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It is a significant task to predict the solar activity for space weather and solar physics. All kinds of approaches have been used to forecast solar activities, and they have been applied to many areas such as the solar dynamo of simulation and space mission planning. In this paper, we employ the long-short-term memory (LSTM) and neural network autoregression (NNAR) deep learning methods to predict the upcoming 25th solar cycle using the sunspot area (SSA) data during the period of May 1874 to December 2020. Our results show that the 25th solar cycle will be 55% stronger than Solar Cycle 24 with a maximum sunspot area of 3115±401 and the cycle reaching its peak in October 2022 by using the LSTM method. It also shows that deep learning algorithms perform better than the other commonly used methods and have high application value.

Light bridges (LBs) are bright lanes that divide one sunspot umbra into two or more parts. Though frequently observed in sunspots, their formation mechanisms have rarely been studied and thus are not well understood. Here we present results from the first statistical investigation on the formation of LBs. Using observations with the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, we identified 144 LBs within 71 active regions (ARs) over the whole year of 2014. The formation processes of these LBs can be categorized into three groups: penumbral intrusion (type-A), sunspot merging (type-B) and umbral-dot emergence (type-C). The numbers of events in these three categories are 74, 57 and 13, respectively. The duration of the LB formation process is mostly less than 40 hours, with an average of ∼20 hours. Most LBs have a maximum length of less than 20″. For type-A LBs, we found a positive correlation between the LB length and the duration of the LB formation process, suggesting a similar speed of penumbral intrusion in different sunspots.

The solar wind is one of the main properties of the Sun which has a stream of charged particles released from the corona of the Sun. The study of this parameter has started in 1957 and there are a few models that related to prove how the solar wind could escape from the Sun’s gravity. In this paper, we choose the latest solar event that occurred on 16th October 2020 in this new 25th solar cycle. During these months, the Sun considered as active mode and the active region AR2776 potentially contributes high solar activities. Uniquely, a micro solar flare class B formed together with solar burst type II. A very intense flashing which also known as Ellerman bombs can be detected in the optical region. The sunspot number is only 14 and solar wind exceeds up to 306 kms -1 with a density of 4.0 protons/cm 3. We confirmed that AR2776 is a member of Solar Cycle 25.

Given the infrequency of extreme geomagnetic storms, it is significant to note the concentration of three extreme geomagnetic storms in 1941, whose intensities ranked fourth, twelfth, and fifth within the aa index between 1868–2010. Among them, the geomagnetic storm on 1941 March 1 was so intense that three of the four Dst station magnetograms went off scale. Herein, we reconstruct its time series and measure the storm intensity with an alternative Dst estimate (Dst*). The source solar eruption at 09:29–09:38 GMT on February 28 was located at RGO AR 13814 and its significant intensity is confirmed by large magnetic crochets of ∣35∣ nT measured at Abinger. This solar eruption most likely released a fast interplanetary coronal mass ejection with estimated speed 2260 km s^−1. After its impact at 03:57–03:59 GMT on March 1, an extreme magnetic storm was recorded worldwide. Comparative analyses on the contemporary magnetograms show the storm peak intensity of minimum Dst* ≤ −464 nT at 16 GMT, comparable to the most and the second most extreme magnetic storms within the standard Dst index since 1957. This storm triggered significant low-latitude aurorae in the East Asian sector and their equatorward boundary has been reconstructed as 38fdg5 in invariant latitude. This result agrees with British magnetograms, which indicate an auroral oval moving above Abinger at 53fdg0 in magnetic latitude. The storm amplitude was even more enhanced in equatorial stations and consequently casts caveats on their usage for measurements of the storm intensity in Dst estimates.

Quasi-biennial Oscillations (QBOs) of the Sun have a significant meaning as a benchmark of solar cycle, not only for understanding the dynamo action but also in terms of space weather prediction. In this paper, the hand-drawn sunspot images recorded from the Purple Mountain Observatory are used to investigate the solar QBOs and the Gnevyshev gap of the sunspot relative numbers (Rs) and group sunspot numbers (Rg) during the period 1954–2011. The main results are as follows: (1) both the Rs and Rg exhibit similar periods including the 22-year magnetic cycle, the 11-year Schwabe cycle, and the QBOs modes; (2) the reconstructed QBOs of both data sets exhibit coherent behavior and tend to have a high amplitude during the maximum phase of each solar cycle; (3) the Gnevyshev gap is produced by the superposition of the QBOs and the 11-year Schwabe cycle, and the Rs is better to study the variation of the Gnevyshev gap rather than the Rg.

It is well-known that there is a gradient, there will drive a flow inevitably. For example, a density-gradient may drive a diffusion flow, an electrical potential-gradient may drive an electric current in plasmas, etc. Then, what will be driven when a magnetic-gradient occurs in solar atmospheric plasmas? Considering the ubiquitous distribution of magnetic-gradient in solar plasma loops, this work demonstrates that magnetic-gradient pumping (MGP) mechanism is valid even in the partial ionized solar photosphere, chromosphere as well as in the corona. It drives energetic particle flows which carry and convey kinetic energy from the underlying atmosphere to move upwards, accumulate around the looptop and increase there temperature and pressure, and finally lead to eruptions around the looptop by triggering ballooning instabilities. This mechanism may explain the formation of the observing hot cusp-structures above flaring loops in most preflare phases, therefore, the magnetic-gradient should be a natural driver of solar eruptions. Furthermore, we may also apply to understand many other astrophysical phenomena, such as the temperature distribution above sunspots, the formation of solar plasma jets, type-II spicule, and fast solar wind above coronal holes, as well as the fast plasma jets related to white dwarfs, neutron stars and black holes., Comment: 16 pages, 7 figures, 2 tables, accepted by RAA

The differential rotation is the difference in the rate of rotation of each latitude in the Sun indicating that the Sun is not a solid body. The differential rotation is the result of the interaction between rotation and convection and causes dynamo circulation that affects the cycle of solar activity. In this research, we measured the coordinates of 304 sunspots umbra as tracer in the rising phase of the Solar Cycle 24 to obtain the differential rotation equation. Coordinates of sunspots were measured using AIA images at a wavelength of 4500 Å from SDO (Solar Dynamic Observatory) with JHelioviewer software. The areas of sunspots were measured using HMI (Helioseismic Magnetic Imager) images with ImageJ software. From the measurement, we derived the differential rotation equation and the relation of sidereal rotation and area of sunspots umbra. The differential rotation equation obtained in this research is ω(B) = (14.27 ± 0.01) - (0.78 ± 0.10) sin2B (°/day). There is a difference between the differential rotation equation of the northern and southern hemispheres that indicates the asymmetry between different hemispheres. We got the sidereal rotation of sunspots with area < 5 MH is 0.70% higher than sunspots with area > 15 MH.

Sunspots are the most striking and easily observed magnetic structures of the Sun, and statistical analysis of solar historical data could reveal a wealth of information on the long-term variation of solar activity cycle. The hand-drawn sunspot records of Yunnan Observatories, Chinese Academy of Sciences have been accumulating for more than 60 years, and nearly 16 000 images have been preserved. In the future, the observation mode of recording sunspots by hand-drawing will be replaced inevitably by digital images observed either at ground or in space. To connect the hand-drawn sunspot data and the purely digital sunspot data in future, it is necessary to analyze the systematic errors of the data which are observed by the two observation modes in the period of transition. In this paper, we choose 268 round sunspots (H-type in modified Zurich sunspot classification) from the drawing of Yunnan Observatories to compare their positions and areas with the CCD observations made by Helioseismic and Magnetic Imager (HMI) on board Solar Dynamic Observatory (SDO) and Global Oscillation Network Group (GONG). We find that the latitude and longitude accuracy of hand-drawn sunspot are within −0.127 and 2.29 degree respectively, and the area accuracy is about 16.36 sunspot unit (μHem). Systematic errors apparently decrease with large sunspot.

Predictions of the strength of solar cycles are important and are necessary for planning long-term missions. A new solar cycle 25 is coming soon, and the amplitude is needed for space weather operators. Some predictions have been made using differentmethods and the values are drastically different. However, since 2015 July 1, the original sunspot number data have been entirely replaced by the Version 2.0 data series, and the sunspot number values have changed greatly. In this paper, using Version 2 smoothed sunspot numbers and aa indices, we verify the predictions for cycles 18–24 based on Ohl’s PrecursorMethod. Then a similar-cycles method is used to evaluate the aa minimum of 9.7 (±1.1) near the start of cycle 25 and based on the linear regression relationship between sunspot maxima and aa minima, our predicted Version 2 maximum sunspot number for cycle 25 is 121.5 (±32.9).

We test recent claims that the polar field at the end of Cycle 23 was weakened by a small number of large, abnormally oriented regions, and investigate what this means for solar cycle prediction. We isolate the contribution of individual regions from magnetograms for Cycles 21, 22 and 23 using a 2D surface flux transport model, and find that although the top ~10% of contributors tend to define sudden large variations in the axial dipole moment, the cumulative contribution of many weaker regions cannot be ignored. In order to recreate the axial dipole moment to a reasonable degree, many more regions are required in Cycle 23 than in Cycles 21 and 22 when ordered by contribution. We suggest that the negative contribution of the most significant regions of Cycle 23 could indeed be a cause of the weak polar field at the following cycle minimum and the low-amplitude Cycle 24. We also examine the relationship between a region's axial dipole moment contribution and its emergence latitude, flux, and initial axial dipole moment. We find that once the initial dipole moment of a given region has been measured, we can predict the long-term dipole moment contribution using emergence latitude alone., 15 pages, 10 figures, accepted for publication in ApJ

This paper focuses on the study of active region (AR) 486 from the 171 Å wavelength in conjunction with solar radio burst data from the e-CALLISTO. This active region produced quite a strong solar flare with the X 17 class on 28th October 2003. The intense solar flare was detected by the CALLISTO system as the type III solar burst. Another data for this study were collected from the online database of Solar Monitor and Space Weather Live website where they provided the data from NOAA and SDO/AIA publicly. The study of the solar flare event was done by observing the sunspot for the past six days to see the changes in the magnetic field of the active region 486 and compared it to the solar radio data for the nature of the solar flares. The active region 486 alone had a sunspot number of 74 which is quite high, hence it produced a flare with the solar wind speed of 800 km/s and a solar radio burst type III with the storm type. The frequency drift rate for the solar burst was 2.15 MHz/s which proved that this type III is a fast drift burst. It was also recorded that the coronal mass ejection followed this solar flare event with the speed of nearly 2000 km/s and directed toward the Earth which then produced intense geomagnetic storm on the Earth the next day.

EUV cyclones are rotating structures in the solar corona, and they are usually rooted in the underlying rotating network magnetic fields in the photosphere. However, their connection with the surrounding magnetic fields remains unknown. Here we report an observational study of four typical cyclones which are rooted in different kinds of magnetic fields. We use Solar Dynamics Observatory /Atmospheric Imaging Assembly data to investigate the rotation of EUV features in cyclones and Helioseismic and Magnetic Imager data to study the associated magnetic fields. The results show that, (1) an EUV cyclone rooted in a sunspot rotates with the photospheric magnetic field; (2) two EUV cyclones in two faculae of an active region are connected to the same sunspot of the active region but rotate oppositely; (3) an EUV cyclone is rooted in a coronal hole with weak open magnetic fields; (4) a pair of conjugated cyclones is rooted in magnetic fields that have opposite polarity with opposite directions of rotation. The differences in the spatial extent of a cyclone, characteristics of its rotation and underlying fields indicate that cyclones are ubiquitous over the solar atmosphere and that the magnetic structures relevant to the cyclones are more complicated than expected.

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 axially symmetric sunspot AR 11131 (2010 Dec 08) were investigated. Mode numbers m = 2, 3, 4, 7, 10 were obtained in both 1700 A and 1600 A bandpasses. The 1600 A 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 atmosphere 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.

Solar conventional adaptive optics (CAO) with one deformable-mirror uses a small field-of-view (FOV) for wave-front sensing, which yields a small corrected FOV for high-resolution imaging. Solar activities occur in a two-dimensional extended FOV and studies of solar magnetic fields need high-resolution imaging over a FOV at least 60''. Recently, solar Tomography Adaptive Optics (TAO) and Multi-Conjugate Adaptive Optics (MCAO) were being developed to overcome this problem of small AO corrected FOV. However, for both TAO and MCAO, wavefront distortions need to be tomographically reconstructed from measurements on multiple guide stars, which is a complicated and time-consuming process. Solar Ground-Layer Adaptive Optics (S-GLAO) uses one or several guide stars, and does not rely on a tomographic reconstruction of the atmospheric turbulence. In this publication, we present two unique wavefront sensing approaches for the S-GLAO. We show that our S-GLAO can deliver good to excellent performance at variable seeing conditions in the Near Infrared (NIR) J and H bands, and is much simpler to implement. We discuss details of our S-GLAO associated wavefront approaches, which make our S-GLAO a unique solution for sunspot high-resolution imaging that other current adaptive optics systems, including the solar MCAO, cannot offer.

This paper reviews the studies of solar photospheric magnetic field evolution in active regions and its relationship to solar flares. It is divided into two topics, the magnetic structure and evolution leading to solar eruptions and rapid changes in the photospheric magnetic field associated with eruptions. For the first topic, we describe the magnetic complexity, new flux emergence, flux cancelation, shear motions, sunspot rotation and magnetic helicity injection, which may all contribute to the storage and buildup of energy that trigger solar eruptions. For the second topic, we concentrate on the observations of rapid and irreversible changes of the photospheric magnetic field associated with flares, and the implication on the restructuring of the three-dimensional magnetic field. In particular, we emphasize the recent advances in observations of the photospheric magnetic field, as state-of-the-art observing facilities (such as Hinode and Solar Dynamics Observatory ) have become available. The linkages between observations, theories and future prospectives in this research area are also discussed.

We present properties of intensity oscillations of a sunspot in the photosphere and chromosphere using G band and Ca II H filtergrams from Hinode . Intensity power maps as function of magnetic field strength and frequency reveal reduction of power in the G band with an increase in photospheric magnetic field strength at all frequencies. In Ca II H, however, stronger fields exhibit more power at high frequencies, particularly in the 4.5–8.0 mHz band. Power distributions in different locations of the active region show that the oscillations in Ca II H exhibit more power compared to that of the G band. We also relate the power in intensity oscillations with different components of the photospheric vector magnetic field using near simultaneous spectro-polarimetric observations of the sunspot from the Hinode spectropolarimeter. The photospheric umbral power is strongly anti-correlated with the magnetic field strength and its line-of-sight component but there is a good correlation with the transverse component. A reversal of this trend is observed in the chromosphere except at low frequencies ( ν ≤ 1.5 mHz). The power in sunspot penumbrae is anti-correlated with the magnetic field parameters at all frequencies (1.0 ≤ ν ≤ 8.0 mHz) in both the photosphere and chromosphere, except that the chromospheric power shows a strong correlation in the frequency range 3 – 3.5 mHz.

We aim to numerically study evolution of Alfv e n waves that accompany short-lasting swirl events in a solar magnetic flux-tube that can be a simple model of a magnetic pore or a sunspot. With the use of the FLASH code we numerically solve three-dimensional ideal magnetohydrodynamic equations to simulate twists which are implemented at the top of the photosphere in magnetic field lines of the flux-tube. Our numerical results exhibit swirl events and Alfv e n waves with associated clockwise and counterclockwise rotation of magnetic lines, with the largest values of vorticity at the bottom of the chromosphere, and a certain amount of energy flux.

Penumbrae are the manifestation of magnetoconvection in highly inclined (to the vertical direction) magnetic field. The penumbra of a sunspot tends to form, initially, along the arc of the umbra antipodal to the main region of flux emergence. The question of how highly inclined magnetic field can concentrate along the antipodal curves of umbrae, at least initially, remains to be answered. Previous observational studies have suggested the existence of some form of overlying magnetic canopy which acts as the progenitor for penumbrae. We propose that such overlying magnetic canopies are a consequence of how the magnetic field emerges into the atmosphere and are, therefore, part of the emerging region. We show, through simulations of twisted flux tube emergence, that canopies of highly inclined magnetic field form preferentially at the required locations above the photosphere., Accepted for ApJL

The morphological asymmetry of leading and following sunspots is a well-known characteristic of the solar surface. In the context of large-scale evolution of the surface magnetic field, the asymmetry has been assumed to have only a negligible effect. Using the surface flux transport model, we show that the morphological asymmetry of leading and following sunspots has a significant impact on the evolution of the large-scale magnetic field on the solar surface. By evaluating the effect of the morphological asymmetry of each bipolar magnetic region (BMR), we observe that the introduction of the asymmetry in the BMR model significantly reduces its contribution to the polar magnetic field, especially for large and high-latitude BMRs. Strongly asymmetric BMRs can even reverse the regular polar field formation. The surface flux transport simulations based on the observed sunspot record shows that the introduction of the morphological asymmetry reduces the root-mean-square difference from the observed axial dipole strength by 30--40 percent. These results indicate that the morphological asymmetry of leading and following sunspots has a significant effect on the solar cycle prediction., 21 pages, 11 figures, accepted for publication in ApJ

The differential rotation is the result of the interaction between rotation and convection and causes dynamo circulation that affect the cycle of solar activity. Tracer method using features in the photosphere such as sunspot is a simple method to measure the differential rotation. In this study, 98 individual sunspots on January 8 - 22, 2013 and August 25 - September 7, 2013 were used to measure the differential rotation of the Sun. The Sun’s continuum images were obtained from HMI (Helioseismic Magnetic Imager) instrument at SDO (Solar Dynamic Observatory). Coordinate and area of sunspot were measured using ImageJ software and converted to Carrington coordinates. From the measurement, we derived the differential rotation equation, the relation of velocity and area of sunspot, and the relation of sunspot’s velocity and Zurich classification. The differential rotation equation obtained in this study is ω (B) = (14.376 ± 0.04) + (0.6 ± 0.38) sin2B (°/day). For the relation between velocity and area of sunspot, we got the sidereal rotation rate of sunspots with area < 100 pixels2 is about 0.8% higher than sunspots with area > 100 pixels2.

Two primary solar-activity indicators− sunspot numbers (SNs) and sunspot areas (SAs) in the time interval from November 1874 to December 2012 − are used to determine the chaotic and fractal properties of solar activity. The results show that (1) the long-term solar activity is governed by a low-dimensional chaotic strange attractor, and its fractal motion shows a long-term persistence on large scales; (2) both the fractal dimension and maximal Lyapunov exponent of SAs are larger than those of Sns, implying that the dynamical system of SAs is more chaotic and complex than SNs; (3) the predictions of solar activity should only be done for short- to mid-term behaviors due to its intrinsic complexity; moreover, the predictability time of SAs is obviously smaller than that of SNs and previous results.

Wavelet analysis is becoming more popular in geophysics. It is used for numerous researches, including tropical convection, the El Nino-Southern Oscillation, atmospheric cold fronts, temperature variations, the dispersion of ocean waves, and coherent structures in turbulent flows, number of sunspots etc. In this paper we research how informative is the application of wavelet analysis to the analysis of geomagnetic field variations at the mid-latitude observatory "Mikhnevo" of Institute of Geosphere Dynamics of Russian Academy of Science. We review continuous wavelet transform by focusing attention on such aspects as choice of mother wavelet, choice of scales, cone of influence, visualization of results, reconstruction of time series from wavelet transform and its application to estimate the Holder exponents and singularity spectra. In our work we use Morlet wavelet with frequency parameter of 6. In so doing, the reconstruction of the time series from the wavelet transform has a mean square error of 3.4%. The application of wavelet analysis made it possible to distinguish pronounced periodicities of the geomagnetic field with periods of 27, 13.5, 9, 6 days. In solar quiet-day variations is dominated by the 24- 12-, 8-, and 6-hour period components. An analysis of the modulus of the wavelet transform coefficients qualitatively indicates a scaling (close to the monofractal) character of the variations of the geomagnetic field in the diurnal range. Moreover, the intensity of periodic variations of geomagnetic variation isn't constant in time. The application of the method of wavelet transform modulus maxima confirmed the monofractal character of the diurnal variation for any solar activity. In contrast to the 1-day variation, the 27-day variation and its harmonics show a higher degree of multifractality during a maximum of solar activity in comparison with the minimum of solar activity.

It is widely believed that the evolution of solar active regions leads to solar flares. However, information about the evolution of solar active regions is not employed in most existing solar flare forecasting models. In the current work, a short-term solar flare forecasting model is proposed, in which sequential sunspot data, including three days of information about evolution from active regions, are taken as one of the basic predictors. The sunspot area, the McIntosh classification, the magnetic classification and the radio flux are extracted and converted to a numerical format that is suitable for the current forecasting model. Based on these parameters, the sliding-window method is used to form the sequential data by adding three days of information about evolution. Then, multi-layer perceptron and learning vector quantization are employed to predict the flare level within 48 h. Experimental results indicate that the performance of the proposed flare forecasting model works better than previous models.

We examine the solar cycle distribution of major geomagnetic storms (Dst ≤ − 100 nT), including intense storms at the level of −200 nT < Dst ≤ −100 nT, great storms at −300 nT< Dst ≤ −200 nT, and super storms at Dst ≤ −300 nT, which occurred during the period of 1957-2006, based on Dst indices and smoothed monthly sunspot numbers. Statistics show that the majority (82%) of the geomagnetic storms at the level of Dst ≤ −100 nT that occurred in the study period were intense geomagnetic storms, with 12.4% ranked as great storms and 5.6% as super storms. It is interesting to note that about 27% of the geomagnetic storms that occurred at all three intensity levels appeared in the ascending phase of a solar cycle, and about 73% in the descending one. Statistics also show that 76.9% of the intense storms, 79.6% of the great storms and 90.9% of the super storms occurred during the two years before a solar cycle reached its peak, or in the three years after it. The correlation between the size of a solar cycle and the percentage of major storms that occurred, during the period from two years prior to maximum to three years after it, is investigated. Finally, the properties of the multi-peak distribution for major geomagnetic storms in each solar cycle is investigated.

Solar rotation rates can be measured from changes in sunspot positions. In this paper, we propose using digital camera images taken with small telescopes to determine the solar rotation rate at different heliographic latitudes. This low-cost practical experiment can be performed easily by undergraduate students, introducing them to topics related to solar physics. The data obtained in this work from the analysis of sunspots observed in 2010, 2011 and 2012 were compared with current models of solar rotation, showing good agreement.

The magnetic non-potentiality is important for understanding flares and other solar activities in active regions (ARs). Five non-potential parameters, i.e., electric current, current helicity, source field, photospheric free energy, and angular shear, are calculated in this work to quantify the non-potentiality of NOAA AR 11158. Benefited from high spatial resolution, high cadence, and continuously temporal coverage of vector magnetograms from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, both the long-term evolution of the AR and the rapid change during flares have been studied. We confirmed that, comparing with the magnetic flux, the magnetic non-potentiality has a closer connection with the flare, and the emerging flux regions are important for the magnetic non-potentiality and flares. The main results of this work are as follows. (1) The vortex in the source field directly displays the deflection of horizontal magnetic field. The deflection is corresponding to the fast rotated sunspot with a time delay, which suggests that the sunspot rotation leads to an increase of the non-potentiality. (2) Two areas that have evident changes of the azimuth of the vector magnetic field are found near the magnetic polarity inversion line. The change rates of the azimuth are about 1.3 deg/h and 3.6 deg/h, respectively. (3) Rapid and prominent increases are found in the variation of helicity during four flares in their initial brightening regions. The recovery of the increases takes 3-4 h for the two biggest flares (X2.2 and M6.6), while only takes about 2 h for the other two smaller flares (M2.2 and M1.6)., Comment: 13 pages, 7 figures, accepted to Research in Astronomy and Astrophysics (RAA)

Cross-correlation analysis and wavelet transform methods are proposed to investigate the phase relationship between the monthly sunspot group numbers in the solar northern and southern hemispheres. It is found that (1) the monthly sunspot group numbers in the northern hemisphere begin two months earlier than those in the southern one, which should lead to phase asynchrony between them but with a slight effect; (2) the Schwabe cycle length for the monthly sunspot group numbers in the two hemispheres obviously differs from each other, and the mean Schwabe cycle length of the monthly sunspot group numbers in the northern hemisphere is slightly larger than that in the southern one; (3) the monthly sunspot group numbers in the northern hemisphere precede those in the southern hemisphere during the years of about 1874-1927, after which, the southern hemisphere leads the northern hemisphere in the years 1928-1964, and then the northern hemisphere leads in time till the present.

The relationships between solar flare parameters (total importance, time duration, flare index, and flux) and sunspot activity (Rz) as well as those between geomagnetic activity (aa index) and the flare parameters can be well described by an integral response model with the response time scales of about eight and thirteen months, respectively. Compared with linear relationships, the correlation coefficients of the flare parameters with Rz, of aa with the flare parameters, and of aa with Rz based on this model have increased about 6%, 17%, and 47% on average, respectively. The time delays of the flare parameters to Rz, of aa to the flare parameters, and of aa to Rz at their peaks in solar cycle can be predicted in part by this model (82%, 47%, and 78%, respectively). These results may be further improved when using a cosine filter with a wider window. It implies that solar flares are related to the accumulation of solar magnetic energies in the past through a time decay factor. The above results may help to understand the mechanism of the solar cycle and to improve the solar flare prediction., Comment: 9 pages, 6 figures, accepted for publication in RAA (Res. Astron. Astrophys.)

The daily sunspot numbers of the whole disk as well as the northern and southern hemispheres from January 1, 1945 to December 31, 2010 are used to investigate the temporal variation of the rotational cycle length through the continuous wavelet transformation analysis method. The auto-correlation function analysis of daily hemispheric sunspot numbers shows that the southern hemisphere rotates faster than the northern hemisphere. The results obtained from the wavelet transformation analysis are: there exists no direct relationship between the variation trend of the rotational cycle length and the variation trend of solar activity in the two hemispheres; the rotational cycle length of both hemispheres has no significant period appearing at the 11 years, but has significant period of about 7.6 years. Analysis concerning the solar cycle dependence of the rotational cycle length shows that in the whole disk and the northern hemisphere acceleration seems to appear before the minimum time of solar activity. Furthermore, the cross-correlation study indicates that the rotational cycle length of the two hemispheres has different phases, and the rotational cycle length of the whole disk as well as the northern and southern hemispheres also has phase shifts with the corresponding solar activity. What's more, the temporal variation of North-South (N-S) asymmetry of the rotational cycle length is also studied; it displays the same variation trend as the N-S asymmetry of solar activity in a solar cycle as well as in the considered time interval, and it has two significant periods of 7.7 and 17.5 years. Moreover, the N-S asymmetry of the rotational cycle length and the N-S asymmetry of solar activity are highly correlated. It's inferred that the northern hemisphere should rotate faster at the beginning of solar cycle 24.

In general, it is believed that plages and sunspots are the main contributors to solar irradiance. There are small-scale structures on the Sun with intermediate magnetic fields that could also contribute to solar irradiance, but it has not yet been quantified how many of these small scale structures contribute and how much this varies over the solar cycle. We used Ca II K images obtained from the telescope at the Kodaikanal observatory. We report a method to separate the network elements from the background structure and plage regions, and compute the changes in the network element area index during the minimum phase of the solar cycle and part of the ascending phase of cycle 24. The measured area occupied by the network elements is about 30% and the plages cover less than 1% of the solar disk during the observation period from February 2008 to 2011. During the extended period of minimum activity, it is observed that the network element area index decreases by about 7% compared to the area occupied by the network elements in 2008. A long term study of the network element area index is required to understand the variations over the solar cycle.

The magnetic field of the umbrae is sometimes found to be saturated in the magnetograms taken by the Michelson Doppler Imager (MDI) onboard the Solar and Heliospheric Observatory (SOHO). It is suggested that the combination of the low intensity of sunspot umbrae and the limitation of the 15-bit onboard numerical data acquisition leads to this saturation. In this paper, we propose to use the MDI's intensity data to correct this saturation. This method is based on the well-established relationship between the continuum intensity and the magnetic field (the so-called I-B relationship). A comparison between the corrected magnetic field and the data taken by the Stokes-Polarimeter of the Solar Optical Telescope (SOT/SP) onboard Hinode shows a reasonable agreement, suggesting that this correction is effective.

Data analysis of sunspot oscillation based on 6-hr SDO run of observation showed that low frequency (0.2 < ! < 1 mHz) oscillations are local 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 scenario for sunspot oscillations leads to conclusion that local sunspot oscillations occur due to subphotospheric resonator for slow mhd waves. Empirical models of sunspot atmosphere and the theory of slow waves in thin magnetic flux tubes is applied to the modeling of subphotospheric resonator. Spectrum of local oscillations consists of a great number of lines. This kind of spectrum can occur only if the subphospheric 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 the monolithic sunspots. The interrelation of local oscillations with umbral dots and wave fronts of traveling waves in sunspots is discussed., 17 pages, 8 figures, accepted to the Research in Astronomy and Astrophysics (RAA)

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.

Previous statistical analyses of a large number of SOHO/MDI full disk longitudinal magnetograms provided a result that demonstrated how responses of solar flares to photospheric magnetic properties can be fitted with sigmoid functions. A logistic model reveals that these fitted sigmoid functions might be related to the free energy storage process in solar active regions. Although this suggested model is rather simple, the free energy level of active regions can be estimated and the probability of a solar flare with importance over a threshold can be forecast within a given time window.

We fi nd that the solar cycles 9, 11, and 20 are similar to cycle 23 in their respective descending phases. Using this similarity and the observed data of smoothed monthly mean sunspot numbers (SMSNs) available for the descending phase of cycle 23, we make a date calibration for the average time sequence made of the three descending phases of the three cycles, and predict the start of March or April 2008 for cycle 24. For the three cycles, we also fi nd a linear correlation of the length of the descending phase of a cycle with the difference between the maximum epoch of this cycle and that of its next cycle. Using this relationship along with the known relationship between the rise-time and the maximum amplitude of a slowly rising solar cycle, we predict the maximum SMSN of cycle 24 of 100.2 ± 7.5 to appear during the period from May to October 2012.

We study the properties of the He I 10830 A line in nine selected solar flares, using spectral data obtained with the Multi-channel Infrared Solar Spectrograph (MISS) at Purple Mountain Observatory (PMO) and photospheric images from the Michelson Doppler Imager (MDI) onboard the Solar and Heliospheric Observatory (SOHO). Our results indicate that, over an area of 3''– 8'', the He I 10830 A line shows emission exceeding the continuum in nearby quiet region when the Geostationary Operations Environmental Satellite (GOES) X-ray class of the flare reaches a threshold value (C4.5). The He I 10830 A line emission is detected only in the kernels of the Hα brightenings, but is not associated with the size of the flare. It is found that, whenever the He I 10830 A line shows excess emission over the nearby continuum both the Hα and the Ca II 8542 A lines display enhanced intensities exceeding their preflare intensities. The He I 10830 A line emission can occasionally extend into the umbra of the involved sunspot, which is inconsistent with previous studies. The weak component of He I 10830 A line changes from emission to absorption earlier than does the main component. Our results favor the photoionization-reconnection mechanism for the excitation of the He I 10830 A line.

The running correlation coefficient between the solar cycle amplitudes and the max-max cycle lengths at a given cycle lag is found to vary roughly in a cyclical wave with the cycle number, based on the smoothed monthly mean Group sunspot numbers available since 1610. A running average method is proposed to predict the size and length of a solar cycle by the use of the varying trend of the coefficients. It is found that, when a condition (that the correlation becomes stronger) is satisfied, the mean prediction error (16.1) is much smaller than when the condition is not satisfied (38.7). This result can be explained by the fact that the prediction must fall on the regression line and increase the strength of the correlation. The method itself can also indicate whether the prediction is reasonable or not. To obtain a reasonable prediction, it is more important to search for a running correlation coefficient whose varying trend satisfies the proposed condition, and the result does not depend so much on the size of the correlation coefficient. As an application, the peak sunspot number of cycle 24 is estimated as 140.4±15.7, and the peak as May 2012±11 months.

The Empirical Mode Decomposition (EMD) and Auto-Regressive model (AR) are applied to a long-term prediction of sunspot numbers. With the sample data of sunspot numbers from 1848 to 1992, the method is evaluated by examining the measured data of the solar cycle 23 with the prediction: different time scale components are obtained by the EMD method and multi-step predicted values are combined to reconstruct the sunspot number time series. The result is remarkably good in comparison to the predictions made by the solar dynamo and precursor approaches for cycle 23. Sunspot numbers of the coming solar cycle 24 are obtained with the data from 1848 to 2007, the maximum amplitude of the next solar cycle is predicted to be about 112 in 2011–2012.

Based on physical backgrounds, the four time series of the Guliya (Tibetan plateau) ice core (GIC) δ18O, and three natural factors, i.e. the rotation rate of earth, sunspots, and El Nino–Southern Oscillation (ENSO) signals, are decomposed into two hierarchies, i.e. more and less than 10-year hierarchies respectively, and then the running t-test is used to reanalyse the data before and after filtering with the purpose of investigating the contribution of natural factors to the abrupt climate changes in the last one hundred years. The results show that the GIC δ18O evolved with a quasi-period of 7–9 years, and the abrupt climate changes in the early 1960s and in the period from the end of the 1970s to the beginning of the 1980s resulted from the joint effect of the two hierarchies, in other words, the two interdecadal abrupt changes of climate in the last one hundred years were global. The interannual variations of ENSO and sunspots were the important triggering factors for the abrupt climate changes in the last one hundred years. At the same time, the method of Information Transfer (IT) is employed to estimate the contributions of ENSO signals and sunspots activities to the abrupt climate changes, and it is found that the contribution of the interannual variation of ENSO signals is relatively large.

We use wavelet transform to analyze the daily relative sunspot number series over solar cycles 10–23. The characteristics of some of the periods shorter than ~600-day are discussed. The results exhibit not only the variation of some short periods in the 14 solar cycles but also the characteristics and differences around solar peaks and valley years. The short periodic components with larger amplitude such as ~27, ~150 and ~360-day are obvious in some solar cycles, all of them are time-variable, also their lengths and amplitudes are variable and intermittent in time. The variable characteristics of the periods are rather different in different solar cycles.

We reported recently some rapid changes of sunspot structure in white-light (WL) associated with major flares. We extend the study to smaller events and present here results of a statistical study of this phenomenon. In total, we investigate 403 events from 1998 May 9 to 2004 July 17, including 40 X-class, 174 M-class, and 189 C-class flares. By monitoring the structure of the flaring active regions using the WL observations from the Transition Region and Coronal Explorer (TRACE), we find that segments in the outer sunspot structure decayed rapidly right after many flares; and that, on the other hand, the central part of sunspots near the flare-associated magnetic neutral line became darkened. These rapid and permanent changes are evidenced in the time profiles of WL mean intensity and are not likely resulted from the flare emissions. Our study further shows that the outer sunspot structure decay as well as the central structure darkening are more likely to be detected in larger solar flares. For X-class flares, over 40% events show distinct sunspot structure change. For M- and C-class flares, this percentage drops to 17% and 10%, respectively. The results of this statistical study support our previously proposed reconnection picture, i.e., the flare-related magnetic fields evolve from a highly inclined to a more vertical configuration.

An important issue affecting operation of ground-based observatories is the local environmental conditions, including dust in the atmosphere. Dust "events" can appear suddenly and without warning, and can be very detrimental to a telescope's optics. Due to these dust events, optics may be required to undergo cleaning and recoating which can cost the observatory a substantial amount of money, in addition to lost observing time. This research involves the statistical analysis of dust event data obtained from the Apache Point Observatory (APO) in Sunspot, New Mexico, which has similar weather conditions to our observatory, the Magdalena Ridge Observatory. The objective of this work is to determine whether there are any correlations between dust events and basic weather effects, such as levels or changes in pressure, humidity, wind speed, and wind direction, which could be used to predict the likelihood of such an event. We have identified one correlation between a drop in humidity and concurrent rise in temperature which precedes 76.23% of the measured dust events at APO during a 17 month period.

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 10 cm 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.

We examine the nonlinear dynamical properties of the monthly smoothed group sunspot number R-g and find that the solar activity underlying the time series of R-g, 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 R-g 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 R-z. 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.

Solar activity measurements in the far‐ to mid‐IR range are receiving renewed interest as part of an effort to complement recent results obtained at submillimeter wavelengths. A new setup has been developed to measure solar activity in the infrared spectral region centered at 10 μm (30 THz) by means of a camera with focal plane array of uncooled microbolometers. An optical arrangement of concave‐convex‐concave mirrors magnifies and focuses the full‐disk solar image to fit into the field of view of the camera. Techniques were developed to characterize the camera and calibrate the measurements in brightness temperature and flux units. Test observations were made at the Bernard Lyot Solar Observatory, Campinas, Brazil, and were continued at El Leoncito Astronomical Complex, San Juan, Argentina. The sky was found to be almost transparent at 10 μm at both sites. The first measurements of the solar disk have confirmed the presence of quiescent bright ring, or "plagelike," regions around sunspots, and "disappearances" of sunspots coincident with small soft X‐ray bursts. Small mid‐IR flares were found, consisting of multiple rapid brightenings (tens of seconds to several minutes) at different locations in the solar active regions, corresponding to soft X‐ray bursts reported by GOES satellites. At a wavelength of 10 μm, the sizes of some flare sources were found to be smaller than the diffraction‐limited photometric beam of 25'' set by the 10.5 cm diameter objective lens. The intensities of such small mid‐IR flares were high, of the order of (8–14) × 10−19 W m−2 Hz−1 (or [8–14] × 104 solar flux units).