David Farrelly

Formation of Kuiper-belt binaries through multiple chaotic scattering encounters with low-mass intruders

The discovery that many trans-Neptunian objects exist in pairs, or binaries, is proving invaluable for shedding light on the formation, evolution and structure of the outer Solar system. Based on recent systematic searches it has been estimated that up to 10 per cent of Kuiper-belt objects might be binaries. However, all examples discovered to date are unusual, as compared with near-Earth and main-belt asteroid binaries, for their mass ratios of the order of unity and their large, eccentric orbits. In this article we propose a common dynamical origin for these compositional and orbital properties based on four-body simulations in the Hill approximation. Our calculations suggest that binaries are produced through the following chain of events. Initially, long-lived quasi-bound binaries form by two bodies getting entangled in thin layers of dynamical chaos produced by solar tides within the Hill sphere. Next, energy transfer through gravitational scattering with a low-mass intruder nudges the binary into a nearby non-chaotic, stable zone of phase space. Finally, the binary hardens (loses energy) through a series of relatively gentle gravitational scattering encounters with further intruders. This produces binary orbits that are well fitted by Kepler ellipses. Dynamically, the overall process is strongly favoured if the original quasi-bound binary contains comparable masses. We propose a simplified model of chaotic scattering to explain these results. Our findings suggest that the observed preference for roughly equal-mass ratio binaries is probably a real effect; that is, it is not primarily due to an observational bias for widely separated, comparably bright objects. Nevertheless, we predict that a sizeable population of very unequal-mass Kuiper-belt binaries is probably awaiting discovery.

Chaos-assisted capture of irregular moons

It has been thought that the capture of irregular moons—with non-circular orbits—by giant planets occurs by a process in which they are first temporarily trapped by gravity inside the planets Hill sphere (the region where planetary gravity dominates over solar tides). The capture of the moons is then made permanent by dissipative energy loss (for example, gas drag) or planetary growth. But the observed distributions of orbital inclinations, which now include numerous newly discovered moons, cannot be explained using current models. Here we show that irregular satellites are captured in a thin spatial region where orbits are chaotic, and that the resulting orbit is either prograde or retrograde depending on the initial energy. Dissipation then switches these long-lived chaotic orbits into nearby regular (non-chaotic) zones from which escape is impossible. The chaotic layer therefore dictates the final inclinations of the captured moons. We confirm this with three-dimensional Monte Carlo simulations that include nebular drag, and find good agreement with the observed inclination distributions of irregular moons at Jupiter and Saturn. In particular, Saturn has more prograde irregular moons than Jupiter, which we can explain as a result of the chaotic prograde progenitors being more efficiently swept away from Jupiter by its galilean moons.

Capture and escape in the elliptic restricted three-body problem

Several families of irregular moons orbit the giant planets. These moons are thought to have been captured into planetocentric orbits after straying into a region in which the gravitation of the planet dominates solar perturbations (the Hill sphere). This mechanism requires a source of dissipation, such as gas drag, in order to make capture permanent. However, capture by gas drag requires that particles remain inside the Hill sphere long enough for dissipation to be effective. Recently we have proposed that in the circular restricted three-body problem (CRTBP) particles may become caught up in sticky chaotic layers, which tends to prolong their sojourn within the Hill sphere of the planet thereby assisting capture. Here, we show that this mechanism survives perturbations due to the ellipticity of the orbit of the planet. However, Monte Carlo simulations indicate that the ability of the planet to capture moons decreases with increasing orbital eccentricity. At the actual orbital eccentricity of Jupiter, this results in approximately an order of magnitude lower capture probability than estimated in the circular model. Eccentricities of planetary orbits in the Solar system are moderate but this is not necessarily the case for extrasolar planets, which typically have rather eccentric orbits. Therefore, our findings suggest that these extrasolar planets are unlikely to have substantial populations of irregular moons. Ke yw ords: methods: N-body simulations ‐ celestial mechanics ‐ planets and satellites: formation ‐ planetary systems: formation.

Production of trans-Neptunian binaries through chaos-assisted capture

The recent discovery of binary objects in the Kuiper Belt opens an invaluable window into past and present conditions in the trans-Neptunian part of the Solar System. For example, knowledge of how these objects formed can be used to impose constraints on planetary formation theories. We have recently proposed a binary object formation model based on the notion of chaosassisted capture (CAC). In this model two potential binary partners may become trapped for long times inside chaotic layers within their mutual Hill sphere. The binary may then be captured permanently through gravitational scattering with a third ‘intruder’ body. The creation of binaries having similarly sized partners is an ab initio prediction of the model which also predicts large binary semimajor axes and moderately eccentric mutual orbits similar to those observed. Here we present a more detailed analysis with calculations performed in the spatial (three-dimensional) three- and four-body Hill approximations. It is assumed that the potential binary partners are initially following heliocentric Keplerian orbits and that their relative motion becomes perturbed as these objects undergo close encounters. First, the mass, velocity and orbital element distributions which favour binary formation are identified in the circular and elliptical Hill limits. We then consider intruder scattering to the circular Hill four-body problem and find that the CAC mechanism is consistent with observed, apparently randomly distributed, binary mutual orbit inclinations. It also predicts asymmetric distributions of retrograde versus prograde orbits. The time-delay induced by chaos on particle transport through the Hill sphere is analogous to the formation of a resonance in a chemical reaction. Implications for binary formation rates are considered and the ‘fine-tuning’ problem recently identified by Noll et al. is also addressed.

Integral-field spectroscopy of (90482) Orcus-Vanth

Aims. We seek to constrain the surface composition of the trans-Neptunian object (90482) Orcus and its small satellite Vanth, as well as their mass and density. Methods. We acquired near-infrared spectra (1.4−2.4 μm) of (90482) Orcus and its companion Vanth using the adaptive-optics-fed integral-field spectrograph SINFONI mounted on Yepun/UT4 at the European Southern Observatory Very Large Telescope. We took advantage of a very favorable appulse (separation of only 4 �� ) between Orcus and the UCAC2 29643541 star (mR = 11.6) to use the adaptive optics mode of SINFONI, allowing both components to be spatially resolved and Vanth colors to be extracted independently from Orcus. Results. The spectrum of Orcus we obtain has the highest signal-to-noise ratio to date, and we confirm the presence of H2 Oi ce in crystalline form, together with the presence of an absorption band at 2.2 μm. We set an upper limit of about 2% to the presence of methane, and 5% for ethane. Since the methane alone cannot account for the 2.2 μm band, the presence of ammonia is suggested to the level of a couple of percent. The colors of Vanth are found to be slightly redder than those of Orcus, but the large measurement uncertainties prevent us from drawing any firm conclusions about the origin of the pair (capture or co-formation). Finally, we reset the orbital phase of Vanth around Orcus, and confirm the orbital parameters derived by Brown and collaborators.

Quantum solvation dynamics of HCN in a helium-4 droplet

Ultracold nanodroplets of helium-4, containing several thousands of He atoms, offer considerable promise as microscopic cryogenic chambers. Potential applications include the creation of tailor-made chemical or biomolecular complexes and studies of superfluidity in nanoscale systems. Recent experiments have succeeded in interrogating droplets of quantum solvent which consist of as few as 1-20 helium-4 atoms and which contain a single solute molecule. This allows the transition from a floppy, but essentially molecular, complex to a dissolved molecule to be followed and, surprisingly, the transition is found to occur quite rapidly, in some cases for as few as N = 7-20 solvent atoms. For example, in experiments on helium-4 droplets seeded with CO molecules [Tang and McKellar, J. Chem. Phys. 119, 754 (2003)], two series of transitions are observed which correlate with the a-type (Delta K = 0) and b-type (Delta K = +/-1) lines of the binary complex, CO-He (K is the quantum number associated with the projection of the total angular momentum onto the vector connecting the atom and the molecular center of mass). The a-type series, which evolves from the end-over-end rotational motion of the CO-He binary complex, saturates to the nanodroplet limit for as few as 10-15 helium-4 atoms, i.e., the effective moment of inertia of the molecule converges to its asymptotic (solvated) value quite rapidly. In contrast, the b-type series, which evolves from the free-molecule rotational mode, disappears altogether for N approximately 7 atoms. Similar behavior is observed in recent computational studies of HCN(4He)N droplets [Paolini et al., J. Chem. Phys. 123, 114306 (2005)]. In this article the quantum solvation of HCN in small helium-4 droplets is studied using a new fixed-node diffusion Monte Carlo (DMC) procedure. In this approach a Born-Oppenheimer-type separation of radial and angular motions is introduced as a means of computing nodal surfaces of the many-body wave functions which are required in the fixed-node DMC method. Excited rotational energies are calculated for HCN(4He)N droplets with N = 1-20: the adiabatic node approach also allows concrete physical mechanisms to be proposed for the predicted disappearance of the b-type series as well as the rapid convergence of the a-type series to the nanodroplet limit with increasing N. The behavior of the a-type series is traced directly to the mechanics of angular momentum coupling-and decoupling-between identical bosons and the molecular rotor. For very small values of N there exists significant angular momentum coupling between the molecule and the helium atoms: at N approximately 10 solvation appears to be complete as evidenced by significant decoupling of the molecule and solvent angular momenta. The vanishing of the b-type series is predicted to be a result of increasing He-He repulsion as the number of solvent atoms increases.

Collisional population of ultra-high, ultra-long-living Rydberg states under zero-electron-kinetic-energy conditions

Zero-electron-kinetic-energy photoelectron spectroscopy (“ZEKE-PES”) is based on the pulsed field ionization of long lived Rydberg states (ZEKE states); it is generally accepted that ZEKE states have large angular momentum l, which quenches electron-core interactions, but how they acquire it remains a matter of dispute. We show that {nl}→{nl′} ion-Rydberg collisions are a viable and prominent mechanism for the excitation of large-l Rydberg states. We elucidate the dynamics by an exactly solvable classical model which provides a transparent and intuitive picture of the excitation of high-l states. By a geometric interpretation of the dynamics we are able to predict for which values of the impact parameter and reduced velocity of the incoming ion a change of the angular momentum of the state becomes possible. We pay particular attention to the influence of the quantum defect, δl, on the {nl}→{nl′} cross section and demonstrate that, for small initial angular momenta, δl is itself a major contributor to the ...

QUANTUM-CLASSICAL CORRESPONDENCE IN THE HYDROGEN ATOM IN WEAK EXTERNAL FIELDS

The complex processes leading to the collisional population of ultra-long-lived Rydberg states with very high angular momentum can be explained surprisingly well using classical mechanics. In this paper, we explain the reason behind this striking agreement between classical theory and experiment by showing that the classical and quantum dynamics of Rydberg electrons in weak, slowly varying external fields agree beyond the mandates of Ehrenfests theorem. In particular, we show that the expectation values of angular momentum and Runge-Lenz vectors in hydrogenic eigenstates obey exactly the same perturbative equations of motion as the time averages of the corresponding classical variables. By time averaging the quantum dynamics over a Kepler period, we extend this special quantum-classical equivalence to Rydberg wave packets relatively well localized in energy. Finally, the perturbative equations hold well also for external fields beyond the Inglis-Teller limit, and in the case of elliptic states, which yield the appropriate quasiclassical initial conditions, the matching with classical mechanics is complete.

Core-induced stabilization and autoionization of molecular Rydberg states

Abstract Stabilization of molecular Rydberg states through interaction with the core is demonstrated. Core rotation is shown to provide a mechanism for recent, unexplained, experimental observations that long-living Rydberg states, under ZEKE conditions, exist both below and above the ionization threshold.

Integrability of the Paul trap and generalized van der Waals Hamiltonians

Abstract We obtain global invariants for a Hamiltonian that includes the Paul trap and generalized van der Waals Hamiltonians as special cases. Similarities and differences in the dynamics of the systems are pointed out. In particular, we discover a double well in the trap potential possessing stable dynamical equilibria for experimentally realized parameter values.