On the origin of the Trojan asteroids: Effects of Jupiter's mass accretion and radial migration

We present analytic and numerical results which illustrate the effects of Jupiter's accretion of nebular gas and the planet's radial migration on its Trojan companions. Initially, we approximate the system by the planar circular restricted three-body problem and assume small Trojan libration amplitudes. Employing an adiabatic invariant calculation, we show that Jupiter's thirty-fold growth from a $10 M_\oplus$ core to its present mass causes the libration amplitudes of Trojan asteroids to shrink by a factor of about 2.5 to $\sim 40$ of their original size. The calculation also shows that Jupiter's radial migration has comparatively little effect on the Trojans; inward migration from 6.2 to 5.2 AU causes an increase in Trojan libration amplitudes of $\sim4$. In each case, the area enclosed by small tadpole orbits, if made dimensionless by using Jupiter's semimajor axis, is approximately conserved. Similar adiabatic invariant calculations for inclined and eccentric Trojans show that Jupiter's mass growth leaves the asteroid's eccentricities and inclinations essentially unchanged, while one AU of inward migration causes an increase in both of these quantities by $\sim 4$. Numerical integrations confirm and extend these analytic results. We demonstrate that our predictions remain valid for Trojans with small libration amplitudes even when the asteroids have low, butComment: Submitted to Icarus - 13 Fig

Debris about asteroids: Where and how much?

We summarize several recent findings on the size and shape of the region within which material can stably orbit an asteroid. If the asteroid (with assumed density 2.38 g/cu cm) circles the Sun at 2.55 AU, co-planar prograde material will remain trapped whenever started on unperturbed circular orbits at less than about 220 R(sub A) (asteroid radii); co-planar retrograde particles are stable out twice as far. Our 3-D stability surface, which encloses several hundred numerically calculated orbits that start with various inclinations, is shaped like a sphere with its top and bottom sliced off; its dimensions scale like the Hill radius =(mu/3)(exp 1/3)R, where mu is the asteroid-to-solar mass ratio and R is the asteroid's orbital radius. If the asteroid moves along an elliptical orbit, a fairly reliable indicator of the dimensions of the hazard zone is the size of its Hill sphere at the orbit's pericenter. Grains with radii less than a few mm will be lost through the action of radiation forces which can induce escape or cause collisions with the asteroid on times scales of a few years; interplanetary micrometeoroids produce collisional break-up of these particles in approximately 10(exp 4) yrs. The effects of Jupiter and of asteroids that pass close to the target asteroid allow particles to diffuse from the system, again shrinking the hazard zone. None of the considered sources-primordial formation, debris spalled off the asteroid during micrometeoroid impact, captured interplanetary particles, feeder satellites, etc., seem capable of densely populating distant orbits from the asteroid. No certain detections of debris clouds or of binary asteroids have been made. Thus, it seems highly unlikely that a spacecraft fly-by targeted at 100 R(sub A) from the asteroid over its orbital pole would encounter any material

Three-Body Capture of Irregular Satellites: Application to Jupiter

We investigate a new theory of the origin of the irregular satellites of the giant planets: capture of one member of a ~100-km binary asteroid after tidal disruption. The energy loss from disruption is sufficient for capture, but it cannot deliver the bodies directly to the observed orbits of the irregular satellites. Instead, the long-lived capture orbits subsequently evolve inward due to interactions with a tenuous circumplanetary gas disk. We focus on the capture by Jupiter, which, due to its large mass, provides the most stringent test of our model. We investigate the possible fates of disrupted bodies, the differences between prograde and retrograde captures, and the effects of Callisto on captured objects. We make an impulse approximation and discuss how it allows us to generalize capture results from equal-mass binaries to binaries with arbitrary mass ratios. We find that at Jupiter, binaries offer an increase of a factor of ~10 in the capture rate of 100-km objects as compared to single bodies, for objects separated by tens of radii that approach the planet on relatively low-energy trajectories. These bodies are at risk of collision with Callisto, but may be preserved by gas drag if their pericenters are raised quickly enough. We conclude that our mechanism is as capable of producing large irregular satellites as previous suggestions, and it avoids several problems faced by alternative models.Comment: 39 pages, 12 figures, 1 table, submitted to Icaru

Three-Body Encounters of Black Holes in Globular Clusters

Evidence has been mounting for the existence of black holes with masses from 10^2 to 10^4 M_Solar associated with stellar clusters. Such intermediate-mass black holes (IMBHs) will encounter other black holes in the dense cores of these clusters. The binaries produced in these interactions will be perturbed by other objects as well thus changing the orbital characteristics of the binaries. These binaries and their subsequent mergers due to gravitational radiation are important sources of gravitational waves. We present the results of numerical simulations of high mass ratio encounters, which help clarify the interactions of intermediate-mass black holes in globular clusters and help determine what types of detectable gravitational wave signatures are likely.Comment: 4 pages, 3 figures to appear in the proceedings of The Astrophysics of Gravitational Wave Sources, College Park, MD, 24-26 April 200

Three-Body Dynamics with Gravitational Wave Emission

We present numerical three-body experiments that include the effects of gravitational radiation reaction by using equations of motion that include the 2.5-order post-Newtonian force terms, which are the leading order terms of energy loss from gravitational waves. We simulate binary-single interactions and show that close approach cross sections for three 1 solar mass objects are unchanged from the purely Newtonian dynamics except for close approaches smaller than 1.0e-5 times the initial semimajor axis of the binary. We also present cross sections for mergers resulting from gravitational radiation during three-body encounters for a range of binary semimajor axes and mass ratios including those of interest for intermediate-mass black holes (IMBHs). Building on previous work, we simulate sequences of high-mass-ratio three-body encounters that include the effects of gravitational radiation. The simulations show that the binaries merge with extremely high eccentricity such that when the gravitational waves are detectable by LISA, most of the binaries will have eccentricities e > 0.9 though all will have circularized by the time they are detectable by LIGO. We also investigate the implications for the formation and growth of IMBHs and find that the inclusion of gravitational waves during the encounter results in roughly half as many black holes ejected from the host cluster for each black hole accreted onto the growing IMBH.Comment: 34 pages, 14 figures, minor corrections to match version accepted by Ap