The Accelerated Kepler Problem

The accelerated Kepler problem is obtained by adding a constant acceleration to the classical two-body Kepler problem. This setting models the dynamics of a jet-sustaining accretion disk and its content of forming planets as the disk loses linear momentum through the asymmetric jet-counterjet system it powers. The dynamics of the accelerated Kepler problem is analyzed using physical as well as parabolic coordinates. The latter naturally separate the problem's Hamiltonian into two unidimensional Hamiltonians. In particular, we identify the origin of the secular resonance in the accelerated Kepler problem and determine analytically the radius of stability boundary of initially circular orbits that are of particular interest to the problem of radial migration in binary systems as well as to the truncation of accretion disks through stellar jet acceleration.Comment: 16 pages, 9 figures, in press at Celestial Mechanics and Dynamical Astronom

Retrograde resonance in the planar three-body problem

We continue the investigation of the dynamics of retrograde resonances initiated in Morais & Giuppone (2012). After deriving a procedure to deduce the retrograde resonance terms from the standard expansion of the three-dimensional disturbing function, we concentrate on the planar problem and construct surfaces of section that explore phase-space in the vicinity of the main retrograde resonances (2/-1, 1/-1 and 1/-2). In the case of the 1/-1 resonance for which the standard expansion is not adequate to describe the dynamics, we develop a semi-analytic model based on numerical averaging of the unexpanded disturbing function, and show that the predicted libration modes are in agreement with the behavior seen in the surfaces of section.Comment: Celestial Mechanics and Dynamical Astronomy, in pres

Asteroids in retrograde resonance with Jupiter and Saturn

We identify a set of asteroids among Centaurs and Damocloids, that orbit contrary to the common direction of motion in the Solar System and that enter into resonance with Jupiter and Saturn. Their orbits have inclinations I >= 140 deg and semi-major axes a < 15 AU. Two objects are currently in retrograde resonance with Jupiter: 2006 BZ8 in the 2/-5 resonance and 2008 SO218 in the 1/-2 resonance. One object, 2009 QY6, is currently in the 2/-3 retrograde resonance with Saturn. These are the first examples of Solar System objects in retrograde resonance. The present resonant configurations last for several thousand years. Brief captures in retrograde resonance with Saturn are also possible during the 20,000 years integration timespan, particularly in the 1/-1 resonance (2006 BZ8) and the 9/-7 resonance (1999 LE31).Comment: 6 pages, 7 figures, accepted for publication in MNRAS Letter

Dynamics of Jupiter Trojans during the 2:1 mean motion resonance crossing of Jupiter and Saturn

We study the dynamics of Jupiter Trojans in the early phase of the Solar system while the outer planets migrated due to their interaction with the planetesimal disk.Comment: 10 pages, 17 figure

On the Flaring of Jet-sustaining Accretion Disks

Jet systems with two unequal components interact with their parent accretion disks through the asymmetric removal of linear momentum from the star-disk system. We show that as a result of this interaction, the disk's state of least energy is not made up of orbits that lie in a plane containing the star's equator as in a disk without a jet. The disk's profile has the shape of a sombrero curved in the direction of acceleration. For this novel state of minimum energy, we derive the temperature profile of thin disks. The flaring geometry caused by the sombrero profile increases the disk temperature especially in its outer regions. The jet-induced acceleration disturbs the vertical equilibrium of the disk leading to mass loss in the form of a secondary wind emanating from the upper face of the disk. Jet time variability causes the disk to radially expand or contract depending on whether the induced acceleration increases or decreases. Jet time variability also excites vertical motion and eccentric distortions in the disk and affects the sombrero profile's curvature. These perturbations lead to the heating of the disk through its viscous stresses as it tries to settle into the varying state of minimum energy. The jet-disk interaction studied here will help estimate the duration of the jet episode in star-disk systems and may explain the origin of the recently observed one-sided molecular outflow of the HH 30 disk-jet system.Comment: 18 pages, 4 figures, accepted for publication in the Astrophysical Journa

Phase-Space Volume of Regions of Trapped Motion: Multiple Ring Components and Arcs

The phase--space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, sudden reductions in the phase-space volume or gaps are observed at specific values of the parameter which tunes the dynamics; these locations are approximated by the stability resonances. The latter are defined by a resonant condition on the stability exponents of a central linearly stable periodic orbit. We show that, for more than two degrees of freedom, these resonances can be excited opening up gaps, which effectively separate and reduce the regions of trapped motion in phase space. Using the scattering approach to narrow rings and a billiard system as example, we demonstrate that this mechanism yields rings with two or more components. Arcs are also obtained, specifically when an additional (mean-motion) resonance condition is met. We obtain a complete representation of the phase-space volume occupied by the regions of trapped motion.Comment: 19 pages, 17 figure

Rings in the Solar System: a short review

Rings are ubiquitous around giant planets in our Solar System. They evolve jointly with the nearby satellite system. They could form either during the giant planet formation process or much later, as a result of large scale dynamical instabilities either in the local satellite system, or at the planetary scale. We review here the main characteristics of rings in our solar system, and discuss their main evolution processes and possible origin. We also discuss the recent discovery of rings around small bodies.Comment: Accepted for the Handbook of Exoplanet

Dynamical friction in a gaseous medium with a large-scale magnetic field

The dynamical friction force experienced by a massive gravitating body moving through a gaseous medium is modified by sufficiently strong large-scale magnetic fields. Using linear perturbation theory, we calculate the structure of the wake generated by, and the gravitational drag force on, a body traveling in a straight-line trajectory in a uniformly magnetized medium. The functional form of the drag force as a function of the Mach number (V_0/c_s, where V_0 is the velocity of the body and c_s the sound speed) depends on the strength of the magnetic field and on the angle between the velocity of the perturber and the direction of the magnetic field. In particular, the peak value of the drag force is not near Mach number 1 for a perturber moving in a sufficiently magnetized medium. As a rule of thumb, we may state that for supersonic motion, magnetic fields act to suppress dynamical friction; for subsonic motion, magnetic fields tend to enhance dynamical friction. For perturbers moving along the magnetic field lines, the drag force at some subsonic Mach numbers may be stronger than it is at supersonic velocities. We also mention the relevance of our findings to black hole coalescence in galactic nuclei.Comment: 21 pages, 14 figures, accepted for publication in Ap