231 research outputs found
Modeling the secular evolution of migrating planet pairs
The subject of this paper is the secular behaviour of a pair of planets
evolving under dissipative forces. In particular, we investigate the case when
dissipative forces affect the planetary semi-major axes and the planets move
inward/outward the central star, in a process known as planet migration. To
perform this investigation, we introduce fundamental concepts of conservative
and dissipative dynamics of the three-body problem. Based on these concepts, we
develop a qualitative model of the secular evolution of the migrating planetary
pair. Our approach is based on analysis of the energy and the orbital angular
momentum exchange between the two-planet system and an external medium; thus no
specific kind of dissipative forces is invoked. We show that, under assumption
that dissipation is weak and slow, the evolutionary routes of the migrating
planets are traced by the Mode I and Mode II stationary solutions of the
conservative secular problem. The ultimate convergence and the evolution of the
system along one of these secular modes of motion is determined uniquely by the
condition that the dissipation rate is sufficiently smaller than the proper
secular frequency of the system. We show that it is possible to reassemble the
starting configurations and migration history of the systems on the basis of
their final states and consequently to constrain the parameters of the physical
processes involved.Comment: 20 pages, 17 figures. Accepted for publication in MNRA
Dynamics of two planets in co-orbital motion
We study the stability regions and families of periodic orbits of two planets
locked in a co-orbital configuration. We consider different ratios of planetary
masses and orbital eccentricities, also we assume that both planets share the
same orbital plane. Initially we perform numerical simulations over a grid of
osculating initial conditions to map the regions of stable/chaotic motion and
identify equilibrium solutions. These results are later analyzed in more detail
using a semi-analytical model. Apart from the well known quasi-satellite (QS)
orbits and the classical equilibrium Lagrangian points L4 and L5, we also find
a new regime of asymmetric periodic solutions. For low eccentricities these are
located at , where \sigma is
the difference in mean longitudes and \Delta\omega is the difference in
longitudes of pericenter. The position of these Anti-Lagrangian solutions
changes with the mass ratio and the orbital eccentricities, and are found for
eccentricities as high as ~ 0.7. Finally, we also applied a slow mass variation
to one of the planets, and analyzed its effect on an initially asymmetric
periodic orbit. We found that the resonant solution is preserved as long as the
mass variation is adiabatic, with practically no change in the equilibrium
values of the angles.Comment: 9 pages, 11 figure
The Dynamics of Neptune Trojan: I. the Inclined Orbits
The stability of Trojan type orbits around Neptune is studied. As the first
part of our investigation, we present in this paper a global view of the
stability of Trojans on inclined orbits. Using the frequency analysis method
based on the FFT technique, we construct high resolution dynamical maps on the
plane of initial semimajor axis versus inclination . These maps show
three most stable regions, with in the range of and respectively, where the Trojans
are most probably expected to be found. The similarity between the maps for the
leading and trailing triangular Lagrange points and confirms the
dynamical symmetry between these two points. By computing the power spectrum
and the proper frequencies of the Trojan motion, we figure out the mechanisms
that trigger chaos in the motion. The Kozai resonance found at high inclination
varies the eccentricity and inclination of orbits, while the secular
resonance around pumps up the eccentricity. Both mechanisms
lead to eccentric orbits and encounters with Uranus that introduce strong
perturbation and drive the objects away from the Trojan like orbits. This
explains the clearance of Trojan at high inclination () and an
unstable gap around on the dynamical map. An empirical theory is
derived from the numerical results, with which the main secular resonances are
located on the initial plane of . The fine structures in the
dynamical maps can be explained by these secular resonances.Comment: 12 pages, 11 figures, accepted by Mon. Not. R.A.
Tidal decay and orbital circularization in close-in two-planet systems
The motion of two planets around a Sun-like star under the combined effects
of mutual interaction and tidal dissipation is investigated. The secular
behaviour of the system is analyzed using two different approaches. First, we
solve the exact equations of motion through the numerical simulation of the
system evolution. In addition to the orbital decay and circularization, we show
that the final configuration of the system is affected by the shrink of the
inner orbit. Our second approach consist in the analysis of the stationary
solutions of mean equations of motion based on a Hamiltonian formalism. We
consider the case of a hot super-Earth planet with a more massive outer
companion. As a real example, the CoRoT-7 system is analyzed solving the exact
and mean equations of motion. The star-planet tidal interaction produces
orbital decay and circularization of the orbit of CoRoT-7b. In addition, the
long-term tidal evolution is such that the eccentricity of CoRoT-7c is also
circularized and a pair of final circular orbits is obtained. A curve in the
space of eccentricities can be constructed through the computation of
stationary solutions of mean equations including dissipation. The application
to CoRoT-7 system shows that the stationary curve agrees with the result of
numerical simulations of exact equations. A similar investigation performed in
a super-Earth-Jupiter two-planet system shows that the doubly circular state is
accelerated when there is a significant orbital migration of the inner planet,
in comparison with previous results were migration is neglected.Comment: Accepted for publication in MNRAS; 10 pages, 13 figure
Tidal evolution of close-in exoplanets in co-orbital configurations
In this paper, we study the behavior of a pair of co-orbital planets, both
orbiting a central star on the same plane and undergoing tidal interactions.
Our goal is to investigate final orbital configurations of the planets,
initially involved in the 1/1 mean-motion resonance (MMR), after long-lasting
tidal evolution. The study is done in the form of purely numerical simulations
of the exact equations of motions accounting for gravitational and tidal
forces. The results obtained show that, at least for equal mass planets, the
combined effects of the resonant and tidal interactions provoke the orbital
instability of the system, often resulting in collision between the planets. We
first discuss the case of two hot-super-Earth planets, whose orbital dynamics
can be easily understood in the frame of our semi-analytical model of the 1/1
MMR. Systems consisting of two hot-Saturn planets are also briefly discussed.Comment: 18 pages, 8 figures. Accepted for publication in Celestial Mechanics
and Dynamical Astronom
Extrasolar Planets in Mean-Motion Resonance: Apses Alignment and Asymmetric Stationary Solutions
In recent years several pairs of extrasolar planets have been discovered in
the vicinity of mean-motion commensurabilities. In some cases, such as the
Gliese 876 system, the planets seem to be trapped in a stationary solution, the
system exhibiting a simultaneous libration of the resonant angle theta_1 = 2
lambda_2 - lambda_1 - varpi_1 and of the relative position of the pericenters.
In this paper we analyze the existence and location of these stable
solutions, for the 2/1 and 3/1 resonances, as function of the masses and
orbital elements of both planets. This is undertaken via an analytical model
for the resonant Hamiltonian function. The results are compared with those of
numerical simulations of the exact equations.
In the 2/1 commensurability, we show the existence of three principal
families of stationary solutions: (i) aligned orbits, in which theta_1 and
varpi_1 - varpi_2 both librate around zero, (ii) anti-aligned orbits, in which
theta_1=0 and the difference in pericenter is 180 degrees, and (iii) asymmetric
stationary solutions, where both the resonant angle and varpi_1 - varpi_2 are
constants with values different of 0 or 180 degrees. Each family exists in a
different domain of values of the mass ratio and eccentricities of both
planets. Similar results are also found in the 3/1 resonance.
We discuss the application of these results to the extrasolar planetary
systems and develop a chart of possible planetary orbits with apsidal
corotation. We estimate, also, the maximum planetary masses in order that the
stationary solutions are dynamically stable.Comment: 25 pages, 10 figures. Submitted to Ap
Scalar field in a minimally coupled brane world: no-hair and other no-go theorems
In the brane-world framework, we consider static, spherically symmetric
configurations of a scalar field with the Lagrangian (\d\phi)^2/2 - V(\phi),
confined on the brane. We use the 4D Einstein equations on the brane obtained
by Shiromizu et al., containing the usual stress tensor T\mN, the tensor
\Pi\mN, quadratic in T\mN, and E\mN describing interaction with the bulk.
For models under study, the tensor \Pi\mN has zero divergence, so we can
consider a "minimally coupled" brane with E\mN = 0, whose 4D gravity is
decoupled from the bulk geometry. Assuming E\mN =0, we try to extend to brane
worlds some theorems valid for scalar fields in general relativity (GR). Thus,
the list of possible global causal structures in all models under consideration
is shown to be the same as is known for vacuum with a term in GR:
Minkowski, Schwarzschild, (A)dS and Schwarzschild-(A)dS. A no-hair theorem,
saying that, given a potential , asymptotically flat black holes
cannot have nontrivial external scalar fields, is proved under certain
restrictions. Some objects, forbidden in GR, are allowed on the brane, e.g,
traversable wormholes supported by a scalar field, but only at the expense of
enormous matter densities in the strong field region.Comment: 8 pages, Latex2e. Numerical estimates and a few references adde
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