On the formation of pulsar radiation diagrmas

A model of pulsars is discussed in which formation of a polar diagram of the radiation is influenced by the motion of the source around a neutron star with a velocity close to that of light. For a power-law frequency-spectrum of the radiation and isotropy of the diagram in a system of coordinates rotating with the source, the width of the observed pulse is shown to be independent of frequency.The proposed explanation of the second period characteristics of type CP 1919 pulsars is based on the effect of relativistic motion of the radiation source. The positions are established (relative to the axis of rotation of the star) of the local sources of radiation in the optical and in the radio ranges for the pulsar NP 0532. It is shown how the polarization characteristics of the optical radiation of this pulsar may be connected with the effects of relativistic orbiting of the source of radiation about the star.     

Spectral and thermodynamic constraints on the existence of gypsum at the Juventae Chasma on Mars

The spectral imaging of the Mars obtained with the Mars Express/OMEGA experiment demonstrates that a majority of the sulfates-rich regions are associated with the interior light-toned layered deposits within the canyon system in the equatorial zone of the planet. While all sulfates-rich deposits inside the canyons are characterized by the presence of the kieserite and hydrated magnesium sulfates, the spectral features of gypsum were detected only in the Juventae Chasma and the Iani Chaos. The detection of gypsum in the upper part of the layered deposits, stacking the erosional remnant on the floor of the Juventae Chasma (above the spectral signature of the kieserite and polyhydrated sulfates detected on the flanks of the remnant) represents a more intriguing case. To clarify the question of the presence of gypsum in the Juventae Chasma, we present reanalyzed OMEGA spectra within that area and performed the chemical equilibrium modelling of sulfates precipitation sequence at the freezing and the evaporation of a hypothetical aqueous solution which could have existed within the Chasma in the past. Our results did not confirm the presence of distinct spectral signatures of gypsum. The results of equilibrium modelling also exclude significant precipitation of gypsum during the latest stage of the aqueous sedimentation, responsible for the formation of the upper part of the erosional remnant.     

Two-integral distribution functions for axisymmetric systems

Some formulae are presented for finding two-integral distribution functions (DFs) which depend only on the two classical integrals of the energy and the magnitude of the angular momentum with respect to the axis of symmetry for stellar systems with known axisymmetric densities. They come from a combination of the ideas of Eddington and Fricke and they are also an extension of those shown by Jiang and Ossipkov for finding anisotropic DFs for spherical galaxies. The density of the system is required to be expressed as a sum of products of functions of the potential and of the radial coordinate. The solution corresponding to this type of density is in turn a sum of products of functions of the energy and of the magnitude of the angular momentum about the axis of symmetry. The product of the density and its radial velocity dispersion can be also expressed as a sum of products of functions of the potential and of the radial coordinate. It can be further known that the density multiplied by its rotational velocity dispersion is equal to a sum of products of functions of the potential and of the radial coordinate minus the product of the density and the square of its mean rotational velocity. These formulae can be applied to the Binney and the Lynden-Bell models. An infinity of the odd DFs for the Binney model can be also found under the assumption of the laws of the rotational velocity.     

On the Formation of Planetesimals: Radial Contraction of the Dust Layer Interacting with the Protoplanetary Disk Gas

Radial contraction of the dust layer in the midplane of a gas–dust protoplanetary disk that consists of large dust aggregates is modeled. Sizes of aggregates vary from centimeters to meters assuming the monodispersion of the layer. The highly nonlinear continuity equation for the solid phase of the dust layer is solved numerically. The purpose of the study is to identify the conditions under which the solid matter is accumulated in the layer, which contributes to the formation of planetesimals as a result of gravitational instability of the dust phase of the layer. We consider the collective interaction of the layer with the surrounding gas of the protoplanetary disk: shear stresses act on the gas in the dust layer that has a higher orbital velocity than the gas outside the layer, this leads to a loss of angular momentum and a radial drift of the layer. The stress magnitude is determined by the turbulent viscosity, which is represented as the sum of the α-viscosity associated with global turbulence in the disk and the viscosity associated with turbulence that is localized in a thin equatorial region comprising the dust layer and is caused by the Kelvin–Helmholtz instability. The evaporation of water ice and the continuity of the mass flux of the nonvolatile component on the ice line is also taken into account. It is shown that the accumulation of solid matter on either side of the ice line and in other regions of the disk is determined primarily by the ratio of the radii of dust aggregates on either side of the ice line. If after the ice evaporation the sizes (or density) of dust aggregates decrease by an order of magnitude or more, the density of the solid phase of the layer’s matter in the annular zone adjacent to the ice line from the inside increases sharply. If, however, the sizes of the aggregates on the inner side of the ice line are only a few times smaller than behind the ice line, then in the same zone there is a deficit of mass at the place of the modern asteroid belt. We have obtained constraints on the parameters at which the layer compaction is possible: the global turbulence viscosity parameter (α < 10^?5), the initial radial distribution of the surface density of the dust layer, and the distribution of the gas surface density in the disk. Restrictions on the surface density depend on the size of dust aggregates. It is shown that the timescale of radial contraction of a dust layer consisting of meter-sized bodies is two orders of magnitude and that of decimeter ones, an order of magnitude greater than the timescale of the radial drift of individual particles if there is no dust layer.     

Tectonics and Evolution of Novae and Coronae on Venus: Tectonophysical Modeling Based on Gravitational Models

This paper describes the results of tectonophysical modeling of the formation and evolution of novae and coronae—radial/concentric volcanotectonic structures typical of the surface of Venus. The formation of these structures is usually associated with the effect of the rising and subsequently relaxing mantle diapirs on the surface layers of the lithosphere. Two series of experiments with gravitational models reproduce the topographic changes and the evolution of structural patterns in the course of the formation of novae and coronae on Venus. For model materials, we chose (1) rubber (a Bingham liquid) to reproduce the behavior of the elastoviscous diapir material in one series of experiments and the lower part of the lithosphere in the other series and (2) flour to model tectonic structures in the upper, brittle part of the lithosphere. Regularities in the formation of the topographic and structural characteristics of novae and coronae have been demonstrated on models of different geometry. The process of formation of the dense radial fracturing in novae due to the mechanical elevation caused by the formation of a rising dome, which was suggested by many authors, is not corroborated by our models. In the course of modeling, we studied the influence of the relative dimensions of the diapir and the thickness of the overlying structures, or the relative depth of the neutral buoyancy surface of the diapir, on the topographic, morphological, and structural features of novae and coronae and on the possible paths of their evolution. Regularities are also revealed in the formation of tectonic structures in relation to the environment in which the diapir evolution occurs—in the brittle upper part of the lithosphere or in its lower, viscoplastic part.     

A theory of integration for the extended Delaunay method

In this paper a method for the integration of the equations of the extended Delaunay method is proposed. It is based on the equations of the characteristic curves associated with the partial differential equation of Delaunay-Poincaré. The use of the method of characteristics changes the partial differential equation for higher order approximations into a system of ordinary differential equations. The independent variable of the equations of the characteristics is used instead of the angular variables of the Jacobian methods and the averaging principle of Hori is applied to solve the equations for higher orders. It is well known that Jacobian methods applied to resonant problems generally lead to the singularity of Poincaré. In the ideal resonance problem, this singularity appears when higher order approximations of the librational motion are considered. The singularity of Poincaré is non-essential and is caused by the choice of the critical arguments as integration variables. The use of the independent variable of the equation of the characteristics in the place of the critical angles eliminates the singularity of Poincaré.     

Solar oscillations and the equation of state

Summary Accurate measurements of observed frequencies of solar oscillations are providing a wealth of data on the properties of the solar interior. The frequencies depend on solar structure, and on the properties of the plasma in the Sun. Here we consider in particular the dependence on the thermodynamic state. From an analysis of the equations of stellar structure, and the relevant aspects of the properties of the oscillations, we argue that in the convection zone one can isolate information about the equation of state which is relatively unaffected by other uncertainties in the physics of the solar interior. We review the different treatments that have been used to describe the thermodynamics of stellar plasmas. Through application of several of these to the computation of models of the solar envelope we demonstrate that the sensitivity of the observed frequencies is in fact sufficient to distinguish even quite subtle features of the physics of solar matter. This opens up the possibility of using the Sun as a laboratory for statistical mechanics, under conditions that are out of reach in a terrestrial laboratory.     

On the storage of high-energy protons in the solar corona: The cyclotron instability

We consider the problem of long-time storage of high-energy protons, accelerated in the process of a flare, in coronal magnetic traps. From the viewpoint of the storage, one of the most important plasma instabilities is the kinetic cyclotron instability of the Alfvén waves. We carry out a detailed theoretical analysis of the instability for typical conditions of the solar corona. It is the refraction of the Alfvén waves in combination with a drastic decrease of the instability growth rate with an increase of the angle between the directions of the wave vector and the stationary magnetic field that leads to the possibility of the long-term storage of the flare protons. Sufficient conditions of the storage are determined.     

Precision of the ephemerides of outer planetary satellites

Ephemerides of planetary satellites are needed to address many problems. These ephemerides are used for subsequent observations. A comparison of the available ephemerides with new observations allows the accuracy of the former to be assessed. However, the precision of the ephemerides must be known a priori when solving the tasks. In this paper we formulate and solve the problem of estimating the precision of the ephemerides of outer planetary satellites derived from observations when applied up to the future moments.The methods of assessing the precision of ephemerides involve producing a set of samples of the same ephemeris inferred from observations with different samples of Monte Carlo generated random errors (RO) superimposed onto it. The statistical parameters of simulated observational errors are based on the results of the reduction of real satellite observations. We compute the deviations of the samples of the ephemeris from the standard ephemeris inferred from real observations and adopt the root-mean-square deviation of the apparent coordinates as the precision of the ephemeris. We also use alternative methods: one based on the matrix of covariances of parameter errors (RP), and another one based on bootstrap samples of observations (BS).We use three methods (RO, RP, and BS) to estimate the precision of the ephemerides of all the 107 outer planetary satellites over the 2010-2020 time interval. The precision of the ephemerides of different satellites varies from 0.05 to 4.0 arcsec. For a number of satellites new observations are of vital importance for maintaining the precision of the ephemerides at a level that would allow identification of satellites during the reduction of observations. For some satellites the precision of their ephemerides is of the order of the sizes of their orbits and such satellites can be considered to have been lost. We show that the method of bootstrap samples (BS) can give doubtful results in the cases where there are few observations, which covered a time interval that is shorter than the orbital period of the satellite.Our results suggest obtaining more precise ephemeris making new observations at the times of maximum estimated errors of the ephemeris.All the inferred estimates of the precision of ephemerides are available from the MULTI-SAT ephemeris server: www.imcce.fr/sat (IMCCE), www.sai.msu.ru/neb/nss/index.htm (SAI).     

Reflectance model for densely packed media: Estimates of the surface properties of the high-albedo satellites of Saturn

Interpretation of photometric and polarimetric observations of atmosphereless celestial bodies faces the problems connected with both the insufficient accuracy and level of details in groundbased observations and the current state of the theory of the multiple scattering of light. In application to sparse media, where the electromagnetic waves, propagating between the scatterers, can be considered as spherical (the socalled far-field approximation), this theory is rather well developed for both the diffuse and coherent components of the scattered radiation. In this paper, we show that this theory can be also successfully applied to the measurements of polarization of light scattered by densely packed, though nonabsorbing or weakly absorbing, media. For this purpose, we calculated the models for a semi-infinite layer of the medium composed of randomly oriented clusters of spherical particles and compared them with the data of laboratory and astronomical measurements. The potential of the present approach is illustrated by an example of the interpretation of the polarization measurements of the ice satellites of Saturn—Rhea and Enceladus—which allowed some properties of the surface of these celestial bodies to be estimated. In particular, the ratio of the surface area that makes no contribution to the negative polarization of light reflected at small phase angles to the area producing the negative polarization branch was found. Under the assumption of the same albedo of these areas, this ratio turned out to be 3.31–3.66 and 1.7–3.8 for Rhea and Enceladus, respectively. For Enceladus, it is difficult to obtain a sufficiently narrow range of the estimated parameters, since the number of measurement points in the phase dependence of polarization of this satellite is small. For the surface of Rhea, the estimated packing density of particles, participating in the opposition effects, is approximately 15%, while their smallest size is of the order of the wavelength of visible light.     

Double Plasma Resonance for Decimetric dot-Emissions

The mechanism of the double plasma resonance has been applied to the dot-like emission structures observed in the decimetric band. In particular, the existence of dot-emissions on definite trajectories in the dynamic spectra offers a rare opportunity to delineate the details of the double resonance mechanism as well as the diagnostics of the radio source and the ambient corona. The modeling of the chains of dots points to the excitation of the electron Bernstein modes predominantly at the second cyclotron harmonic and their subsequent coalescence to produce the observed dot-emissions. The coalescence process doubles the cyclotron harmonic number and thereby reduces the cyclotron absorption significantly. The discrete nature of the emissions results from the finite extent of the resonant region due to the presence of inhomogeneities. The determination of the relative scales of spatial variation of the magnetic field and the electron density in the region of the decimetric emission is particularly desirable as it has important consequences for the energy release, acceleration processes and the configuration of the participating plasma structures.     

Dynamic Structure of the GLONASS and GPS Orbital Space: Problem of Disposal of Retired Objects

The paper presents the results of a study of the dynamic structure of the orbital space of the navigation systems GLONASS and GPS. It is shown that the dynamic structure of the GLONASS region is determined by the action of one stable Lidov–Kozai secular resonance. The motion of almost all the retired objects of the GLONASS system is stable throughout the 100-year study period. In the GPS region, there is an orbital resonance and a large number of secular resonances. Their combined influence leads to a rapid increase in the eccentricity of the orbits of the retired objects of the system. Features of the dynamic structure of the orbital space are used to find the graveyard (parking) orbits of the retired objects of navigation systems.     

The 1997 Campaign of Observations of Mutual Occultations and Eclipses in the System of Jupiter's Galilean Satellites: Final Results

This paper presents the final results of the campaign of photometric observations of the Galilean satellites of Jupiter at the time of their mutual occultations and eclipses at the epoch of 1997 at observatories of Kazakhstan, Russia, and Ukraine. These results essentially contribute to the worldwide database of this type. They will help to refine the models of motion of the Galilean satellites of Jupiter. A comparison is made of the obtained data with the results of the worldwide campaign of observations of mutual occultations and eclipses in 1997. From the results of these observations, the differences of planetocentric coordinates of two satellites are calculated for a sequence of instants of time. Processing is based on the theory and the model of mutual occultations and eclipses of natural planetary satellites, which were developed by one of the authors in previous papers (Emel'yanov, 1999, 2000). In this paper, some new elements of the technique were used. We estimated the accuracy of observations. The paper contains information on the observing conditions and describes briefly the instruments employed.     

Shock jump relations for a dusty gas atmosphere

This paper presents simplified forms of jump relations for one dimensional shock waves propagating in a dusty gas. The dusty gas is assumed to be a mixture of a perfect gas and spherically small solid particles, in which solid particles are continuously distributed. The simplified jump relations for the pressure, the temperature, the density, the velocity of the mixture and the speed of sound have been derived in terms of the upstream Mach number. The expressions for the adiabatic compressibility of the mixture and the change-in-entropy across the shock front have also been derived in terms of the upstream Mach number. Further, the handy forms of shock jump relations have been obtained in terms of the initial volume fraction of small solid particles and the ratio of specific heats of the mixture, simultaneously for the two cases viz., (i) when the shock is weak and, (ii) when it is strong. The simplified shock jump relations reduce to the Rankine-Hugoniot conditions for shock waves in an ideal gas when the mass fraction (concentration) of solid particles in the mixture becomes zero. Finally, the effects due to the mass fraction of solid particles in the mixture, and the ratio of the density of solid particles to the initial density of the gas are studied on the pressure, the temperature, the density, the velocity of the mixture, the speed of sound, the adiabatic compressibility of the mixture and the change-in-entropy across the shock front. The results provided a clear picture of whether and how the presence of dust particles affects the flow field behind the shock front. The aim of this paper is to contribute to the understanding of how the shock waves behave in the gas-solid particle two-phase flows.     

Simple Model of a Stochastically Excited Solar Dynamo

The aim of this paper is to investigate the dynamical nature of the complexity observed in the time evolution of the sunspot number. We report a detailed analysis of the sunspot number time series, and use the daily records to build the phase space of the underlying dynamical system. The observed features of the phase space prompted us to describe the global behavior of the solar cycle in terms of a noise-driven relaxation oscillator. We find the equations whose solutions best fit the observed series, which adequately describe the shape of the peaks and the oscillations of the system. The system of equations obtained from this fitting procedure is shown to be equivalent to a truncation of the dynamo equations. A linear transformation maps the phase space of these equations into the phase space reconstructed from the observations. The irregularities of the solar cycle were modeled through the introduction of a stochastic parameter in the equations to simulate the randomness arising in the process of eruption of magnetic flow to the solar surface. The mean values and deviations obtained for the periods, rise times and peak values, are in good agreement with the values obtained from the sunspot time series.     

低纬子午环测微器的视栅形式及其观测原理

根据低纬子午环绝对测定的要求，在原来的测微器方案〔１〕的基础上，针对斜狭缝用于卯酉方向测定天顶距时所存在的问题，对原来的视栅形式作了进一步改进。本文对改进后的视栅形式及观测原理加以说明，并讨论了视栅的狭缝倾斜对测定量的影响及测定狭缝倾斜的方法。     

Holomorphy of coordinates with respect to eccentricities in the planetary three-body problem

The boundaries of the domains of holomorphy of the coordinates of unperturbed elliptic motion with respect to the eccentricities of planetary orbits are determined for the cases when any of the five anomalies of one of the planets-eccentric, true, tangential, or one of two mutual anomalies suggested by M.F. Subbotin—is used as an independent variable. The resulting equations are a generalization of the known equations for the boundaries of the domains of the holomorphy of coordinates for the cases when the time is the independent variable and determine the bisymmetric ovals, whose size and shape depend on the eccentricities and on the ratio of the planetary mean motions. The largest domains of holomorphy are obtained when the tangential anomaly or one of the Subbotin mutual anomalies is used. A function was found that conformally maps the domain of holomorphy to the unit disk. It was demonstrated that the application of any anomaly of the outer planet as the independent variable can result in a significant shrinking of the domain of the holomorphy of the coordinates of the inner planet, so that the analytic continuation of the initial power series with the center at the origin of the coordinates of a complex plane becomes impossible.     

Excitation of Chandler Wobble by Pacific,Indian and Atlantic Oceans from 1980 to 2005

In addition to the atmosphere, the oceans play important roles in the excitation of the Chandler wobble. The contributions made by the Pacific Ocean, the Indian Ocean and the Atlantic Ocean from 1980 to 2005 to the excitation of the Chandler wobble are first and systematically researched by taking advantage of the data of the current velocity field and ocean floor pressure provided by the marine circulation model of the Estimating the Circulation and Climate of the Ocean (ECCO). Studies show that the contributions of the three oceans to the excitation of the Chandler wobble are different from one another: the excitation energy of the Pacific Ocean makes up about 22.2% of the observational excitation energy, the largest one among the three oceans, that of the Indian Ocean accounts for about 12.7% and that of the Atlantic Ocean amounts to about 7.1%, the smallest among the three great oceans. The remarkable increase in the excitation energy of the Chandler wobble by the Pacific Ocean may be possibly due to the effect of the strong ENSO event which occurred from 1982 to 1983.     

An infinite family of generalized Kalnajs discs

An infinite family of axially symmetric thin discs of finite radius is presented. The family of discs is obtained by means of a method developed by Hunter and contains, as its first member, the Kalnajs disc. The surface densities of the discs present a maximum at the centre of the disc and then decrease smoothly to zero at the edge, in such a way that the mass distribution of the higher members of the family is more concentrated at the centre. The first member of the family has a circular velocity proportional to the radius, thus representing a uniformly rotating disc. On the other hand, the circular velocities of the other members of the family increase from a value of zero at the centre of the discs to a maximum and then decrease smoothly to a finite value at the edge of the discs, in such a way that, for the higher members of the family, the maximum value of the circular velocity is attained nearest the centre of the discs.