Engineering topics
Publications and source records attributed to Bai, T..
On the basis of analysis of the occurrence rate of major flares (X-ray class greater than or equal to M3.0), we present evidence that the 51-day periodicity was in operation during the interval from May 4, 1991 to November 15, 1992. This periodicity is noted to be two times 25.5 days, which has been proposed as the fundamental period of the Sun.
We have analyzed the longitude distributions of major flares observed in the 1955-1991 interval, referring them to coordinate systems rotating about axes tilted with respect to the rotation axis of the solar envelope. We find that the longitude distribution exhibits the largest modulation in the coordinate system with the following parameters: rotation period, 25.50 days; tilt angle of the rotation axis, 40 deg; tilt direction, toward the position of the earth on December 4 in its orbit around the sun. We interpret this as being due to an obliquely rotating structure (or a wave pattern rotating about an oblique axis) which has two exciters. We identify the period of 25.50 days as the fundamental period of the hypothetical 'clock' proposed by Bai and Sturrock (1991). The periods of the subharmonics are 51.0, 76.5, 102.0, 127.5, and 153.0 days, in agreement with periodicities found from analysis of flare occurrence times.
We study the occurrence frequency of solar flares as a function of the hard X-ray peak count rate, using observations of the Solar Maximum Mission. The size distributions are well represented by power-law distributions with negative indices. As a better alternative to the conventional method, we devise a maximum likelihood method of determining the power-law index of the size distribution. We find that the power-law index of the size distribution changes with time and with the phase of the 154-day periodicity. The size distribution is steeper during the maximum years of solar cycle 21 (1980 and 1981) than during the declining phase (1982-1984). The size distribution, however, is flatter during the maximum phase of the 154-day periodicity than during the minimum phase. The implications of these findings are discussed.
For periodicity analysis of occurrence rates of discrete events, one can use the maximum likelihood method or the 'Rayleigh analysis'. In a maximum likelihood analysis using a sinusoidal distribution, one tries various values of amplitude A and phase angle Theta(0) of the distribution function. We show that these two methods are essentially equivalent to one another in spite of their different mathematical origins. Using the Rayleigh analysis, therefore, we can simply calculate A and Theta(0) which maximize the likelihood. Using the cumulative nature of the logarithmic likelihood, we can identify time intervals during which the periodicity is in operation. When a periodicity operates only in certain time intervals, it is important to identify these intervals. Mathematically, the above technique is applicable only to discrete events. However, with slight modifications we can apply this technique to general cases - periodicity analysis of measurements of continuously varying quantities.
Evidence indicates that the 154-day periodicity in solar activity may be part of a complex of periodicities that are approximate multiples of 25.8 d, which suggests that the sun contains a 'clock' with frequency in the range 440-463 nHz. To search for evidence of this clock, the daily Greenwich sunspot areas and daily Zurich sunspot numbers have been Fourier-analyzed. The Zurich data show a strong peak that may clearly be identified with the fundamental frequency, while the Greenwich data show a peak that may be the harmonic of the fundamental frequency. A model is discussed which provides a kinematical interpretation of the sunspot spectrum.
The ocurrence times of major flares of solar cycle 22 are analyzed to detect periodicities. It is found that a periodicity of 77 d was in operation in the 15-m interval from 1988 November to 1990 February for six cycles. During the rest of 1990 no periodicity was discernible; however, it seems that the 77-d periodicity resumed in 1991. This 77-d period is interpreted as the third subharmonic of the fundamental period of about 25.5 d. In this interpretation, the 154-d periodicity is the sixth subharmonic. It is also found that when the 77-d periodicity or the 154-d periodicity is in operation the occurrence rate of major flares is much higher than is expected form the relative sunspot number.
Evidence that has recently been compiled (Bai and Sturrock 1991) indicates that the enigmatic 154-day periodicity in solar activity may be viewed as part of a complex of periodicities that are approximate multiples of 25.8 days, suggesting that the Sun contains a 'clock' with frequency in the range 440 to 463 nano Hz. The clock may comprise either an oscillator or a rotator, each of which may be either real or virtual. We have reconsidered a previous spectrum analysis of the Zurich sunspot-number sequence by Knight, Schatten, and Sturrock (1979) which revealed a sharp, persistent and significant periodicity with a period of 12.072 days, corresponding to a frequency of about 958.8 nano Hz. This periodicity may be regarded as the (second) upper sideband of the second harmonic (2nu(sub R) + 2nu(sub E)) of a fundamental frequency of 447.7 nano Hz that is clearly within the search band. In this expression, nu(sub R) is the sidereal frequency of the hypothetical rotator and nu(sub E) is the frequency (31.69 nano Hz) of the Earth in its orbital motion around the Sun. In analyzing sunspot area data derived from the Greenwich data set, and on noting that any frequency is defined only to within the Nyquist frequency, we find clear evidence not only for the upper sideband of the second harmonic, but also for the second harmonic (2nu(sub R)) and the lower sideband of the second harmonic (2nu(sub R) - 2nu(sub E)). There is no strong peak at the fundamental frequency in the Greenwich data, but there is in the Zurich sunspot data. The effect of a linear oscillator is, to the lowest order in the amplitude, the same as the combined effect of two rotators of opposite polarities. A rotator that has arbitrary orientation with respect to the ecliptic may influence the outer layers of the Sun and thereby modulate the occurrence of solar activity such as sunspots. By analyzing a simple model, we find that such a rotator would influence surface activity in such a way that the spectrum of a 'signal' (such as the record of sunspots), as seen from the Earth, would contain components with frequencies that are certain integral combinations of nu(sub R) and nu(sub E). The amplitudes of the various components depend sensitively on theta, the angle between the axis of the rotator and the axis of the Earth's orbital motion. This simple model therefore offers a kinematical (but not dynamical) interpretation of the sunspot spectrum. The present analysis, while offering support of our conjectures that the Sun contains a clock that regulates the 154-day complex of periodicities, cannot distinguish between an osillator or a rotator (that might be a traveling wave), nor between a real rotator or a virtual rotator (that might be an apparent traveling wave due to the aliasing effect of an oscillator in a rotating system). Further analysis of sunspot and other data sets will be required to confirm the existence of such clock and (if it is real) to determine its physical nature.
It is shown here that periodicities of 51, 78, 104, and 129 days in addition to the 154-day period found in 1984, can often be detected in flare and sunspot records. These periods are close to integral multiples of 25.8 days, suggesting that they are subharmonics of a fundamental period.
When and where to look is an important issue to observers planning to observe major solar flares. Prediction of major flares is also important because they influence the Earth's environment. Techniques for utilizing recently discovered solar hot spots and a solar activity periodicity of about 154 days in determining when and where to look to catch major flares are discussed.
The historical background of solar flare classification before the SMM launch is reviewed along with recent developments made by observations with SMM, Hinotori, and other contemporary satellite and ground-based observations. Based on these recent findings, solar flares are grouped into five classes: thermal hard X-ray flares, nonthermal hard X-ray flares, impulsive gamma-ray/proton flares, gradual gamma-ray/proton flares, and quiescent filament-eruption flares. The roles of filament eruptions in flare development are examined, and theoretical ideas related to processes occurring in different flare classes are discussed.
The occurrence rate of major flares during solar cycle 19 has been analyzed. A periodicity of 51 d is found, which is one-third of the period found from the flare rates of solar cycles 20 and 21 by various authors. The statistical significance of the periodicity is estimated to be at 99.85-percent confidence level. This periodicity is though to be related to the 153-d periodicity. The template of the phase diagram is well described by a constant plus a sine function. Additionally, an 18-month periodicity is found in the flare rate of the northern hemisphere.
Data is compiled from Solar Maximum Mission and Hinothori satellites, particle detectors in several satellites, ground based instruments, and balloon flights in order to answer fundamental questions relating to: (1) the requirements for the coronal magnetic field structure in the vicinity of the energization source; (2) the height (above the photosphere) of the energization source; (3) the time of energization; (4) transistion between coronal heating and flares; (5) evidence for purely thermal, purely nonthermal and hybrid type flares; (6) the time characteristics of the energization source; (7) whether every flare accelerates protons; (8) the location of the interaction site of the ions and relativistic electrons; (9) the energy spectra for ions and relativistic electrons; (10) the relationship between particles at the Sun and interplanetary space; (11) evidence for more than one acceleration mechanism; (12) whether there is single mechanism that will accelerate particles to all energies and also heat the plasma; and (13) how fast the existing mechanisms accelerate electrons up to several MeV and ions to 1 GeV.
Various observational properties of gamma-ray/proton (GR/P) flares are investigated. The question whether gamma ray line (GRL) flares are different from other flares is reevaluated, and flares with gradual hard X-ray time profiles are searched for and shown to share many common characteristics. Among the gradual flares, the only difference between those with observable nuclear gamma rays and those without is that hard X-ray burst spectrometer peak rates are greater than 4500 counts/s for the former, and less for the latter. It is proposed that GR/P flares be classified into impulsive and gradual flares. The differences between the two classes ofo GR/P flares are studied in phenomena occurring in the high corona and interplanetary medium. By examining the ratio of the number of interplanetary protons to the number of gamma-ray producing protons, it is found that it is small for impulsive GR/P flares but relatively large for gradual GR/P flares.
The success of imaging detectors with small fields of veiw such as HXIS or P/OF (Pinhole/Occulter Facility) depends heavily on pointing to the right place at the right time. During the solar maximum years many active regions coexist on the solar disk. Therefore, in order to point the imaging detector to the right place, it is important to know which active region is most likely to produce major flares. This knowledge is also important for flare prediction. As a first step toward this goal active regions have been identified which produced major flares observed by HXRBS (Hard X-Ray Burst Spectrometer) on SMM during February 1980 through December 1983. For this study the HXRBS Event List, an updated flare list compiled by the HXRBS group, and the Comprehensive Reports of the Solar Geophysical Data were used. During this period, HXRBS detected hard X-rays from approx 7000 solar flares, out of which only 441 flares produced X-rays with peak count rates exceeding 1000 counts/s. Flares with such high peak count rates are major flares. During the same time period about 2100 active regions passed across the solar disk, out of which only 153 were observed to produce major flares. (Some active regions are known to persist for several solar rotations, but at each passage new active region numbers are assigned and the estimate is based on active region numbers.) Out of these 153 active regions, 25 were observed to produce 5 or more major flares. Considering their high productivity of major flares, we may call these active regions super active regions. These 25 super active regions produced 209 major flares, accounting for 51% of all the major flares with identified active regions.
A large data base on solar flares obtained during the last solar maximum years makes it necessary to revise the views on the relationship between the impulsive phase and the second phase of flares. Contrary to the view most popular before the launch of the Solar Maximum Mission, it is now known that relativistic electrons and gamma-ray-producing protons and ions are accelerated during the impulsive phase. Because flares producing nuclear gamma-rays are different from ordinary flares, it is concluded that additional processes take place in gamma-ray-line flares. Recent studies have shown that flares with gradual hard X-ray time profiles not only produce nuclear gamma-rays during the impulsive phase but also develop full-fledged second-phase phenomena. It is proposed that filament eruption plays a key role in gamma-ray-line flares. When an erupting filament interacts with an overlaying flare loop, relativistic electrons and energetic protons are produced during the impulsive phase. When the erupting filament fully distends the overlying flare loop, full-fledged second-phase phenomena, such as shocks, interplanetary energetic particles, mass ejections and etc. are observed. When the overlying flare loop is compact and strong enough to suppress the activated filament, gamma-rays are emitted during the first phase but no second-phase phenomena occur.
Evidence for a periodicity of about 155 + or - 5 days in the production of energetic solar flares was reported in 1984 by Rieger et al. and Kiplinger et al. To see whether this periodicity is a persistent phenomenon, the occurrences of flares inferred from microwave data, which are available for most of the present and previous solar cycles, were examined. Strong confirmation of a 152 day periodicity in the time interval previously studied is found, demonstrating that these flares are a useful indicator for the observed periodicity. Evidence is found for persistence of the periodicity in the previous cycle (cycle 20). In cycle 20 the periodic modulation of the flare occurrence rate was weaker than in cycle 21, but the phase has apparently remained coherent through both cycles.
Observations of solar gamma rays by the Solar Maximum Mission (SMM) demonstrate that energetic protons and ions are rapidly accelerated during the impulsive phase. To understand the acceleration mechanisms for these particles, the characteristics of the gamma ray line flares observed by SMM were studied. Some very intense hard X-ray flares without detectable gamma ray lines were also investigated. Gamma ray line flares are distinguished from other flares by: (1) intense hard X-ray and microwave emissions; (2) delay of high energy hard X-rays, (3) emission of type 2 and/or type 4 radio bursts; and (4) flat hard X-ray spectra (average power law index: 3.1). The majority of the gamma ray line flares shared all these characteristics, and the remainder shared at least three of them. Positive correlations were found between durations of spike bursts and spatial sizes of flare loops as well as between delay times and durations of spike bursts.
Observations of solar gamma rays by the Solar Maximum Mission (SMM) demonstrate that energetic protons and ions are rapidly accelerated during the impulsive phase. To understand the acceleration mechanisms for these particles, the characteristics of the gamma ray line flares observed by SMM were studied. Some very intense hard X-ray flares without detectable gamma ray lines were also investigated. Gamma ray line flares are distinguished from other flares by: (1) intense hard X-ray and microwave emissions; (2) delay of high energy hard X-rays; (3) emission of type 2 and/or type 4 radio bursts; and (4) flat hard X-ray spectra (average power law index: 3.1). The majority of the gamma ray line flares shared all these characteristics, and the remainder shared at least three of them. Positive correlations were found between durations of spike bursts and spatial sizes of flare loops as well as between delay times and durations of spike bursts.