1,397 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

### The potential for Earth-mass planet formation around brown dwarfs

Recent observations point to the presence of structured dust grains in the
discs surrounding young brown dwarfs, thus implying that the first stages of
planet formation take place also in the sub-stellar regime. Here, we
investigate the potential for planet formation around brown dwarfs and very low
mass stars according to the sequential core accretion model of planet
formation. We find that, for a brown dwarfs of mass 0.05M_{\odot}, our models
predict a maximum planetary mass of ~5M_{\oplus}, orbiting with semi-major axis
~1AU. However, we note that the predictions for the mass - semi-major axis
distribution are strongly dependent upon the models chosen for the disc surface
density profiles and the assumed distribution of disc masses. In particular, if
brown dwarf disc masses are of the order of a few Jupiter masses, Earth-mass
planets might be relatively frequent, while if typical disc masses are only a
fraction of Jupiter mass, we predict that planet formation would be extremely
rare in the sub-stellar regime. As the observational constraints on disc
profiles, mass dependencies and their distributions are poor in the brown dwarf
regime, we advise caution in validating theoretical models only on stars
similar to the Sun and emphasise the need for observational data on planetary
systems around a wide range of stellar masses. We also find that, unlike the
situation around solar-like stars, Type-II migration is totally absent from the
planet formation process around brown dwarfs, suggesting that any future
observations of planets around brown dwarfs would provide a direct measure of
the role of other types of migration.Comment: 11 pages, accepted for publication in MNRA

### On the structure of nonarchimedean analytic curves

Let K be an algebraically closed, complete nonarchimedean field and let X be
a smooth K-curve. In this paper we elaborate on several aspects of the
structure of the Berkovich analytic space X^an. We define semistable vertex
sets of X^an and their associated skeleta, which are essentially finite metric
graphs embedded in X^an. We prove a folklore theorem which states that
semistable vertex sets of X are in natural bijective correspondence with
semistable models of X, thus showing that our notion of skeleton coincides with
the standard definition of Berkovich. We use the skeletal theory to define a
canonical metric on H(X^an) := X^an - X(K), and we give a proof of Thuillier's
nonarchimedean Poincar\'e-Lelong formula in this language using results of
Bosch and L\"utkebohmert.Comment: 23 pages. This an expanded version of section 5 of arXiv:1104.0320
which appears in the conference proceedings "Tropical and Non-Archimedean
Geometry

### An Analysis of Jitter and Transit Timing Variations in the HAT-P-13 System

If the two planets in the HAT-P-13 system are coplanar, the orbital states
provide a probe of the internal planetary structure. Previous analyses of
radial velocity and transit timing data of the system suggested that the
observational constraints on the orbital states were rather small. We reanalyze
the available data, treating the jitter as an unknown MCMC parameter, and find
that a wide range of jitter values are plausible, hence the system parameters
are less well constrained than previously suggested. For slightly increased
levels of jitter ($\sim 4.5\,m\,s^{-1}$) the eccentricity of the inner planet
can be in the range $0<e_{inner}<0.07$, the period and eccentricity of the
outer planet can be $440<P_{outer}<470$ days and $0.55<e_{outer}<0.85$
respectively, while the relative pericenter alignment, $\eta$, of the planets
can take essentially any value $-180^{\circ}<\eta<+180^{\circ}$. It is
therefore difficult to determine whether $e_{inner}$ and $\eta$ have evolved to
a fixed-point state or a limit cycle, or to use $e_{inner}$ to probe the
internal planetary structure. We perform various transit timing variation (TTV)
analyses, demonstrating that current constraints merely restrict
$e_{outer}<0.85$, and rule out relative planetary inclinations within $\sim
2^{\circ}$ of $i_{rel}=90^{\circ}$, but that future observations could
significantly tighten the restriction on both these parameters. We demonstrate
that TTV profiles can readily distinguish the theoretically favored
inclinations of i_{rel}=0^{\circ}\,&\,45^{\circ}, provided that sufficiently
precise and frequent transit timing observations of HAT-P-13b can be made close
to the pericenter passage of HAT-P-13c. We note the relatively high probability
that HAT-P-13c transits and suggest observational dates and strategies.Comment: Published in Ap

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