722 research outputs found
The Resonance Overlap and Hill Stability Criteria Revisited
We review the orbital stability of the planar circular restricted three-body
problem, in the case of massless particles initially located between both
massive bodies. We present new estimates of the resonance overlap criterion and
the Hill stability limit, and compare their predictions with detailed dynamical
maps constructed with N-body simulations. We show that the boundary between
(Hill) stable and unstable orbits is not smooth but characterized by a rich
structure generated by the superposition of different mean-motion resonances
which does not allow for a simple global expression for stability.
We propose that, for a given perturbing mass and initial eccentricity
, there are actually two critical values of the semimajor axis. All values
are
unstable in the Hill sense. The first limit is given by the Hill-stability
criterion and is a function of the eccentricity. The second limit is virtually
insensitive to the initial eccentricity, and closely resembles a new resonance
overlap condition (for circular orbits) developed in terms of the intersection
between first and second-order mean-motion resonances.Comment: 33 pages, 14 figures, accepte
MAMA: An Algebraic Map for the Secular Dynamics of Planetesimals in Tight Binary Systems
We present an algebraic map (MAMA) for the dynamical and collisional
evolution of a planetesimal swarm orbiting the main star of a tight binary
system (TBS). The orbital evolution of each planetesimal is dictated by the
secular perturbations of the secondary star and gas drag due to interactions
with a protoplanetary disk. The gas disk is assumed eccentric with a constant
precession rate. Gravitational interactions between the planetesimals are
ignored. All bodies are assumed coplanar. A comparison with full N-body
simulations shows that the map is of the order of 100 times faster, while
preserving all the main characteristics of the full system.
In a second part of the work, we apply MAMA to the \gamma-Cephei, searching
for friendly scenarios that may explain the formation of the giant planet
detected in this system. For low-mass protoplanetary disks, we find that a
low-eccentricity static disk aligned with the binary yields impact velocities
between planetesimals below the disruption threshold. All other scenarios
appear hostile to planetary formation
The stability in the most external region of the Oort Cloud: The evolution of the ejected comets
In this paper, we present a study about the dynamical effects of the Galaxy
on the external region of the Oort Cloud. The aims of this paper are: i) to
determine an outer limit for the Oort Cloud; and ii) to analyse the dynamical
behaviour of the most external objects of the Cloud and how they are ejected
from the Solar System. This is undertaken by following the temporal evolution
of massless test particles in the Galactic environment of the solar
neighbourhood. Here we show that the effect of the perturbations from the
Galactic tide in the particles is similar to that find for the evolution of
wide binary stars population. Moreover, in the Oort Cloud we found a dynamical
structure around 10 5 au conformed by objects unbound of the Sun. This
structure allows us to define a transition region of stability and an outer
boundary for the Oort Cloud, and it is also in agreement with previous results
about the disruption of wide binary stars.Comment: Accepted for publishing in MNRAS. 13 pages, 9 figures, 2 table
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
The population of Comet candidates among quasi-Hilda objects revisited and updated
In this paper, we perform a dynamical study of the population of objects in
the unstable quasi-Hilda region. The aim of this work is to make an update of
the population of quasi-Hilda comets (QHCs) that have recently arrived from the
Centaurs region. To achieve our goal, we have applied a dynamical criteria to
constrain the unstable quasi-Hilda region that allowed us to select 828
potential candidates. The orbital data of the potential candidates was take
from the ASTORB database and we apply backward integration to search by those
that have recently arrived from the outer regions of the Solar System. Then we
studied the dynamical evolution of the candidates from a statistical point of
view by calculating the time-averaged distribution of a number of clones of
each candidate as a function of aphelion and perihelion distances. We found
that 47 objects could have been recently injected into the inner Solar System
from the Centaur or transneptunian regions. These objects may have preserved
volatile material and are candidates to exhibit cometary activity.Comment: 7 pages 3 figure
A new insight into the Galactic potential: a simple secular model for the evolution of binary systems in the solar neighbourhood
Context. Among the main effects that the Milky Way exerts in binary systems, the Galactic tide is the only one that is not probabilistic and can be deduced from a potential. Therefore, it is possible to perform an analysis of the global structure of the phase space of binary systems in the solar neighbourhood using the Galactic potential. Aims. The aim of this work is to obtain a simple model to study the collisionless dynamical evolution of generic wide binaries systems in the solar neighbourhood. Methods. Through an averaging process, we reduced the three-dimensional potential of the Galaxy to a secular one-degree of freedom model. The accuracy of this model was tested by comparing its predictions with numerical simulations of the exact equations of motion of a two-body problem disturbed by the Galaxy. Results. Using the one-degree of freedom model, we developed a detailed dynamical study, finding that the secular Galactic tide period changes as a function of the separation of the pair, which also gives a dynamical explanation for the arbitrary classification between wide and tight binaries. Moreover, the secular phase space for a generic gravitationally bound pair is similar to the dynamical structure of a Lidov-Kozai resonance, but surprisingly this structure is independent of the masses and semimajor axis of the binary system. Thus, the Galactic potential is able to excite the initially circular orbit of binary systems to high values of eccentricity, which has important implications for studies of binary star systems (with and without exoplanets), comets, and Oort cloud objects.Facultad de Ciencias Astronómicas y Geofísica
Formation and evolution of the two 4/3 resonant giants planets in HD 200946
It has been suggested that HD 200964 is the first exoplanetary system with
two Jovian planets evolving in the 4/3 mean- motion resonance. Previous
scenarios to simulate the formation of two giant planets in the stable 4/3
resonance configuration have failed. Moreover, the orbital parameters available
in the literature point out an unstable configuration of the planetary pair.
The purpose of this paper is i) to determine the orbits of the planets from
the RV measurements and update the value of the stellar mass (1.57 M), ii) to
analyse the stability of the planetary evolution in the vicinity and inside the
4/3 MMR, and iii) to elaborate a possible scenario for the formation of systems
in the 4/3 MMR.
The results of the formation simulations are able to very closely reproduce
the 4/3 resonant dynamics of the best-fit config- uration obtained in this
paper. Moreover, the confidence interval of the fit matches well with the very
narrow stable region of the 4/3 mean-motion resonance. The formation process of
the HD 200964 system is very sensitive to the planetary masses and
protoplanetary disk parameters. Only a thin, flat disk allows the embryo-sized
planets to reach the 4/3 resonant configuration. The stable evolution of the
resonant planets is also sensitive to the mass of the central star, because of
overlapping high-order resonances inside the 4/3 resonance. Regardless of the
very narrow domain of stable motion, the confidence interval of our fit closely
matches the stability area
Secular dynamics of planetesimals in tight binary systems: Application to Gamma-Cephei
The secular dynamics of small planetesimals in tight binary systems play a
fundamental role in establishing the possibility of accretional collisions in
such extreme cases. The most important secular parameters are the forced
eccentricity and secular frequency, which depend on the initial conditions of
the particles, as well as on the mass and orbital parameters of the secondary
star. We construct a second-order theory (with respect to the masses) for the
planar secular motion of small planetasimals and deduce new expressions for the
forced eccentricity and secular frequency. We also reanalyze the radial
velocity data available for Gamma-Cephei and present a series of orbital
solutions leading to residuals compatible with the best fits. Finally, we
discuss how different orbital configurations for Gamma-Cephei may affect the
dynamics of small bodies in circunmstellar motion. For Gamma-Cephei, we find
that the classical first-order expressions for the secular frequency and forced
eccentricity lead to large inaccuracies around 50 % for semimajor axes larger
than one tenth the orbital separation between the stellar components. Low
eccentricities and/or masses reduce the importance of the second-order terms.
The dynamics of small planetesimals only show a weak dependence with the
orbital fits of the stellar components, and the same result is found including
the effects of a nonlinear gas drag. Thus, the possibility of planetary
formation in this binary system largely appears insensitive to the orbital fits
adopted for the stellar components, and any future alterations in the system
parameters (due to new observations) should not change this picture. Finally,
we show that planetesimals migrating because of gas drag may be trapped in
mean-motion resonances with the binary, even though the migration is divergent.Comment: 11 pages, 9 figure
Mapping the Secular Resonance for Retrograde Irregular Satellites
Constructing dynamical maps from the filtered output of numerical
integrations, we analyze the structure of the secular resonance for
fictitious irregular satellites in retrograde orbits. This commensurability is
associated to the secular angle , where
is the longitude of pericenter of the satellite and
corresponds to the (fixed) planetocentric orbit of the Sun. Our study is
performed in the restricted three-body problem, where the satellites are
considered as massless particles around a massive planet and perturbed by the
Sun. Depending on the initial conditions, the resonance presents a diversity of
possible resonant modes, including librations of around zero (as found
for Sinope and Pasiphae) or 180 degrees, as well as asymmetric librations (e.g.
Narvi). Symmetric modes are present in all giant planets, although each regime
appears restricted to certain values of the satellite inclination. Asymmetric
solutions, on the other hand, seem absent around Neptune due to its almost
circular heliocentric orbit. Simulating the effects of a smooth orbital
migration on the satellite, we find that the resonance lock is preserved as
long as the induced change in semimajor axis is much slower compared to the
period of the resonant angle (adiabatic limit). However, the librational mode
may vary during the process, switching between symmetric and asymmetric
oscillations. Finally, we present a simple scaling transformation that allows
to estimate the resonant structure around any giant planet from the results
calculated around a single primary mass.Comment: 11 pages, 13 figure
Dynamics of Planetesimals due to Gas Drag from an Eccentric Precessing Disk
We analyze the dynamics of individual kilometer-size planetesimals in
circumstellar orbits of a tight binary system. We include both the
gravitational perturbations of the secondary star and a non-linear gas drag
stemming from an eccentric gas disk with a finite precession rate. We consider
several precession rates and eccentricities for the gas, and compare the
results with a static disk in circular orbit.
The disk precession introduces three main differences with respect to the
classical static case: (i) The equilibrium secular solutions generated by the
gas drag are no longer fixed points in the averaged system, but limit cycles
with frequency equal to the precession rate of the gas. The amplitude of the
cycle is inversely dependent on the body size, reaching negligible values for
km size planetesimals. (ii) The maximum final eccentricity attainable
by small bodies is restricted to the interval between the gas eccentricity and
the forced eccentricity, and apsidal alignment is no longer guaranteed for
planetesimals strongly coupled with the gas. (iii) The characteristic
timescales of orbital decay and secular evolution decrease significantly with
increasing precession rates, with values up to two orders of magnitude smaller
than for static disks.
Finally, we apply this analysis to the -Cephei system and estimate
impact velocities for different size bodies and values of the gas eccentricity.
For high disk eccentricities, we find that the disk precession decreases the
velocity dispersion between different size planetesimals, thus contributing to
accretional collisions in the outer parts of the disk. The opposite occurs for
almost circular gas disks, where precession generates an increase in the
relative velocities.Comment: 11 pages, 9 figures. Accepted in MNRA
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