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1.
We investigate the secular dynamics of three-body circumbinary systems under the effect of tides. We use the octupolar non-restricted approximation for the orbital interactions, general relativity corrections, the quadrupolar approximation for the spins, and the viscous linear model for tides. We derive the averaged equations of motion in a simplified vectorial formalism, which is suitable to model the long-term evolution of a wide variety of circumbinary systems in very eccentric and inclined orbits. In particular, this vectorial approach can be used to derive constraints for tidal migration, capture in Cassini states, and stellar spin–orbit misalignment. We show that circumbinary planets with initial arbitrary orbital inclination can become coplanar through a secular resonance between the precession of the orbit and the precession of the spin of one of the stars. We also show that circumbinary systems for which the pericenter of the inner orbit is initially in libration present chaotic motion for the spins and for the eccentricity of the outer orbit. Because our model is valid for the non-restricted problem, it can also be applied to any three-body hierarchical system such as star–planet–satellite systems and triple stellar systems. 相似文献
2.
The angle between planetary spin and the normal direction of an orbital plane is supposed to reveal a range of information about the associated planetary formation and evolution. Since the orbit's eccentricity and inclination oscillate periodically in a hierarchical triple body and tidal friction makes the spin parallel to the normal orientation of the orbital plane with a short timescale in an isolated binary system, we focus on the comprehensive effect of third body perturbation and tidal mechanism on the angle. Firstly, we extend the Hut tidal model(1981) to the general spatial case, adopting the equilibrium tide and weak friction hypothesis with constant delay time, which is suitable for arbitrary eccentricity and any angle ? between the planetary spin and normal orientation of the orbital plane. Furthermore, under the constraint of angular momentum conservation, the equations of orbital and ratational motion are given. Secondly, considering the coupled effects of tidal dissipation and third body perturbation, and adopting the quadrupole approximation as the third body perturbation effect, a comprehensive model is established by this work. Finally, we find that the ultimate evolution depends on the timescales of the third body and tidal friction. When the timescale of the third body is much shorter than that of tidal friction, the angle ? will oscillate for a long time,even over the whole evolution; when the timescale of the third body is observably larger than that of the tidal friction, the system may enter stable states, with the angle ? decaying to zero ultimately, and some cases may have a stable inclination beyond the critical value of Lidov-Kozai resonance. In addition, these dynamical evolutions depend on the initial values of the orbital elements and may aid in understanding the characteristics of the orbits of exoplanets. 相似文献
3.
The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the equations of motion of the unaveraged perturbed two-body problem in terms of planetary orbital elements by using a generalized form of Gauss’ equations. We consider a varied set of position and velocity-dependent perturbations, and also derive relevant specific cases of the equations: when they are averaged over fast variables (the “adiabatic” approximation), and in the prograde and retrograde planar cases. In each instance, we delineate the properties of the equations. As brief demonstrations of potential applications, we consider the effect of Galactic tides. We measure the effect on the widest-known exoplanet orbit, Sedna-like objects, and distant scattered disk objects, particularly with regard to where the adiabatic approximation breaks down. The Mathematica code which can help derive the equations of motion for a user-defined perturbation is freely available upon request. 相似文献
4.
Frédéric Pont 《Monthly notices of the Royal Astronomical Society》2009,396(3):1789-1796
Most transiting planets orbit very close to their parent star, causing strong tidal forces between the two bodies. Tidal interaction can modify the dynamics of the system through orbital alignment, circularization, synchronization and orbital decay by exchange of angular moment. Evidence for tidal circularization in close-in giant planet is well known. Here, we review the evidence for excess rotation of the parent stars due to the pull of tidal forces towards spin-orbit synchronization. We find suggestive empirical evidence for such a process in the present sample of transiting planetary systems. The corresponding angular momentum exchange would imply that some planets have spiralled towards their star by substantial amounts since the dissipation of the protoplanetary disc. We suggest that this could quantitatively account for the observed mass–period relation of close-in gas giants. We discuss how this scenario can be further tested and point out some consequences for theoretical studies of tidal interactions and for the detection and confirmation of transiting planets from radial velocity and photometric surveys. 相似文献
5.
通过结合理论分析和数值模拟方法,可以对热海王星系统HD 106315轨道迁移中的近2:1平运动共振捕获机制以及潮汐作用下的演化过程进行研究.在轨道迁移阶段,初始轨道半长径、初始偏心率以及行星c的偏心率衰减系数K会对系统轨道构型产生影响.数值模拟结果显示当初始轨道半长径分别为ab～0.4 au、ac～0.8 au,偏心率eb和ec均小于0.03时, HD 106315b和HD 106315c在中央恒星的引力作用以及原行星盘粘滞作用下向内迁移, 65000 yr左右两颗行星均可迁移至当前观测位置附近并形成近2:1平运动共振捕获.此外,中央恒星的潮汐效应也可能会对行星系统共振构型产生影响,理论分析表明当行星潮汐耗散系数Q=100时,潮汐效应造成的轨道半长径衰减使系统轨道周期比发生的变化可能是系统脱离共振构型的原因.数值模拟结果显示, HD 106315系统内两颗行星Q103时,来自中央恒星的潮汐效应并不会使行星系统产生明显的偏心率和轨道半长径衰减,不足以使HD 106315行星系统在剩余寿命内脱离2:1平运动共振轨道构型. 相似文献
6.
François Farago Jacques Laskar Jocelyn Couetdic 《Celestial Mechanics and Dynamical Astronomy》2009,104(3):291-306
Exploring the global dynamics of a planetary system involves computing integrations for an entire subset of its parameter
space. This becomes time-consuming in presence of a planet close to the central star, and in practice this planet will be
very often omitted. We derive for this problem an averaged Hamiltonian and the associated equations of motion that allow us
to include the average interaction of the fast planet. We demonstrate the application of these equations in the case of the μ Arae system where the ratio of the two fastest periods exceeds 30. In this case, the effect of the inner planet is limited
because the planet’s mass is one order of magnitude below the other planetary masses. When the inner planet is massive, considering
its averaged interaction with the rest of the system becomes even more crucial. 相似文献
7.
We provide a generalized discussion of tidal evolution to arbitrary order in the expansion of the gravitational potential
between two spherical bodies of any mass ratio. To accurately reproduce the tidal evolution of a system at separations less
than 5 times the radius of the larger primary component, the tidal potential due to the presence of a smaller secondary component
is expanded in terms of Legendre polynomials to arbitrary order rather than truncated at leading order as is typically done
in studies of well-separated system like the Earth and Moon. The equations of tidal evolution including tidal torques, the
changes in spin rates of the components, and the change in semimajor axis (orbital separation) are then derived for binary
asteroid systems with circular and equatorial mutual orbits. Accounting for higher-order terms in the tidal potential serves
to speed up the tidal evolution of the system leading to underestimates in the time rates of change of the spin rates, semimajor
axis, and mean motion in the mutual orbit if such corrections are ignored. Special attention is given to the effect of close
orbits on the calculation of material properties of the components, in terms of the rigidity and tidal dissipation function,
based on the tidal evolution of the system. It is found that accurate determinations of the physical parameters of the system,
e.g., densities, sizes, and current separation, are typically more important than accounting for higher-order terms in the
potential when calculating material properties. In the scope of the long-term tidal evolution of the semimajor axis and the
component spin rates, correcting for close orbits is a small effect, but for an instantaneous rate of change in spin rate,
semimajor axis, or mean motion, the close-orbit correction can be on the order of tens of percent. This work has possible
implications for the determination of the Roche limit and for spin-state alteration during close flybys. 相似文献
8.
Piotr Wąż 《Celestial Mechanics and Dynamical Astronomy》2006,96(3-4):159-167
The dynamics of planetary and star systems including perturbing forces due to the flattering and quadrupole distortion of the bodies is studied. The analytical model describing the perturbations which influence on the orbital motion of extrasolar planetary systems is presented. The calculations of the secular evolution of the mean orbital elements have shown that the effects related to the shape of the body are more important than the ones due to the quadrupole distortion. 相似文献
9.
Using numerical simulations, we studied several coupled translational and rotational solutions of the two-finite-body problem with one spherical and one triaxial body. The aim was to investigate which types of orbits and planetary bodies could produce spin-induced orbital perturbations relevant enough to add to models dealing with other perturbations. To fully assess the strengths and consequences of this perturbation, we did not include any other perturbation even when a more realistic scenario would have required it. Interesting results concern planet–star mass ratios like a hot Jupiter or a super-Jupiter around a star like the Sun or the red dwarf Proxima Centauri. The short-period chaotic effect of the gravitational spin–orbit perturbation on highly eccentric orbits in the vicinity of the Roche limit can be a prominent feature. It should be taken into account when studying the tidal evolution of such a planet or its interactions with any companion in the neighborhood of the star. 相似文献
10.
We consider an algorithm to construct averaged motion equations for four-planetary systems by means of the Hori–Deprit method. We obtain the generating function of the transformation, change-variable functions and right-hand sides of the equations of motion in elements of the second Poincaré system. Analytical computations are implemented by means of the Piranha echeloned Poisson processor. The obtained equations are to be used to investigate the orbital evolution of giant planets of the Solar system and various extrasolar planetary systems. 相似文献
11.
Since 20 years, a large population of close-in planets orbiting various classes of low-mass stars (from M-type to A-type stars) has been discovered. In such systems, the dissipation of the kinetic energy of tidal flows in the host star may modify its rotational evolution and shape the orbital architecture of the surrounding planetary system. In this context, recent observational and theoretical works demonstrated that the amplitude of this dissipation can vary over several orders of magnitude as a function of stellar mass, age and rotation. In addition, stellar spin-up occurring during the Pre-Main-Sequence (PMS) phase because of the contraction of stars and their spin-down because of the torque applied by magnetized stellar winds strongly impact angular momentum exchanges within star–planet systems. Therefore, it is now necessary to take into account the structural and rotational evolution of stars when studying the orbital evolution of close-in planets. At the same time, the presence of planets may modify the rotational dynamics of the host stars and as a consequence their evolution, magnetic activity and mixing. In this work, we present the first study of the dynamics of close-in planets of various masses orbiting low-mass stars (from \(0.6~M_\odot \) to \(1.2~M_\odot \)) where we compute the simultaneous evolution of the star’s structure, rotation and tidal dissipation in its external convective envelope. We demonstrate that tidal friction due to the stellar dynamical tide, i.e. tidal inertial waves excited in the convection zone, can be larger by several orders of magnitude than the one of the equilibrium tide currently used in Celestial Mechanics, especially during the PMS phase. Moreover, because of this stronger tidal friction in the star, the orbital migration of the planet is now more pronounced and depends more on the stellar mass, rotation and age. This would very weakly affect the planets in the habitable zone because they are located at orbital distances such that stellar tide-induced migration happens on very long timescales. We also demonstrate that the rotational evolution of host stars is only weakly affected by the presence of planets except for massive companions. 相似文献
12.
Dane Quinn Brett Gladman Phil Nicholson Richard Rand 《Celestial Mechanics and Dynamical Astronomy》1997,67(2):111-130
We study the rotational evolution under tidal torques of axisymmetric natural satellites in inclined, precessing orbits. In
the spin- and orbit-averaged equations of motion, we find that a global limit cycle exists for parameter values near the stability
limit of Cassini state
. The limit cycle involves an alternation between states of near-synchronous spin at low obliquity, and strongly subsynchronous
spin at an obliquity near 90°. This dynamical feature is characterized as a relaxation oscillation, arising as the system
slowly traverses two saddle-node bifurcations in a reduced system. This slow timescale is controlled by ε, the nondimensional
tidal dissipation rate. Unfortunately, a straightforward expansion of the governing equations for small ε is shown to be insufficient
for understanding the underlying structure of the system. Rather, the dynamical equations of motion possess a singular term,
multiplied by ε, which vanishes in the unperturbed system. We thus provide a demonstration that a dissipatively perturbed
conservative system can behave qualitatively differently from the unperturbed system.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
13.
Pavol Pástor 《Celestial Mechanics and Dynamical Astronomy》2014,120(1):77-104
Circumstellar dust particles can be captured in a mean-motion resonance (MMR) with a planet and simultaneously be affected by non-gravitational effects. It is possible to describe the secular variations of a particle orbit in the MMR analytically using averaged resonant equations. We derive the averaged resonant equations from the equations of motion in near-canonical form. The secular variations of the particle orbit depending on the orientation of the orbit in space are taken into account. The averaged resonant equations can be derived/confirmed also from Lagrange’s planetary equations. We apply the derived theory to the case when the non-gravitational effects are the Poynting–Robertson effect, the radial stellar wind, and an interstellar wind. The analytical and numerical results obtained are in excellent agreement. We found that the types of orbits correspond to libration centers of the conservative problem. The averaged resonant equations can lead to a system of equations which holds for stationary points in a subset of resonant variables. Using this system we show analytically that for the considered non-gravitational effects, all stationary points should correspond to orbits which are stationary in interplanetary space after an averaging over a synodic period. In an exact resonance, the stationary orbits are stable. The stability is achieved by a periodic repetition of the evolution during the synodic period. Numerical solutions of this system show that there are no stationary orbits for either the exact or non-exact resonances. 相似文献
14.
The majority of confirmed terrestrial exoplanets orbits close to their host stars and their evolution was likely altered by tidal interaction. Nevertheless, due to their viscoelastic properties on the tidal frequencies, their response cannot be described exactly by standardly employed constant-lag models. We therefore introduce a tidal model based on the numerical evaluation of a continuum mechanics problem describing the deformation of viscoelastic (Maxwell or Andrade) planetary mantles subjected to external force. We apply the method on a model Earth-size planet orbiting a low-mass star and study the effect of the orbital eccentricity, the mantle viscosity and the chosen rheology on the tidal dissipation, the complex Love numbers and the tidal torque. The number of stable spin states (i.e., zero tidal torque) grows with increasing mantle viscosity, similarly to the analytical model of Correia et al. (Astron Astrophys 571:A50, 2014) for homogeneous bodies. This behavior is only slightly influenced by the rheology used. Similarly, the Love numbers do not distinctly depend on the considered rheological model. The increase in viscosity affects the amplitude of their variations. The tidal heating described by the Maxwell rheology attains local minima associated with low spin-orbit resonances, with depth and shape depending on both the eccentricity and the viscosity. For the Andrade rheology, the minima at low resonances are very shallow and the tidal heating for all viscosities resembles a “fluid limit.” The tidal heating is the quantity influenced the most by the rheology, having thus possible impact on the internal thermal evolution. 相似文献
15.
D. V. Mikryukov 《Astronomy Letters》2018,44(5):337-350
A system of averaged equations of planetary motion around a central star is constructed. An astrocentric coordinate system is used. The two-planet problem is considered, but all constructions are easily generalized to an arbitrary number N of planets. The motion is investigated in modified (complex) Poincarécanonical elements. The averaging is performed by the Hori–Deprit method over the fast mean longitudes to the second order relative to the planetary masses. An expansion of the disturbing function is constructed using the Laplace coefficients. Some terms of the expansion of the disturbing function and the first terms of the expansion of the averaged Hamiltonian are given. The results of this paper can be used to investigate the evolution of orbits with moderate eccentricities and inclinations in various planetary systems. 相似文献
16.
Bruce G. Bills 《Icarus》2005,175(1):233-247
The obliquity, or angular separation between orbit normal and spin pole, is an important parameter for the geodynamics of most Solar System bodies. Tidal dissipation has driven the obliquities of the Galilean satellites of Jupiter to small, but non-zero values. We present estimates of the free and forced obliquities of these satellites using a simple secular variation model for the orbits, and spin pole precession rate estimates based on gravity field parameters derived from Galileo spacecraft encounters. The free obliquity values are not well constrained by observations, but are presumed to be very small. The forced obliquity variations depend only on the orbital variations and the spin pole precession rate parameters, which are quite well known. These variations are large enough to influence spatial and temporal patterns of tidal dissipation and tidal stress. 相似文献
17.
《New Astronomy》2024
A very well-known property of close binary stars is that they usually rotate slowly than a similar type single star. Massive stars in close binary systems are supposed to experience an exchange of mass and angular momentum via mass transfer and tidal interaction, and thus the evolution of binary stars becomes more complex than that of individual stars. In recent times, it has become clear that a large number of massive stars interact with binary companions before they die. The observation also reveals that in close pairs the rotation tends to be synchronized with the orbital motion and the companions are naturally tempted to invoke tidal friction. We here introduce the effect of tidal angular momentum in the model of wind driven non-conservative mass transfer taking mass accretion rate as uniform with respect to time. To model the angular momentum evolution of a low mass main sequence companion star can be a challenging task. So, to make the present study more interesting, we have considered initial masses of the donor and gainer stars at the proximity of bottom-line main sequence stars and they are taken with lower angular momentum. We have produced a graphical profile of the rate of change of tidal angular momentum and the variation of tidal angular momentum with respect to time under the present consideration. 相似文献
18.
V.V. Kouprianov 《Icarus》2005,176(1):224-234
The problem of observability of chaotic regimes in the rotation of planetary satellites is studied. The analysis is based on the inertial and orbital data available for all satellites discovered up to now. The Lyapunov spectra of the spatial chaotic rotation and the full range of variation of the spin rate are computed numerically by integrating the equations of the rotational motion; the initial data are taken inside the main chaotic layer near the separatrices of synchronous resonance in phase space. The model of a triaxial satellite in a fixed elliptic orbit is adopted. A short Lyapunov time along with a large range of variation of the spin rate are used as criteria for observability of the chaotic motion. Independently, analysis of stability of the synchronous state with respect to tilting the axis of rotation provides a test for the physical opportunity for a satellite to rotate chaotically. Finally, a calculation of the times of despinning due to tidal evolution shows whether a satellite's spin could evolve close to the synchronous state. Apart from Hyperion, already known to rotate chaotically, only Prometheus and Pandora, the 16th and 17th satellites of Saturn, pass all these four tests. 相似文献
19.
极端质量比旋进系统是空间引力波探测器最重要的波源之一。对引力波的探测需要高精度波形模版。当前主流的极端质量比旋进系统引力波计算模型中,人们一般将小质量天体当作试验粒子进行计算,而忽略了其结构及自身引力对背景引力场的影响。利用Mathisson-Papapetrou-Dixon方程研究延展体在弯曲时空中的运动,以及小天体自旋和质量多极矩对引力波信号识别产生的影响。结果表明,质量比在10?6-10?4范围的旋进系统,其自旋达到很大时,自旋对延展体的轨道运动有不可忽略的影响;在质量比10?4-10?2区间内,需要考虑中心黑洞潮汐作用导致的白矮星形变;在质量比大于10?4,且白矮星自旋很大时,其自旋产生的形变会对小天体轨道运动产生不可忽略的影响。大质量黑洞潮汐作用导致的恒星级黑洞或中子星产生的形变可以忽略,中子星和黑洞的自旋会对轨道运动产生不可忽略的影响,而自旋产生的四极矩对轨道运动不产生影响。 相似文献
20.
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