Dynamical Cusp Regeneration

After being destroyed by a binary supermassive black hole, a stellar density cusp can regrow at the center of a galaxy via energy exchange between stars moving in the gravitational field of the single, coalesced hole. We illustrate this process via high-accuracy N-body simulations. Regeneration requires roughly one relaxation time and the new cusp extends to a distance of roughly one-fifth the black hole's influence radius, with density rho ~ r^{-7/4}; the mass in the cusp is of order 10% the mass of the black hole. Growth of the cusp is preceded by a stage in which the stellar velocity dispersion evolves toward isotropy and away from the tangentially-anisotropic state induced by the binary. We show that density profiles similar to those observed at the center of the Milky Way and M32 can regenerate themselves in several Gyr following infall of a second black hole; the presence of density cusps at the centers of these galaxies can therefore not be used to infer that no merger has occurred. We argue that Bahcall-Wolf cusps are ubiquitous in stellar spheroids fainter than M_V ~ -18.5 that contain supermassive black holes, but the cusps have not been detected outside of the Local Group since their angular sizes are less than 0.1". We show that the presence of a cusp implies a lower limit of \~10^{-4} per year on the rate of stellar tidal disruptions, and discuss the consequences of the cusps for gravitational lensing and the distribution of dark matter on sub-parsec scales.Comment: Accepted for publication in The Astrophysical Journa

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

Self-consistent models of cuspy triaxial galaxies with dark matter haloes

We have constructed realistic, self-consistent models of triaxial elliptical galaxies embedded in triaxial dark matter haloes. We examined three different models for the shape of the dark matter halo: (i) the same axis ratios as the luminous matter (0.7:0.86:1); (ii) a more prolate shape (0.5:0.66:1); (iii) a more oblate shape (0.7:0.93:1). The models were obtained by means of the standard orbital superposition technique introduced by Schwarzschild. Self-consistent solutions were found in each of the three cases. Chaotic orbits were found to be important in all of the models,and their presence was shown to imply a possible slow evolution of the shapes of the haloes. Our results demonstrate for the first time that triaxial dark matter haloes can co-exist with triaxial galaxies.Comment: Latex paper based on the AASTEX format, 20 pages, 11 figures, 2 tables. Paper submitted to Ap

Australian Glow-worms in Caves

Glow-worms are the larvae of a fly from the family Keroplatidae. Their closest relatives are the “fungus flies” that seek out mushrooms for their larvae to consume. Glow-worms have gone out on an evolutionary limb, albeit a successful one. They have lost their association with fungi and have instead become carnivorous. The unique feature of glow-worms is their ability to bioluminesce—to produce light

"Kludge" gravitational waveforms for a test-body orbiting a Kerr black hole

One of the most exciting potential sources of gravitational waves for low-frequency, space-based gravitational wave (GW) detectors such as the proposed Laser Interferometer Space Antenna (LISA) is the inspiral of compact objects into massive black holes in the centers of galaxies. The detection of waves from such "extreme mass ratio inspiral" systems (EMRIs) and extraction of information from those waves require template waveforms. The systems' extreme mass ratio means that their waveforms can be determined accurately using black hole perturbation theory. Such calculations are computationally very expensive. There is a pressing need for families of approximate waveforms that may be generated cheaply and quickly but which still capture the main features of true waveforms. In this paper, we introduce a family of such "kludge" waveforms and describe ways to generate them. We assess performance of the introduced approximations by comparing "kludge" waveforms to accurate waveforms obtained by solving the Teukolsky equation in the adiabatic limit (neglecting GW backreaction). We find that the kludge waveforms do extremely well at approximating the true gravitational waveform, having overlaps with the Teukolsky waveforms of 95% or higher over most of the parameter space for which comparisons can currently be made. Indeed, we find these kludges to be of such high quality (despite their ease of calculation) that it is possible they may play some role in the final search of LISA data for EMRIs.Comment: 29 pages, 11 figures, requires subeqnarray; v2 contains minor changes for consistency with published versio

The internal structure and formation of early-type galaxies: the gravitational--lens system MG2016+112 at z=1.004

[Abridged] We combine our measurements of the velocity dispersion and the surface brightness profile of the lens galaxy D in the system MG2016+112 (z=1.004) with constraints from gravitational lensing to study its internal mass distribution. We find that: (i) dark matter accounts for >50% of the total mass within the Einstein radius (99% CL), excluding at the 8-sigma level that mass follows light inside the Einstein radius with a constant mass-to-light ratio (M/L). (ii) the total mass distribution inside the Einstein radius is well-described by a density profile ~r^-gamma' with an effective slope gamma'=2.0+-0.1+-0.1, including random and systematic uncertainties. (iii) The offset of galaxy D from the local Fundamental Plane independently constrains the stellar M/L, and matches the range derived from our models, leading to a more stringent lower limit of >60% on the fraction of dark matter within the Einstein radius (99%CL). Under the assumption of adiabatic contraction, the inner slope of the dark matter halo before the baryons collapsed is gamma_i<1.4 (68 CL), marginally consistent with the highest-resolution cold dark matter simulations that indicate gamma_i~1.5. This might indicate that either adiabatic contraction is a poor description of E/S0 formation or that additional processes play a role as well. Indeed, the apparently isothermal density distribution inside the Einstein radius, is not a natural outcome of adiabatic contraction models, where it appears to be a mere coincidence. By contrast, we argue that isothermality might be the result of a stronger coupling between luminous and dark-matter, possibly the result of (incomplete) violent relaxation processes. Hence, we conclude that galaxy D appears already relaxed 8 Gyr ago.Comment: 8 pages, 4 figures, ApJ, in press, minor change