439 research outputs found
First order resonance overlap and the stability of close two planet systems
Motivated by the population of multi-planet systems with orbital period
ratios 1<P2/P1<2, we study the long-term stability of packed two planet
systems. The Hamiltonian for two massive planets on nearly circular and nearly
coplanar orbits near a first order mean motion resonance can be reduced to a
one degree of freedom problem (Sessin & Ferraz Mello (1984), Wisdom (1986),
Henrard et al. (1986)). Using this analytically tractable Hamiltonian, we apply
the resonance overlap criterion to predict the onset of large scale chaotic
motion in close two planet systems. The reduced Hamiltonian has only a weak
dependence on the planetary mass ratio, and hence the overlap criterion is
independent of the planetary mass ratio at lowest order. Numerical integrations
confirm that the planetary mass ratio has little effect on the structure of the
chaotic phase space for close orbits in the low eccentricity (e <~0.1) regime.
We show numerically that orbits in the chaotic web produced primarily by first
order resonance overlap eventually experience large scale erratic variation in
semimajor axes and are Lagrange unstable. This is also true of the orbits in
this overlap region which are Hill stable. As a result, we can use the first
order resonance overlap criterion as an effective stability criterion for pairs
of observed planets. We show that for low mass (<~10 M_Earth) planetary systems
with initially circular orbits the period ratio at which complete overlap
occurs and widespread chaos results lies in a region of parameter space which
is Hill stable. Our work indicates that a resonance overlap criterion which
would apply for initially eccentric orbits needs to take into account second
order resonances. Finally, we address the connection found in previous work
between the Hill stability criterion and numerically determined Lagrange
instability boundaries in the context of resonance overlap.Comment: Accepted for publication in Ap
Liberating exomoons in white dwarf planetary systems
Previous studies indicate that more than a quarter of all white dwarf (WD)
atmospheres are polluted by remnant planetary material, with some WDs being
observed to accrete the mass of Pluto in 10^6 years. The short sinking
timescale for the pollutants indicate that the material must be frequently
replenished. Moons may contribute decisively to this pollution process if they
are liberated from their parent planets during the post-main-sequence evolution
of the planetary systems. Here, we demonstrate that gravitational scattering
events among planets in WD systems easily triggers moon ejection. Repeated
close encounters within tenths of a planetary Hill radii are highly destructive
to even the most massive, close-in moons. Consequently, scattering increases
both the frequency of perturbing agents in WD systems, as well as the available
mass of polluting material in those systems, thereby enhancing opportunities
for collision and fragmentation and providing more dynamical pathways for
smaller bodies to reach the WD. Moreover, during intense scattering, planets
themselves have pericenters with respect to the WD of only a fraction of an AU,
causing extreme Hill-sphere contraction, and the liberation of moons into
WD-grazing orbits. Many of our results are directly applicable to exomoons
orbiting planets around main sequence stars.Comment: Published (MNRAS): First published online January 19, 201
The Fate of Exomoons in White Dwarf Planetary Systems
Roughly 1000 white dwarfs are known to be polluted with planetary material,
and the progenitors of this material are typically assumed to be asteroids. The
dynamical architectures which perturb asteroids into white dwarfs are still
unknown, but may be crucially dependent on moons liberated from parent planets
during post-main-sequence gravitational scattering. Here, we trace the fate of
these exomoons, and show that they more easily achieve deep radial incursions
towards the white dwarf than do scattered planets. Consequently, moons are
likely to play a significant role in white dwarf pollution, and in some cases
may be the progenitors of the pollution itself.Comment: 9 pages, 5 figures, accepted for publication in MNRA
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