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.     

Time variations of the Magnetic Field at the Heliospheric Termination Shock – Galactic Cosmic-Ray modulation

The microwave circular polarization of the active region (AR) NOAA 7260 on 21–23 August 1992 is analyzed. Two-dimensional images at 1.76 cm with spatial resolution of =10 from the Nobeyama radioheliograph and one-dimensional scans at 9 wavelengths in the range of 1.81–3.43 cm and =16.3–31.1 from the radio telescope RATAN-600 were used. An inversion of the sense of circular polarization through the wavelength range was recorded on 22 August. It is shown that both the wavelength and the time dependence of the inversion are consistent with quasi-transverse (QT) propagation of the radiation in the solar corona. From this, the strength of the coronal magnetic field in the active region was found to be H=20–65 G at a height of h= (5.7–8.7)×109 cm above the photosphere on 22 and 30 August and 125 G at the lower height of (3.7–6.4)×109 cm on 23 August. We present a new technique, based on the radio mapping (in both Stokes I and V) of an AR undergoing circular polarization inversion; applying this method to the Nobeyama data we obtained, for the first time, a magnetogram of the coronal magnetic field. For AR 7260 we found values in the range of 70–100 G at heights of (4–6)×109 cm on 23 August, adopting a constant value of NL (where N is the electron density and L is the scale of the coronal field divergence) of 2.5×1018 cm–2. We compare our results with force-free extrapolations of the photospheric magnetic field from a MSFC magnetogram obtained on 20 August.     

The application of a non-static spherically-symmetric metric to clusters of galaxies

An approximate metric is found which represents a sphere of matter embedded in a background of dust. The use of this metric in conjunction with the Friedmann equations gives values of for the three possible values ofk as +6×10^–36 (k=+1), +3×10^–35 (k=0), +10^–36 (k=–1). These values depend on data regarding clusters of galaxies, and are probably accurate to within an order of magnitude given the correctness of the assumptions on which their derivation rests.     

Ionization equilibrium and spectrum formation in QSOs' absorption regions

The behaviour of the primary and secondary components in a sample of double-lined Algol-type eclipsing binaries in the logg-logT _e diagram is analyzed. Our results indicate that the hotter components behave like normal Main-Sequence stars while the effect of irradiation may partly explain the overluminosity of the cool components.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

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.     

Models of clusters of point masses with large central redshifts

Conclusions In the Newtonian case we have obtained an isotropic self-consistent distribution of gravitationally interacting point masses which satisfies the transport equation without collisions, and the gravitational equation for an arbitrary powerfunction density distribution =r^–s, s<3.For =r^–2 the analogous self-consistent solution was obtained for the anisotropic distribution function both in Newtonian and GTR cases.The GTR solutions with =r^–2 have central redshifts which increase without limit in accordance with the law 1+zr^–1/ as we approach the center. In the isotropic case, they appear to be stable when the mean velocities are much less than the velocity of light u<0.2c, >21.The hydrodynamic GTR solution was found for a perfect gas at constant temperature (but variable T=T(g₀₀)^1/2) which also has z for r0.We should like to thank K. Thorne, L. Hazin, and M. Podurets for valuable discussions. K. Thorne was particularly helpful in supplying unpublished results on circular orbits obtained by American authors.Astrofizika, Vol. 5, No. 2, pp. 223–234, 1969     

Study of the nonradial directional property of the rays of the streamer belt and chains in the solar corona

Based on analyzing corona images taken by the LASCO C1, C2, and C3 instruments, a study is made of the behavior of the streamer belt spanning one half of the 1996–2001 cycle of solar activity, from minimum to maximum activity, in the absence of coronal mass ejections. It is shown that: (1) The position of the streamer belt relative to the solar equator is generally characterized by two angles: _o and _E, where _o is the latitudinal position (near the solar surface) of the middle of the base of the helmet, the top of which gradually transforms to a ray of the streamer belt with a further distance from the Sun, and _E is the latitude of this ray for R>5–6 R from the Sun's center where the ray becomes radial. (2) Only rays lying at some of the selected latitudes _o retain their radial orientation (_oE) throughout their extent. Namely: _o0° (equator), _o±90° (north and south poles), and the angle _o lying in the range ±(65°–75°) in the N- and S-hemispheres. (3) A deviation of rays from their radial orientation in the direction normal to the surface of the streamer belt occurs: for latitudes _o<|65°–75°| toward the equator (>0°) reaching a maximum in the N and S hemispheres, respectively, when _OM40°, and _OM–42° for latitudes _o>|65°–75°| toward the pole (<0°). The regularities obtained here are a numerical test which can be used to assess of the validity of the theory for describing the behavior of the Sun's quasi-stationary corona over a cycle of solar activity.     

Wolf-Rayet binaries: Evolutionary causes for their distribution in the Galaxy

On the basis of the most recent data, the fraction of known Wolf-Rayet binaries is 0.22. In the solar neighbourhood (d<2.5 kpc) this fraction is 0.34In order to assess the relative importance of massive binary evolution as one of the ways to produce WR stars, the galactic distribution of WR binaries is compared with that of single WR stars using improved intrinsic parameters and new data for the fainter WR stars.In the galactic plane the increase of the binary frequency with galactocentric distance is confirmed.In a direction perpendicular to the galactic plane it is demonstrated at all distances from the Sun that the single-line spectroscopic WR binaries with small mass functions have definitely larger -distances than the single WR stars and the WR binaries with massive companions. This is consistent with the evolutionary scenario for massive binaries summarized by van den Heuvel (1976). Among the single WR stars the fraction of those with large |z|-distances is increasing with galactocentric distance, like the fraction of the known binaries. This implies that among the high-|z| single WR stars as well as among the WR stars with lower |z|-values many binaries are still to be discovered.The total WR binary frequency in the Galaxy could be well above 50%.Contribution from the Bosscha Observatory No. 79.Invited paper presented at the Lembang-Bamberg IAU Colloquium No. 80 on Double Stars: Physical Properties and Generic Relations, held at Bandung, Indonesia, 3–7 June, 1983.     

A search for the Hα emission in spectroscopic binaries of the spectral types B0–B9

The H emission is searched for 67 spectroscopic binaries of the spectral types B0–B9 and of the orbital period 1–1000 days. Among them the H emission is detected in 13 stars with various intensity. The results of this inspection are presented. When combined with the previous data, our results show that the Be-star frequency in spectroscopic binaries along the orbital periods exhibits a sharp maximum in the period range 100–300 days, and that the stars of strong H emission concentrate in the same period range.     

On the stability of small quasiperiodic motions in the hamiltonian systems

Orbital stability of quasiperiodic motions in the many dimensional autonomic hamiltonian systems is considered. Studied motions are supposed to be not far from equilibrium, the number of their basic frequencies may be not equal to the number of degrees of freedom, and the procedure of their construction is supposed to be converged. The stability problem is solved in the strict nonlinear mode.Obtained results are used in the stability investigation of small plane motions near the lagrangian solutions of the three-dimensional circular restricted three-body problem. The values of parameters for which the plane motions are unstable have been found.

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Statistical models for HIPPARCOS binaries

A statistical model for the binaries in the solar neighbourhood is constructed, using schematic but plausible distribution functions for the semi-major axes, the mass-ratios, and the eccentricities. The model is calibrated to give correct numbers of observed visual binaries and is then used to study the (closer) binaries of relevance for the HIPPARCOS mission. One main purpose is to estimate the influence of astrometric binaries observed by their photocentres. It is found that some 500 such systems (out of the 100000 stars observed by HIPPARCOS) should show a detectably curved motion, while more than ten times more show an orbital proper motion bias greater than the HIPPARCOS accuracy 0.002 yr^–1. Also, a non-negligible fraction (1%) of all stars will be binaries with periods close to 1 year causing problems for the parallax determination. The main contribution to these figures is from faint Main-Sequence stars. The period-distribution for the resolved HIPPARCOS binaries is also obtained, and for many of them the periods are fairly short (<100 yr). Such data as these are to be used as guidelines in the construction of reduction software for the HIPPARCOS observations.Communication presented at the International Conference on Astrometric Binaries, held on 13–15 June, 1984, at the Remeis-Sternwarte Bamberg, Germany, to commemorate the 200th anniversary of the birth of Friedrich Wilhelm Bessel (1784–1846).     

The eclipses of starspots

Formulae are set out from which the light loss may be derived in a close binary system in which a component affected by a starspot, of the type considered previously (Budding, 1977) is also in eclipse, in such a way that the starspot itself is undergoing eclipse. In this way the hitherto postponed problem of thecombination of eclipse and maculation effects — which are sometimes believed to be present, e.g., in RS CVn-stars — is treated, and shown to be reducible to expressions involving algebraic or elliptic integrals.A more practical approach using a small-spot approximation is given, and demonstrated on an example. Such an approach should be easy to manage by computer, and is expected to find a ready application in the analysis of active cool, close binaries.     

Radial pulsation of less-massive yellow supergiants

The conclusions of the present paper broadly are: (a) The galactic concentration of doubles by comparing the distributions in galactic latitudes 0°<20° and >40° is nearly twice as large as the galactic concentration of stars in general. (b) The astrographic catalogues are not complete in the fainter magnitudes. (c) The large value of the ratioT:O _k (observed to optical number of pairs) from Kreiken's formula shows that almost all stars in the group 0<d5 and quite a few in the other two groups, viz., 5<d10 and 10<d15 might be shown true binaries. Consequently, Aitken's working definition of a true binary should be extended if it were to include all true binaries. (d) The doubles are probably stars of Population I. (e) The logarithm to the base 10 of the cumulative counts can be represented by an empirical relationA+B(m–1.5)+C(m–1.5)².Communication presented at the International Conference on Astrometric Binaries, held on 13–15 June, 1984, at the Remeis-Sternwarte Bamberg, Germany, to commemorate the 200th anniversary of the birth of Friedrich Wilhelm Bessel (1784–1846)     

Sur les solutions Lagrangiennes et euleriennes du probleme generalise des trois corps en axes absolus

Résumé Le présent travail est une continuation d'un autre, publié plus tôt (Doubochine, 1970). On montre ici, que les propriétés des mouvements Lagrangiens et Euleriens établies en mécanique céleste classique sont vraies aussi dans les cas plus généraux, envisagés dans le travail indiqué. On montre de plus, que les trajectoires des points en ces mouvements en axes absolus sont les spirales infinies s'enroulant sur les surfaces des cylindres curvilignes infinis.

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Оπорная селенодезическая система координат по гелиометрическим наБлюдениям луны В казани

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The spectroscopic study of astrometric binaries

The spectroscopic observations of several astrometric binaries, obtained by the author during the past 20 years, are described. Main emphasis is placed on the determination of orbital elements of visual binaries, and the detection of unseen companions.Communication presented at the International Conference on Astrometric Binaries, held on 13–15 June, 1984, at the Remeis-Sternwarte Bamberg, Germany, to commemorate the 200th anniversary of the birth of Friedrich Wilhelm Bessel (1784–1846).     

A search for soft X-ray emission from stellar sources

With the soft X-ray detector (0.2–0.284 keV) aboard the Astronomical Netherlands Satellite (ANS) we have searched for X-ray emission from hot star coronae and peculiar stars. On Sirius ( CMa) and Capella ( Aur) X-ray emission has been measured at 6 and 5 level, respectively, above background. In all other cases the search revealed no evidence for soft X-ray emission. Upper limits to the luminosities of about 25 star coronae (main-sequence stars, (sub)giants, and supergiants) and of 4 peculiar stars ( Sco, Lyr, P Cyg, and Car) have been obtained.Paper presented at the COSPAR/IAU Symposium on Fast Transients in X-and Gamma-Rays, held at Varna, Bulgaria, 29–31 May, 1975.     

On the Power in the Legendre Modes of the Solar Radial Magnetic Field

The power in the different modes of an expansion of the solar radial magnetic field at the surface in terms of Legendre polynomials,P , is calculated with the help of a solar dynamo model studied earlier. The model is of the Babcock–Leighton type, i.e., the surface eruptions of the toroidal magnetic field – through the tilt angle, , formed by the magnetic axis of a bipolar magnetic region with the east-west line – are the sources for the poloidal field. In this paper it is assumed that the tilt angle is subject to fluctuations of the form, = ()+ <> where <> is the average value and () is a random normal fluctuation with standard deviation which is taken from Howard's observations of the distribution of tilt angles. For numerical considerations, negative values of were not allowed. If this occurred, was recalculated. The numerical integrations were started with a toroidal magnetic field antisymmetric across the equator, large enough to generate eruptions, and a negligible poloidal field. The fluctuations in the tilt angle destroy the antisymmetry as time increases. The power of the antisymmetric modes across the equator (i.e., odd values of ) is concentrated in frequencies, _p, corresponding to the cycle period. The maximum power lies in the =3 mode with considerable power in the =5 mode, in broad agreement with Stenflo's results who finds a maximum power at =5. For the symmetric modes, there is considerable power in frequencies larger than _p, again in broad agreement with Stenflo's power spectrum.     

The rate of growth of density perturbations in simple big-bang model universes

In this paper we present exact solutions to the density perturbation equation derived by Bonnor for the cases where = _c ,k=1 and = – _c ,k=–1. The solutions when =0,k=1 and =0,k=–1 have been previously published. Using these solutions a quantitative analysis has been carried out that has enabled us to estimate the size of the fluctuations that must be postulated at decoupling in order to explain the formation of the galaxies in these model universes.     

Околозвездньiе облака поданньiм ультрафиолетовьiх спектров свезл

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