996 research outputs found
Origin of the peculiar eccentricity distribution of the inner cold Kuiper belt
Dawson and Murray-Clay (2012) pointed out that the inner part of the cold
population in the Kuiper belt (that with semi major axis a<43.5 AU) has orbital
eccentricities significantly smaller than the limit imposed by stability
constraints. Here, we confirm their result by looking at the orbital
distribution and stability properties in proper element space. We show that the
observed distribution could have been produced by the slow sweeping of the 4/7
mean motion resonance with Neptune that accompanied the end of Neptune's
migration process. The orbital distribution of the hot Kuiper belt is not
significantly affected in this process, for the reasons discussed in the main
text. Therefore, the peculiar eccentricity distribution of the inner cold
population can not be unequivocally interpreted as evidence that the cold
population formed in-situ and was only moderately excited in eccentricity; it
can simply be the signature of Neptune's radial motion, starting from a
moderately eccentric orbit. We discuss how this agrees with a scenario of giant
planet evolution following a dynamical instability and, possibly, with the
radial transport of the cold population.Comment: in press in Icaru
Did the Hilda collisional family form during the late heavy bombardment?
We model the long-term evolution of the Hilda collisional family located in
the 3/2 mean-motion resonance with Jupiter. Its eccentricity distribution
evolves mostly due to the Yarkovsky/YORP effect and assuming that: (i) impact
disruption was isotropic, and (ii) albedo distribution of small asteroids is
the same as for large ones, we can estimate the age of the Hilda family to be
. We also calculate collisional activity in the J3/2
region. Our results indicate that current collisional rates are very low for a
200\,km parent body such that the number of expected events over Gyrs is much
smaller than one.
The large age and the low probability of the collisional disruption lead us
to the conclusion that the Hilda family might have been created during the Late
Heavy Bombardment when the collisions were much more frequent. The Hilda family
may thus serve as a test of orbital behavior of planets during the LHB. We
tested the influence of the giant-planet migration on the distribution of the
family members. The scenarios that are consistent with the observed Hilda
family are those with fast migration time scales to
, because longer time scales produce a family that is depleted
and too much spread in eccentricity. Moreover, there is an indication that
Jupiter and Saturn were no longer in a compact configuration (with period ratio
) at the time when the Hilda family was created
Constraining the cometary flux through the asteroid belt during the late heavy bombardment
In the Nice model, the late heavy bombardment (LHB) is related to an orbital
instability of giant planets which causes a fast dynamical dispersion of a
transneptunian cometary disk. We study effects produced by these hypothetical
cometary projectiles on main-belt asteroids. In particular, we want to check
whether the observed collisional families provide a lower or an upper limit for
the cometary flux during the LHB.
We present an updated list of observed asteroid families as identified in the
space of synthetic proper elements by the hierarchical clustering method,
colour data, albedo data and dynamical considerations and we estimate their
physical parameters. We selected 12 families which may be related to the LHB
according to their dynamical ages. We then used collisional models and N-body
orbital simulations to gain insight into the long-term dynamical evolution of
synthetic LHB families over 4 Gyr. We account for the mutual collisions, the
physical disruptions of comets, the Yarkovsky/YORP drift, chaotic diffusion, or
possible perturbations by the giant-planet migration.
Assuming a "standard" size-frequency distribution of primordial comets, we
predict the number of families with parent-body sizes D_PB >= 200 km which
seems consistent with observations. However, more than 100 asteroid families
with D_PB >= 100 km should be created at the same time which are not observed.
This discrepancy can be nevertheless explained by the following processes: i)
asteroid families are efficiently destroyed by comminution (via collisional
cascade), ii) disruptions of comets below some critical perihelion distance (q
<~ 1.5 AU) are common.
Given the freedom in the cometary-disruption law, we cannot provide stringent
limits on the cometary flux, but we can conclude that the observed distribution
of asteroid families does not contradict with a cometary LHB.Comment: accepted in Astronomy and Astrophysic
A new perspective on the irregular satellites of Saturn - I Dynamical and collisional history
The dynamical features of the irregular satellites of the giant planets argue
against an in-situ formation and are strongly suggestive of a capture origin.
Since the last detailed investigations of their dynamics, the total number of
satellites have doubled, increasing from 50 to 109, and almost tripled in the
case of Saturn system. We have performed a new dynamical exploration of Saturn
system to test whether the larger sample of bodies could improve our
understanding of which dynamical features are primordial and which are the
outcome of the secular evolution of the system. We have performed detailed
N--Body simulations using the best orbital data available and analysed the
frequencies of motion to search for resonances and other possible perturbing
effects. We took advantage of the Hierarchical Jacobian Symplectic algorithm to
include in the dynamical model of the system also the gravitational effects of
the two outermost massive satellites, Titan and Iapetus. Our results suggest
that Saturn's irregular satellites have been significantly altered and shaped
by the gravitational perturbations of Jupiter, Titan, Iapetus and the Sun and
by the collisional sweeping effect of Phoebe. In particular, the effects on the
dynamical evolution of the system of the two massive satellites appear to be
non-negligible. Jupiter perturbs the satellites through its direct
gravitational pull and, indirectly, via the effects of the Great Inequality,
i.e. its almost resonance with Saturn. Finally, by using the Hierarchical
Clustering Method we found hints to the existence of collisional families and
compared them with the available observational data.Comment: 26 Pages, 27 Figures, 4 Table
On the relationship between instability and Lyapunov times for the 3-body problem
In this study we consider the relationship between the survival time and the
Lyapunov time for 3-body systems. It is shown that the Sitnikov problem
exhibits a two-part power law relationship as demonstrated previously for the
general 3-body problem. Using an approximate Poincare map on an appropriate
surface of section, we delineate escape regions in a domain of initial
conditions and use these regions to analytically obtain a new functional
relationship between the Lyapunov time and the survival time for the 3-body
problem. The marginal probability distributions of the Lyapunov and survival
times are discussed and we show that the probability density function of
Lyapunov times for the Sitnikov problem is similar to that for the general
3-body problem.Comment: 9 pages, 19 figures, accepted for publication in MNRA
Massive planet migration: Theoretical predictions and comparison with observations
We quantify the utility of large radial velocity surveys for constraining
theoretical models of Type II migration and protoplanetary disk physics. We
describe a theoretical model for the expected radial distribution of extrasolar
planets that combines an analytic description of migration with an empirically
calibrated disk model. The disk model includes viscous evolution and mass loss
via photoevaporation. Comparing the predicted distribution to a uniformly
selected subsample of planets from the Lick / Keck / AAT planet search
programs, we find that a simple model in which planets form in the outer disk
at a uniform rate, migrate inward according to a standard Type II prescription,
and become stranded when the gas disk is dispersed, is consistent with the
radial distribution of planets for orbital radii 0.1 AU < a < 2.5 AU and planet
masses greater than 1.65 Jupiter masses. Some variant models are disfavored by
existing data, but the significance is limited (~95%) due to the small sample
of planets suitable for statistical analysis. We show that the favored model
predicts that the planetary mass function should be almost independent of
orbital radius at distances where migration dominates the massive planet
population. We also study how the radial distribution of planets depends upon
the adopted disk model. We find that the distribution can constrain not only
changes in the power-law index of the disk viscosity, but also sharp jumps in
the efficiency of angular momentum transport that might occur at small radii.Comment: ApJ, in press. References updated to match published versio
The three-body problem and the Hannay angle
The Hannay angle has been previously studied for a celestial circular
restricted three-body system by means of an adiabatic approach. In the present
work, three main results are obtained. Firstly, a formal connection between
perturbation theory and the Hamiltonian adiabatic approach shows that both lead
to the Hannay angle; it is thus emphasised that this effect is already
contained in classical celestial mechanics, although not yet defined nor
evaluated separately. Secondly, a more general expression of the Hannay angle,
valid for an action-dependent potential is given; such a generalised expression
takes into account that the restricted three-body problem is a time-dependent,
two degrees of freedom problem even when restricted to the circular motion of
the test body. Consequently, (some of) the eccentricity terms cannot be
neglected {\it a priori}. Thirdly, we present a new numerical estimate for the
Earth adiabatically driven by Jupiter. We also point out errors in a previous
derivation of the Hannay angle for the circular restricted three-body problem,
with an action-independent potential.Comment: 11 pages. Accepted by Nonlinearit
On the connection between the Nekhoroshev theorem and Arnold Diffusion
The analytical techniques of the Nekhoroshev theorem are used to provide
estimates on the coefficient of Arnold diffusion along a particular resonance
in the Hamiltonian model of Froeschl\'{e} et al. (2000). A resonant normal form
is constructed by a computer program and the size of its remainder
at the optimal order of normalization is calculated as a function
of the small parameter . We find that the diffusion coefficient
scales as , while the size of the optimal remainder
scales as in the range
. A comparison is made with the numerical
results of Lega et al. (2003) in the same model.Comment: Accepted in Celestial Mechanics and Dynamical Astronom
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