Relaxational effects in radiating stellar collapse

Relaxational effects in stellar heat transport can in many cases be significant. Relativistic Fourier–Eckart theory is inherently quasi-stationary, and cannot incorporate these effects. The effects are naturally accounted for in causal relativistic thermodynamics, which provides an improved approximation to kinetic theory. Recent results, based on perturbations of a static star, show that relaxation effects can produce a significant increase in the central temperature and temperature gradient for a given luminosity. We use a simple stellar model that allows for non-perturbative deviations from staticity, and confirms qualitatively the predictions of the perturbative models.     

Planetary perturbations on Mercury’s libration in longitude

Two space missions dedicated to Mercury (MESSENGER and BepiColombo) aim at understanding its rotation and confirming the existence of a liquid core. This double challenge requires much more accurate models for the spin-orbit resonant rotation of Mercury. The purpose of this paper is to introduce planetary perturbations on Mercury’s rotation using an analytical method and to analyse the influence of the perturbations on the libration in longitude. Applying a perturbation theory based on the Lie triangle, we were able to re-introduce short periodic terms into the averaged Hamiltonian and to compute the evolution of the rotational variables. The perturbations on Mercury’s forced libration in longitude mainly come from the orbital motion of Mercury (with an amplitude around 41 arcsec that depends on the momenta of inertia). It is completed by various effects from Jupiter (11.86 and 5.93 year-periods), Venus (with a 5.66 year-period), Saturn (14.73 year-period), and the Earth (6.58 year-period). The amplitudes of the oscillations due to Jupiter and Venus are approximately 33% and 10% of those from the orbital motion of Mercury and the amplitudes of the oscillations due to Saturn and the Earth are approximately 3% and 2%. We compare the analytical results with the solution obtained from the spin-orbit numerical model SONYR.     

On the Dynamical Foundations of the Lidov–Kozai Theory

The Lidov–Kozai theory developed by each of the authors independently in 1961–1962 is based on qualitative methods of studying the evolution of orbits for the satellite version of the restricted three-body problem (Hill’s problem). At present, this theory is in demand in various fields of science: in the field of planetary research within the Solar system, the field of exoplanetary systems, and the field of high-energy physics in interstellar and intergalactic space. This has prompted me to popularize the ideas that underlie the Lidov–Kozai theory based on the experience of using this theory as an efficient tool for solving various problems related to the study of the secular evolution of the orbits of artificial planetary satellites under the influence of external gravitational perturbations with allowance made for the perturbations due to the polar planetary oblateness.     

Dynamical supersymmetric inflation

We propose a new class of inflationary models in which the scalar field potential governing inflation is generated by the same nonperturbative gauge dynamics that may lead to supersymmetry breaking. Such models satisfy constraints from cosmic microwave background measurements for natural values of the fundamental parameters in the theory. In addition, they have two particularly interesting characteristics: a “blue” spectrum of scalar perturbations, and an upper bound on the total amount of inflation possible.     

Nonlinear theory of secular perturbations of satellites of an oblate planet

Anonlinear analytical theory of secular perturbations in the problem of the motion of a systemof small bodies around a major attractive center has been developed. Themutual perturbations of the satellites and the influence of the oblateness of the central body are taken into account in the model. In contrast to the classical Laplace-Lagrange theory based on linear equations for Lagrange elements, the third-degree terms in orbital eccentricities and inclinations are taken into account in the equations. The corresponding improvement of the solution turns out to be essential in studying the evolution of orbits over long time intervals. A program inC has been written to calculate the corrections to the fundamental frequencies of the solution and the third-degree secular perturbations in orbital eccentricities and inclinations. The proposed method has been applied to investigate the motion of the major Uranian satellites. Over time intervals longer than 100 years, allowance for the nonlinear terms in the equations is shown to give corrections to the coordinates of Miranda on the order of the orbital eccentricity, which is several thousand kilometers in linear measure. For other satellites, the effect of allowance for the nonlinear terms turns out to be smaller. Obviously, when a general analytical theory of motion for the major Uranian satellites is constructed, the nonlinear terms in the equations for the secular perturbations should be taken into account.     

Higher order moments of the density field in a parametrized sequence of non-Gaussian theories

We calculate the higher order moments in a sequence of models where the initial density fluctuations are drawn from a     distribution with a power-law power spectrum. For large values of , the distribution is approximately Gaussian, and we reproduce the values known from perturbation theory. As is lowered the distribution becomes progressively more non-Gaussian, approximating models with rare, high-amplitude peaks. The limit   =1  is a realization of recently proposed isocurvature models for producing early galaxy formation, where the density perturbations are quadratic in a Gaussian field.     

A second order analytical atmospheric drag theory based on the TD88 thermospheric density model

A second order atmospheric drag theory based on the usage of TD88 model is constructed. It is developed to the second order in terms of TD88 small parameters K _n,j . The short periodic perturbations, of all orbital elements, are evaluated. The secular perturbations of the semi-major axis and of the eccentricity are obtained. The theory is applied to determine the lifetime of the satellites ROHINI (1980 62A), and to predict the lifetime of the microsatellite MIMOSA. The secular perturbations of the nodal longitude and of the argument of perigee due to the Earth’s gravity are taken into account up to the second order in Earth’s oblateness.     

Period changes in the pulsating extreme helium stars V652 Her and BX Cir

A new statement of the eigenvalue problem of studying small perturbations in arbitrary integrable self-gravitating systems is presented. An example of such a system, a 2D stellar disc, is considered in detail. The theory, based on the general equation for disc eigenmodes, reveals mechanisms for the formation and growth of global galactic structures. This new point of view specifies the limits of the unified theory of bar-like and spiral modes that was based on the assumption that global galactic structures could be understood in terms of low-frequency disc modes.     

Statistical theory of thermal instability

A new statistical approach is presented to study the thermal instability of an optically thin unmagnetized plasma. In the framework of this approach the time evolution of the mass distribution function over temperature φ( T ) is calculated. Function φ( T ) characterizes the statistical properties of the multiphase medium of arbitrarily spaced three-dimensional structure of arbitrary (small or large) temperature perturbations. We construct our theory under the isobarical condition ( P  = constant over space), which is satisfied in the short-wavelength limit of the perturbations. The developed theory is illustrated for the case of the thermal instability of a slowly expanding interstellar cloud (smooth scenario). Numerical solutions of equations of the statistical theory are constructed and compared with hydrodynamical solutions. The results of both approaches are identical in the short-wavelength range when the isobarity condition is satisfied. Also the limits of applicability of the statistical theory are estimated. The possible evolution of the initial spectrum of perturbations is discussed. The proposed theory and numerical models can be relevant to the formation of the two-phase medium in the ∼ 1 pc region around quasars. Then small warm ( T  ≃ 10⁴  K ) clouds are formed as the result of thermal instability in an expanded gas fragment, which is a product of either star–star or star–accretion disc collision.     

Current‐driven instabilities in weakly ionized disks

Cool weakly ionized gaseous rotating disk form the basis for many models in astrophysics objects. Instabilities against perturbations in such disks play an important role in the theory of the formation of stars and planets. Traditionally, axisymmetric magnetohydrodynamic (MHD) and recently Hall‐MHD instabilities have been thoroughly studied as providers of an efficient mechanism for radial transfer of angular momentum, and of density radial stratification. In the current work, the Hall instability against axisymmetric perturbations in incompressible rotating fluid in external poloidal and toroidal magnetic field is considered. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Secular dynamics of S-type planetary orbits in binary star systems: applicability domains of first- and second-order theories

We analyse the secular dynamics of planets on S-type coplanar orbits in tight binary systems, based on first- and second-order analytical models, and compare their predictions with full N-body simulations. The perturbation parameter adopted for the development of these models depends on the masses of the stars and on the semimajor axis ratio between the planet and the binary. We show that each model has both advantages and limitations. While the first-order analytical model is algebraically simple and easy to implement, it is only applicable in regions of the parameter space where the perturbations are sufficiently small. The second-order model, although more complex, has a larger range of validity and must be taken into account for dynamical studies of some real exoplanetary systems such as \(\gamma \) Cephei and HD 41004A. However, in some extreme cases, neither of these analytical models yields quantitatively correct results, requiring either higher-order theories or direct numerical simulations. Finally, we determine the limits of applicability of each analytical model in the parameter space of the system, giving an important visual aid to decode which secular theory should be adopted for any given planetary system in a close binary.     

Scalar perturbations in two-temperature cosmological plasmas

We study the properties of density perturbations of a two-component plasma with a temperature difference on a homogeneous and isotropic background. For this purpose, we extend the general relativistic gauge-invariant and covariant (GIC) perturbation theory to include a multifluid with a particular equation of state (ideal gas) and imperfect fluid terms due to the relative energy flux between the two species. We derive closed sets of GIC vector and subsequently scalar evolution equations. We then investigate solutions in different regimes of interest. In particular, we study long-wavelength and arbitrary-wavelength Langmuir and ion-acoustic perturbations. The harmonic oscillations are superposed on a Jeans-type instability. We find a generalized Jeans criterion for collapse in a two-temperature plasma, which states that the species with the largest sound velocity determines the Jeans wavelength. Furthermore, we find that within the limit for gravitational collapse, initial perturbations in either the total density or charge density lead to a growth in the initial temperature difference. These results are relevant for the basic understanding of the evolution of inhomogeneities in cosmological models.     

Direct perturbations of the planets on the Moon's motion

The aim of the present paper is to present the theoretical background of a method to compute the planetary perturbations on the Moon's motion. We formulate an algorithm based upon the Lie transform method and well-suited to the particular problem at hand.This algorithm is being implemented using Henrard's Semi-Analytical Lunar Ephemeris (SALE) as solution of the Main Problem and Bretagnon's planetary theory. The accuracy of the solution is intended to be about 0".001 for terms of period up to 2000 years.To illustrate the interest of our approach, we comment on some preliminary results obtained about the direct perturbations due to Venus on the Moon's longitude. The final results will be the subject of another paper.     

Orbits near critical inclination,including lunisolar perturbations

An improved theory is presented of long period perigee motion for orbits near the critical inclinations 63.4° and 116.6°. Inclusion of lunisolar perturbations andall measured zonal harmonic coefficients from a recent Earth model are significant improvements over existing theories. Phase portraits are used to depict the interaction between eccentricity magnitude and argument of perigee. The Hamiltonian constant can be chosen as the parameter to display a family of phase plane trajectories consisting of libration, circulation, and asymptotic motion along separatrices near equilibrium points. A two parameter family of phase portraits is defined by the other two integrals, the average semimajor axis and component of angular momentum resolved along the Earth's polar axis. There are regions of the parameter space where the stability and total number of equilibria can change, or two separatrices can coalesce. These phenomena signal large qualitative changes in phase portrait topology. Numerical studies show that lunisolar perturbations control stability of equilibria for orbits with semimajor axes exceeding 1.4 Earth radii. Moreover, a theory which includes lunisolar perturbations predicts larger maximum fluctuations in eccentricity and faster oscillations near stable equilibria compared to a theory which models only the zonal harmonics.     

Elimination of the perigee in the satellite problem

Developed in this paper is a new approach to an analytic satellite theory which is based on Deprit's elimination of the parallax. The first step in the theory is the elimination of the parallax canonical transformation which eliminates the short period terms in the perturbations to within a factor of (1/r)². A new approach is then taken. The perigee terms are eliminated while retaining the short period terms in (1/r)². A Delaunay normalization of the short period terms in the (1/x)² factor is then constructed to complete the theory.     

Thermal force effects on slowly rotating, spherical artificial satellites-I. Solar heating

The heating of a spinning artificial satellite by natural radiation sources such as the Sun and the Earth results in temperature gradients arising across the satellite's surface. The corresponding anisotropic emission of thermal radiation leads to a recoil force, commonly referred to as “thermal force”. A quantitative theory of this effect is developed, based on more general assumptions than used so far, to model such radiation forces on spherically symmetric LAGEOS-like satellites. In particular, the theory holds for any ratio of the three basic timescales of the problem: the rotation period of the satellite, the orbital period around the Earth, and the relaxation time for the thermal processes. Thus, the simplifying assumption of a comparatively fast rotational motion is avoided, which will fail for LAGEOS within the next decade, owing to magnetic dissipation effects. A number of predictions about the future behaviour of non-gravitational long-term orbital perturbations of LAGEOS become possible with the new theory. In particular the Yarkovsky-Schach thermal force effects are studied arising as a consequence of the solar radiation flux onto the satellite, periodically interrupted by eclipses. Starting on about year 2005, the orbital perturbation effects predicted by the new theory are substantially different from those inferred in the fast-rotation case. This holds not only for the long-term semimajor axis effects, but also for eccentricity and inclination perturbations.     

Density perturbations in cosmological models

Differential equations are derived, following the methods ofLifshitz (1946) andLifshitz andKhalatnikov (1963), for density perturbations in isotropic, spatially homogeneous cosmological models of arbitrary space curvature. The unperturbed models contain both matter and radiation. An explicit third-order equation is obtained for the time development of the perturbations, and it is shown that one of the solutions is not covariantly defined. The two remaining solutions are compared with existing solutions for the limiting cases of radiation-filled and dust-filled models. The results ofBonnor's (1957) Newtonian analysis are shown to be a valid limiting case of our equation when the pressurep is finite, but small compared with the densityp timesc ².A detailed analysis is given of a model containing coupled radiation (p=pc ²/3) and dust (p=0). It is shown that density perturbations with long wavelengths are unstable (with slow growth rate) for all time. The instability exists because for a long-wavelength disturbance, the time scale governing the propagation of pressure effects (which stabilize perturbations) is longer than the time scale for which pressure falls to the point of ineffectiveness. The present value of the critical wavelength is 60 Mpc in models based on flat space sections in which the present background radiation temperature is 3 °K.The research reported herein was supported in part by the Atomic Energy Commission under contract number AT(11-1)-34, Project Agreement No. 125, and by the National Science Foundation, under Grant GP-4975.     

Elliptic-type motion in Fock's gravitational field

The elliptic-type motion in the gravitational field found by Fock as exact solution of Einstein's vacuum equations in the case of spherical symmetry (Solution called here Fock's gravitational field) is studied by means of a classic method based on the perturbation theory. Regarding the deviations of the orbit from a Kepleian orbit as perturbations, the first and second order variations of the Keplerian orbital elements over one nodal period as well as those of the nodal period itself are determined.     

Analytical Proper Elements for the Hilda Asteroids I: Construction of a Formal Solution

In this paper, we present the mathematical basis for the calculation of proper elements for asteroids in 3:2 mean-motion resonance with Jupiter from their osculating Keplerian elements. The method is based on a new resonant Lie-series perturbation theory (Ferraz-Mello, 1997, 2002), which allows the construction of formal solutions in cases where resonant and long-period angles appear simultaneously. For the disturbing function, we used the Beaugé’s expansion (Beaugé, 1996), adapted to include short period terms. In this paper, the theory is restricted to the planar case and only the perturbations due to Jupiter are considered.