On convergence of an asymmetrical body potential expansion in spherical harmonics

The gravity potential of an arbitrary bodyT is expanded in a series of spherical harmonics and rigorous evaluations of the general termV _n of the expansion are obtained. It is proved thatV _n decreases on the sphere envelopingT according to the power law if the body structure is smooth. For a body with analytic structure,V _n decreases in geometric progression. The exactness of these evaluations is proved for bodies having irregular and analytic structures. For the terrestrial planetsV _n =O (n ^–5/2).

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I I V _n IV _n I . . IV _n I . I. IV _n =O(n ^–5/2 )

     

Time Evolution of low-Frequency Periodicities in Cosmic ray Intensity

The long-time series of daily means of cosmic-ray intensity observed by four neutron monitors at different cutoff rigidities (Calgary, Climax, Lomnický tít and Huancayo/Haleakala) were analyzed by means of the wavelet transform method in the period range 60 to 1000 days. The contributions of the time evolution of three quasi-periodic cosmic-ray signals (150 d, 1.3 yr and 1.7 yr) to the global one are obtained. While the 1.7-yr quasi-periodicity, the most remarkable one in the studied interval, strongly contributes to the cosmic ray intensity profile of solar cycle 21 (particularly in 1982), the 1.3-yr one, which is better correlated with the same periodicity of the interplanetary magnetic field strength, is present as a characteristic feature for the decreasing phases of the cycles 20 and 22. Transitions between these quasi-periodicities are seen in the wavelet power spectra plots. Obtained results support the claimed difference in the solar activity evolution during odd and even solar activity cycles.     

Periodicity in filamentary activity

This paper presents the results of the study on the periodicity in filament activity. The spectral analysis of the number of filaments shows a basic period at 141 (10.5 yr), at 138 (10.3 yr), and at 144 (10.7 yr) Carrington rotation in the northern and southern hemisphere, respectively.The time series concerning the index of filament activity shows also a typical period at 135 Carrington rotation (10.1 yr) at 144 Carrington rotation (10.7 yr) and at 133 Carrington rotation (9.9 yr), respectively, in the northern and southern hemisphere.The power spectrum analysis of the time series of the filamentary activity in the short-term also yields less pronounced but still noticeable peaks which are statistically significant.     

Rapid changes in the fine structure of a coronal ‘bright point’ and a small coronal ‘active region’

A coronal bright point is resolved into a pattern of emission which, at any given time, consists of 2 or 3 miniature loops (each 2500 km in diameter and 12 000 km long). During the half-day lifetime of the bright point individual loops evolved on a time scale 6 min. A small ctive region seemed to evolve in this way, but the occasional blurring together of several loops made it difficult to follow individual changes.     

Low noise beam-lead diode mixer for the 3 mm radio astronomical receiver at the metsähovi radio research station

A 3 mm low noise beam-lead Schottky diode mixer has been developed. At cryogenic temperatures the conversion loss is 6.3 dB, and the DSB mixer noise temperature is 75 K, respectively. The mixer was installed into the cooled receiver for radioastronomical observations at the Metsähovi 13.7-m radio telescope. Total DSB noise temperature of the cooled receiver with an ultra low noise HEMT IF amplifier was 110 K at 103 GHz. The tuning range of the mixer mount was from 70 GHz to 115 GHz.     

Short-Term Periodicities in the Time Series of Solar Radio Emissions at Different Solar Altitudes

A spectral analysis of the time series of daily values of 12 parameters, namely, ten solar radio emissions in the range 275–1755 MHz, 2800 MHz solar radio flux, and sunspot numbers for six continuous intervals of 132 values each during June 1997–July 1999 showed considerable differences from one interval to the next, indicating a nonstationary nature. A 27-day periodicity was noticed in Interval 2 (26.8 days), 3 (27.0 days), 5 (25.5 days), 6 (27.0 days). Other periodicities were near 11.4, 12.3, 13.3, 14.5, 15.5, 16.5, 35, 40, 50–70 days. Periodicities were very similar in a large vertical span of the coronal region corresponding to 670–1755 MHz. Above this region, the homogeneity disappeared. Below this region, there were complications and distortions due to localized solar surface phenomena.     

Structure and evolution of solar radio bursts at 26.4 MHz

Two dimensional source brightness distributions at 26.4 MHz for solar bursts of spectral type II, III, IV, and V are derived from observations with a multiple-baseline, time-sharing interferometer system. It was designed explicitly to study the large angle (40 halo) component of low frequency solar bursts first reported by Weiss and Sheridan (1962). Thirty-two bursts occurring in the interval of June–August, 1975, were fit with a circular gaussian core and an elliptical gaussian halo component. Half-power halo diameters (E-W×N-S) averaged 30×28 for type III bursts and 42×27, 28×37, 30×25 for type V, II and IV bursts respectively. Typical core sizes fell in the range of 10±4 giving 31 halo to core size ratio. All burst types were found to have some large angle structure: the specific intensity was 10% compared to the core but the total power in each component was comparable. Two processes for producing the core-halo structure of type III bursts are compared: scattering and refraction of a point source and refraction from many sources over an extended region. It is concluded that the core can be explained by either model but the halo is more consistent with emission from an extended source region of 40° in longitude.     

A model for interstellar extinction

From an analysis of the interstellar extinction we conclude that interstellar grains are of three main kinds: graphite spheres of radii 0.02 m making up 10% of the total grain mass, small dielectric spheres of radius about 0.04 m making up 25% of the mass, and hollow dielectric cylinders containing metallic iron with diameters of 2/3 m making up 45% of the mass. The remaining 20% consists of other metals and metal oxides. The main dielectric component of the grains appears to be comprised of organic material.     

Sub-arcsecond 10 micron imaging of newly-formed stars

We describe initial results of a program to image massive newly-formed stars with sub-arc second spatial resolution. We discuss high-precision diffraction-limited size measurements at =10 m made using the 3 m Lick telescope. The point-spread function has FWHM 0.7; deconvolution yields a spatial resolution of 0.35. We find that the core component of one such object, LkH 101, is unresolved at these scales, and we are able to set a 95%-confidence upper limit of 270 AU for the diameter of the circumstellar dust shell. This places the dust at the same radial scale as a strong ionized stellar wind region seen at radio wavelengths. Our observations, when combined with published spectral observations, rule out an optically thick circumstellar disk but allow a radially thin, anisotropic distribution of dust, or alternatively an isotropic distribution of dust with a narrow range of large grain sizes.     

Massive accretion disks

Recent high resolution near infrared (HST-NICMOS) and mm-interferometric imaging have revealed dense gas and dust accretion disks in nearby ultra-luminous galactic nuclei. In the best studied ultraluminousIR galaxy, Arp 220, the 2m imaging shows dust disks in both of the merging galactic nuclei and mm-CO line imaging indicates molecular gasmasses 10⁹M for each disk. The two gas disks in Arp 220 are counterrotating and their dynamical masses are 2×10⁹ M , that is, only slightly largerthan the gas masses. These disks have radii 100 pc and thickness 10-50 pc. The high brightness temperatures of the CO lines indicatethat the gas in the disks has area filling factors 25-50% and mean densitiesof 10⁴ cm^-3. Within these nuclear disks, the rate of massive star formation is undoubtedly prodigious and, given the high viscosity of the gas, there will also be high radial accretion rates, perhaps 10 M yr ^-1. If this inflow persists to very small radii, it is enough to feed even the highest luminosity AGNs.     

In situ acceleration and gradients of charged particles in the outer solar system observed by the voyager spacecraft

The probable connection between cosmic rays and the electromagnetic state of the interplanetary medium was recognized by Hannes Alfvén as early as 1949 (Alfvén, 1949, 1950); he pointed out that the properties of cosmic rays necessitate a mechanism, external to Earth but within the solar system, capable of accelerating particles to extremely high energies. In advocating the view of local origin for part of the cosmic-ray spectrum, Alfvén and his colleagues developed a very general type of acceleration mechanism called magnetic pumping. The unique data set of the two Voyagers extends over an entire decade (1977–1987) and is most suitable to explore the problem of acceleration of charged particles in the heliosphere. The energy coverage of the Low Energy Charged Particle (LECP) experiment covers the range 30 keV to several hundred MeV for ions and 22 keV to several MeV for electrons. Selected observations of interplanetary acceleration events from 1 to 25 AU are presented and reviewed. These show frequent acceleration of ions to several tens of MeV in association with shocks; highest energies (220 MeV oxygen) were measured in the near-perpendicular ( _Bn 87.5°) shock of January 5, 1978 at 1.9 AU, where electron acceleration was also observed. Examples of ion acceleration in association with corotating interaction regions are presented and discussed. It is shown that shock structures have profound effects on high-energy (70 MeV) cosmic rays, especially during solar minimum, when a negative latitudinal gradient was observed after early 1985 at all energies from 70 MeV down to 30 keV. By early 1987, most shock acceleration activity in the outer heliosphere (25 to 30 AU) had ceased both in the ecliptic (Voyager-2) and at higher (30°) ecliptic latitudes (Voyager-1). The totality of observations demonstrate that local acceleration to a few hundred MeV, and as high as a few GeV is continually present throughout the heliosphere. It should be noted that in 1954 when Alfvén suggested local acceleration and containment of cosmic rays within the solar system, no one treated his suggestion seriously, at any energy. The observations reviewed in this paper illustrate once more Alfvén's remarkable prescience and demonstrate how unwise it is to dismiss his ideas.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

The fundamental role of giant comets in earth history

We discuss some fundamental aspects of Earth history as predicted by what has come to be called coherent rather than stochastic catastrophism. The latter essentially seeks to provide an understanding of terrestrial evolution in terms of occasional kilometre-plus impactors from the asteroid belt whereas the former recognises a far more complex extraterrestrial regime arising from the streams of sub-kilometre and kilometre-plus debris due to the disintegration of successive giant comets in sub-Jovian orbits. Periodicities of 15 Myr during the later Phanerozoic (i.e. 250 to 0 Myr BP) and 200 yr during the Holocene (i.e. 10,000 to 0 yr 1313) are likely fundamental signatures in the terrestrial record relating to the action of past and present giant cornets respectively.     

Optically thick accretion onto black holes

Spherically symmetric, steady-state, optically thick accretion onto a nonrotating black hole with the mass of is studied. The gas accreting onto the black hole is assumed to be a fully ionized hydrogen plasma withn ₀=10⁸ cm^–3 andT ₀=10⁴ K far from the black hole, and a new approximate expression for the Eddington factor is introduced. The luminosity is estimated to beL=1.875×10³³ erg s^–1, which primarily arises from the optical surface (1) ofT10⁴ K. The accretion flow is characterized by 1 and (v/c)10. In the optically thin region, the flow remains isothermal, and the increase of temperature occurs at 1. The radiative equilibrium is strictly realized at (v/c)10.     

The solar O i λ 7773 triplet

The reduction of observations of the O i 7773 triplet obtained at high spatial resolution (0.5) at two disk positions is described. Two sets of triplet profile data are presented at each disk position. One set represents data taken from 0.5 regions centered on the brightest granules, while the other set represents data taken from 0.5 regions centered on the cooler infalling intergranular material.     

The virial-based solution for the velocity of gaseous sphere gravitational contraction

It is found that the relationship between the potential energy and the moment of the inertia independent of the radial mass distribution obtained earlier for the sphere also holds in the case of the ellipsoidal mass distribution for the ellipsoid of rotation.The possibility of application of the energy virial relations for solution of the evolutionary problems of the gravitating gaseous sphere, with the help of the relationship found earlier, is demonstrated. The physical conditions on the gaseous sphere boundary are introduced. The existence of two branches of evolution, the proton one and the electron one, is established. The problem of the gravitational contraction velocity during sphere evolution is solved. The relationship between the boundary temperature and the gaseous sphere radius as well as between the luminosity and the body mass is obtained. Some limiting relations for the final stage of the gaseous sphere evolution are found.

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, , , . . . — . . , . .

     

Impulsive phenomena in a small active region

The temporal and spatial variations of EUV emission from a small growing active region were investigated. Frequent localized short term ( few minutes) fluctuations in EUV emission were observed throughout the 7.2 hr interval when the most continuous observations were acquired. Approximately 20% of the 5 x 5 pixels had intensity variations exceeding a factor of 1.3 for the chromospheric L line, a factor of 1.5 for lines formed in the chromospheric-coronal transition region and a factor of 1.4 for the coronal Mg x line. A subflare in the region produced the largest intensity enhancements, ranging from a factor of 2.3 for the chromospheric L line to 8 for the transition region and coronal lines. The EUV fluctuations in this small active region are similar to those observed in coronal bright points, suggesting that impulsive heating is an important, perhaps dominant form of heating the upper chromospheric and lower coronal plasmas in small magnetic bipolar regions. The responsible mechanism most likely involves the rapid release of magnetic energy, possibly associated with the emergence of magnetic flux from lower levels into the chromosphere and corona.     

Different ages of lunar light plains

The crater populations of 18 lunar light plains (Cayley plains) show a variation in relative ages by a factor of about 4 in crater frequency of regions in the surroundings of the Orientale resp. Imbrium basin, and by a factor of greater than 25 for more distant sites. Thus the idea of a Moonwide synchronism in the emplacement of the lunar light plains with the formation of the basins Imbrium or Orientale cannot be supported.Some light plains are younger than the youngest basin Orientale. Since these plains cannot have been emplaced by any other basin-forming event and local impact-derived origin can certainly be excluded, an endogenic (magmatic) origin is proposed for these plains.Age determination data (D _L -values) by Soderblom and Lebofsky (1972) and Soderblom and Boyce (1972) are shown to be correlated with own cumulative crater frequency data (N) for surfaces younger than 3.8 × 10⁹ years; we findD _L × N ^0.6, different from the originally proposed relationD _L × N. For ages > 3.8 × 10⁹ years, theD _L data by those authors, especially their light plains data, are incompatible with our crater frequency data.     

Implications of a strongly peaked polar magnetic field

Using the flux-transport equation in the absence of sources, we study the relation between a highly peaked polar magnetic field and the poleward meridional flow that concentrates it. If the maximum flow speed _m greatly exceeds the effective diffusion speed /R, then the field has a quasi-equilibrium configuration in which the poleward convection of flux via meridional flow approximately balances the equatorward spreading via supergranular diffusion. In this case, the flow speed () and the magnetic field B() are related by the steady-state approximation () (/R)B()/B() over a wide range of colatitudes from the poles to midlatitudes. In particular, a general flow profile of the form sin ^p cos ^q which peaks near the equator (q p) will correspond to a cos ⁿ magnetic field at high latitudes only if p = 1 and _m = n /R. Recent measurements of n 8 and 600 km² s^–1 would then give _m 7 m s^–1.     

Inverse compton effect and the colorimetric characteristics of flare stars

It is shown that the observed color diagrams(U-B) _f (B-V) _f for pure flare emission of UV Cet type flare stars may be explained within the framework of a fast electron hypothesis. We point out the essential influence on these color indices of the two following factors: (a) the deviations of the normal radiation capability of the star in the infrared region of spectra (on 3.6 m, 4.4 m, and 5.5 m) from the Planckian distribution; (b) the location of the cloud (source) of fast electrons around the star (flare geometry effect). Under the real conditions of the generation of flares around the star the frequency transformation law at the photon-electron interaction has a view =n²₀, wheren may take the different values-from 0.15 up to 4; it depends on the cloud-star-observer geometry. By the observed colors of the flare emission may be understood, in principle, the location of flare source around the star. A possible role of reflection effect at the generation of stellar flares is outlined.     

Theory of the Trojan asteroids

In the previously published Parts I and II of the paper, the author has constructed a formal long-periodic solution for the case of 11 resonance in the restricted problem of three bodies to 0(m ^3/2), wherem is the small mass parameter of the system. The time-dependencet(, ,m), where is the mean synodic longitude and is related to the Jacobi constant, has been expressed by ahyperelliptic integral. It is shown here that with the approximationm=0 in the integrand, the functiont(, , 0) can be expanded in a series involving standardelliptic functions. Then the problem of inversion can be formally solved, yielding the function (t, , 0).Similarly, the normalized period (,m) of the motion can be approximated by theHagihara hyperelliptic integral (, 0), corresponding tom=0. This integral is also expanded into elliptic functions. Asymptotic forms for (, 0) are derived for 0 and for 1, corresponding to the extreme members of thetadpole branch of the family of orbits.