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1.
We study the various approximations used to investigate the eigenmode spectrum for systems with highly elongated stellar orbits. The approximation in which the elongated orbits are represented by thin rotating spokes, with the rotation imitating the precession of real orbits, is the simplest and most natural one. However, we show that using this pictorial approximation does not allow the picture of stability to be properly presented. We show that for stellar systems with a plane disk geometry, this approach does not allow unstable spectral modes to be obtained even in the leading order in small parameter, which characterizes the spread of nearly radial orbits in angular momentum. For spherical systems, where the situation is more favorable, the spectrum can be determined but only in the leading order in this parameter. A rigorous approach based on the solution of more complex integral equations given here should be used to properly investigate the stability of stellar systems. 相似文献
2.
Using a consistent perturbation theory for collisionless disk-like and spherical star clusters, we construct a theory of slow
modes for systems having an extended central region with a nearly harmonic potential due to the presence of a fairly homogeneous
(on the scales of the stellar system) heavy, dynamically passive halo. In such systems, the stellar orbits are slowly precessing,
centrally symmetric ellipses (2: 1 orbits). Depending on the density distribution in the system and the degree of halo inhomogeneity,
the orbit precession can be both prograde and retrograde, in contrast to systems with 1: 1 elliptical orbits where the precession
is unequivocally retrograde. In the first paper, we show that in the case where at least some of the orbits have a prograde
precession and the stellar distribution function is a decreasing function of angular momentum, an instability that turns into
the well-known radial orbit instability in the limit of low angular momenta can develop in the system. We also explore the
question of whether the so-called spoke approximation, a simplified version of the slow mode approximation, is applicable
for investigating the instability of stellar systems with highly elongated orbits. Highly elongated orbits in clusters with
nonsingular gravitational potentials are known to be also slowly precessing 2: 1 ellipses. This explains the attempts to use
the spoke approximation in finding the spectrum of slow modes with frequencies of the order of the orbit precession rate.
We show that, in contrast to the previously accepted view, the dependence of the precession rate on angular momentum can differ
significantly from a linear one even in a narrow range of variation of the distribution function in angular momentum. Nevertheless,
using a proper precession curve in the spoke approximation allows us to partially “rehabilitate” the spoke approach, i.e.,
to correctly determine the instability growth rate, at least in the principal (O(α
T−1/2) order of the perturbation theory in dimensionless small parameter α
T, which characterizes the width of the distribution function in angular momentum near radial orbits. 相似文献
3.
We discuss contradictions existing in the literature in the problem on the stability of collisionless spherical stellar systems,
which are the simplest anisotropic generalization of the well-known polytropic models. On the one hand, calculations of the
growth rates within the framework of a linear stability theory and N-body simulations suggest that these systems should become stable when the parameter s characterizing the degree of anisotropy of the stellar velocity distribution becomes lower than some critical value s
crit > 0. On the other hand, according to Palmer and Papaloizou, the growth rate should be nonzero up to the isotropic limit s = 0. Using our method of determining the eigenmodes of stellar systems, we show that even though the mode growth rates in
weakly radially anisotropic systems of this type are nonzero, they are exponentially small, i.e., decrease as γ ∝ exp(−a/s) when s → 0. For slightly radially anisotropic systems with a finite lifetime, this actually implies stability. 相似文献
4.
D. Kilkenny L. A. Crause F. van Wyk 《Monthly notices of the Royal Astronomical Society》2005,361(2):559-564
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. 相似文献
5.
Photometric and Doppler imaging observations of active binaries indicate the existence of starspots at preferred longitudes (position angles with respect to the companion star). We investigate the stability of magnetic flux tubes in the convection zone of close, fast‐rotating binary stars and explore whether the observed preferred longitudes could be caused by tidal forces and the deformation of the active star. We assume a synchronized binary system with spin axes perpendicular to the orbital plane and a rotation period of a few days. The tidal force and the deviation from spherical structure are considered in lowest‐order perturbation theory. The magnetic field is in the form of toroidal magnetic flux rings, which are stored in mechanical equilibrium within the stably stratified overshoot region beneath the convection zone until the field has grown sufficiently strong for the undulatory instability to initiate the formation of rising loops. Frequencies and geometry of stable as well as growth rates of unstable eigenmodes are determined by linear stability analysis. Particular consideration is given to the question whether the effects of tidal forces and perturbations of the stellar structure can force a rising flux loop to enter the convection zone at specific longitudes. 相似文献
6.
H. Kjeldsen 《Astrophysics and Space Science》2003,284(1):1-12
Measuring eigenfrequencies and identifying eigenmodes provide the observational basis for a significant improvement in our understanding of stellar evolution and structure.Development throughout the last few years show that we may be at the dawn of a `Golden Age'for Asteroseismology. For this to become a reality we only need two things:Better data and better models. In this paper I describe some aspectsof how one detects stellar oscillations. 相似文献
7.
Robert S. Harrington 《Celestial Mechanics and Dynamical Astronomy》1972,6(3):322-327
A wide variety of equal-mass stellar triple systems has been numerically integrated in order to establish factors pertinent to stability. The significant parameters appear to be whether the relative revolution is direct or retrograde, and the ratio of the periastron distance in the outer orbit to the semi-major axis of the inner orbit. For stability, this ratio must be at least 3.5 for direct orbits and at least 2.75 for retrograde orbits. 相似文献
8.
Using a consistent perturbation theory for collisionless disk-like and spherical star clusters, we construct a theory of slow
modes for systems having an extended central region with a nearly harmonic potential due to the presence of a fairly homogeneous
(on the scales of the stellar system) heavy, dynamically passive halo. In such systems, the stellar orbits are slowly precessing,
centrally symmetric ellipses (2: 1 orbits). We consider star clusters with monoenergetic distribution functions that monotonically
increase with angular momentum in the entire range of angular momenta (from purely radial orbits to circular ones) or have
a growing region only at low angular momenta. In these cases, there are orbits with a retrograde precession, i.e., in a direction
opposite to the orbital rotation of the star. The presence of a gravitational loss-cone instability, which is also observed
in systems of 1: 1 orbits in near-Keplerian potentials, is associated with such orbits. In contrast to 1: 1 systems, the loss-cone
instability takes place even for distribution functions monotonically increasing with angular momentum, including those for
systems with circular orbits. The regions of phase space with retrograde orbits do not disappear when the distribution function
is smeared in energy. We investigate the influence of a weak inhomogeneity of a heavy halo with a density that decreases with
distance from the center. 相似文献
9.
F. J. Sánchez-Salcedo † A. Brandenburg † 《Monthly notices of the Royal Astronomical Society》2001,322(1):67-78
The dynamical friction experienced by a body moving in a gaseous medium is different from the friction in the case of a collisionless stellar system. Here we consider the orbital evolution of a gravitational perturber inside a gaseous sphere using three-dimensional simulations, ignoring however self-gravity. The results are analysed in terms of a 'local' formula with the associated Coulomb logarithm taken as a free parameter. For forced circular orbits, the asymptotic value of the component of the drag force in the direction of the velocity is a slowly varying function of the Mach number in the range 1.0–1.6. The dynamical friction time-scale for free decay orbits is typically only half as long as in the case of a collisionless background, which is in agreement with E. C. Ostriker's recent analytic result. The orbital decay rate is rather insensitive to the past history of the perturber. It is shown that, similarly to the case of stellar systems, orbits are not subject to any significant circularization. However, the dynamical friction time-scales are found to increase with increasing orbital eccentricity for the Plummer model, whilst no strong dependence on the initial eccentricity is found for the isothermal sphere. 相似文献
10.
John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》1981,23(3):277-286
Recent results on periodic orbits are presented and it is shown that the periodic orbits can be used in the study of planetary systems and triple or multiple stellar systems. Triple stellar systems are stable even for close approaches of the three components. Also stable triple systems exist with nearly zero angular momentum. For the planetary systems a global view is obtained from which it is clear which configurations are stable or unstable and also what factors affect the stability. Also, the relation between resonance and instability is studied by making use of periodic orbits. 相似文献
11.
《Planetary and Space Science》2007,55(5):651-660
In this paper we estimate the likelihood to find habitable Earth-like planets on stable orbits for 86 selected extrasolar planetary systems, where luminosity, effective temperature and stellar age are known. For determining the habitable zone (HZ) an integrated system approach is used taking into account a variety of climatological, biogeochemical, and geodynamical processes. Habitability is linked to the photosynthetic activity on the planetary surface. We find that habitability strongly depends on the age of the stellar system and the characteristics of a virtual Earth-like planet. In particular, the portion of land/ocean coverages plays an important role. We approximated the conditions for orbital stability using a method based on the Hill radius. Almost 60% of the investigated systems could harbour habitable Earth-like planets on stable orbits. In 18 extrasolar systems we find even better prerequisites for dynamic habitability than in our own solar system. In general our results are comparable to those with an HZ determination based only on climatic constraints. However, there are remarkable differences for land worlds and for systems older than about 7 Gyr. 相似文献
12.
Analysis of Families of Triple Close Approaches Occurring inStellar Systems in Three Dimensions (II)
This is the second paper of a trilogy dealing with the role of triple encounters with low initial velocities and equal masses
in the evolution of stellar systems in three dimensional space. It shows how a condition of complete collapse may be perturbed
to obtain well-established families of asymmetric triple close approaches with systematic regularity of escape with the formation
of a binary. The main result is that when perturbation is introduced two close approaches called the first close approach
and the second close approach occur in the same plane but the binary formed and the escaper are not in that plane. Further
it is observed that the conjecture of Szebehely (1977) viz. `The measure of escaping orbits is significantly higher than the
measure of stable orbits' is likely to be true. The third and last paper offers applications in stellar systems.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
13.
Cosmogonical theories as well as recent observations allow us to expect the existence of planets around many stars other than the Sun. On an other hand, double and multiple star systems are established to be more numerous than single stars (such as the Sun), at least in the solar neighborhood. We are then faced to the following dynamical problem: assuming that planets can form in a binary early environment (I do not deal here with), does long-term stability for planetary orbits exist in double star systems.Although preliminary studies were rather pessimistic about the possibility of existence of stable planetary orbits in double or multiple star systems, modern computation have shown that many such stable orbits do exist (but possible chaotic behavior), either around the binary as a whole (P-type) or around one component of the binary (S-type), this latter being explored here.The dynamical model is the elliptic plane restricted three-body problem; the phase space of initial conditions is systematically explored, and limits for stability have been established. Stable S-type planetary orbits are found up to distance of their "sun" of the order of half the periastron distance of the binary; moreover, among these stable orbits, nearly-circular ones exist up to distance of their "sun" of the order of one quarter the periastron distance of the binary; finally, among the nearly-circular stable orbits, several stay inside the "habitable zone", at least for two nearby binaries which components are nearly of solar type.Nevertheless, we know that chaos may destroy this stability after a long time (sometimes several millions years). It is therefore important to compute indicators of chaos for these stable planetary orbits to investigate their actual very long-term stability. Here we give an example of such a computation for more than a billion years. 相似文献
14.
In this paper, we study the existence of transversal homoclinic orbits in a planar circular restricted four-body problem, based on the perturbation theory of integrable Hamiltonian systems. We start from a planar circular restricted four-body model and regard it as a perturbation of the two-body model. Then, in order to conveniently study unbounded orbits, we transform the infinite points to finite points by a non-canonical transformation, arriving at a non-Hamiltonian system with degenerate fixed points. According to the extended Melnikov method, we finally prove that there exist transversal homoclinic orbits in this four-body model. 相似文献
15.
In this paper we extend the theory of close encounters of a giant planet on a parabolic orbit with a central star developed in our previous work (Ivanov and Papaloizou in MNRAS 347:437, 2004; MNRAS 376:682, 2007) to include the effects of tides induced on the central star. Stellar rotation and orbits with arbitrary inclination to the stellar rotation axis are considered. We obtain results both from an analytic treatment that incorporates first order corrections to normal mode frequencies arising from stellar rotation and numerical treatments that are in satisfactory agreement over the parameter space of interest. These results are applied to the initial phase of the tidal circularisation problem. We find that both tides induced in the star and planet can lead to a significant decrease of the orbital semi-major axis for orbits having periastron distances smaller than 5?C6 stellar radii with tides in the star being much stronger for retrograde orbits compared to prograde orbits. Assuming that combined action of dynamic and quasi-static tides could lead to the total circularisation of orbits this corresponds to observed periods up to 4?C5 days. We use the simple Skumanich law to characterise the rotational history of the star supposing that the star has its rotational period equal to one month at the age of 5 Gyr. The strength of tidal interactions is characterised by circularisation time scale, t ev , which is defined as a typical time scale of evolution of the planet??s semi-major axis due to tides. This is considered as a function of orbital period P obs , which the planet obtains after the process of tidal circularisation has been completed. We find that the ratio of the initial circularisation time scales corresponding to prograde and retrograde orbits, respectively, is of order 1.5?C2 for a planet of one Jupiter mass having P obs ~ 4 days. The ratio grows with the mass of the planet, being of order five for a five Jupiter mass planet with the same P orb . Note, however, this result might change for more realistic stellar rotation histories. Thus, the effect of stellar rotation may provide a bias in the formation of planetary systems having planets on close orbits around their host stars, as a consequence of planet?Cplanet scattering, which favours systems with retrograde orbits. The results reported in the paper may also be applied to the problem of tidal capture of stars in young stellar clusters. 相似文献
16.
Stefano Casotto 《Celestial Mechanics and Dynamical Astronomy》1995,62(1):1-22
A new method for calculating the perturbation spectrum in the framework of Kaula's linear satellite theory (LST) is introduced. The novelty of this approach consists in using recent results on the spectral decomposition of the perturbation frequencies in LST to provide a closed formulation for the amplitude and the phase of each line in the perturbation spectrum. The theory presented here can be applied to perturbations in the elements or in the radial and transverse directions due to the geopotential or to the tides. Separate algorithms are developed for application to orbits with circulating or frozen perigee. 相似文献
17.
By linear perturbation theory, a sensitivity study is presented to calculate the contribution of the Mars gravity field to the orbital perturbations in velocity for spacecrafts in both low eccentricity Mars orbits and high eccentricity orbits(HEOs). In order to improve the solution of some low degree/order gravity coefficients, a method of choosing an appropriate semimajor axis is often used to calculate an expected orbital resonance, which will significantly amplify the magnitude of the position and velocity perturbations produced by certain gravity coefficients. We can then assess to what degree/order gravity coefficients can be recovered from the tracking data of the spacecraft. However, this existing method can only be applied to a low eccentricity orbit, and is not valid for an HEO. A new approach to choosing an appropriate semimajor axis is proposed here to analyze an orbital resonance. This approach can be applied to both low eccentricity orbits and HEOs. This small adjustment in the semimajor axis can improve the precision of gravity field coefficients and does not affect other scientific objectives. 相似文献
18.
E. V. Polyachenko V. L. Polyachenko I. G. Shukhman 《Monthly notices of the Royal Astronomical Society》2007,379(2):573-596
We study spherical and disc clusters in a near-Keplerian potential of galactic centres or massive black holes. In such a potential orbit precession is commonly retrograde, that is, the direction of the orbit precession is opposite to the orbital motion. It is assumed that stellar systems consist of nearly-radial orbits. We show that if there is a loss-cone at low angular momentum (e.g. due to consumption of stars by a black hole), an instability similar to loss-cone instability in plasma may occur. The gravitational loss-cone instability is expected to enhance black hole feeding rates. For spherical systems, the instability is possible for the number of spherical harmonics l ≥ 3 . If there is some amount of counter-rotating stars in flattened systems, they generally exhibit the instability independent of azimuthal number m . The results are compared with those obtained recently by Tremaine for distribution functions monotonically increasing with angular momentum.
The analysis is based on simple characteristic equations describing small perturbations in a disc or a sphere of stellar orbits highly elongated in radius. These characteristic equations are derived from the linearized Vlasov equations (combining the collisionless Boltzmann kinetic equation and the Poisson equation), using the action-angle variables. We use two techniques for analysing the characteristic equations: the first one is based on preliminary finding of neutral modes, and the second one employs a counterpart of the plasma Penrose–Nyquist criterion for disc and spherical gravitational systems. 相似文献
The analysis is based on simple characteristic equations describing small perturbations in a disc or a sphere of stellar orbits highly elongated in radius. These characteristic equations are derived from the linearized Vlasov equations (combining the collisionless Boltzmann kinetic equation and the Poisson equation), using the action-angle variables. We use two techniques for analysing the characteristic equations: the first one is based on preliminary finding of neutral modes, and the second one employs a counterpart of the plasma Penrose–Nyquist criterion for disc and spherical gravitational systems. 相似文献
19.
M. R.Burleigh F. J.Clarke S. T.Hodgkin 《Monthly notices of the Royal Astronomical Society》2002,331(4):L41-L45
We suggest that Jovian planets will survive the late stages of stellar evolution, and that white dwarfs will retain planetary systems in wide orbits (≳5 au). Utilizing evolutionary models for Jovian planets, we show that infrared imaging with 8-m class telescopes of suitable nearby white dwarfs should allow us to resolve and detect companions ≳3 M JUP . Detection of massive planetary companions to nearby white dwarfs would prove that such objects can survive the final stages of stellar evolution, place constraints on the frequency of main-sequence stars with planetary systems dynamically similar to our own and allow direct spectroscopic investigation of their composition and structure. 相似文献
20.
Hideyuki Saio Norman H. Baker & Alfred Gautschy 《Monthly notices of the Royal Astronomical Society》1998,294(4):622-634
Properties of the so-called strange modes occurring in linear stability calculations of stellar models are discussed. The behaviour of these modes is compared for two different sets of stellar models, for very massive zero-age main-sequence stars and for luminous hydrogen-deficient stars, both with high luminosity-to-mass ratios. We have found that the peculiar behaviour of the frequencies of the strange modes with the change of a control parameter is caused by the pulsation amplitude of a particular eigenmode being strongly confined to the outer part of the envelope, around the density inversion zone. The frequency of a strange mode changes because the depth of the confinement zone changes with the control parameter. Weakly non-adiabatic strange modes tend to be overstable because the amplitude confinement quenches the effect of radiative damping. On the other hand, extremely non-adiabatic strange modes become overstable because the perturbation of radiation force (gradient of radiation pressure) provides a restoring force that can be out of phase with the density perturbation. We discuss this mechanism by using a plane-parallel two-zone model. 相似文献