Stability of the solar system

If the solar system is considered as a mechanical clockwork consisting of its present members which attract each other as mass-points, the extent of its present approach to secular stability (i.e., the state of minimum potential energy) — manifested by the existence of a number of nearcommensurabilities of the present orbital periods, not only of the planets, but also of their satellites —could not have been attained in a time-span of 4.6×10⁹ yr of its age by gravitational perturbations alone.The existence of such commensurabilities — striking in many instances— could then be understood only on the assumption that either (a) the solar system was actually born with the present 2-, 3- and 4-term couplings between the orbital period of the planets already built-in from the outset (which is improbable on any known grounds); or (b) that these couplings — in particular, the 25 Jupiter-Saturn commensurability — have arisen as a result of tidal interaction between proto-planetary globes of much larger dimensions than these planets possess today. For the present dimensions and mutual distances of these planets, their tidal interaction in 10⁹ yr would exert but negligible effects; and during that time neither their masses, nor the scale of the solar system underwent any essential change.Therefore, a hypothesis is proposed that the situation now obtaining had its origin in the early days of the formation of the solar system, when the planetary globes — in particular, those of Jupiter and Saturn (now in the terminal stage of Kelvin contraction) — were very much larger than they are today; and when, as a result, the tidal coupling between them operated at a much higher rate than at the present time.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

A river erosion estimate on the Loess Plateau: a case study from Luohe River, a second-order tributary of the Yellow River

Based on fieldwork and terrace ages, which were determined using ¹⁴C, TL and paleosol stratigraphy, a general model was established for the development of the Yellow River terrace system. The ages for the terraces and valley flats of the Yellow River system are T₆—1.67–0.85 Ma BP, T₅—0.85–0.47 Ma BP, T₄—0.47–0.10 Ma BP, T₃—0.10–0.007 Ma BP, T₂—7.0–0.7 ka BP, T₁—0.7–0.3 ka BP, the higher valley flat—0.3–0.15 ka BP and the lower valley flat 0.15–0 ka BP, respectively. Each terrace or valley flat and corresponding paleo-valley represents a river erosion/deposition cycle. Using this model and selected geomorphic parameters of terraces and paleo-valleys from 10 typical cross sections of Luohe River, a tributary of the Yellow River, an attempt is made here to estimate paleo-river erosion since the Pleistocene on the Loess Plateau.     

The host galaxies of nearby Seyfert 1 nuclei

We use optical and infrared imaging data of a complete hard X-ray selected sample of AGN to investigate the host galaxies of nearby Seyfert 1 nuclei. We disentangle the emission due to the unresolved point source and the resolved host galaxy by means of luminosity profile fitting. The stellar colours in the nucleus are redder inB — V andV — K than in normal spiral bulges or current stellar evolutionary models, probably due to dust obscuration.J — H colour is quite normal butH — K usually very red, probably indicating a large contribution from reradiating hot dust to the IR colours. No significant difference in IR colours oi the stellar component is found with respect to a comparison sample of Liners and starbursts, except that the reradiating dust in Seyferts tends to be hotter and lie closer to the nucleus.B — V colour gets slightly bluer towards the nucleus, whereasV — K andJ — K have red gradients.B — V andJ — K gradients are not correlated and are likely to be caused by different mechanisms. There is a clear correlation between the AGN and host luminosity. Finally, we present optical colour ratio maps of two Seyfert nuclei, NGC 3227 and NGC 7469. The blue, ringlike or elongated structure in the maps and its correspondence with molecular CO geometry is interpreted as evidence for circumnuclear star formation in these AGN.     

Expression of the initial Poincaré canonical variables as functions of the new in a ninth order J-S theory

We establish the solution of the ninth order — in masses — canonical J-S equations of motion by Hori-Lie technique — i.e., by expressing the initial Poincaré canonical variables as functions of the new variables through the Hori-Lie canonical transformation. Terms of order higher than 9 in the masses are neglected.     

Method of density moment sums for photometric calibration of photographic plates

A new method — the method of moment density sums — is suggested for determining the characteristic curve of a plate as well as the magnitude zero point, using PDS microdensitometer measurements of stars of known brightness. It may be used for surface photometry of plates without sensitometer spots.     

Tectonics of Venus: A review

The article presents a new tectonic scheme of Venus and gives the following interpretation of the planet's main structural units: (1) plains — areas of flood volcanism over stretched crust; (2) dome-like uplifts — areas of uplifting and volcanic activity above the mantle hot-spots; (3) coronae —former dome-like uplifts, partially subsided and diffused by gravity; (4) ridge belts — fold zones; (5) tesserae — fragments of ductile compression and shortening of crust; (6) supercoronae — coronae formed in the course of further evolution and relaxation of Beta-type uplifts. Ishtar Terra is considered to be a fragment of an ancient tessera paleocontinent, on the edge of which the Lakshmi supercorona is superimposed. Aphrodite Terra is considered as a belt of mantle hot-spot structures (dome-like uplifts, coronae, supercoronae, volcanoes, rifts).Three types of planetary belts have been distinguished on Venus: uplifted 'weakened' belts with an abundance of mantle hot-spot structures; a northern fan of ridge belts; and belts of low basalt plains. The center of the planetary system of uplifted weakened belts is situated in Atla Regio.The present tectonic structure of Venus is inferred to have formed during two stages of evolution characterized by different tectonic regimes. Stage I is a regime of soft ductile plates (formation of tessera uplifts and volcanic plains). Stage II is a formation of 'weakened' uplifted planetary belts, various tectonic regimes of mantle hot-spots, and plains-forming volcanism.'Geology and Tectonics of Venus', special issue edited by Alexander T. Basilevsky (USSR Acad. of Sci. Moscow), James W. Head (Brown University, Providence), Gordon H. Pettengill (MIT, Cambridge, Massachusetts) and R. S. Saunders (J.P.L., Pasadena).     

Strained co-ordinate methods in rotating stars

It was shown in a previous paper, Smith (1975), that the determination of the structure of rotating polytropes by expansion in the small rotational parameter constitutes asingular perturbation problem as arises also, for example, in large Reynolds' number approximations in fluid dynamics. The technique used by him — the method of matched asymptotic expansions — is, in fact, just an extension of the Prandtl boundary layer theory familiar in this latter context. In this paper — the first of two — we introduce an alternative procedure: the method of strained co-ordinates; and for comparison purposes again consider rotating polytropes. In Paper II we extend this approach to differentially rotating stars and present an illustrative example.     

The Sun as a system of elementary particles

No unusual observation of the Sun is described here. No new theory is proposed. The paper — based on known facts of solar physics — is a modest attempt to interpret the Sun as a selfgravitating system of about 10⁵⁷ nucleons and electrons. These elementary particles are endowed with strong, electromagnetic, weak and gravitational interactions. Origin of the Sun, its evolution, structure and physiology are consequences of the four interactions.     

The Influences of Shock Thickness and Alfven Waves on the Particle Acceleration by Diffusive Shocks

The influences of the shock thickness and Alfven waves on the particle acceleration by diffusive shock waves are numerically studied through solving one-dimensional diffusive equation including the second-order Fermi effect. It is shown that the spectral index of the energetic particles strongly depends on the shock thickness. For example, the spectral index increases from 2.1 to 3.7 in the low energy range of 3—10 MeV and from 2.5 to 5.0 in the high energy range of 20—60 MeV as the thickness increases. The spectral index decreases from 4.3 to 3.1 as the particle injection energy increases. The spectral index decreases from 4.0 to 1.8 at the quasi-steady stage with the enhancement of the compression ratio from 2 to 4. The results indicate that under the influence of Alfven waves, the energetic particle spectrum at lower energy becomes flat and the spectral index decreases from 2.5 to 0.6 in the low energy range of 3—10 MeV and from 11.6 to 5.0 in the high energy range of 20—60 MeV. At the same time, the turning point energy reaches 19.6 MeV. The spectral index decreases from 5.8 to 2.9 as the energy density of Alfven waves increases. All these results are basically consistent with the theoretical models, as well as the observations of typical energetic particle events.     

A discussion of the Cepheid amplitude behaviour in the instability strip

An analysis is presented which seeks to reveal the possible causes for discrepancy in the results on the dependence of Cepheid amplitudes on star positions in the instability strip noted by different investigators.A comparison of the data used in two of these investigations—that of Yakimova (1970) and that of Sandage and Tammann (1971)—shows that it is most unlikely to be able to explain completely the conflicting results obtained in these studies. But if we analyse the data of Sandage and Tammann following the approach of Yakimova — namely, by considering the Cepheids in only one stellar system and taking into account the stellar colours in maximum light — we obtain Yakimova's result: the light amplitude is the larger, the nearer to the low temperature edge of the instability strip a Cepheid is. Therefore, it appears that differences between the various approaches contribute greatly to the different results of Sandage and Tammann and Yakimova (and the other investigators).     

Sources of error in the photoclinometric determination of planetary topography: A reappraisal

The technique of photoclinometry has frequently been used to determine planetary topography without proper consideration of possible sources of error. Previous studies of error sources have been limited in extent and have overlooked the importance of factors such as atmospheric scattering and the choice of a surface photometric function. This paper adopts a thorough and more direct approach to error analysis, whereby known topography is compared with photoclinometric profiles derived from synthetic quantised reflectance scans.Instrumental and geometric sources of error are found to exert a minimal influence on profiles in practice, provided that sufficient care is taken in the selection of images and the extraction of scans from those images. Environmental factors — relating to the scattering properties of the surface and, if present, atmosphere — are far more important. It is found that a simple Lommel-Seeliger law is unlikely to be appropriate to the majority of planetary terrains, given its inability to model the effects of multiple scattering or unresolved macroscopic roughness. It is further demonstrated that a Minnaert function or combination of Lommel-Seeliger and Lambert laws may empirically compensate for the first of these phenomena but not the second; in this respect, Hapke's equation is a far superior model of surface optical properties. In the case of an atmosphere, the need to correct for scattering by aerosols or suspended dust becomes more acute as atmospheric opacity increases and as particle scattering becomes more forward-biased. To perform this correction, a model for the combined reflectance of surface and atmosphere must be used when deriving profiles.Two case studies — of a small impact crater on Triton and a dust-mantled basaltic lava flow on Mars - are presented here. Regarding the latter, the implications that errors in photoclinometric flow thickness measurements have for inferred lava rheology are examined. Conservative estimates of errors in yield strength and apparent viscosity easily exceed 100% when one of the simplest photometric models possible — a Lommel-Seeliger law — is used to derive a profile.In the light of these findings, strategies are suggested for improving the results obtained from photoclinometry in the future.     

Velocities and birthplaces of pulsars

The values of the proper motions of 36 pulsars are analysed. It is shown that the birthplaces of pulsars are located within the OB-associations and/or in the galactic arms. Eleven cases of pulsar formation in associations, and fourteen cases of formation in the galactic arms, have been established. More precise parameters of pulsars — such as: distances, ages, spatial velocity components —, and the spatial velocity distribution of pulsars is constructed.     

A new word on the spectral classification of stars

With the deepening of our knowledge on the stellar Universe, the problem is set forth concerning a further development of the spectral classification of stars —the actual means for investigation of the realm of stars.A new word on the spectral classification of stars — the idea of the MK Process — has been coined by Morgan; it marks a new stage in the study of our Universe.     

Dynamical tides in close binary systems,I

The aim of the present paper will be to develop from the fundamental equations of hydrodynamics a theory of dynamical tides in close binary systems, the components of which are regarded to consist of heterogeneous viscous fluid, and to revolve around their common centre of gravity in eccentric orbits; moreover, the equatorial planes of their axial rotation and the orbital plane need not be co-planar, but all may be inclined to the invariable plane of the system of arbitrary amounts. The changes in the pressure or density invoked by time-dependent deformation will be regarded as adiabatic; but, in the equilibrium state, both the density and viscosity of the material of our components may be arbitrary functions of the radial distance.Following a brief exposition in Section 2 of the fundamental equations linearized to small oscillations — be these free or forced — in Section 3 we shall particularize them to describe spheroidal deformations; with due regard to all terms arising from viscosity. Section 4 will contain a specification of the boundary conditions to be imposed upon such oscillations; and in Section 5 we shall solve the problem of non-radial oscillations of self-gravitating inviscid configurations in terms of hypergeometric series. The remaining Sections 6–8 will be devoted to a discussion of the phenomena arising from viscosity: in particular, we shall solve in a closed form the problem of non-radial oscillations of incompressible viscous globes in the terms of Bessel functions. It will be shown that the effect of viscosity — like those of compressibility — tend to de-stabilize all non-radial oscillations of homogeneous configurations.At the other extreme, a similar treatment of a mass-point model — as well as of one exhibiting high but finite degree of central condensation — is being postponed for a subsequent communication.     

Particle motion in the vicinity of the protosun with variable luminosity

Variations of luminosity of the protosun during its Hayashi stage produced variations of its repulsive radiative action on small particles in its vicinity — or, in other words, variations of the effective mass of the protosun. Changes of the effective mass produced changes of size of orbits for particles circling around the protosun. When the luminosity increased, the effect of variable luminosity (EVL) diminished or overbalanced the Poynting-Robertson effect (PRE), hindering the small particles in their drift toward the protosun, and reinforced PRE when the luminosity decreased. An analysis of quasicircular motion of small uncharged particles moving in transparent circumsolar space under both effects — EVL and PRE — is given.     

A Note on Second Species Solutions Generated from p–q Resonant Orbits

The first image under the flow of the restricted three-body problem of the p—q resonant strips — that appear in the study of the p—q resonant orbits — do not have, in general, intersection with the strip. In this paper we show some particular situations in which the above intersections exist for some very simple p—q resonant orbits which, at the same time, are periodic second species solutions.This revised version was published online in October 2005 with corrections to the Cover Date.     

On the state of ionization of the local interstellar medium

The abundance ratio of neutral hydrogen to helium, as deduced from interplanetary observations of Lyman-alpha and He 584 Å radiation by Mariner 10, is significantly lower than the cosmic abundance ratio of these elements, thus showing that the local interstellar medium (LISM) is partly ionized. The effect of various sources of ionization — especially electron impact and EUV photon flux — on hydrogen and helium is discussed. It is shown that the observational data on the temperature of the LISM, on the diffuse EUV flux and on the neutral and electron densities in the nearby interstellar medium (NISM) are not all compatible. However, if the diffuse EUV flux below 912 Å as deduced from the preliminary analysis of Voyager observations is not representative, then it is easy to reconcile all observations. In this case an important source of ionization of the LISM would be electron impact, yielding an ionization degree of about 50% for the hydrogen component.     

The design of the Central-Axis Reflector (ZAS)

The Central-Axis Reflector, the design principle which is presented below is a segmented-mirror telescope. The inventions relate mainly to the optical system and to the tracking apparatus.A large number of small individual mirror bodies, ground off-axis (hexagonal/polygonal) produce one primary mirror with closed circular aperture when joined together.The overall design of the tracking apperatus results directly —and thus without unnecessary adornment — from the two planes of to aminimum but which are required for tracking of the telescope.Paper presented at the Symposium on the JNLT and Related Engineering Developments, Tokyo, November 29–December 2, 1988.     

The search for brown dwarfs with infrared surveys

I compute the maximum number of observable brown dwarfs for various infrared surveys by combining the maximum possible Oort limit (0.1 missing Mpc^–3 with all possible brown dwarf mass and age distributions. This approach shows what limits will be placed on the contribution of brown dwarfs to any possible missing mass if no brown dwarfs are observed. I consider brown dwarfs with masses of 0.01—0.08 M and ages of 10⁹—10¹⁰ years.The full range of predicted numbers of brown dwarfs above 6 times the noise of each of the below surveys is: IRAS Point Source Catalog 0.02—6 IRAS Faint Source Catalog |b| > 10° 0.05—16 ISO (2 week 12µm survey) 0.15—80 SIRTF (2 week 12µm survey) 2.50—1600 WIRE (4 month 12µm survey) 21.80—6000 DENIS (half sky) |b| > 10° 0.00—2000 2MASS (full sky) |b| > 10° 0.00—8000A failure to find brown dwarfs in the IRAS FSC would just barely rule out about half of the mass—age range for Oort limit total masses. A failure to find brown dwarfs in 2MASS/DENIS would rule out roughly the same mass—age range, but would set a limit of 0.1—0.01 times the Oort mass in that mass—age region. No limits would be set for the other half of the mass—age range since both IRAS and 2MASS/DENIS have insufficient sensitivity for brown dwarfs with T < 750 K.A failure to find brown dwarfs with ISO would rule out almost all of the mass—age range for Oort limit total masses, but would not set a significantly lower limit to the brown dwarf mass limit. A failure to find brown dwarfs with SIRTF or WIRE would rule out the entire mass—age range for Oort limit total masses and set an upper limit of 0.1—0.001 times the Oort mass.To date, about 18% of the IRAS FSC has been searched down to 6, and no brown dwarfs have been found. This sets a 95% upper limit of 3 in 18% of the sky, or 13 in the entire FSC for |b| > 10°. To begin to set useful limits from 2MASS or DENIS, approximately 400 square degrees needs to be analyzed. To date, only a few square degrees of results from the 2MASS prototype camera have been examined, with no brown dwarfs found so far.     

Interstellar polyynes and related species

The existence of the polyynes — molecules consisting essentially of long chains of carbon atoms — in the interstellar medium is a discovery that appears to be critical to our understanding of interstellar chemistry. The family relationships of these species to other interstellar species are explored as are their significance to theories of interstellar chemistry. Methods for deducing the numbers of related molecules are presented.