The State of Self-organized Criticality of the Sun During the Last Three Solar Cycles. I. Observations

We analyze the occurrence-frequency distributions of peak fluxes [P], total fluxes [E], and durations [T] of solar flares over the last three solar cycles (during 1980??C?2010) from SMM/HXRBS, CGRO/BATSE, and RHESSI hard X-ray data. From the synthesized data we find powerlaw slopes with mean values of ?? _P =1.73±0.07 for the peak flux, ?? _E =1.62±0.12 for the total flux, and ?? _T =1.99±0.35 for flare durations. We find a tendency of an anti-correlation of the powerlaw slope of peak fluxes with the flare rate or sunspot number as a function of the solar cycle. The occurrence powerlaw slope is always steeper by ??????0.1 during a solar-cycle minimum compared with the previous solar-cycle maximum, but the relative amplitude varies for each cycle or instrument. Since each solar cycle has been observed with a different instrument, part of the variation could be attributed to instrumental characteristics and different event selection criteria used in generating the event catalogs. The relatively flatter powerlaw slopes during solar maxima could indicate more energetic flares with harder electron-energy spectra, probably due to a higher magnetic complexity of the solar corona. This would imply a non-stationarity (or solar-cycle dependence) of the coronal state of self-organized criticality.     

Proton Enhancements and Their Relation to the X-Ray Flares During the Three Last Solar Cycles

Energetic proton measurements obtained from the GOES and IMP-8 satellites as well as from ground-based neutron monitors are compared with the GOES soft X-ray measurements of the associated solar flares for the period 1975–2003. The present study investigates a broad range of phenomenology relating proton events to flares (with some references to related interplanetary disturbances), including correlations of occurrence, intensities, durations and timing of both the particle event and the flare as well as the role of the heliographic location of the designated active region. 1144 proton events of > 10 MeV energy were selected from this 28-year period. Owing primarily to the low particle flux threshold employed more than half of this number was found to be reliably connected with an X-ray flare. The statistical analysis indicates that the probability and magnitude of the near-Earth proton enhancement depends critically on the flare's importance and its heliolongitude. In this study all flares of X-ray importance > X5 and located in the most propitious heliolongitude range, 15^∘W to 75^∘W, were succeeded by a detectable proton enhancement. It was also found that the heliolongitude frequently determines the character of the proton event time profile. In addition to intensity, duration and timing, proton events were found to be related to the other flare properties such as lower temperatures and longer loop lengths.     

The Variation of Solar Wind Correlation Lengths Over Three Solar Cycles

We present the results of a study of solar wind velocity and magnetic field correlation lengths over the last 35 years. The correlation length of the magnetic field magnitude λ _|B| increases on average by a factor of two at solar maxima compared to solar minima. The correlation lengths of the components of the magnetic field l_BXYZ\lambda_{B_{XYZ}} and of the velocity l_VYZ\lambda_{V_{YZ}} do not show this change and have similar values, indicating a continual turbulent correlation length of around 1.4×10⁶ km. We conclude that a linear relation between λ _|B|, VB ², and Kp suggests that the former is related to the total magnetic energy in the solar wind and an estimate of the average size of geoeffective structures, which is, in turn, proportional to VB ². By looking at the distribution of daily correlation lengths we show that the solar minimum values of λ _|B| correspond to the turbulent outer scale. A tail of larger λ _|B| values is present at solar maximum causing the increase in mean value.     

Self-Organized Criticality Model of Solar Plasma Eruption Processes

We propose a new two-dimensional self-organized critical model of eruption process based on the concept of magnetic elements. Solar flares are considered as avalanches of annihilations of magnetic elements. This approach allows to describe eruptive processes in the solar atmosphere in the physically clear manner and easily simulate their basic properties. The model proposed yields a power law distribution of flare energy in a good agreement with observations. One can also expand the model to take into account new factors and ideas. This revised version was published online in July 2006 with corrections to the Cover Date.     

Solar Modulation of Cosmic Rays during the Declining and Minimum Phases of Solar Cycle 23: Comparison with Past Three Solar Cycles

We study solar modulation of galactic cosmic rays (GCRs) during the deep solar minimum, including the declining phase, of solar cycle 23 and compare the results of this unusual period with the results obtained during similar phases of the previous solar cycles 20, 21, and 22. These periods consist of two epochs each of negative and positive polarities of the heliospheric magnetic field from the north polar region of the Sun. In addition to cosmic-ray data, we utilize simultaneous solar and interplanetary plasma/field data including the tilt angle of the heliospheric current sheet. We study the relation between simultaneous variations in cosmic ray intensity and solar/interplanetary parameters during the declining and the minimum phases of cycle 23. We compare these relations with those obtained for the same phases in the three previous solar cycles. We observe certain peculiar features in cosmic ray modulation during the minimum of solar cycle 23 including the record high GCR intensity. We find, during this unusual minimum, that the correlation of GCR intensity is poor with sunspot number (correlation coefficient R=?0.41), better with interplanetary magnetic field (R=?0.66), still better with solar wind velocity (R=?0.80) and much better with the tilt angle of the heliospheric current sheet (R=?0.92). In our view, it is not the diffusion or the drift alone, but the solar wind convection that is the most likely additional effect responsible for the record high GCR intensity observed during the deep minimum of solar cycle 23.     

Acoustic Mode Frequencies of the Sun During the Minimum Phase Between Solar Cycles 23 and 24

We investigate the spatial and temporal variations of the high-degree mode frequencies calculated over localized regions of the Sun during the extended minimum phase between solar cycles 23 and 24. The frequency shifts measured relative to the spatial average over the solar disk indicate that the correlation between the frequency shift and magnetic field strength during the low-activity phase is weak. The disk-averaged frequency shifts computed relative to a minimal activity period also reveal a moderate correlation with different activity indices, with a maximum linear correlation of about 72?%. From the investigation of the frequency shifts at different latitudinal bands, we do not find a consensus period for the onset of solar cycle 24. The frequency shifts corresponding to most of the latitudes in the northern hemisphere and 30° south of the equator indicate the minimum epoch to be February 2008, which is earlier than inferred from solar activity indices.     

磁通量喷发的大气响应Ⅱ.太阳附近的慢激波

日冕物质喷射的观测速度常低于阿尔芬波速的估计值而高于背景日冕声速,这说明日冕物质喷射可能在日冕中形成慢激波。本文取带赤道电流片的冕流结构作为背景,用冕流底部的磁通量喷发作为驱动机制,对日冕物质喷射触发的慢激波进行数值模拟。结果表明,电流片对激波结构有着重要影响。慢激波只出现在电流片的外部,在电流片中逐渐过渡为快激波,慢激波前方的背景磁场在快磁声波的作用下显著偏转,背景密度下降超过10％。慢激波的纬度范围有限,从电流片的外沿大约延伸到±20°,且具有凹向上方的外形。     

Time-Latitudinal Dynamics of Magnetic Fields and the Green Corona Over Three Solar Cycles

Time-latitudinal distributions of the solar-surface magnetic fields and the green corona (530.3 nm, Fe XIV) intensities in the period 1975 – 2004 are analyzed. Meridional migration maps show that time-varying components consist of both the poleward and equatorward belts over a solar cycle. The green-corona maps are, for the first time, directly compared with magnetic flux charts, yielding a good association between the green corona and magnetic fields; this is most reliably seen at high latitudes.     

Relation of CME Speed and Magnetic Helicity in CME Source Regions on the Sun during the Early Phase of Solar Cycles 23 and 24

To investigate the relations between coronal mass ejection (CME) speed and magnetic field properties measured in the photospheric surface of CME source regions, we selected 22 disk CMEs in the rising and early maximum phases of the current Solar Cycle 24. For the CME speed, we used two-dimensional (2D) projected speed observed by the Large Angle and Spectroscopic Coronagraph onboard the Solar and Heliospheric Observatory (SOHO/LASCO), as well as a 3D speed calculated from the triangulation method using multi-point observations. Two magnetic parameters of CME source regions were considered: the average of magnetic helicity injection rate and the total unsigned magnetic flux. We then classified the selected CMEs into two groups, showing: i) a monotonically increasing pattern with one sign of helicity (group A: 16 CMEs) and ii) a pattern of significant helicity injection followed by its sign reversal (group B: 6 CMEs). We found that: 1) 3D speed generally shows better correlations with the magnetic parameters than the 2D speed for 22 CME events in Solar Cycle 24; 2) 2D speed and the magnetic parameters of 22 CME events in this solar cycle have lower values than those of 47 CME events in Solar Cycle 23; 3) all events of group B in Solar Cycle 24 occur only after the beginning of the maximum phase, a trend well consistent with that shown in Solar Cycle 23; 4) the 2D speed and the helicity parameter of group B events continue to increase in the declining phase of Solar Cycle 23, while those of group A events abruptly decrease in the same period. Our results indicate that the two CME groups have a different tendency in the solar cycle variations of CME speed and the helicity parameters. Active regions that show a complex helicity evolution pattern tend to appear in the maximum and declining phases, while active regions with a relatively simple helicity evolution pattern appear throughout the whole solar cycle.     

Features of the Solar Active Cycles

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The Shape of Sunspots and Solar Activity Cycles

Solar Physics - A new open-source software, called SunMap, has been developed to obtain synoptic maps in an easy and quick way from multiple full-disc solar images. Our objective is to provide a...     

Investigation of Hemispherical Variations of Soft X-Ray Solar Flares during Solar Cycles 21 to 24

Solar System Research - In the current investigation we have studied the distribution as well as the asymmetry of solar X-ray flares during the period 1976–2017 which corresponds to solar...     

The Relation between the Amplitude and the Period of Solar Cycles

The maximum amplitudes of solar activity cycles are found to be well anti-correlated (r = -0.72) with the newly defined solar cycle lengths three cycles before (at lag -3) in 13-month running mean sunspot numbers during the past 190 years. This result could be used for predicting the maximum sunspot numbers. The amplitudes of Cycles 24 and 25 are estimated to be 149.5±27.6 and 144.3±27.6, respectively.     

The Prediction of Maximum Amplitudes of Solar Cycles and the Maximum Amplitude of Solar Cycle 24

We present a brief review of predictions of solar cycle maximum amplitude with a lead time of 2 years or more. It is pointed out that a precise prediction of the maximum amplitude with such a lead-time is still an open question despite progress made since the 1960s. A method of prediction using statistical characteristics of solar cycles is developed: the solar cycles are divided into two groups, a high rising velocity (HRV) group and a low rising velocity (LRV) group, depending on the rising velocity in the ascending phase for a given duration of the ascending phase. The amplitude of Solar Cycle 24 can be predicted after the start of the cycle using the formula derived in this paper. Now, about 5 years before the start of the cycle, we can make a preliminary prediction of 83.2-119.4 for its maximum amplitude.     

Prediction of the Length of Upcoming Solar Cycles

The forecast of solar cycle (SC) characteristics is crucial particularly for several space-based missions. In the present study, we propose a new model for predicting the length of the SC. The model uses the information of the width of an autocorrelation function that is derived from the daily sunspot data for each SC. We tested the model on Versions 1 and 2 of the daily international sunspot number data for SCs 10?–?24. We found that the autocorrelation width \(A_{\mathrm{w}} ^{n}\) of SC \(n\) during the second half of its ascending phase correlates well with the modified length that is defined as \(T_{\mathrm{cy}}^{n+2} - T_{\mathrm{a}}^{n}\). Here \(T_{\mathrm{cy}}^{n+2}\) and \(T_{ \mathrm{a}}^{n}\) are the length and ascent time of SCs \(n+2\) and \(n\), respectively. The estimated correlation coefficient between the model parameters is 0.93 (0.91) for Version 1 (Version 2) sunspot series. The standard errors in the observed and predicted lengths of the SCs for Version 1 and Version 2 data are 0.38 and 0.44 years, respectively. The advantage of the proposed model is that the predictions of the length of the upcoming two SCs (i.e., \(n+1\), \(n+2\)) are readily available at the time of the peak of SC \(n\). The present model gives a forecast of 11.01, 10.52, and 11.91 years (11.01, 12.20, and 11.68 years) for the length of SCs 24, 25, and 26, respectively, for Version 1 (Version 2).     

Long-term Evolution of Solar Activity and Prediction of the Following Solar Cycles

Solar activities have a great impact on modern high-tech systems, such as human aerospace activities, satellite communication and navigation, deep space exploration, and related scientific research. Therefore, studying the long-term evolution trend of solar activity and accurately predicting the future solar cycles are highly anticipated.Based on the wavelet transform and empirical function fitting of the longest recorded data of the annual average relative sunspot number(ASN) series of 323 yr t...     

The Temperature of the Low Corona During Solar Cycles 21–23

Observations of the forbidden coronal lines Fe xiv 530.3 nm and Fe x 637.4 nm obtained at the National Solar Observatory at Sacramento Peak are used to determine the variation of coronal temperature at latitudes above 30^∘ during solar activity cycles 21–23. Features of the long-term variation of emission in the two lines are also discussed. Temperatures at latitudes below 30^∘ are not studied because the technique used to determine the coronal temperature is not applicable in active regions. The polar temperature varies cyclically from approximately 1.3 to 1.7 MK. The temperatures are similar in both hemispheres. The temperature near solar minimum decreases strongly from mid-latitudes to the poles. The temperature of the corona above 80^∘ latitude generally follows the sunspot cycle, with minima in 1985 and 1995–1996 (cf. 1986 and 1996 for the smoothed sunspot number, Rz) and maxima in 1989 and 2000 (cf. 1989 and 2000 for Rz). The temperature of the corona above 30^∘ latitude at solar maximum is nearly uniform, i.e., there is little latitude dependence. If the maximum temperatures of cycles 22 and 23 are aligned in time (superposed epochs), the average annual N + S temperature (average of the northern and southern hemisphere) in cycle 23 is hotter than that in cycle 22 at all times both above 80^∘ latitude and above 30^∘ latitude. The difference in the average annual N + S maximum temperature between cycles 23 and 22 was 56 kK near the poles and 64 kK for all latitudes above 30^∘. Cycle 23 was also hotter at mid-latitudes than cycle 22 by 60 kK. The last 3 years of cycle 21 were hotter than the last 3 years of cycle 22. The difference in average annual N + S temperatures at the end of cycles 21 and 22 was 32 kK near the poles and 23 kK for all latitudes above 30^∘. Cycle 21 was also hotter at mid-latitudes than cycle 22 by at least 90 kK. Thus, there does not seem to be a solar-cycle trend in the low-coronal temperature outside of active regions.     

太阳黑子的世纪周期及对24、25活动周的预报

太阳活动除了具有公认的11 a周期以外,还存在着一个80～120 a变化的世纪周期,也称为Gleissberg周期.使用傅里叶变换和小波分析的方法,分析了1700～2008年的年均黑子数世纪周期的变化规律.得到结果:在太阳活动世纪周期的低谷期,所对应11 a太阳周的极大年和极小年的黑子数目都比其他太阳周的低.在这300多年里,世纪周期的周期长度也有变化.由世纪周期的变化趋势,预测第24、25太阳活动周将处于世纪周期的低谷期.通过对以前3个世纪周期的谷期黑子数求平均的方法,得到第24,25太阳周极大年年均黑子数为63.6±21.1,极小年的为2.2±2.1.这些结果有助于理解当前太阳活动反常宁静这一现象.     

The Effect of Helicity Dissipation on the Critical State of an Avalanche Model for Solar Flares

We perform numerical simulations using an avalanche model for solar flares, in which the effect of avalanche event duration is included and the lateral boundary condition can be either open or periodic. The results from the simulations show that self-organized criticality (SOC) exists under a variety of conditions of helicity dissipation, and they are similar in the sense that the indices of power-law distributions of avalanche sizes are the same, while the duration and waiting time distributions differ little. Of interest are: (1) if there exists helicity dissipation in the course of avalanches, SOC exists only when the amount of helicity dissipation per avalanche is small; (2) sudden reductions in the total helicity of the system do not severely disturb SOC, if the amount reduced is moderate; (3) the distribution of waiting times is shown to be exponential, in consistent with the Poisson statistics other avalanche models have predicted, and the exponent increases as the effect of event duration becomes larger. The self-similar structure of the avalanche time series is also examined. These results imply that, although helicity is dissipated in resistive diffusion of flares, the amount of dissipation should be small and the conservation law of helicity thus holds in an approximate sense. Also, the coronal mass ejections (CMEs), observed to take helicity out of the solar corona in an eruptive way, may disrupt the statistical equilibrium of the corona only temporarily.