76 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
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
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
A new scenario for the origin of the 3/2 resonant system HD 45364
We revise the model for the origin of the HD 45364 exoplanetary system proposed by Rein et al. (2010, A&A, 510, A4), which is currently known to host two planets close to the 3/2 mean-motion resonance (MMR). We show that due to the high surface density of the protoplanetary disk needed for type III migration, this model can only lead to planets in a quasi-resonant regime of motion and thus is not consistent with the resonant configuration obtained by Correia et al. (2009, A&A, 496, 521). Although both resonant and quasi-resonant solutions are statistically indistinguishable with respect to radial velocity measurements, their distinct dynamical behavior is intriguing. We used the semi-analytical model to confirm the quantitative difference between two configurations. To form a system that evolves inside the 3/2 resonance, we developed a different model. Our scenario includes an interaction between different (but slower) planetary migration types, planet growth, and gap formation in the protoplanetary disk. The evolutionary path was chosen due to a detailed analysis of the phase space structure in the vicinity of the 3/2 MMR that employed dynamical mapping techniques. The outcomes of our simulations are able to very closely reproduce the 3/2 resonant dynamics obtained from the best fit presented by Correia et al. In addition, by varying the strength of the eccentricity damping, we can also simulate the quasi-resonant configuration similar to that reported in Rein et al. We furthermore show that our scenario is reliable with respect to the physical parameters involved in the resonance-trapping process. However, our scenario can only be confirmed with additional radial velocities measurements.Fil: Correa Otto, J. A.. Universidade do Sao Paulo. Instituto Astronomia, Geofisica e Ciencias Atmosfericas; Brasil;Fil: Michtchenko, T. A.. Universidade do Sao Paulo. Instituto Astronomia, Geofisica e Ciencias Atmosfericas; Brasil;Fil: Beauge, Cristian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico - CONICET - Córdoba. Instituto de Astronomía Teórica y Experimental; Argentina
Evolution of Migrating Planet Pairs in Resonance
In this paper we present numerical simulations of the evolution of planets or massive satellites captured in the 2/1 and 3/1 resonances, under the action of an anti-dissipative tidal force. The evolution of resonant trapped bodies show a richness of solutions: librations around stationary symmetric solutions with aligned periapses (w1-w2=0) or anti-aligned periapses (w1-w2=180 deg), and librations around stationary solutions in which the periapses configuration is fixed, but with w1-w2 taking values in a wide range of angles. Many of these solutions exist for large values of the eccentricities and, during the semimajor axis drift, the solutions show turnabouts from one configuration to another. These results are valid for other non-conservative forces leading to adiabatic covergent migration and capture into one of these resonances
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