spike of SEP/GLE by 07 UT, are likely to have occurred nearly simultaneously within the flare region. However, our analysis does not rule out a probable contribution from particles accelerated in the CME-driven shock for the leading GLE spike, which seemed to dominate at later stages of the SEP event. S.N. Kuznetsov deceased 17 May 2007.     

Relationship of great soft X-ray flares with other solar activity phenomena

We present study of relationship of GSXR flares with Hα flares, hard X-ray (HXR) bursts, microwave (MW) bursts at 15.4 GHz, type II/IV radio bursts, coronal mass ejections (CMEs), protons flares (>10 MeV) and ground level enhancement (GLE) events we find that about 85.7%, 93%, 97%, 69%, 60%, 11.1%, 79%, 46%, and 23%% GSXR flares are related/associated with observed Hα flares, HXR bursts, MW bursts at 15.4 GHz, type II radio bursts, type IV radio bursts, GLE events, CMEs, halo CMEs, and proton flares (>10 MeV), respectively. In the paper we have studied the onset time delay of GSXR flares with Hα flares, HXR, and MW bursts which shows the during majority GSXR flares SXR emissions start before the Hα, HXR and MW emissions, respectively while during 15–20% of GSXR flares the SXR emissions start after the onset of Hα, HXT and MW emissions, respectively indicating two types of solar flares. The, onset time interval between SXR emissions and type II radio bursts, type IV radio bursts, GLE events CMEs, halo CMEs, and protons flares are 1–15 min, 1–20 min, 21–30 min, 21–40 min, 21–40 min, and 1–4 hrs, respectively. Following the majority results we are of the view that the present investigations support solar flares models which suggest flare triggering first in the corona and then move to chromospheres/ photosphere to starts emissions in other wavelengths. The result of the present work is largely consistent with “big flare syndrome” proposed by Kahler (1982).     

Spatial and Spectral Behaviors of Solar Flares Observed in Microwaves

The spatial and spectral behaviors of two solar flares observed by the Nobeyama Radioheliograph (NoRH) on 24 August 2002 and 22 August 2005 are explored. They were observed with a single loop-top source and double footpoint sources at the beginning, then with looplike structures for the rest of the event. NoRH has high spatial and temporal resolution at the two frequencies of 17 and 34 GHz where a nonthermal radio source is often optically thin. Such capabilities give us an opportunity to study the spatial and spectral behaviors of different microwave sources. The 24 August 2002 flare displayed a soft – hard – soft (SHS) spectral pattern in the rising – peak – decay phases at 34 GHz, which was also observed for the spectral behavior of both loop-top and footpoint sources. In contrast, the 22 August 2005 flare showed a soft – hard – harder (SHH) spectral pattern for its both loop-top and footpoint sources. It is interesting that this event showed a harder spectrum in the early rising phase. We found a positive correlation between the spectral index and microwave flux in both the loop-top source and the footpoint sources in both events. The conclusions drawn from the flux index could apply to the electron index as well, because of their simple linear relationship under the assumption of nonthermal gyrosynchrotron mechanism. Such a property of spatial and spectral behaviors of microwave sources gives an observational constraint on the electron acceleration mechanism and electron propagation.     

Analysis of Magnetic Shear in An X17 Solar Flare on October 28, 2003

An X17 class (GOES soft X-ray) two-ribbon solar flare on October 28, 2003 is analyzed in order to determine the relationship between the timing of the impulsive phase of the flare and the magnetic shear change in the flaring region. EUV observations made by the Transition Region and Coronal Explorer (TRACE) show a clear decrease in the shear of the flare footpoints during the flare. The shear change stopped in the middle of the impulsive phase. The observations are interpreted in terms of the splitting of the sheared envelope field of the greatly sheared core rope during the early phase of the flare. We have also investigated the temporal correlation between the EUV emission from the brightenings observed by TRACE and the hard X-ray (HXR) emission (E > 150 keV) observed by the anticoincidence system (ACS) of the spectrometer SPI on board the ESA INTEGRAL satellite. The correlation between these two emissions is very good, and the HXR sources (RHESSI) late in the flare are located within the two EUV ribbons. These observations are favorable to the explanation that the EUV brightenings mainly result from direct bombardment of the atmosphere by the energetic particles accelerated at the reconnection site, as does the HXR emission. However, if there is a high temperature (T > 20 MK) HXR source close to the loop top, a contribution of thermal conduction to the EUV brightenings cannot be ruled out.     

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 Magnetic Structure and Generation of EUV Flare Ribbons

The `ribbons' of two-ribbon flares show complicated patterns reflecting the linkages of coronal magnetic field lines through the lower solar atmosphere. We describe the morphology of the EUV ribbons of the July 14, 2000 flare, as seen in SOHO, TRACE, and Yohkoh data, from this point of view. A successful co-alignment of the TRACE, SOHO/MDI and Yohkoh/HXT data has allowed us to locate the EUV ribbon positions on the underlying field to within ∼ 2′′, and thus to investigate the relationship between the ribbons and the field, and also the sites of electron precipitation. We have also made a determination of the longitudinal magnetic flux involved in the flare reconnection event, an important parameter in flare energetic considerations. There are several respects in which the observations differ from what would be expected in the commonly-adopted models for flares. Firstly, the flare ribbons differ in fine structure from the (line-of-sight) magnetic field patterns underlying them, apparently propagating through regions of very weak and probably mixed polarity. Secondly, the ribbons split or bifurcate. Thirdly, the amount of line-of-sight flux passed over by the ribbons in the negative and positive fields is not equal. Fourthly, the strongest hard X-ray sources are observed to originate in stronger field regions. Based on a comparison between HXT and EUV time-profiles we suggest that emission in the EUV ribbons is caused by electron bombardment of the lower atmosphere, supporting the hypothesis that flare ribbons map out the chromospheric footpoints of magnetic field lines newly linked by reconnection. We describe the interpretation of our observations within the standard model, and the implications for the distribution of magnetic fields in this active region.     

Relative Timing and Spectra of Solar Flare Hard X-ray Sources

Hard X-ray lightcurves, spectrograms, images, and spectra of three medium-sized flares observed by the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) are presented. Imaging spectroscopy of the 20 February 2002, 11:06 UT flare at 10′′ spatial resolution, comparable to the best previous hard X-ray imaging from Yohkoh, shows two footpoints with an ∼ 8 s delay of peak emission between footpoints. Subsequent imaging at le4′′ shows three sources consistent with two separate loops and simultaneous brightening in connected footpoints. Imaging for the simple two footpoint flare of 2 June 2002 also shows simultaneous footpoint brightening. The more complex 17 March 2002 flare shows at least four different sources during the main peak of the event, and it is difficult to clearly demonstrate simultaneous brightening of connected footpoints. Non-thermal power laws are observed down to ∼ 12–13 keV without flattening in all these events, indicating the energy content in energetic electrons may be significantly greater than previously estimated from assumed 25 keV low energy cutoff. Simultaneously brightening footpoints show similar spectra, at least in the three flares investigated. Double-power-law spectra with a relatively sharp break are often observed. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1022469902940     

Low-Energy Cutoffs in Electron Spectra of Solar Flares: Statistical Survey

The Reuven Ramaty High Energy Spectroscopic Imager (RHESSI) X-ray data base (February 2002 – May 2006) has been searched to find solar flares with weak thermal components and flat photon spectra. Using a regularized inversion technique, we determine the mean electron flux distribution from count spectra for a selection of events with flat photon spectra in the 15 – 20 keV energy range. Such spectral behavior is expected for photon spectra either affected by photospheric albedo or produced by electron spectra with an absence of electrons in a given energy range (e.g., a low-energy cutoff in the mean electron spectra of nonthemal particles). We have found 18 cases that exhibit a statistically significant local minimum (a dip) in the range of 13 – 19 keV. The positions and spectral indices of events with low-energy cutoff indicate that such features are likely to be the result of photospheric albedo. It is shown that if the isotropic albedo correction is applied, all low-energy cutoffs in the mean electron spectrum are removed, and hence the low-energy cutoffs in the mean electron spectrum of solar flares above ∼ 12 keV cannot be viewed as real features. If low-energy cutoffs exist in the mean electron spectra, their energies should be less than ∼ 12 keV.     

Type II Radio Bursts with High and Low Starting Frequencies

We report on the detailed analysis of i) differences between the properties of type IIs with various starting frequencies (high: ≥100 MHz; low: ≤50 MHz; mid: 50 MHz ≤f≤ 100 MHz) and ii) the properties of CMEs and flares associated with them. For this study, we considered a sample of type II radio bursts observed by Culgoora radio spectrograph from January 1998 to December 2000. The X-ray flares and CMEs associated with these events are identified using GOES and SOHO/LASCO data. The secondary aim is to study the frequency dependence on other properties of type IIs, flares, and CMEs. We found that the type IIs with high starting frequencies have larger drift rate, relative drift rate, and shock speed than the type IIs with low starting frequencies. The flares associated with high frequency type IIs are of impulsive in nature with shorter rise time, duration and delay between the flare start and type II start times than the low frequency type IIs. There is a distinct power – law relationship between the flare parameters and the starting frequencies of type II bursts, whereas the trend in the CME parameters shows low correlation. While the mean speed of CMEs is larger for the mid-frequency group, it is nearly the same for the high and low frequency groups. On the other hand, the percentage of CME association (90%) is larger for low frequency type IIs than for the high frequency type IIs (75%).     

Energy-Dependent Timing of Thermal Emission in Solar Flares

We report solar flare plasma to be multi-thermal in nature based on the theoretical model and study of the energy-dependent timing of thermal emission in ten M-class flares. We employ high-resolution X-ray spectra observed by the Si detector of the “Solar X-ray Spectrometer” (SOXS). The SOXS onboard the Indian GSAT-2 spacecraft was launched by the GSLV-D2 rocket on 8 May 2003. Firstly we model the spectral evolution of the X-ray line and continuum emission flux F(ε) from the flare by integrating a series of isothermal plasma flux. We find that the multi-temperature integrated flux F(ε) is a power-law function of ε with a spectral index (γ)≈−4.65. Next, based on spectral-temporal evolution of the flares we find that the emission in the energy range E=4 – 15 keV is dominated by temperatures of T=12 – 50 MK, while the multi-thermal power-law DEM index (δ) varies in the range of −4.4 and −5.7. The temporal evolution of the X-ray flux F(ε,t) assuming a multi-temperature plasma governed by thermal conduction cooling reveals that the temperature-dependent cooling time varies between 296 and 4640 s and the electron density (n _e) varies in the range of n _e=(1.77 – 29.3)×10¹⁰ cm⁻³. Employing temporal evolution technique in the current study as an alternative method for separating thermal from nonthermal components in the energy spectra, we measure the break-energy point, ranging between 14 and 21±1.0 keV.     

Are There Radio-quiet Solar Flares?

Some 15% of solar flares having a soft X-ray flux above GOES class C5 are reported to lack coherent radio emission in the 100 – 4000 MHz range (type I – V and decimetric emissions). A detailed study of 29 such events reveals that 22 (76%) of them occurred at a radial distance of more than 800″ from the disk center, indicating that radio waves from the limb may be completely absorbed in some flares. The remaining seven events have statistically significant trends to be weak in GOES class and to have a softer non-thermal X-ray spectrum. All of the non-limb flares that were radio-quiet above 100 MHz were accompanied by metric type III emission below 100 MHz. Out of 201 hard X-ray flares, there was no flare except near the limb (R>800″) without coherent radio emission in the entire meter and decimeter range. We suggest that flares above GOES class C5 generally emit coherent radio waves when observed radially above the source.     

Spectroscopic Properties of Dynamical Chromospheric Processes in a Confined Solar Flare

We present our results of high temporal resolution spectroscopic observation and study in Hα, Ca II, and He I lines for the 2B/M1.9 confined disk flare on September 9, 2001, combining with GOES soft X-ray (SXR) and Yohkoh hard X-ray (HXR) observations. Apparent redshifted and red-asymmetric profiles were observed in the initial phase. The redshift lasted until the late phase. The derived velocity depends on both the spectral line and the used method. The redshift velocities computed from the line centers of the observed emission profiles (υ₀) are of the order of 10 km s⁻¹ both inside and outside the streak area. However, the velocities determined from the excess profiles by the bisector method (υ) are larger in the streak (18–50 km s⁻¹). Both υ and the red full widths (RFWs) derived from the excess profiles show temporal variations similar to the HXR light-curve in the streak area. Moreover, the Hα line wings of nonthermal characteristics, the redshift velocities, and the lifetime of impulsive broadening suggest that the streak is related to nonthermal electron bombardment. Spectral simulations reveal that we cannot reproduce the observed profiles in the three lines simultaneously with a set of parameters, indicating that the flare atmosphere was not homogeneous along the line-of-sight. Most of the observed Hα profiles showed a ‘flat-top’ structure, implying the flare plasma was optically thick for this line. The electron temperatures (T_e) deduced from the line-center intensity of the three lines are similar and estimated to be higher than 7200 K. The obvious central reversal of the Hα profiles due to absorption of materials in the impulsive phase lasted more than 2 min. However, the far blue wings of the Ca II profiles in the impulsive phase showed low-intensity emission, which is suggestive of the existence of large turbulence or macroscopic motion (> 50 km s⁻¹), which is inconsistent with the current flare model.     

Origin of the Submillimeter Radio Emission During the Time-Extended Phase of a Solar Flare

Solar flares observed in the 200 – 400 GHz radio domain may exhibit a slowly varying and time-extended component which follows a short (few minutes) impulsive phase and can last for a few tens of minutes to more than one hour. The few examples discussed in the literature indicate that such long-lasting submillimeter emission is most likely thermal bremsstrahlung. We present a detailed analysis of the time-extended phase of the 27 October 2003 (M6.7) flare, combining 1 – 345 GHz total-flux radio measurements with X-ray, EUV, and Hα observations. We find that the time-extended radio emission is, as expected, radiated by thermal bremsstrahlung. Up to 230 GHz, it is entirely produced in the corona by hot and cool materials at 7 – 16 MK and 1 – 3 MK, respectively. At 345 GHz, there is an additional contribution from chromospheric material at a few 10⁴ K. These results, which may also apply to other millimeter–submillimeter radio events, are not consistent with the expectations from standard semiempirical models of the chromosphere and transition region during flares, which predict observable radio emission from the chromosphere at all frequencies where the corona is transparent.     

Simultaneous observations of second and sub-second time structures in H α , radio and hard X-ray data due to the periodical particle acceleration and MHD waves in the November 1, 2004 flare

Second and sub-second structures were simultaneously detected in optical, radio and hard X-ray (HXR) band, respectively by the GanYu Station of Purple Mountain Observatory, Nobeyama Radio Observatory, and RHESSI satellite in the November 1, 2004 flare (Ji et al., in Astrophys. J. 636:L173, 2006), which may be contributed to the energy transport of the continuous heat flux from the hot corona or chromosphere evaporation and of the accelerated electrons. The linear correlations between the amplitudes of these fluctuations and their flare emissions, and those between the cross-correlation coefficients of the fluctuations at two H _α kernels, or two radio frequencies, or two X-ray energies and their flare emissions may support the causal relationship of the flare and these time structures. While, the cross-correlations of the fluctuations at three different bands suggest that the fluctuations are caused by the common thermal or nonthermal processes in the flare. Moreover, some new features of the fluctuations are reported in the flare: (1) The sub-second fluctuations in radio and HXR bands have a same timescale, which is evidently larger than that in H-alpha band. The difference may be explained by the downward movements of nonthermal electrons or the upward motion of chromosphere evaporation. (2) The power-law distributions of the amplitudes of the second and the sub-second structures are obtained at optical, radio and HXR bands with different indices. (3) The peak-to-peak correspondence of Stokes I and V components in the sub-second structures at radio band suggests that they may be resulted from a periodical particle acceleration and particle injection in this event. However, the second structures may be caused by the modulations of Alfvén waves with an upward speed of 10³ km/s.     

The RHESSI Microflare Height Distribution

We present the first in-depth statistical survey of flare source heights observed by RHESSI. Flares were found using a flare-finding algorithm designed to search the 6 – 10 keV count-rate when RHESSI’s full sensitivity was available in order to find the smallest events (Christe et al. in Astrophys. J. 677, 1385, 2008). Between March 2002 and March 2007, a total of 25 006 events were found. Source locations were determined in the 4 – 10 keV, 10 – 15 keV, and 15 – 30 keV energy ranges for each event. In order to extract the height distribution from the observed projected source positions, a forward-fit model was developed with an assumed source height distribution where height is measured from the photosphere. We find that the best flare height distribution is given by g(h)∝exp (−h/λ) where λ=6.1±0.3 Mm is the scale height. A power-law height distribution with a negative power-law index, γ=3.1±0.1 is also consistent with the data. Interpreted as thermal loop-top sources, these heights are compared to loops generated by a potential-field model (PFSS). The measured flare heights distribution are found to be much steeper than the potential-field loop height distribution, which may be a signature of the flare energization process.     

Radio Observations of the 20 January 2005 X-class Flare

We present a multi-frequency and multi-instrument study of the 20 January 2005 event. We focus mainly on the complex radio signatures and their association with the active phenomena taking place: flares, CMEs, particle acceleration, and magnetic restructuring. As a variety of energetic-particle accelerators and sources of radio bursts are present, in the flare – ejecta combination, we investigate their relative importance in the progress of this event. The dynamic spectra of ARTEMIS-IV – Wind/Waves – HiRAS, with 2000 MHz – 20 kHz frequency coverage, were used to track the evolution of the event from the low corona to the interplanetary space; these were supplemented with SXR, HXR, and γ-ray recordings. The observations were compared with the expected radio signatures and energetic-particle populations envisaged by the Standard Flare – CME model and the reconnection outflow termination shock model. A proper combination of these mechanisms seems to provide an adequate model for the interpretation of the observational data.     

Homologous Flares and Magnetic Field Topology in Active Region NOAA 10501 on 20 November 2003

We present and interpret observations of two morphologically homologous flares that occurred in active region (AR) NOAA 10501 on 20 November 2003. Both flares displayed four homologous Hα ribbons and were both accompanied by coronal mass ejections (CMEs). The central flare ribbons were located at the site of an emerging bipole in the centre of the active region. The negative polarity of this bipole fragmented in two main pieces, one rotating around the positive polarity by ≈ 110° within 32 hours. We model the coronal magnetic field and compute its topology, using as boundary condition the magnetogram closest in time to each flare. In particular, we calculate the location of quasi-separatrix layers (QSLs) in order to understand the connectivity between the flare ribbons. Though several polarities were present in AR 10501, the global magnetic field topology corresponds to a quadrupolar magnetic field distribution without magnetic null points. For both flares, the photospheric traces of QSLs are similar and match well the locations of the four Hα ribbons. This globally unchanged topology and the continuous shearing by the rotating bipole are two key factors responsible for the flare homology. However, our analyses also indicate that different magnetic connectivity domains of the quadrupolar configuration become unstable during each flare, so that magnetic reconnection proceeds differently in both events.     

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.