Multiple cycles of magnetic activity in the Sun and Sun-like stars and their evolution

The wavelet transform method for high-quality time-frequency analysis is applied to sets of observations of relative sunspot numbers and stellar chromosphere fluxes of 10 Sun-like stars. Wavelet analysis of solar data shows that in a certain interval of time there are several cycles of activity with pe- riods of duration which vary considerably from each other： from quasi-biennial cycles to lO0-yr cycles. Cyclic activity was detected in almost all Sun-like stars that we examined, even those that previously were not considered as stars with cyclic activity according to analysis using a Scargle periodogram. The durations of solar and stellar cycles significantly change during the observation period.

A Confined Two-peaked Solar Flare Observed by EAST and SDO

The solar flare is one of the most violent explosions,and can disturb the near-Earth space weather.Except for commonly single-peaked solar flares in soft X-ray,some special flares show intriguing a two-peak feature that is deserved much more attentions.Here,we reported a confined two-peaked solar flare and analyzed the associated eruptions using high-quality observations from Educational Adaptive-optics Solar Telescope and Solar Dynamics Observatory.Before the flare,a magnetic flux rope(MFR)formed through partially tether-cutting reconnection between two sheared arches.The flare occurred after the MFR eruption that was confined by the overlying strong field.Interestingly,a small underlying filament immediately erupted,which was possibly destabilized by the flare ribbon.The successive eruptions were confirmed by the analysis of the emission measure and the reconnection fluxes.Therefore,we suggest that the two peaks of the confined solar flare are corresponding to two episodes of magnetic reconnection during the successive eruptions of the MFR and the underlying filament.

Evolution of the Level of Sunspot Activity in Solar Cycles I. Evolution in the Descending Phase

Taking the 13-point smoothed monthly sunspot number,Ri, and the deviation of the 13 associated monthly sunspot numbers from the smoothed one, Di, as a number-pair describing the global level of sunspot activity, the evolution of the level is statistically studied for the period from the month which is just 48 months before the minimum to the minimum in the descending phase, using the observed data of Solar Cycles 10 to 22. Our results show （1） for 46 months （94%） of the studied 49 months it is found that for a given month, the distribution of the 13 pairs which come from the 13 solar cycles on a log Ri - Di plane may be fitted by a straight line with a correlation coefficient larger than the critical one at confidence level a = 5%, and for 36 months （73%） the fitting is even better, for a = 1%; （2） time variations of these two parameters and their correlations in the studied period can be described respectively by functions of time, whose main trends may be expressed by a linear or simple curvilinear function; （3） the evolutionary path of the level of sunspot activity may be represented by a logarithmic function as log/~ = 0.704 lnDi - 0.291.

Evolution of a Long-lived Sunspot Group and Its Associated Solar-terrestrial Events

A long-lived sunspot group (AR9604) on the south hemisphere that lasted five solar rotations and produced some strong bursts is analyzed. The focus is on its evolving features. Its whole life was successfully maintained by four Emerging Flux Regions (EFRs). Apart from the one that lasted only a short time and did not produce any bursts, the other three EFRs have the following common features: (1) A positive writhe of magnetic flux tubes and a twist of the field lines of the same sign, indicating kink instability. (2) A clockwise rotation and a high tilt because the writhe was right-handed. (3) A compact 'island δ' structure of the sunspot group indicating concentrated kink instability. Since magnetic reconnection easily occurs at the kinked point of a very kink-unstable flux tube, these features should be the inducement of the strong bursts.

The causality between the rapid rotation of a sunspot and an X3.4 flare

Using multi-wavelength data of Hinode, the rapid rotation of a sunspot in active region NOAA 10930 is studied in detail. We found extraordinary counterclockwise rotation of the sunspot with positive polarity before an X3.4 flare. From a series of vector magnetograms, it is found that magnetic force lines are highly sheared along the neutral line accompanying the sunspot rotation. Furthermore, it is also found that sheared loops and an inverse S-shaped magnetic loop in the corona formed gradually after the sunspot rotation. The X3.4 flare can be reasonably regarded as a result of this movement. A detailed analysis provides evidence that sunspot rotation leads to magnetic field lines twisting in the photosphere. The twist is then transported into the corona and triggers flares.

The Role of Nuclei-Nuclei Interactions in the Production of Gamma-ray Lines in Solar Flares

Dramatic extensions of experimental possibilities (spacecraft RHESSI, CORONAS-F and others) in solar gamma-ray astronomy call for urgent, detailed theoretical consideration of a set of physical problems of solar activity and solar-terrestrial relationships that earlier may have only been outlined. Here we undertake a theoretical analysis of issues related to the production of gamma-radiation in the processes of interactions of energetic (accelerated) heavy and middle nuclei with the nuclei of the solar atmosphere (the so-called i-j interactions). We also make an estimate of the contribution of these interactions to the formation of nuclear and isotopic abundances of the solar atmosphere in the range of light and rare elements. The analysis is carried out for solar flares in the wide range of their intensities. We compare our theoretical estimates with RHESSI observations for the flare of 2002 July 23. It was shown that the 24Mg gamma-ray emission in this event was produced by the newly generated Mg nuclei. With a high probability, the gamma-ray line emission of 28Si nuclei from this flare was generated by the same processes.

Analysis of the coronal source of the partially limb-occulted flare on 2002 July 20

We carry out a detailed analysis of the X3.5 solar flare that occurred on 2002 July 20, which is the strongest partially limb-occulted flare ever observed by the RHESSI satellite. The main results are： （1） during the main impulsive phase that lasts ,-10 minutes, the motion of the thermal sources follows a U-shaped trajectory. Nonthermal sources move in a similar way, but in a series of larger zigzags. We further show that the non-thermal sources are actually leading the contraction motion. （2） During the main impulsive phase, X-ray sources at different energies continuously form a loop-like configuration, with the highest energy source （up to ,- 100 keV） and the lowest energy source （down to ,- 10 keV） being located at two ends. The entire loop-like configuration moves in a U-shaped trajectory, while keeping the order of descending energy from highest to lowest during motion. Two non-thermal hard X- ray sources with different energies are spatially well separated in the distribution. The unusual complexities of the X-ray emissions in the tenuous solar corona challenge interpretations using bremsstrahlung in a simple magnetic configuration.

Study of temporal and spectral characteristics of the X-ray emission from solar flares

Temporal and spectral characteristics of X-ray emission from 60 flares of intensity ≥C class observed by the Solar X-ray Spectrometer （SOXS） during 2003-2011 are presented. We analyze the X-ray emission observed in four and three energy bands by the Si and Cadmium-Zinc-Telluride （CZT） detectors, respectively. The number of peaks in the intensity profile of the flares varies between 1 and 3. We find moderate correlation （R ~=0.2） between the rise time and the peak flux of the first peak of the flare irrespective of energy band, which is indicative of its energy-independent nature. Moreover, the magnetic field complexity of the flaring region is found to be highly anti-correlated （R = 0.61） with the rise time of the flares while positively correlated （R = 0.28） with the peak flux of the flare. The time delay between the peak of the X-ray emission in a given energy band and that in 25-30keV decreases with increasing energy, suggesting conduction cooling is dominant in the lower energies. Analysis of 340 spectra from 14 flares reveals that the peak of differential emission measure （DEM） evolution is delayed by 60-360 s relative to that of the temperature, and this time delay is inversely proportional to the peak flux of the flare. We conclude that temporal and intensity characteristics of flares are dependent on energy as well as the magnetic field configuration of the active region.

A magnetic bald-patch flare in solar active region 11117

With SDO observations and a data-constrained magnetohydrodynamics （MHD） model, we identify a confined multi-ribbon flare that occurred on 2010 October 25 in solar active region 11117 as a magnetic bald patch （BP） flare with strong evidence. From the photospheric magnetic field observed by SDO/HMI, we find there are indeed magnetic BPs on the polarity inversion lines （PILs） which match parts of the flare ribbons. From the 3D coronal magnetic field derived from an MHD relaxation model constrained by the vector magnetograms, we find strikingly good agreement of the BP separatrix surface （BPSS） footpoints with the flare ribbons, and the BPSS itself with the hot flaring loop system. Moreover, the triggering of the BP flare can be attributed to a small flux emergence under the lobe of the BPSS, and the relevant change of coronal magnetic field through the flare is reproduced well by the pre-flare and post-flare MHD solutions, which match the corresponding pre- and post-flare AIA observations, respectively. Our work contributes to the study of non-typical flares that constitute the majority of solar flares but which cannot be explained by the standard flare model.

Study of white-light flares observed by Hinode

White-light flares are considered to be the most energetic flaring events that are observable in the optical broad-band continuum of the solar spectrum. They have not been commonly observed. Observations of white-light flares with sub-arcsecond resolution have been very rare. The continuous high resolution observations of Hinode provide a unique opportunity to systematically study the white-light flares with a spatial resolution around 0.2 arcsec. We surveyed all the flares above GOES magnitude C5.0 since the launch of Hinode in 2006 October. 13 of these kinds of flares were covered by the Hinode G-band observations. We analyzed the peak contrasts and equivalent areas （calculated via integrated excess emission contrast） of these flares as a function of the GOES X-ray flux, and found that the cut-off visibility is likely around M1 flares under the observing limit of Hinode. Many other observational and physical factors should affect the visibility of white-light flares; as the observing conditions are improved, smaller flares are likely to have detectable white-light emissions. We are cautious that this limiting visibility is an overestimate, because G-band observations contain emissions from the upper atmosphere. Among the 13 events analyzed, only the M8.7 flare of 2007 June 4 had near-simultaneous observations in both the G-band and the blue continuum. The blue continuum had a peak contrast of 94% vs. 175% in G-band for this event. The equivalent area in the blue continuum is an order of magnitude lower than that in the G-band. Very recently, Jess et al. studied a C2.0 flare with a peak contrast of 300% in the blue continuum. Compared to the events presented in this letter, that event is probably an unusual white-light flare： a very small kernel with a large contrast that can be detected in high resolution observations.

The Energetics of White-light Flares Observed by SDO/HMI and RHESSI

White-light （WL） flares have been observed and studied for more than a century since their first discovery. However, some fundamental physics behind the brilliant emission remains highly controversial. One of the important facts in addressing the flare energetics is the spatio-temporal correlation between the WL emission and the hard X-ray （HXR） radiation, presumably suggesting that energetic electrons are the energy sources. In this study, we present a statistical analysis of 25 strong flares （〉M5） observed simultaneously by the Helioseismic and Magnetic Imager （HMI）, on board the Solar Dynamics Observatory （SDO）, and the Reuven Ramaty High Energy Solar Spectroscopic lmager （RHESS1）. Among these events, WL emission was detected by SDO/HMI in 13 flares, associated with HXR emission. To quantitatively describe the strength of WL emission, equivalent area （EA） is defined as the integrated contrast enhancement over the entire flaring area. Our results show that the EA is inversely proportional to the HXR power-law index, indicating that stronger WL emission tends to be associated with a larger population of high energy electrons. However, no obvious correlation is found between WL emission and flux of non-thermal electrons at 50 keV. For the other group of 13 flares without detectable WL emission, the HXR spectra are softer （larger power-law index） than those flares with WL emission, especially for the X-class flares in this group.

Three-dimensional Distribution of the Escape Photons of Hα Flares

A technique for obtaining a three-dimensional distribution of received photons in Hα flares in the solar atmosphere is presented. It is well known that during flares hydrogen atoms in the chromosphere and photosphere are excited （even ionized） by the downward heating of non-thermal particles and then emit Hα photons. We trace back these Hα photons to their original layers by use of the contribution function in the theory of spectral line formation, and so acquire their three-dimensional （3D） distribution. This technique is applied to the two-ribbon flare of 2002 January 20. The atmospheric models are obtained by fitting the ＂quasi-profiles＂ with the help of the generally used model atmospheres. Since the variety of the 3D images reflects the response of the atmospheric layers to the impact of energy transport, an analysis of the development of the flare is given through a comparison of the 3D images with the 2D temperature distribution.

Application of a data-driven simulation method to the reconstruction of the coronal magnetic field

Ever since the magnetohydrodynamic （MHD） method for extrapolation of the solar coronal magnetic field was first developed to study the dynamic evolution of twisted magnetic flux tubes, it has proven to be efficient in the reconstruction of the solar coronal magnetic field. A recent example is the so-called data-driven simu- lation method （DDSM）, which has been demonstrated to be valid by an application to model analytic solutions such as a force-free equilibrium given by Low and Lou. We use DDSM for the observed magnetograms to reconstruct the magnetic field above an active region. To avoid an unnecessary sensitivity to boundary conditions, we use a classical total variation diminishing Lax-Friedrichs formulation to iteratively compute the full MHD equations. In order to incorporate a magnetogram consistently and sta- bly, the bottom boundary conditions are derived from the characteristic method. In our simulation, we change the tangential fields continually from an initial potential field to the vector magnetogram. In the relaxation, the initial potential field is changed to a nonlinear magnetic field until the MHD equilibrium state is reached. Such a stable equilibrium is expected to be able to represent the solar atmosphere at a specified time. By inputting the magnetograms before and after the X3.4 flare that occurred on 2006 December 13, we find a topological change after comparing the magnetic field before and after the flare. Some discussions are given regarding the change of magnetic con- figuration and current distribution. Furthermore, we compare the reconstructed field line configuration with the coronal loop observations by XRT onboard Hinode. The comparison shows a relatively good correlation.

Support Vector Machine combined with K-Nearest Neighbors for Solar Flare Forecasting

A method combining the support vector machine （SVM） the K-Nearest Neighbors （KNN）, labelled the SVM-KNN method, is used to construct a solar flare forecasting model. Based on a proven relationship between SVM and KNN, the SVM-KNN method improves the SVM algorithm of classification by taking advantage of the KNN algorithm according to the distribution of test samples in a feature space. In our flare forecast study, sunspots and 10cm radio flux data observed during Solar Cycle 23 are taken as predictors, and whether an M class flare will occur for each active region within two days will be predicted. The SVM- KNN method is compared with the SVM and Neural networks-based method. The test results indicate that the rate of correct predictions from the SVM-KNN method is higher than that from the other two methods. This method shows promise as a practicable future forecasting model.

Synthetic analysis of a two-ribbon microflare

High-resolution Stokes spectral data of Hα, Ca Ⅱ 8542A, and Fe 16302.5A lines for a two-ribbon microflare （TRMF） were simultaneously obtained by the THEMIS telescope on 2002 September 5. We derive the intensity, velocity, and longitudinal magnetic field maps. The hard X-ray emission observed by RHESSI provides evidence of nonthermal particle acceleration in the TRMF. Using Ha and Ca Ⅱ 8542A line profiles and a non-LTE calculation, we obtain semi-empirical atmospheric models for the two brightest kernels of the TRME Our result indicates that the temperature enhancement in the chromosphere is more than 2500 K. The kinetic and radiative energies at the kernels are also estimated, resulting in an estimate of the total energy of the TRMF of about 2.4×10^29 erg. Observations indicate that the TRMF results from the low coronal magnetic reconnection following the eruption of a small fila- ment. However, the local temperature ＂bump＂ in the chromosphere presents a puzzle for such a standard flare model. A possible solution to this is discussed.

Wavelet Analysis of Several Important Periodic Properties in the Relative Sunspot Numbers

We investigate the wavelet transform of yearly mean relative sunspot number series from 1700 to 2002. The curve of the global wavelet power spectrum peaks at 11-yr, 53-yr and 101-yr periods. The evolution of the amplitudes of the three periods is studied. The results show that around 1750 and 1800, the amplitude of the 53-yr period was much higher than that of the the 11-yr period, that the ca. 53-yr period was apparent only for the interval from 1725 to 1850, and was very low after 1850, that around 1750, 1800 and 1900, the amplitude of the 101-yr period was higher than that of the 11-yr period and that, from 1940 to 2000, the 11-yr period greatly dominates over the other two periods.

A comparison between magnetic shear and flare shear in a well-observed M-class flare

We give an extensive multi-wavelength analysis of an eruptive M1.0/1N class solar flare, which occurred in the active region NOAA 10044 on 2002 July 26. Our emphasis is on the relationship between magnetic shear and flare shear. Flare shear is defined as the angle formed between the line connecting the centroids of the two ribbons of the flare and the line perpendicular to the magnetic neutral line. The magnetic shear is computed from vector magnetograms observed at Big Bear Solar Observatory （BBSO）, while the flare shear is computed from Transition Region and Coronal Explorer （TRACE） 1700A images. By a detailed comparison, we find that; 1） The magnetic shear and the flare shear of this event are basically consistent, as judged from the directions of the transverse magnetic field and the line connecting the two ribbons＇ centroids. 2） During the period of the enhancement of magnetic shear, flare shear had a fast increase followed by a fluctuated decrease. 3） When the magnetic shear stopped its enhancement, the fluctuated decreasing behavior of the flare shear became very smooth. 4） Hard X-ray （HXR） spikes are well correlated with the unshearing peaks on the time profile of the rate of change of the flare shear. We give a discussion of the above phenomena.

Low Dimensional Chaos from the Group Sunspot Numbers

We examine the nonlinear dynamical properties of the monthly smoothed group sunspot number Rg and find that the solar activity underlying the time series of Rg is globally governed by a low-dimensional chaotic attractor. This finding is consistent with the nonlinear study results of the monthly Wolf sunspot numbers. We estimate the maximal Lyaponuv exponent （MLE） for the Rg series to be positive and to equal approximately 0.0187 ± 0.0023 （month^- 1）. Thus, the Lyaponuv time or predictability time of the chaotic motion is obtained to be about 4.46 ± 0.5 years, which is slightly different with the predictability time obtained from Rz. However, they both indicate that solar activity forecast should be done only for a short to medium term due to the intrinsic complexity of the time behavior concerned.

Short-term solar flare prediction using multi-model integration method

A multi-model integration method is proposed to develop a multi-source and heterogeneous model for short-term solar flare prediction. Different prediction models are constructed on the basis of extracted predictors from a pool of observation databases. The outputs of the base models are normal- ized first because these established models extract predictors from many data resources using different prediction methods. Then weighted integration of the base models is used to develop a multi-model integrated model （MIM）. The weight set that single models assign is optimized by a genetic algorithm. Seven base models and data from Solar and Heliospheric Observatory/Michelson Doppler Imager lon- gitudinal magnetograms are used to construct the MIM, and then its performance is evaluated by cross validation. Experimental results showed that the MIM outperforms any individual model in nearly every data group, and the richer the diversity of the base models, the better the performance of the MIM. Thus, integrating more diversified models, such as an expert system, a statistical model and a physical model, will greatly improve the performance of the MIM.

A Multi-Wavelength Study of the 3B/X1.2 Flare Observed on 2003 October 26

We report results from a multi-wavelength study of the 3B/X1.2 tworibbon disk flare （S15E44）, which was well observed by both ground-based and space-borne instruments. Two pairs of conjugate kernels - K1 and K4, and K2 and K3 - in the Ha images are identified. These kernels are linked by two different systems of EUV loops. K1 and K4 correspond to the two 17 GHz and 34 GHz microwave sources observed by the Nobeyama Radioheliograph （NoRH）, while K2 and K3 have no corresponding microwave sources. Optical spectroscopic observations suggest that all the four kernels are possible precipitating sites of non-thermal electrons. Thus the energy of electron deposited in K2 and K3 should be less than 100keV. Two-dimensional distributions of the full widths at half maximum （FWHM） of the Ha profiles and the line-of-sight （LOS） velocities derived from the Ca n 8542 A profiles indicate that the largest FWHM and LOS velocity tends to be located near the outer edges of Hα kernels, which is consistent with the scenario of current two-ribbon flare models and previous results. When non-thermal electron bombardment is present, the observed Hα and Ca II 8542 A profiles are similar to previous observational and theoretical results, while the He I 10830 A profiles are different from the theoretical ones. This puts some constraints on future theoretical calculation of the He I 10830 A line.