Irregular Satellites of the Planets: Products of Capture in the Early Solar System

All four giant planets in the Solar system possess irregular satellites, characterized by large, highly eccentric and/or inclined orbits that are distinct from the nearly circular, uninclined orbits of the regular satellites. This difference can be traced directly to different modes of formation. Whereas the regular satellites grew by accretion within circumplanetary disks the irregular satellites were captured from initially heliocentric orbits at an early epoch. Recently, powerful survey observations have greatly increased the number of known irregular satellites, permitting a fresh look at the group properties of these objects and motivating a re-examination of the mechanisms of capture. None of the suggested mechanisms, including gas-drag, pull-down, and three-body capture, convincingly fit the group characteristics of the irregular satellites. The sources of the satellites also remain unidentified.Comment: 51 pages, 17 figures, 5 tables, to appear in ARAA 200

Revisiting the ABC flow dynamo

The ABC flow is a prototype for fast dynamo action, essential to the origin of magnetic field in large astrophysical objects. Probably the most studied configuration is the classical 1:1:1 flow. We investigate its dynamo properties varying the magnetic Reynolds number Rm. We identify two kinks in the growth rate, which correspond respectively to an eigenvalue crossing and to an eigenvalue coalescence. The dominant eigenvalue becomes purely real for a finite value of the control parameter. Finally we show that even for Rm = 25000, the dominant eigenvalue has not yet reached an asymptotic behaviour. Its still varies very significantly with the controlling parameter. Even at these very large values of Rm the fast dynamo property of this flow cannot yet be established

Capture of field stars by globular clusters in dense bulge regions

The recent detection of a double Red Giant Branch in the optical color-magnitude diagram (CMD) of the bulge globular cluster HP1 (Ortolani et al. 1997), a more populated metal-poor steep one corresponding to the cluster itself, and another metal-rich curved, led us to explore in the present Letter the possibility of capture of field stars by a globular cluster orbiting in dense bulge regions over several gigayears. Analytical arguments, as well as N-body calculations for a cluster model of 10^5 solar masses in a bulge-like environment, suggest that a significant fraction of cluster stars may consist of captures. Metal-poor globular clusters in the inner bulge, like HP1, contrasting at least in Delta [Fe/H] = 1.0 dex with respect to the surrounding metal-rich stars, are ideal probes to further test the capture scenario. In turn, if this scenario is confirmed, the double RGB of HP1 could provide direct estimates of blanketing amounts, which is fundamental for the photometric calibration of metal-rich stellar populations.Comment: 6 pages, 2 included figures, aas2pp4,sty Latex style. To be published in Astrophysical Journal Letter

Two-Component Fokker-Planck Models for the Evolution of Isolated Globular Clusters

Two-component (normal and degenerate stars) models are the simplest realization of clusters with a mass spectrum because high mass stars evolve quickly into degenerates, while low mass stars remain on the main-sequence for the age of the universe. Here we examine the evolution of isolated globular clusters using two-component Fokker-Planck (FP) models that include heating by binaries formed in tidal capture and in three-body encounters. Three-body binary heating dominates and the postcollapse expansion is self-similar, at least in models with total mass M <= 3 x 10^5 M_\odot, initial half-mass radius r_{h,i} >= 5 pc, component mass ratio m_2/m_1 <= 2, and number ratio N_1/N_2 <= 300 when m_2=1.4 M_\odot. We derive scaling laws for \rho_c, v_c, r_c, and r_h as functions of m_1/m_2, N, M, and time t from simple energy-balance arguments, and these agree well with the FP simulations. We have studied the conditions under which gravothermal oscillations (GTOs) occur. If E_{tot} and E_c are the energies of the cluster and of the core, respectively, and t_{rh} and t_c are their relaxation times, then \epsilon \equiv (E_{tot}/t_{rh})/(E_c/t_{rc}) is a good predictor of GTOs: all models with \epsilon>0.01 are stable, and all but one with \epsilon < 0.01 oscillate. We derive a scaling law for \epsilon against N and m_1/m_2 and compared with our numerical results. Clusters with larger m_2/m_1 or smaller N are stabler.Comment: 15 pages (LaTeX) with 8 figures. To appear in ApJ March 10, 1998 issu

Long-Term Evolution of Massive Black Hole Binaries. III. Binary Evolution in Collisional Nuclei

[Abridged] In galactic nuclei with sufficiently short relaxation times, binary supermassive black holes can evolve beyond their stalling radii via continued interaction with stars. We study this "collisional" evolutionary regime using both fully self-consistent N-body integrations and approximate Fokker-Planck models. The N-body integrations employ particle numbers up to 0.26M and a direct-summation potential solver; close interactions involving the binary are treated using a new implementation of the Mikkola-Aarseth chain regularization algorithm. Even at these large values of N, two-body scattering occurs at high enough rates in the simulations that they can not be simply scaled to the large-N regime of real galaxies. The Fokker-Planck model is used to bridge this gap; it includes, for the first time, binary-induced changes in the stellar density and potential. The Fokker-Planck model is shown to accurately reproduce the results of the N-body integrations, and is then extended to the much larger N regime of real galaxies. Analytic expressions are derived that accurately reproduce the time dependence of the binary semi-major axis as predicted by the Fokker-Planck model. Gravitational wave coalescence is shown to occur in <10 Gyr in nuclei with velocity dispersions below about 80 km/s. Formation of a core results from a competition between ejection of stars by the binary and re-supply of depleted orbits via two-body scattering. Mass deficits as large as ~4 times the binary mass are produced before coalescence. After the two black holes coalesce, a Bahcall-Wolf cusp appears around the single hole in one relaxation time, resulting in a nuclear density profile consisting of a flat core with an inner, compact cluster, similar to what is observed at the centers of low-luminosity spheroids.Comment: 21 page

A Method for Determining the Transient Process Duration in Dynamic Systems in the Regime of Chaotic Oscillations

We describe a method for determining the transient process duration in a standard two-dimensionaldynamic system with discrete time (Henon map), occurring in the regime of chaotic oscillationsComment: 4 pages, 2 figure

Analytic Central Orbits and their Transformation Group

A useful crude approximation for Abelian functions is developed and applied to orbits. The bound orbits in the power-law potentials A*r^{-alpha} take the simple form (l/r)^k = 1 + e cos(m*phi), where k = 2 - alpha > 0 and 'l' and 'e' are generalisations of the semi-latus-rectum and the eccentricity. 'm' is given as a function of 'eccentricity'. For nearly circular orbits 'm' is sqrt{k}, while the above orbit becomes exact at the energy of escape where 'e' is one and 'm' is 'k'. Orbits in the logarithmic potential that gives rise to a constant circular velocity are derived via the limit of small alpha. For such orbits, r^2 vibrates almost harmonically whatever the 'eccentricity'. Unbound orbits in power-law potentials are given in an appendix. The transformation of orbits in one potential to give orbits in a different potential is used to determine orbits in potentials that are positive powers of r. These transformations are extended to form a group which associates orbits in sets of six potentials, e.g. there are corresponding orbits in the potentials proportional to r, r^{-2/3}, r^{-3}, r^{-6}, r^{4/3} and r^{-4}. A degeneracy reduces this to three, which are r^{-1}, r^2 and r^{-4} for the Keplerian case. A generalisation of this group includes the isochrone with the Kepler set.Comment: 12 pages, 8 figures; updated version with minor typographical corrections; published in MNRA

Forming Galaxies with MOND

Beginning with a simple model for the growth of structure, I consider the dissipationless evolution of a MOND-dominated region in an expanding Universe by means of a spherically symmetric N-body code. I demonstrate that the final virialized objects resemble elliptical galaxies with well-defined relationships between the mass, radius, and velocity dispersion. These calculations suggest that, in the context of MOND, massive elliptical galaxies may be formed early (z > 10) as a result of monolithic dissipationless collapse. Then I reconsider the classic argument that a galaxy of stars results from cooling and fragmentation of a gas cloud on a time scale shorter than that of dynamical collapse. Qualitatively, the results are similar to that of the traditional picture; moreover, the existence, in MOND, of a density-temperature relation for virialized, near isothermal objects as well as a mass-temperature relation implies that there is a definite limit to the mass of a gas cloud where this condition can be met-- an upper limit corresponding to that of presently observed massive galaxies.Comment: 9 pages, 9 figures, revised in response to comments of referee. Table added, extended discussion, accepted MNRA

Analytical solutions of the lattice Boltzmann BGK model

Analytical solutions of the two dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plain Poiseuille flow and the plain Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time $\tau$ and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation.Comment: 10 pages, no postscript figure provide

A Two-Temperature Model of the Intracluster Medium

We investigate evolution of the intracluster medium (ICM), considering the relaxation process between the ions and electrons. According to the standard scenario of structure formation, ICM is heated by the shock in the accretion flow to the gravitational potential well of the dark halo. The shock primarily heats the ions because the kinetic energy of an ion entering the shock is larger than that of an electron by the ratio of masses. Then the electrons and ions exchange the energy through coulomb collisions and reach the equilibrium. From simple order estimation we find that the region where the electron temperature is considerably lower than the ion temperature spreads out on a Mpc scale. We then calculate the ion and electron temperature profiles by combining the adiabatic model of two-temperature plasma by Fox & Loeb (1997) with spherically symmetric N-body and hydrodynamic simulations based on three different cosmological models. It is found that the electron temperature is about a half of the mean temperature at radii $\sim$ 1 Mpc. This could lead to an about 50 % underestimation in the total mass contained within $\sim$ 1 Mpc when the electron temperature profiles are used. The polytropic indices of the electron temperature profiles are $\simeq 1.5$ whereas those of mean temperature $\simeq 1.3$ for $r \geq 1$ Mpc. This result is consistent both with the X-ray observations on electron temperature profiles and with some theoretical and numerical predictions about mean temperature profiles.Comment: 20 pages with 6 figures. Accepted for publication in Ap