Ejection of high-velocity stars from the Galactic Center by an inspiraling Intermediate-Mass Black Hole

The presence of young stars in the immediate vicinity and strong tidal field of SgrA* remains unexplained. One currently popular idea for their origin posits that the stars were bused in by an Intermediate-Mass Black Hole (IMBH) which has inspiraled into the Galactic Center a few million years ago. Yu and Tremaine (2003) have argued that in this case some of the old stars in the SgrA* cusp would be ejected by hard gravitational collisions with the IMBH. Here we derive a general expression for the phase-space distribution of the ejected high-velocity stars, given the distribution function of the stars in the cusp. We compute it explicitly for the Peebles-Young distribution function of the cusp, and make a detailed model for the time-dependent ejection of stars during the IMBH inspiral. We find that (1) the stars are ejected in a burst lasting a few dynamical friction timescales; if the ejected stars are detected by Gaia they are likely to be produced by a single inspiral event, (2) if the inspiral is circular than in the beginning of the burst the velocity vectors of the ejected stars cluster around the inspiral plane, but rapidly isotropise as the burst proceeds, (3) if the inspiral is eccentric, then the stars are ejected in a broad jet roughly perpendicular to the Runge-Lenz vector of the IMBH orbit. In a typical cusp the orbit will precess with a period of \sim 10^5 years, and the rate of ejection into our part of the Galaxy (as defined by e.g. the Gaia visibility domain) will be modulated periodically. Gaia, together with the ground-based follow-up observations, will be able to clock many high-velocity stars back to their ejection from the Galactic Center, thus measuring some of the above phenomena. This would provide a clear signature of the IMBH inspiral in the past 10--20 Myr.Comment: 12 pages, including 7 figure

Approximating Stellar Orbits: Improving on Epicycle Theory

Already slightly eccentric orbits, such as those occupied by many old stars in the Galactic disk, are not well approximated by Lindblad's epicycle theory. Here, alternative approximations for flat orbits in axisymmetric stellar systems are derived and compared to results from numeric integrations. All of these approximations are more accurate than Lindblad's classical theory. I also present approximate, but canonical, maps from ordinary phase-space coordinates to a set of action-angle variables. Unfortunately, the most accurate orbit approximation leads to non-analytical R(t). However, from this approximation simple and yet very accurate estimates can be derived for the peri- and apo-centers, frequencies, and actions integrals of galactic orbits, even for high eccentricities. Moreover, further approximating this approximation allows for an analytical R(t) and still an accurate approximation to galactic orbits, even with high eccentricities.Comment: accepted for publication in AJ; 12 pages LaTeX, 9 figures (coloured only here, not in AJ) uses aas2pp4.st

Self Similar Spherical Collapse Revisited: a Comparison between Gas and Dark Matter Dynamics

We reconsider the collapse of cosmic structures in an Einstein-de Sitter Universe, using the self similar initial conditions of Fillmore & Goldreich (1984). We first derive a new approximation to describe the dark matter dynamics in spherical geometry, that we refer to the "fluid approach". This method enables us to recover the self-similarity solutions of Fillmore & Goldreich for dark matter. We derive also new self-similarity solutions for the gas. We thus compare directly gas and dark matter dynamics, focusing on the differences due to their different dimensionalities in velocity space. This work may have interesting consequences for gas and dark matter distributions in large galaxy clusters, allowing to explain why the total mass profile is always steeper than the X-ray gas profile. We discuss also the shape of the dark matter density profile found in N-body simulations in terms of a change of dimensionality in the dark matter velocity space. The stable clustering hypothesis has been finally considered in the light of this analytical approach.Comment: 14 pages, 2 figures, accepted for publication in The Astrophysical Journa

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

A Note on the Toda Criterion for Interacting Dipole-Quadrupole Vibrations

The Toda criterion of the Gaussian curvature is applied to calculate analytically the transition energy from regular to chaotic motion in a schematic model describing the interaction between collective dipole and quadrupole modes in atomic nuclei.Comment: Latex, 9 pages, 2 figures (available upon request), to be published in Modern Physics Letters

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

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

Variation of the Dependence of the Transient Process Duration on the Initial Conditions in Systems with Discrete Time

Dependence of the transient process duration on the initial conditions is considered in one- and two-dimensional systems with discrete time, representing a logistic map and the Eno map, respectively.Comment: 4 pages, 2 figure

Exact Quantum Solutions of Extraordinary N-body Problems

The wave functions of Boson and Fermion gases are known even when the particles have harmonic interactions. Here we generalise these results by solving exactly the N-body Schrodinger equation for potentials V that can be any function of the sum of the squares of the distances of the particles from one another in 3 dimensions. For the harmonic case that function is linear in r^2. Explicit N-body solutions are given when U(r) = -2M \hbar^{-2} V(r) = \zeta r^{-1} - \zeta_2 r^{-2}. Here M is the sum of the masses and r^2 = 1/2 M^{-2} Sigma Sigma m_I m_J ({\bf x}_I - {\bf x}_J)^2. For general U(r) the solution is given in terms of the one or two body problem with potential U(r) in 3 dimensions. The degeneracies of the levels are derived for distinguishable particles, for Bosons of spin zero and for spin 1/2 Fermions. The latter involve significant combinatorial analysis which may have application to the shell model of atomic nuclei. For large N the Fermionic ground state gives the binding energy of a degenerate white dwarf star treated as a giant atom with an N-body wave function. The N-body forces involved in these extraordinary N-body problems are not the usual sums of two body interactions, but nor are forces between quarks or molecules. Bose-Einstein condensation of particles in 3 dimensions interacting via these strange potentials can be treated by this method.Comment: 24 pages, Latex. Accepted for publication in Proceedings of the Royal Societ

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