Global dynamics of the Gliese 876 planetary system

The Gliese 876 planetary system consists of two Jupiter-like planets having a nearly commensurate 2:1 orbital periods ratio. Because the semimajor axes of the planets are very small (of the order 0.1 au and 0.2 au, respectively), and the eccentricity of the inner companion is ≃0.3, the mutual perturbations are extremely large. However, many authors claim the long-term orbital stability of the system, at least over 500 Myr for initial conditions found by Rivera & Lissauer. Results of investigations of a migration of initially separated planets into the close 2:1 mean motion resonance lock from Lee & Peale also support the conclusion that the system should be stable for the lifetime of the parent star. Initial conditions of the system, found from non-linear N -body fits by Laughlin & Chambers and Rivera & Lissauer, to the radial velocity curve, formally allow for a variety of orbital configurations of the GJ 876 system, e.g. coplanar, with planetary inclinations in the range [≃30°, 90°], and with relative inclinations of orbital planes as high as 80°. Our work is devoted to the stability investigation of the systems originating from the fitted initial conditions. We study neighbourhoods of these initial states in the orbital parameter space. We found estimations of the 2:1 mean motion resonance width and dynamical limitations on the planetary masses. We also obtain a global representation of the domains of the orbital parameters space in which initial conditions leading to stable evolutions can be found. Our results can be useful in localization of the best, stable fits to the observational data. In our investigations we use the MEGNO technique (the Mean Exponential Growth factor of Nearby Orbits) invented by Cincotta & Simó. It allows us to distinguish efficiently and precisely between chaotic and regular behaviour of a planetary system.     

Encounters between spherical galaxies – I. Systems without a dark halo

We report here on a survey of N -body simulations of encounters between spherical galaxies. Initial systems are isotropic Jaffe models. Different sets of mass ratios, impact parameters and orbital energies are studied. Both merger remnants and systems perturbed after a non-merging encounter are analysed and compared to real-life elliptical galaxies. The properties of merger remnants show a large variety. Merger remnants resulting from head-on encounters are mainly non-rotating prolate spheroids. Merger remnants from models with   J _orb≠ 0  are tri-axial or mildly oblate spheroids, supported in part by rotation. The velocity distributions are biased towards the radial direction in the prolate case and the tangential direction in the oblate case. Non-mergers are affected in various ways, depending on the orbital characteristics. We conclude that many of the global properties of real-life ellipticals can, in principle, be attributed to a merger of spherical progenitors.     

Numerical simulation of the landslide-induced tsunami of 1988 on Vulcano Island, Italy

 On 20 April 1988 a landslide of approximately 200,000 m³ occurred on the northeastern flank of the volcano La Fossa on the island of Vulcano. The landslide fell into the sea, producing a small tsunami in the bay between Punte Nere and Punta Luccia that was observed locally in the neighbouring harbour called Porto Levante. The slide occurred during a period of unrest at the volcano that was monitored very accurately. The study of this event is composed of two parts, the simulation of the landslide and the simulation of the ensuing tsunami; the former is studied by means of a Lagrangian-type numerical model in which the landslide is seen as a multibody system, an ensemble of material-deforming blocks interacting together during their motion; the latter is simulated according to the Eulerian view by solving the shallow-water approximation to Navier-Stokes equations of fluid dynamics, with the incorporation of a forcing term depending on the slide motion. Technically, the slide evolution is computed first, and this result is then used to evaluate the excitation term of the hydraulic equations and to calculate the tsunami propagation. Computed wave fronts radiate both toward the open sea, with rapid amplitude decay, and along the shore, in the form of edge waves that lose energy slowly. Comparison between model outputs and observations can be carried out only in a qualitative way owing to the absence of tide-gauge records, and results are satisfactory. Received: 14 September 1998 / Accepted: 18 December 1998