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

A Tale of Two Cases

Professor Agnor here traces the development of what he suggests is a bad rule of law which originated in a poor decision of a jurisdiction highly respected for its decisions on the law of future interests. The author\u27s demonstration of how the case has been blindly followed by both bench and bar underscores his message that members of the legal profession must not rely on encyclopedic statements of the law without an examination into the policies and problems involved

On the Migration of Jupiter and Saturn: Constraints from Linear Models of Secular Resonant Coupling with the Terrestrial Planets

We examine how the late divergent migration of Jupiter and Saturn may have perturbed the terrestrial planets. We identify six secular resonances between the nu_5 apsidal eigenfrequency of Jupiter and Saturn and the four eigenfrequencies of the terrestrial planets (g_{1-4}). We derive analytic upper limits on the eccentricity and orbital migration timescale of Jupiter and Saturn when these resonances were encountered to avoid perturbing the eccentricities of the terrestrial planets to values larger than the observed ones. If Jupiter and Saturn migrated with eccentricities comparable to their present day values, smooth migration with exponential timescales characteristic of planetesimal-driven migration (\tau~5-10 Myr) would have perturbed the eccentricities of the terrestrial planets to values greatly exceeding the observed ones. This excitation may be mitigated if the eccentricity of Jupiter was small during the migration epoch, migration was very rapid (e.g. \tau<~ 0.5 Myr perhaps via planet-planet scattering or instability-driven migration) or the observed small eccentricity amplitudes of the j=2,3 terrestrial modes result from low probability cancellation of several large amplitude contributions. Further, results of orbital integrations show that very short migration timescales (\tau<0.5 Myr), characteristic of instability-driven migration, may also perturb the terrestrial planets' eccentricities by amounts comparable to their observed values. We discuss the implications of these constraints for the relative timing of terrestrial planet formation, giant planet migration, and the origin of the so-called Late Heavy Bombardment of the Moon 3.9+/-0.1 Ga ago. We suggest that the simplest way to satisfy these dynamical constraints may be for the bulk of any giant planet migration to be complete in the first 30-100 Myr of solar system history.Comment: Accepted for publication in The Astrophysical Journa

Christian and Non-Religious Sociopaths Compared: Self-Concept, Locus of Control, Guilt, and Quality of Religious Experience

Criminal sociopaths frequently claim commitment to Christianity, a religion which philosophically is counter to a sociopath\u27s world view. Ascertaining whether or not religious commitment is a variable relevant to corrections is confusing in light of a lack of research which addresses this problem. In this study 25 non-religious and 27 orthodox Christian male sociopaths, inmates from Oregon State Penitentiary, were administered the Tennessee Self-Concept Scale, the Rotter Internal/External Locus of Control Scale, and the Mosher Forced Choice Guilt Scales. To gather data on the religious experience of the sociopath, the Spiritual Well-Being Scale, the Intrinsic/Extrinsic Religious Orientation Scale, and the God Concept Semantic Differential Scale were also given. Christian sociopaths had significantly higher guilt and had significantly more internal locus of control than non-religious sociopaths. There were no self-esteem differences, but Christian sociopaths had higher behavior self-concept. It was concluded that the Christian and non-religious sociopaths were distinct populations, and since higher guilt and more internal locus of control are signs in the direction of psychological health, Christian sociopaths were better positioned than non-religious sociopaths. The Christian sociopaths were possibly better prospects for rehabilitation, an idea deserving further consideration in longitudinal research

Constraints on the Orbital Evolution of Triton

We present simulations of Triton's post-capture orbit that confirm the importance of Kozai-type oscillations in its orbital elements. In the context of the tidal orbital evolution model, these variations require average pericenter distances much higher than previously published, and the timescale for the tidal orbital evolution of Triton becomes longer than the age of the Solar System. Recently-discovered irregular satellites present a new constraint on Triton's orbital history. Our numerical integrations of test particles indicate a timescale for Triton's orbital evolution to be less than $10^5$ yrs for a reasonable number of distant satellites to survive Triton's passage. This timescale is inconsistent with the exclusively tidal evolution (time scale of $>10^8$ yrs), but consistent with the interestion with the debris from satellite-satellite collisions. Any major regular satellites will quickly collide among themselves after being perturbed by Triton, and the resulting debris disk would eventually be swept up by Triton; given that the total mass of the Uranian satellite system is 40% of that of Triton, large scale evolution is possible. This scenario could have followed either collisional or the recently-discussed three-body-interaction-based capture.Comment: 10 pages, 4 figures, accepted for ApJ

Minimum Radii of Super-Earths: Constraints from Giant Impacts

The detailed interior structure models of super-Earth planets show that there is degeneracy in the possible bulk compositions of a super-Earth at a given mass and radius, determined via radial velocity and transit measurements, respectively. In addition, the upper and lower envelopes in the mass--radius relationship, corresponding to pure ice planets and pure iron planets, respectively, are not astrophysically well motivated with regard to the physical processes involved in planet formation. Here we apply the results of numerical simulations of giant impacts to constrain the lower bound in the mass--radius diagram that could arise from collisional mantle stripping of differentiated rocky/iron planets. We provide a very conservative estimate for the minimum radius boundary for the entire mass range of large terrestrial planets. This envelope is a readily testable prediction for the population of planets to be discovered by the Kepler mission.Comment: 8 pages, 4 figures, Accepted for publication in ApJ Letter

Embryo impacts and gas giant mergers II: Diversity of Hot Jupiters' internal structure

We consider the origin of compact, short-period, Jupiter-mass planets. We propose that their diverse structure is caused by giant impacts of embryos and super-Earths or mergers with other gas giants during the formation and evolution of these hot Jupiters. Through a series of numerical simulations, we show that typical head-on collisions generally lead to total coalescence of impinging gas giants. Although extremely energetic collisions can disintegrate the envelope of gas giants, these events seldom occur. During oblique and moderately energetic collisions, the merger products retain higher fraction of the colliders' cores than their envelopes. They can also deposit considerable amount of spin angular momentum to the gas giants and desynchronize their spins from their orbital mean motion. We find that the oblateness of gas giants can be used to infer the impact history. Subsequent dissipation of stellar tide inside the planets' envelope can lead to runaway inflation and potentially a substantial loss of gas through Roche-lobe overflow. The impact of super-Earths on parabolic orbits can also enlarge gas giant planets' envelope and elevates their tidal dissipation rate over $\sim$ 100 Myr time scale. Since giant impacts occur stochastically with a range of impactor sizes and energies, their diverse outcomes may account for the dispersion in the mass-radius relationship of hot Jupiters.Comment: 19 pages, 7 figures, 7 tables. Accepted for publication in MNRA

Water/Icy Super-Earths: Giant Impacts and Maximum Water Content

Water-rich super-Earth exoplanets are expected to be common. We explore the effect of late giant impacts on the final bulk abundance of water in such planets. We present the results from smoothed particle hydrodynamics simulations of impacts between differentiated water(ice)-rock planets with masses between 0.5 and 5 M_Earth and projectile to target mass ratios from 1:1 to 1:4. We find that giant impacts between bodies of similar composition never decrease the bulk density of the target planet. If the commonly assumed maximum water fraction of 75wt% for bodies forming beyond the snow line is correct, giant impacts between similar composition bodies cannot serve as a mechanism for increasing the water fraction. Target planets either accrete materials in the same proportion, leaving the water fraction unchanged, or lose material from the water mantle, decreasing the water fraction. The criteria for catastrophic disruption of water-rock planets are similar to those found in previous work on super-Earths of terrestrial composition. Changes in bulk composition for giant impacts onto differentiated bodies of any composition (water-rock or rock-iron) are described by the same equations. These general laws can be incorporated into future N-body calculations of planet formation to track changes in composition from giant impacts.Comment: 9 pages, 4 figures, Accepted for publication in ApJ Letter