A solar cycle timing predictor - the latitude of active regions

The Schatten and Sofia (1987) dynamo theory prediction for the amplitude of smoothed annual sunspot number in the present solar cycle, No. 22, of 170 ± 25 was predicted to peak in 1990 ± 1 year. This peak was earlier and larger than most other estimates made in early 1987. New observational evidence shows sunspot values rising very rapidly, generally supporting the exceptionally large cycle predicted, however, solar cycle 22 appears even more exceptional than expected, in that the early cycle rise has exceeded all previous cycle increases. We use a Spörer butterfly method to examine solar cycle 22. We show from the latitude of active regions, that the cycle can now be expected to peak near November 1989 ±8 months, basically near the latter half of 1989.This paper was presented at the third meeting of the Solar Cycle Workshop, held in Sydney, Australia, January 9–13, 1989.     

Eclipse Observations of Compact Sources in the Outer Solar Corona

We report here on high angular resolution observations of solar noise storm sources at a frequency of 75 MHz. The data for the study were obtained at the Gauribidanur Radio Observatory (long.: 77°2612 E, lat.: 13°3612 N) about 100 km north of Bangalore, India, during the solar eclipse of 24 October 1995. Our main conclusion is that there are structures of angular size 2.5 arc min in the outer solar corona.     

Pitch angle scattering of solar particles: Comparison of ‘particle’ and ‘field’ approach

In the quasi-linear theory of pitch angle scattering the power spectrum of magnetic field fluctuations is related to the shape of the pitch angle diffusion coefficient D(), the absolute value of the mean free path , and the rigidity dependence of the mean free path (R). We discuss these relations in detail during the solar particle event of 11 April, 1978 which was observed on HELIOS-2 at a distance of 0.49 AU from the Sun. Magnetic field measurements obtained during the time of the event are used as a basis for the layer model in which the method of particle trajectories in an actually measured field is used to simulate pitch angle diffusion. The values of D() and based on the trajectory simulation for 100 MeV protons (field approach) are compared with results obtained from solar proton data (particle approach) and with predictions from quasi-linear theory based on the additional assumption of the slab model for magnetic field fluctuations (QLT approach). The time of the event is characterized by a high level of field fluctuations, the observed mean free path of about 0.03 AU for 100 MeV protons is smaller than the average value near 1 AU. Results from the field and particle approaches agree surprisingly well. The remaining difference in the mean free path of about a factor of 2 could be due to tangential discontinuities which are measured by the magnetometer, but not seen by the real particles traveling along the average field. The results from the field and QLT approaches based on the same set of magnetic field measurements differ by about a factor of 4. One of the reasons for this discrepancy is that the conditions for resonance scattering are only marginally valid. In addition, the wave vectors representing Alfvén-type fluctuations may not be totally field aligned. This deviation from the slab model would cause an increase of the theoretically predicted mean free path and lead to better agreement with the other two approaches.     

Non-restricted double-averaged three body problem in Hill's case

A limiting case of the problem of three bodies (m ₀,m ₁,m ₂) is considered. The distance between the bodiesm ₀ andm ₁ is assumed to be much less than that between their barycenter and the bodym ₂ so that one may use Hill's approximation for the potential of interaction between the bodiesm ₁ andm ₂. In the absence of resonant relations the potential, double-averaged by the mean longitudes ofm ₁ andm ₂, describes the secular evolution of the orbits in the first approximation of the perturbation theory.As Harrington has shown, this problem is integrable. In the present paper a qualitative investigation of the evolution of the orbits and comparison with the analogous case in the restricted problem are carried out.The set of initial data is found, for which a collision between the bodiesm ₀ andm ₁ takes place.The region of the parameters of the problem is determined, for which plane retrograde motion is unstable.In a special example the results of approximate analysis are compared with those of numerical integration of the exact equations of the three body problem.

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m ₀,m ₁,m ₂. , m ₀ m ₁. m ₂, m ₁ m ₂ m ₁ m ₂ . , . . , m ₀ m ₁. , . .

     

The distribution of the angular momenta of galaxies

Since the average relation between the angular momentaP and the massesM of galaxies can be represented by a power lawPM , we can define a relative angular momentum =P/M (or a constant timeP/M ). For a random motion picture within protogalaxies, should follow a Maxwellian distribution and consequently the dispersion of log should be 0.210.For the reasonable range of ( to 2), the limited sample of galaxies with known dynamical parameters gives between and 1 times the Maxwellian value. For the plausible special case =2 the reciprocal of the maximum rotational velocityv _m is already a measure of and the larger sample ofv _m-values not only yields the Maxwellian but, moreover, shows the shape of the distribution.

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PM , =constP/M . , (lg )=0.210. 7/42, . =2 v _m- .

     

Микрофлуктуации электрического поля на фронте ударной волны в модельном эксперименте

, . , , . . . . . , , .     

Повевхное магнитосферное течение С силяными разрывами

=qm . . ¶, I . — , ¶, 5. , . : , , . =ah 4. . . , -, ( ). .     

An apparent ‘even-odd’ cycle distribution in Mt. Wilson ‘numbers of spots’ data

Mt. Wilson numbers of spots data (as defined in Howard et al., 1984) appear to be distributed according to even-odd cycle numbering. Linear fits of annual numbers of spots versus annual sunspot number for even- and odd-numbered cycles have slopes which are statistically different at the 5% level of significance. The existence of an even-odd split in Mt. Wilson numbers of spots data may be due either to a real difference in even- and odd-numbered cycles on the Sun or to a difference in weather at Mt. Wilson (perhaps, related to the 22-yr rhythm of drought in the western United States) during even- and odd-numbered cycles, or both. For cycle 22, an even-numbered cycle, the peak numbers of spots is estimated to be near 2600.     

THE RELATIONSHIP BETWEEN SOLAR FLARE GAMMA-RAY EMISSION AND NEUTRON PRODUCTION

We have examined six solar neutron events measured by satellite instruments and/or neutron monitors (NM) to understand the relationship between the intensity–time profiles of the -ray lines, the pion-related -rays, and the neutron production. In all six events the solar neutron production was clearly time-extended. We find that neutron emission as detected by NMs most closely follows the emission of pion-related -rays, whereas lower energy neutron production may follow that of nuclear -ray line emissions. Although this distinction is not unexpected, it is safe to say that the 2.223 MeV -ray line from neutron capture on hydrogen is a poor measure of the neutron production at energies >200 MeV. During the three events on 1982, June 3, 1990, May 24 and 1991, June 4 solar neutrons with energies greater than 200 MeV were recorded by NMs. The NM increases on 1982, June 3 and 1990, May 24 can be modeled using the time profile of the pion-related -rays. For the 1991, June 4 event the NM signal was small but lasted for 60 min and the high-energy -ray data available to us are insufficient to conclude unambiguously that the high-energy neutron production followed the pion-related -rays. In the other three events on 1991, June 9, 11, and 15 solar neutrons with energies 10–100 MeV were observed by the COMPTEL -ray instrument on the Compton Gamma Ray Observatory. The duration of the low-energy neutron production on 1991, June 9 corresponded clearly to the high-energy and not to the low-energy -ray emission.     

The solar wind cycle,the sunspot cycle,and the corona

Recent theories of the solar cycle and of coronal heating strongly suggest that solar cycle variations of different quantities (i.e. sunspots, coronal green line, etc.) ought not to be expected to be in phase with one another. In agreement with this notion we note that the shape of the corona typical of a maximum eclipse occurs 1.5yr before sunspot maximum, compared with 2 yr as might be expected from Leighton's standard model. Further, we argue that the phase of the solar wind cycle can be determined from geomagnetic observations. Using this phase, a solar cycle variation of 100 km s^–1 in the solar wind velocity and 1 in the magnetic field intensity becomes apparent. In general, the solar wind cycle lags the coronal-eclipse-form cycle by 3 yr, compared with the 2 yr that might be expected from model calculations.     

Variation of the solar constant during the solar cycle

Measurements of the Nimbus-7 and Solar Maximum Mission satellites reported temporary large decreases of the solar constant of the order of a few tenths of a percent on a time-scale from days to weeks. Our investigations show that these decreases were caused by active sunspot groups with fast development and complex structure. This connection between the solar constant variation and the appearance of the active groups seems to be more clear in the maximum of the solar activity. At the time of the solar minimum, mainly in the second part of 1984, there were not any active sunspot groups practically on the solar disk, the value of the solar constant only fluctuated around its mean without large variation. The results of time series analyses show that the periodicity of the solar constant values, of young and active spot areas was nearly 23.5 days in 1980, which increases to 28 days towards the minimum of the solar cycle till 1983. During this time interval the main periodicity of the old, passive spot areas was around 28 days. In 1984, at the time of the solar minimum, there were not any obvious periodicities practically in the projected areas of the different types of the sunspot groups.     

Energy release in solar flares

We examine observational evidence concerning energy release in solar flares. We propose that different processes may be operative on four different time scales: (a) on the sub-second time scale of sub-bursts which are a prominent feature of mm-wave microwave records; (b) on the few-seconds time scale of elementary bursts which are a prominent feature of hard X-ray records; (c) on the few-minutes time scale of the impulsive phase; and (d) on the tens-of-minutes or longer time scale of the gradual phase.We propose that the concentration of magnetic field into magnetic knots at the photosphere has important consequences for the coronal magnetic-field structure such that the magnetic field in this region may be viewed as an array of elementary flux tubes. The release of the free energy of one such tube may produce an elementary burst. The development of magnetic islands during this process may be responsible for the sub-bursts. The impulsive phase may be simply the composite effect of many elementary bursts.We propose that the gradual phase of energy release, with which flares typically begin and with which many flares end, involves a steady process of reconnection, whereas the impulsive phase involves a more rapid stochastic process of reconnection which is a consequence of mode interaction.In the case of two-ribbon flares, the late part of the gradual phase may be attributed to reconnection of a large current sheet which is being produced as a result of filament eruption. A similar process may be operative in smaller flares.Also, Department of Applied Physics, Stanford University.     

The 1991 March 22 flare: Possible anisotropy of high-energy neutral emission

We made a parameter fit to the Haleakala neutron monitor counting rate during the 1991 March 22 solar flare (Pyle and Simpson, 1991) using the time profiles of -rays at 0.42–80 MeV obtained with the GRANAT satellite (Vilmeret al., 1994) and the microwave data from Owens Valley Radio Observatory. We use a two-component neutron injection function to find that either an impulsive injection or the impulsive-plus-prolonged neutron injection is possible. In both cases, the number of > 300 MeV neutrons emitted towards the Earth is estimated as 2 × 10²⁷ sr^–1, which is less than that of the 1990 May 24 flare by an order of magnitude.We tested if such a big difference in neutron number detected on the Earth can be accounted for solely by their different positions on the solar disk. For the estimation of the degree of anisotropy of high-energy secondary emission, we made use of macroscopic parameters of the flare active region, in particular, the vector magnetogram data from the Big Bear Solar Observatory. In our result, the anisotropy factor for the neutral emissions of the 1991 March 22 flare is only 1 – 10, which is rather small compared with previous theoretical predictions for a disk flare. Such a moderate anisotropy is due to the relatively large inclination angles of the magnetic fields at the footpoints of the flaring loop where accelerated particles are trapped. We thus concluded that the smaller number of neutrons of the 1991 March 22 flare would be not only due to its location on the disk, but also due to fewer protons accelerated during this event as compared with the 1990 May 24 limb event. For a more precise determination of the anisotropy factor in a flare, we need a detailed spectrum of electron bremsstrahlung in 0.1 – 10 MeV and the fluence of -ray emission from the ⁰-decay.Visting Associate from St. Petersburg State Technical University, St. Petersburg, 195251, Russia.     

The velocity field in the atmosphere of δ Cephei

Observations related to the photospheric velocity field of Cephei can be interpreted as follows: during the whole cycle of pulsations the only motion form in the atmosphere is a wave motion with a nearly constant full amplitude of approximately 15 km s^–1, and a wavelength of about 10⁶ km (which are quantities, about equal to the amplitudes of pulsational velocity and radius of the star). There are no significant small-scale turbulent velocity components. The microturbulent and macroturbulent velocities, as derived from spectral line observations, are fully compatible with this picture.     

Study of alpha component dynamics in the solar wind using the Prognoz satellite

The analysis of solar wind He⁺⁺ and H⁺ ion distribution functions, collected over five months by the satellite Prognoz 1, shows that these are in general maxwellian but that often tails appear at higher speeds. The existing relation V-T, the observation of ratios of T/Tp 3.83 and V/Vp 1.035 give evidence of preferential He⁺⁺ ion heating and acceleration. The criteria for heating by dissipation of hydromagnetic waves proposed by Barnes and Hung (1973) are tested experimentally. Finally, multifluid models are likely to predict certain observations such as dependence of the velocity ratio V/Vp on the solar wind flux.     

Toward a model of a two-component solar cycle

In a two-component cycle, the generation of the dipole field by a separate mechanism as well as the strong link occurring, with a 5–6-yr delay, between the sunspot cycle and the preceding dipole cycle, sets in new terms the problem of the mechanisms at the origin of the solar cycle. In this paper, from various series of synoptic solar data, we identify some of the mechanisms to incorporate in a model of a two-component solar cycle. The first one concerns the dipole field which is not a surface phenomenon. We establish the cyclic behaviour and the various properties of the dipole-field sources which are deep-seated in the solar interior and have a rigid rotation of about 27 days. We identify two cyclic phenomena which, in each hemisphere, link with a 5–6-yr delay, the dipole field generation which occurs at high latitudes, to the bipolar field emergence occurring at sunspot latitudes. They are the signatures of a coupling mechanism taking place deep in the solar interior. Then we study the constraints imposed on the mechanisms of the sunspot field generation both by a two-component cycle and by new observational results. These last ones concern the links occurring between the birth of new sunspot groups and the occurrence of pre-existing features of the photospheric field and of pivot-points in rigid rotation at 27.3 days.Our final discussion is devoted to a first sketch of the distribution of the relevant mechanisms among separate regions of the convective zone. Unfortunately neither the helioseismology, nor our data analysis has yet supplied us with appropriate pieces of information for building a physical model of this two-component cycle.     

Solar cycle variation and N-S asymmetry of λ 5303 coronal intensity

It is shown that during the present solar cycle (No-20), the 5303 coronal intensity at heliographic latitudes between 15°–40° in both hemispheres had two maxima. The first maximum occurred in 1967–68 and the second in 1969–70. At lower latitudes ( ± 10°) there was only one clear maximum in 1970. These results are in good agreement with those of Gnevyshev (1967) for the previous solar cycle. The North-South asymmetry of 5303 intensity for the period 1957–1970 is studied and its implications to solar-terrestrial relationships are discussed. It is shown that during the period studied, the N-S asymmetry of 5303 intensity is negatively correlated with sunspot activity.     

Periodicities of solar irradiance and solar activity indices,I

Using a standard FFT time series analysis, our results show an 8–11 months periodicity in the solar total and UV irradiances, 10.7 cm radio flux, Ca-K plage index, and sunspot blocking function. The physical origin of this period is not known, but the evidence in the results exclude the possibility that the observed period is a harmonic due to the FFT transform or detrending. Periods at 150–157 and 51 days are found in those solar data which are related to strong magnetic fields. The 51-day period is the dominant period in the projected areas of developing complex sunspot groups, but it is missing from the old decaying sunspot areas. This evidence suggests that the 51-day period is related to the emergence of new magnetic fields. A strong 13.5-day period is found in the total irradiance and projected areas of developing complex groups. This confirms those results (e.g., Donnelly et al., 1983, 1984; Bai, 1987, 1989) which show that active centers are located 180 deg apart from each other.Our study also shows that the modulation of various solar data due to the 27-day solar rotation is more pronounced during the declining portion of solar cycle than during the rising portion. This arises from that the active regions and their magnetic fields are better organized and more long-lived during the maximum and declining portion of solar cycle than during its rising portion.     

The abelian higgs sunspot endowed with a local conformal symmetry

We show that the requirement of alocal conformal symmetry of the Abelian Higgs sunspot leads, at least formally, to a complex-valued electromagnetic potential, whose imaginary part is a conformal compensating potential. It is shown that there exists a fundamental difference between conformal and ordinary electromagnetic fields; whereas the ordinary total magnetic flux of a spot is quantized its conformal analogue has to vanish if the Higgs field is to be single-valued. We further stress that such a complex-valued Abelian Higgs field configuration mimics quite well, under certain conditions (all the salient features of) the classical Abelian Higgs sunspot.     

Understanding Solar Flare Waiting-Time Distributions

The observed distribution of waiting times t between X-ray solar flares of greater than C1 class listed in the Geostationary Operational Environmental Satellite (GOES) catalog exhibits a power-law tail (t) for large waiting times (t>10hours). It is shown that the power-law index varies with the solar cycle. For the minimum phase of the cycle the index is =–1.4±0.1, and for the maximum phase of the cycle the index is –3.2±0.2. For all years 1975–2001, the index is –2.2±0.1. We present a simple theory to account for the observed waiting-time distributions in terms of a Poisson process with a time-varying rate (t). A common approximation of slow variation of the rate with respect to a waiting time is examined, and found to be valid for the GOES catalog events. Subject to this approximation the observed waiting-time distribution is determined by f(), the time distribution of the rate . If f() has a power-law form for low rates, the waiting time-distribution is predicted to have a power-law tail (t)^–(3+) (>–3). Distributions f() are constructed from the GOES data. For the entire catalog a power-law index =–0.9±0.1 is found in the time distribution of rates for low rates (<0.1hours ^–1). For the maximum and minimum phases power-law indices =–0.1±0.5 and =–1.7±0.2, respectively, are observed. Hence, the Poisson theory together with the observed time distributions of the rate predict power-law tails in the waiting-time distributions with indices –2.2±0.1 (1975–2001), –2.9±0.5 (maximum phase) and –1.3±0.2 (minimum phase), consistent with the observations. These results suggest that the flaring rate varies in an intrinsically different way at solar maximum by comparison with solar minimum. The implications of these results for a recent model for flare statistics (Craig, 2001) and more generally for our understanding of the flare process are discussed.