208 research outputs found
Diversity and Origin of 2:1 Orbital Resonances in Extrasolar Planetary Systems
(Abridged) A diversity of 2:1 resonance configurations can be expected in
extrasolar planetary systems, and their geometry can provide information about
the origin of the resonances. Assembly during planet formation by the
differential migration of planets due to planet-disk interaction is one
scenario for the origin of mean-motion resonances in extrasolar planetary
systems. The stable 2:1 resonance configurations that can be reached by
differential migration of planets with constant masses and initially coplanar
and nearly circular orbits are (1) anti-symmetric configurations with the
mean-motion resonance variables theta_1 and theta_2 (in deg.) librating about 0
and 180, respectively (as in the Io-Europa pair), (2) symmetric configurations
with both theta_1 and theta_2 librating about 0 (as in the GJ 876 system), and
(3) asymmetric configurations with theta_1 and theta_2 librating about angles
far from either 0 or 180. There are, however, stable 2:1 resonance
configurations with symmetric (theta_1 = theta_2 = 0), asymmetric, and
anti-symmetric (theta_1 = 180 and theta_2 = 0) librations that cannot be
reached by differential migration of planets with constant masses and initially
coplanar and nearly circular orbits. If real systems with these configurations
are ever found, their origin would require (1) a change in the planetary mass
ratio m_1/m_2 during migration, (2) a migration scenario involving inclination
resonances, or (3) multiple-planet scattering in crowded planetary systems. We
find that the asymmetric configurations with large e_2 and the theta_1 = 180
and theta_2 = 0 configurations have intersecting orbits and that the theta_1 =
theta_2 = 0 configurations with e_1 > 0.714 have prograde periapse precessions.Comment: 24 pages, including 14 figures; uses AASTeX v5.0; accepted for
publication in Ap
On the Early In Situ Formation of Pluto's Small Satellites
The formation of Pluto's small satellites - Styx, Nix, Keberos and Hydra -
remains a mystery. Their orbits are nearly circular and are near mean-motion
resonances and nearly coplanar with Charon's orbit. One scenario suggests that
they all formed close to their current locations from a disk of debris that was
ejected from the Charon-forming impact before the tidal evolution of Charon.
The validity of this scenario is tested by performing -body simulations with
the small satellites treated as test particles and Pluto-Charon evolving
tidally from an initial orbit at a few Pluto radii with initial eccentricity
or 0.2. After tidal evolution, the free eccentricities of the test particles are extracted by applying fast Fourier
transformation to the distance between the test particles and the center of
mass of the system and compared with the current eccentricities of the four
small satellites. The only surviving test particles with
matching the eccentricities of the current satellites are those not affected by
mean-motion resonances during the tidal evolution in a model with Pluto's
effective tidal dissipation function and an initial = 0.2
that is damped down rapidly. However, these test particles do not have any
preference to be in or near 4:1, 5:1 and 6:1 resonances with Charon. An
alternative scenario may be needed to explain the formation of Pluto's small
satellites.Comment: 27 pages, including 10 figures, accepted for publication in A
Secular Evolution of Hierarchical Planetary Systems
(Abridged) We investigate the dynamical evolution of coplanar hierarchical
two-planet systems where the ratio of the orbital semimajor axes alpha=a_1/a_2
is small. The orbital parameters obtained from a multiple Kepler fit to the
radial velocity variations of a star are best interpreted as Jacobi coordinates
and Jacobi coordinates should be used in any analyses of hierarchical planetary
systems. An approximate theory that can be applied to coplanar hierarchical
two-planet systems with a wide range of masses m_j and orbital eccentricities
e_j is the octupole-level secular perturbation theory (OSPT). The OSPT shows
that if the ratio of the maximum orbital angular momenta, lambda \approx
(m_1/m_2) alpha^{1/2}, for given a_j is approximately equal to a critical value
lambda_{crit}, then libration of the difference in the longitudes of periapse,
w_1-w_2, about either 0 or 180 deg. is almost certain, with possibly large
amplitude variations of both e_j. We establish that the OSPT is highly accurate
for systems with alpha<0.1 and reasonably accurate even for systems with alpha
as large as 1/3, provided that alpha is not too close to a significant
mean-motion commensurability or above the stability boundary. The HD 168443
system is not in a secular resonance and its w_1-w_2 circulates. The HD 12661
system is the first extrasolar planetary system found to have w_1-w_2 librating
about 180 deg. The libration of w_1-w_2 and the large-amplitude variations of
both e_j in the HD 12661 system are consistent with the analytic results on
systems with lambda \approx lambda_{crit}. The HD 12661 system with the best-
fit orbital parameters and sin i = 1 is affected by the close proximity to the
11:2 commensurability, but small changes in the outer orbital period can result
in configurations that are not affected by mean-motion commensurabilities.Comment: 32 pages, including 8 figures; uses AASTeX v5.0; accepted for
publication in Ap
A Primordial Origin of the Laplace Relation Among the Galilean Satellites
Understanding the origin of the orbital resonances of the Galilean satellites
of Jupiter will constrain the longevity of the extensive volcanism on Io, may
explain a liquid ocean on Europa, and may guide studies of the dissipative
properties of stars and Jupiter-like planets. The differential migration of the
newly formed Galilean satellites due to interactions with a circumjovian disk
can lead to the primordial formation of the Laplace relation n_1 - 3 n_2 + 2
n_3 = 0, where the n_i are the mean orbital angular velocities of Io, Europa,
and Ganymede, respectively. This contrasts with the formation of the resonances
by differential expansion of the orbits from tidal torques from Jupiter.Comment: 13 pages, including 4 figures; uses scicite.st
On the Origin of Pluto's Small Satellites by Resonant Transport
The orbits of Pluto's four small satellites (Styx, Nix, Kerberos, and Hydra)
are nearly circular and coplanar with the orbit of the large satellite Charon,
with orbital periods nearly in the ratios 3:1, 4:1, 5:1, and 6:1 with Charon's
orbital period. These properties suggest that the small satellites were created
during the same impact event that placed Charon in orbit and had been pushed to
their current positions by being locked in mean-motion resonances with Charon
as Charon's orbit was expanded by tidal interactions with Pluto. Using the
Pluto-Charon tidal evolution models developed by Cheng et al. (2014), we show
that stable capture and transport of a test particle in multiple resonances at
the same mean-motion commensurability is possible at the 5:1, 6:1, and 7:1
commensurabilities, if Pluto's zonal harmonic . However, the test
particle has significant orbital eccentricity at the end of the tidal evolution
of Pluto-Charon in almost all cases, and there are no stable captures and
transports at the 3:1 and 4:1 commensurabilities. Furthermore, a non-zero
hydrostatic value of destroys the conditions necessary for multiple
resonance migration. Simulations with finite but minimal masses of Nix and
Hydra also fail to yield any survivors. We conclude that the placing of the
small satellites at their current orbital positions by resonant transport is
extremely unlikely.Comment: 22 pages, including 7 figures; accepted for publication in Icaru
Are the Kepler Near-Resonance Planet Pairs due to Tidal Dissipation?
The multiple-planet systems discovered by the Kepler mission show an excess
of planet pairs with period ratios just wide of exact commensurability for
first-order resonances like 2:1 and 3:2. In principle, these planet pairs could
have both resonance angles associated with the resonance librating if the
orbital eccentricities are sufficiently small, because the width of first-order
resonances diverges in the limit of vanishingly small eccentricity. We consider
a widely-held scenario in which pairs of planets were captured into first-order
resonances by migration due to planet-disk interactions, and subsequently
became detached from the resonances, due to tidal dissipation in the planets.
In the context of this scenario, we find a constraint on the ratio of the
planet's tidal dissipation function and Love number that implies that some of
the Kepler planets are likely solid. However, tides are not strong enough to
move many of the planet pairs to the observed separations, suggesting that
additional dissipative processes are at play.Comment: 20 pages, including 7 figures; accepted for publication in Ap
Dynamical analysis of the circumprimary planet in the eccentric binary system HD59686
We present a detailed orbital and stability analysis of the HD~59686
binary-star planet system. HD~59686 is a single-lined moderately close (AU) eccentric () binary, where the primary is an evolved
K giant with mass and the secondary is a star with a
minimum mass of . Additionally, on the basis of precise
radial velocity (RV) data a Jovian planet with a minimum mass of , orbiting the primary on a nearly circular S-type orbit with
and AU, has recently been announced. We investigate
large sets of orbital fits consistent with HD 59686's radial velocity data by
applying bootstrap and systematic grid-search techniques coupled with
self-consistent dynamical fitting. We perform long-term dynamical integrations
of these fits to constrain the permitted orbital configurations. We find that
if the binary and the planet in this system have prograde and aligned coplanar
orbits, there are narrow regions of stable orbital solutions locked in a
secular apsidal alignment with the angle between the periapses, , librating about . We also test a large number of mutually
inclined dynamical models in an attempt to constrain the three-dimensional
orbital architecture. We find that for nearly coplanar and retrograde orbits
with mutual inclination , the
system is fully stable for a large range of orbital solutions.Comment: 17 pages, 11 figures, accepted for publication by A
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