Stability of power-law discs — II. The global spiral modes

This paper reports on the in-plane normal modes in the self-consistent and the cut-out power-law discs. Although the cut-out discs are remarkably stable to bisymmetric perturbations, they are very susceptible to one-armed modes. For this harmonic, there is no inner Lindblad resonance, thus removing a powerful stabilizing influence. A physical mechanism for the generation of the one-armed instabilities is put forward. Incoming trailing waves are reflected as leading waves at the inner cut-out, thus completing the feedback for the swing-amplifier. Growing three-armed and four-armed modes occur only at very low temperatures. However, neutral m  = 3 and m  = 4 modes are possible at higher temperatures for some discs. The rotation curve index β has a marked effect on stability. For all azimuthal wavenumbers, any unstable modes persist to higher temperatures and grow more vigorously if the rotation curve is rising (β < 0) than if the rotation curve is falling (β > 0). If the central regions or outer parts of the disc are carved out more abruptly, any instabilities become more virulent. The self-consistent power-law discs possess a number of unusual stability properties. There is no natural time-scale in the self-consistent disc. If a mode is admitted at some pattern speed and growth rate, then it must be present at all pattern speeds and growth rates. Our analysis — although falling short of a complete proof — suggests that such a two-dimensional continuum of non-axisymmetric modes does not occur and that the self-consistent power-law discs admit no global non-axisymmetric normal modes whatsoever. Without reflecting boundaries or cut-outs, there is no resonant cavity and no possibility of unstable growing modes. The self-consistent power-law discs certainly admit equi-angular spirals as neutral modes, together with a one-dimensional continuum of growing axisymmetric modes.     

Evolution of the mass function of the Galactic globular cluster system

In this work we investigate the evolution of the mass function of the Galactic globular cluster system (GCMF) taking into account the effects of stellar evolution, two-body relaxation, disc shocking and dynamical friction on the evolution of individual globular clusters. We have adopted a lognormal initial GCMF and considered a wide range of initial values for the dispersion, σ, and the mean value, 〈log  M 〉. We have studied in detail the dependence on the initial conditions of the final values of σ, 〈log  M 〉, the fraction of the initial number of clusters surviving after one Hubble time and the difference between the properties of the GCMF of clusters closer to the Galactic Centre and those of clusters located in the outer regions of the Galaxy. In most of the cases considered, evolutionary processes alter significantly the initial population of globular clusters and the disruption of a significant number of globular clusters leads to a flattening in the spatial distribution of clusters in the central regions of the Galaxy. The initial lognormal shape of the GCMF is preserved in most cases and if a power-law in M is adopted for the initial GCMF, evolutionary processes tend to modify it into a lognormal GCMF. The difference between initial and final values of σ and 〈log  M 〉 as well as the difference between the final values of these parameters for inner and outer clusters can be positive or negative depending on initial conditions. A significant effect of evolutionary processes does not necessarily give rise to a strong trend of 〈log  M 〉 with the galactocentric distance. The existence of a particular initial GCMF able to keep its initial shape and parameters unaltered during the entire evolution through a subtle balance between disruption of clusters and evolution of the masses of those which survive, suggested by Vesperini, is confirmed.     

A New Protocol for the Astrometric Follow-up of Near Earth Asteroids

A new protocol was devised to improve the efficiency of astrometric follow-up observations of Near Earth Asteroids for the accurate determination of their orbits. It was implemented in the activities of the Spaceguard Central Node (SCN, a facility of the Spaceguard Foundation, established with the support of the European Space Agency) in the form of a Priority List. Here we describe this protocol and results obtained during five years of activity (2000–2004).     

A Survey of Newtonian Core-Shell Systems with Pseudo High Order Symplectic Integrator and Fast Lyapunov Indicator

Newtonian core-shell systems, as limiting cases of relativistic core-shell models under the two conditions of weak field and slow motion, could account for massive circumstellar dust shells and rings around certain types of star remnants. Because this kind of systems have Hamiltonians that can be split into a main part and a small perturbing part, a good choice of the numerical tool is the pseudo 8th order symplectic integrator of Laskar ＆ Robutel, and, to match the symplectic calculations, a good choice of chaos indicator is the fast Lyapunov indicator （FLI） with two nearby trajectories proposed by Wu, Huang ＆ Zhang. Numerical results show that the FLI is very powerful when describing not only the transition from regular motion to chaos but also the global structure of the phase space of the system.     

Problem of the motion of a star inside a layered inhomogeneous elliptical galaxy with a variable mass

The problem of the motion of a star inside a layered inhomogeneous rotating elliptical galaxy with a variable mass is considered. We have found an analogue of the Jacobi integral and determined the possible regions of motion. A solution to the equations of perturbed motion has been obtained.     

Close encounters in young stellar clusters: implications for planetary systems in the solar neighbourhood

The stars that populate the solar neighbourhood were formed in stellar clusters. Through N -body simulations of these clusters, we measure the rate of close encounters between stars. By monitoring the interaction histories of each star, we investigate the singleton fraction in the solar neighbourhood. A singleton is a star which formed as a single star, has never experienced any close encounters with other stars or binaries, or undergone an exchange encounter with a binary. We find that, of the stars which formed as single stars, a significant fraction is not singletons once the clusters have dispersed. If some of these stars had planetary systems, with properties similar to those of the Solar System, the planets' orbits may have been perturbed by the effects of close encounters with other stars or the effects of a companion star within a binary. Such perturbations can lead to strong planet–planet interactions which eject several planets, leaving the remaining planets on eccentric orbits. Some of the single stars exchange into binaries. Most of these binaries are broken up via subsequent interactions within the cluster, but some remain intact beyond the lifetime of the cluster. The properties of these binaries are similar to those of the observed binary systems containing extrasolar planets. Thus, dynamical processes in young stellar clusters will alter significantly any population of Solar System-like planetary systems. In addition, beginning with a population of planetary systems exactly resembling the Solar System around single stars, dynamical encounters in young stellar clusters may produce at least some of the extrasolar planetary systems observed in the solar neighbourhood.     

The total number of giant planets in debris discs with central clearings

Infrared spectra from the Spitzer Space Telescope ( SSC ) of many debris discs are well fit with a single blackbody temperature which suggest clearings within the disc. We assume that clearings are caused by orbital instability in multiple planet systems with similar configurations to our own. These planets remove dust-generating planetesimal belts as well as dust generated by the outer disc that is scattered or drifts into the clearing. From numerical integrations, we estimate a minimum planet spacing required for orbital instability (and so planetesimal and dust removal) as a function of system age and planet mass. We estimate that a 10⁸ yr old debris disc with a dust disc edge at a radius of 50 au hosted by an A star must contain approximately five Neptune mass planets between the clearing radius and the iceline in order to remove all primordial objects within it. We infer that known debris disc systems contain at least a fifth of a Jupiter mass in massive planets. The number of planets and spacing required is insensitive to the assumed planet mass. However, an order of magnitude higher total mass in planets could reside in these systems if the planets are more massive.