Sergey A. Astakhov

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.

Monte Carlo Algorithm for Least Dependent Non-Negative Mixture Decomposition

We propose a simulated annealing algorithm (stochastic non-negative independent component analysis, SNICA) for blind decomposition of linear mixtures of non-negative sources with non-negative coefficients. The demixing is based on a Metropolis-type Monte Carlo search for least dependent components, with the mutual information between recovered components as a cost function and their non-negativity as a hard constraint. Elementary moves are shears in two-dimensional subspaces and rotations in three-dimensional subspaces. The algorithm is geared at decomposing signals whose probability densities peak at zero, the case typical in analytical spectroscopy and multivariate curve resolution. The decomposition performance on large samples of synthetic mixtures and experimental data is much better than that of traditional blind source separation methods based on principal component analysis (MILCA, FastICA, RADICAL) and chemometrics techniques (SIMPLISMA, ALS, BTEM).

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.

Bifurcational Mechanism of Multistability Formation and Frequency Entrainment in a van der Pol Oscillator with an Additional Oscillatory Circuit

In this paper, the bifurcational mechanism of frequency entrainment in a van der Pol oscillator coupled with an additional oscillatory circuit is studied. It is shown that bistability observed in the system is based on two bifurcations: a supercritical Andronov–Hopf bifurcation and a sub-critical Neimark–Sacker bifurcation. The attracting basin boundaries are determined by stable and unstable invariant manifolds of a saddle two-dimensional torus.