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.

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.

Signature of high-order azimuthal MHD body modes in sunspot's low atmosphere

The five-minute oscillations inside sunspots appear to be the absorption of the solar p-mode. It is a potential tool to probe a sunspot＇s sub-structure. We studied the collective properties of five-minute oscillations in the power and phase distribution at the sunspot＇s umbra-penumbra boundary. The azimuthal distributions of the power and phase of five-minute oscillations enclosing a sunspot＇s umbra were obtained with images taken with the Solar Dynamics Observatory/Atmospheric Imaging Assembly （SDO/AIA）. The azimuthal modes were quantified with periodogram analysis and justified with significance tests. The azimuthal nodal structures in an approximately ax- ially symmetric sunspot AR 11131 （2010 Dec 08） were investigated. Mode numbers ra = 2, 3, 4, 7, 10 were obtained in both 1700 A and 1600A bandpasses. The 1600A channel also revealed an extra mode at m = 9. In the upper atmosphere （304 A）, fewer modes were detected at m = 3, 4, 7. The azimuthal modes in the sunspot＇s low atmo- sphere could be interpreted as high-order azimuthal MHD body modes. They were detected in the power and phase of the five-minute oscillations in sunspot AR 11131 with SDO/AIA data. Fewer modes were detected in the sunspot＇s upper atmosphere.

Latitudinal migration of sunspots based on the ESAI database

The latitudinal migration of sunspots toward the equator,which implies there is propagation of the toroidal magnetic flux wave at the base of the solar convection zone,is one of the crucial observational bases for the solar dynamo to generate a magnetic field by shearing of the pre-existing poloidal magnetic field through differential rotation.The Extended time series of Solar Activity Indices（ESAI）elongated the Greenwich observation record of sunspots by several decades in the past.In this study,ESAI＇s yearly mean latitude of sunspots in the northern and southern hemispheres during the years 1854 to 1985 is utilized to statistically test whether hemispherical latitudinal migration of sunspots in a solar cycle is linear or nonlinear.It is found that a quadratic function is statistically significantly better at describing hemispherical latitudinal migration of sunspots in a solar cycle than a linear function.In addition,the latitude migration velocity of sunspots in a solar cycle decreases as the cycle progresses,providing a particular constraint for solar dynamo models.Indeed,the butterfly wing pattern with a faster latitudinal migration rate should present stronger solar activity with a shorter cycle period,and it is located at higher latitudinal position,giving evidence to support the Babcock-Leighton dynamo mechanism.

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.

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.

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.

Local sunspot oscillations and umbral dots

Data analysis of sunspot oscillations based on a 6-hr SDO run of an observation showed that low frequency （0.2 〈ω 〈 1 mHz） oscillations are locally similar to three and five minute oscillations. The oscillations in the sunspot are concentrated in cells of a few arcsec, each of which has its own oscillation spectrum. The analysis of two scenarios for sunspot oscillations leads to a conclusion that local sunspot oscillations occur due to a subphotospheric resonator for slow MHD waves. Empirical models of a sunspot atmosphere and the theory of slow waves in thin magnetic flux tubes are applied to modeling the subphotospheric resonator. The spectrum of local oscillations consists of a great number of lines. This kind of spectrum can occur only if the subphotospheric resonator is a magnetic tube with a rather weak magnetic field. Magnetic tubes of this sort are umbral dots that appear due to the convective tongues in monolithic sunspots. The interrelation of local oscillations with umbral dots and wavefronts of traveling waves in sunspots is discussed.

An Electron Density Model above the Sunspot from a Mapping of NOAA 7260 at 17 GHz

The brightness temperature distribution of microwave emission in a solar active region generally shows a ring structure, with a dip at the centre. However, no dip was found in the Nobeyama Radioheliograph left handed circular polarization (LCP) image on 1992 August 18; instead, there was a peak. This is a completely LCP source with zero right-handed circular polarization (RCP). We examine this structure in terms of the joint effect of gyroresonance and bremsstrahlung mechanism with a raised electron density above the central part of the sunspot, and the commonly assumed temperature and vertical dipole magnetic field models. The raised electron density is found to be 1.4 × 1011 cm-3 at the chromosphere base.

What does the Sun tell and hint now?

Some historical records, which have held since the beginning of modern solar activity cycles, are being broken by the present Sun： cycle 23 records the longest cycle length and fall time; latitudes of high-latitude sunspots belonging to a new cycle around the minimum time of the cycle are statistically the lowest at present, compared with those of other cycles; there are only one or no sunspots in a month appearing at high latitudes for 58 months, which is the first time that such a long duration has been observed. The solar dynamo is believed to be slowing down due to： （1） the minimum smoothed monthly mean sunspot number is the smallest since cycle 16 onwards, and even probably among all modern solar cycles; and （2） once the time interval between the first observations of two neighboring sunspot groups is larger than 14 d, it should be approximately regarded as an observation of no sunspots on the visible solar disk, called a spotless event. Spotless events occur with the highest frequency around the minimum time of cycle 24, and the longest spotless event also appears around the minimum time for observations of the Sun since cycle 16. Cycle 24 is expected to have the lowest level of sunspot activity from cycle 16 onwards and even probably for all of the modern solar cycles.

Long-term evolution of magnetic fields in flaring Active Region NOAA 12673

During the lifetime of AR 12673,its magnetic field evolved drastically and produced numerous large flares.In this study,using full maps of the Sun observed by the Solar Dynamics Observatory and the Solar Terrestrial Relations Observatory,we identified that AR 12673 emerged in decayed AR 12665,which had survived for two solar rotations.Although both ARs emerged at the same location,they possessed different characteristics and different flare productivities.Therefore,it is important to study the long-term magnetic evolution of both ARs to identify the distinguishing characteristics of an AR that can produce large solar flares.We used the Space-weather Helioseismic and Magnetic Imager Active Region Patch data to investigate the evolution of the photospheric magnetic field and other physical properties of the recurring ARs during five Carrington rotations.All these investigated parameters dynamically evolved through a series of solar rotations.We compared the long-term evolution of AR 12665 and AR 12673 to understand the differences in their flare-producing properties.We also studied the relation of the long-term evolution of these ARs with the presence of active longitude.We found that the magnetic flux and complexity of AR12673 developed much faster than those of AR 12665.Our results confirmed that a strong emerging flux that emerged in the pre-existing AR near the active longitude created a very strong and complex AR that produced large flares.

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.

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.

Solar Magnetism and the Activity Telescope at HSOS

A new solar telescope system is described, which has been operating at Huairou Solar Observing Station （HSOS）, National Astronomical Observatories, Chinese Academy of Sciences （CAS）, since the end of 2005. This instrument, the Solar Magnetism and Activity Telescope （SMAT）, comprises two telescopes which respectively make measurements of full solar disk vector magnetic field and Ha observation. The core of the full solar disk video vector magnetograph is a birefringent filter with 0.1A bandpass, installed in the tele-centric optical system of the telescope. We present some preliminary observational results of the full solar disk vector magnetograms and Ha filtergrams obtained with this telescope system.

Calibration of Vector Magnetogram with the Nonlinear Least-squares Fitting Technique

To acquire Stokes profiles from observations of a simple sunspot with the Video Vector Magnetograph at Huairou Solar Observing Station (HSOS), we scanned the FeI λ5324.19 A line over the wavelength interval from 150mA redward of the line center to 150mA blueward, in steps of 10mA. With the technique of analytic inversion of Stokes profiles via nonlinear least-squares, we present the calibration coefficients for the HSOS vector magnetic magnetogram. We obtained the theoretical calibration error with linear expressions derived from the Unno-Becker equation under weak-field approximation.

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.

Observational Characteristics of Radio Emission Related to Multi-polar Magnetic Configuration

We present a large complex radio burst and its associated fast time structures observed on 2001 April 10 in the frequency range of 0.65-7.6 GHz. The NoRH radio image observation shows very complex radio source structures which include preexisting, newly emerging, submerging/cancelling polarities and a bipolar, a tripolar （a ＇bipolar ＋ remote unipolar＇）, and a quadrupolar structure. This suggests that the radio burst is generated from a very complicated loop structure. According to the spectral and image observations, we assume that the beginning of this flare was caused by a single bipolar loop configuration with a ‘Y-type＇ re- connection structure. A composite of radio continuum and fast time structures is contained in this flare. The various fast radio emission phenomena include normal and reverse drifting type Ⅲ bursts, and slowly drifting and no-drift structures. The tripolar configurations may form a double-loop with a ＇three-legged＇ struc- ture, which is an important source of the various types of fast time structures. The two-loop reconnection model can lead simultaneously to electron acceleration and corona heating. We have also analyzed the behaviors of coronal magnetic polarities and the emission processes of different types radio emission qualitatively. Interactions of a bipolar or multi-polar loop are consistent with our observational results. Our observations favor the magnetic reconnection configurations of the ‘inverted Y-type＇ （bipolar） and the ‘three-legged＇ structures （tripolar or quadrupo- lar）.

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.