Circumbinary Chaos: Using Pluto's Newest Moon to Constrain the Masses of Nix & Hydra

The Pluto system provides a unique local laboratory for the study of binaries with multiple low mass companions. In this paper, we study the orbital stability of P4, the most recently discovered moon in the Pluto system. This newfound companion orbits near the plane of the Pluto-Charon binary, roughly halfway between the two minor moons Nix and Hydra. We use a suite of few body integrations to constrain the masses of Nix and Hydra, and the orbital parameters of P4. For the system to remain stable over the age of the Solar System, the masses of Nix and Hydra likely do not exceed 5e16 kg and 9e16 kg, respectively. These upper limits assume a fixed mass ratio between Nix and Hydra at the value implied by their median optical brightness. Our study finds that stability is more sensitive to their total mass and that a downward revision of Charon's eccentricity (from our adopted value of 0.0035) is unlikely to significantly affect our conclusions. Our upper limits are an order of magnitude below existing astrometric limits on the masses of Nix and Hydra. For a density at least that of ice, the albedos of Nix and Hydra would exceed 0.3. This constraint implies they are icy, as predicted by giant impact models. Even with these low masses, P4 only remains stable if its eccentricity e < 0.02. The 5:1 commensurability with Charon is particularly unstable, Combining stability constraints with the observed mean motion places the preferred orbit for P4 just exterior to the 5:1 resonance. These predictions will be tested when the New Horizons satellite visits Pluto. Based on the results for the Pluto-Charon system, we expect that circumbinary, multi-planet systems will be more widely spaced than their singleton counterparts. Further, circumbinary exoplanets close to the three-body stability boundary, such as those found by Kepler, are less likely to have other companions nearby.Comment: 12 pages, 7 figure

A Brief History of Trans-Neptunian Space

The Edgeworth-Kuiper belt encodes the dynamical history of the outer solar system. Kuiper belt objects (KBOs) bear witness to coagulation physics, the evolution of planetary orbits, and external perturbations from the solar neighborhood. We critically review the present-day belt's observed properties and the theories designed to explain them. Theories are organized according to a possible time-line of events. In chronological order, epochs described include (1) coagulation of KBOs in a dynamically cold disk, (2) formation of binary KBOs by fragmentary collisions and gravitational captures, (3) stirring of KBOs by Neptune-mass planets (``oligarchs''), (4) eviction of excess oligarchs, (5) continued stirring of KBOs by remaining planets whose orbits circularize by dynamical friction, (6) planetary migration and capture of Resonant KBOs, (7) creation of the inner Oort cloud by passing stars in an open stellar cluster, and (8) collisional comminution of the smallest KBOs. Recent work underscores how small, collisional, primordial planetesimals having low velocity dispersion permit the rapid assembly of ~5 Neptune-mass oligarchs at distances of 15-25 AU. We explore the consequences of such a picture. We propose that Neptune-mass planets whose orbits cross into the Kuiper belt for up to ~20 Myr help generate the high-perihelion members of the hot Classical disk and Scattered belt. By contrast, raising perihelia by sweeping secular resonances during Neptune's migration might fill these reservoirs too inefficiently when account is made of how little primordial mass might reside in bodies having sizes of order 100 km. These and other frontier issues in trans-Neptunian space are discussed quantitatively.Comment: Final proofed version for Protostars and Planets V; some numbers adjusted by factors of 2; references update

A Radio Transient 0.1 pc from Sagittarius A*

We report the discovery of a transient radio source 2.7 arcsec (0.1 pc projected distance) South of the Galactic Center massive black hole, Sagittarius A*. The source flared with a peak of at least 80 mJy in March 2004. The source was resolved by the Very Large Array into two components with a separation of ~0.7 arcsec and characteristic sizes of ~0.2 arcsec. The two components of the source faded with a power-law index of 1.1 +/- 0.1. We detect an upper limit to the proper motion of the Eastern component of ~3 x 10^3 km s^-1 relative to Sgr A*. We detect a proper motion of ~10^4 km s^-1 for the Western component relative to Sgr A*. The transient was also detected at X-ray wavelengths with the Chandra X-ray Observatory and the XMM-Newton telescope and given the designation CXOGC J174540.0-290031. The X-ray source falls in between the two radio components. The maximum luminosity of the X-ray source is ~10^36 erg s^-1, significantly sub-Eddington. The radio jet flux density predicted by the X-ray/radio correlation for X-ray binaries is orders of magnitude less than the measured flux density. We conclude that the radio transient is the result of a bipolar jet originating in a single impulsive event from the X-ray source and interacting with the dense interstellar medium of the Galactic Center.Comment: accepted in ApJ; 24 pages; 8 figure

The Intrinsic Size of Sagittarius A* from 0.35 cm to 6 cm

We present new high-resolution observations of Sagittarius A* at wavelengths of 17.4 to 23.8 cm with the Very Large Array in A configuration with the Pie Town Very Long Baseline Array antenna. We use the measured sizes to calibrate the interstellar scattering law and find that the major axis size of the scattering law is smaller by ~6% than previous estimates. Using the new scattering law, we are able to determine the intrinsic size of Sgr A* at wavelengths from 0.35 cm to 6 cm using existing results from the VLBA. The new law increases the intrinsic size at 0.7 cm by ~20% and <5% at 0.35 cm. The intrinsic size is 13^{+7}_{-3} Schwarzschild radii at 0.35 cm and is proportional to lambda^gamma, where gamma is in the range 1.3 to 1.7.Comment: ApJL, in pres

Dissipation in planar resonant planetary systems

Close-in planetary systems detected by the Kepler mission present an excess of periods ratio that are just slightly larger than some low order resonant values. This feature occurs naturally when resonant couples undergo dissipation that damps the eccentricities. However, the resonant angles appear to librate at the end of the migration process, which is often believed to be an evidence that the systems remain in resonance. Here we provide an analytical model for the dissipation in resonant planetary systems valid for low eccentricities. We confirm that dissipation accounts for an excess of pairs that lie just aside from the nominal periods ratios, as observed by the Kepler mission. In addition, by a global analysis of the phase space of the problem, we demonstrate that these final pairs are non-resonant. Indeed, the separatrices that exist in the resonant systems disappear with the dissipation, and remains only a circulation of the orbits around a single elliptical fixed point. Furthermore, the apparent libration of the resonant angles can be explained using the classical secular averaging method. We show that this artifact is only due to the severe damping of the amplitudes of the eigenmodes in the secular motion.Comment: 18 pages, 20 figures, accepted to A&

Dynamical analysis and constraints for the HD 196885 system

The HD\,196885 system is composed of a binary star and a planet orbiting the primary. The orbit of the binary is fully constrained by astrometry, but for the planet the inclination with respect to the plane of the sky and the longitude of the node are unknown. Here we perform a full analysis of the HD\,196885 system by exploring the two free parameters of the planet and choosing different sets of angular variables. We find that the most likely configurations for the planet is either nearly coplanar orbits (prograde and retrograde), or highly inclined orbits near the Lidov-Kozai equilibrium points, i = 44^{\circ} or i = 137^{\circ} . Among coplanar orbits, the retrograde ones appear to be less chaotic, while for the orbits near the Lidov-Kozai equilibria, those around \omega= 270^{\circ} are more reliable, where \omega_k is the argument of pericenter of the planet's orbit with respect to the binary's orbit. From the observer's point of view (plane of the sky) stable areas are restricted to (I1, \Omega_1) \sim (65^{\circ}, 80^{\circ}), (65^{\circ},260^{\circ}), (115^{\circ},80^{\circ}), and (115^{\circ},260^{\circ}), where I1 is the inclination of the planet and \Omega_1 is the longitude of ascending node.Comment: 10 pages, 7 figures. A&A Accepte

A shallow-water theory for annular sections of Keplerian Disks

A scaling argument is presented that leads to a shallow water theory of non-axisymmetric disturbances in annular sections of thin Keplerian disks. To develop a theoretical construction that will aid in physically understanding the relationship of known two-dimensional vortex dynamics to their three-dimensional counterparts in Keplerian disks. Using asymptotic scaling arguments varicose disturbances of a Keplerian disk are considered on radial and vertical scales consistent with the height of the disk while the azimuthal scales are the full $2\pi$ angular extent of the disk. The scalings lead to dynamics which are radially geostrophic and vertically hydrostatic. It follows that a potential vorticity quantity emerges and is shown to be conserved in a Lagrangian sense. Uniform potential vorticity linear solutions are explored and the theory is shown to contain an incarnation of the strato-rotational instability under channel flow conditions. Linearized solutions of a single defect on an infinite domain is developed and is shown to support a propagating Rossby edgewave. Linear non-uniform potential vorticity solutions are also developed and are shown to be similar in some respects to the dynamics of strictly two-dimensional inviscid flows. Based on the framework of this theory, arguments based on geophysical notions are presented to support the assertion that the strato-rotational instability is in a generic class of barotropic/baroclinic potential vorticity instabilities. Extensions of this formalism are also proposed. The shallow water formulation achieved by the asymptotic theory developed here opens a new approach to studying disk dynamics.Comment: Accepted (July 21, 2008), now in final for