The kinematic signature of the inspiral phase of massive binary black holes

Supermassive black holes are expected to pair as a result of galaxy mergers, and form a bound binary at parsec or sub-parsec scales. These scales are unresolved even in nearby galaxies, and thus detection of non-active black hole binaries must rely on stellar dynamics. Here we show that these systems could be indirectly detected through the trail that the black holes leave as they spiral inwards. We analyze two numerical simulations of inspiralling black holes (equal masses and 10:1 mass ratio) in the stellar environment of a galactic centre. We studied the effect of the binary on the structure of the stellar population, with particular emphasis on projected kinematics and directly measurable moments of the velocity distribution. We present those moments as high-resolution 2D maps. As shown in past scattering experiments, a torus of stars counter-rotating with respect to the black holes exists in scales ~ 5 to 10 times larger than the binary separation. While this is seen in the average velocity map in the unequal mass case, it is obscured by a more strongly co-rotating outer region in the equal mass case; however, the inner counter-rotation could still be detected by studying the higher moments of the velocity distribution. Additionally, the maps reveal a dip in velocity dispersion in the inner region, as well as more pronounced signatures in the higher distribution moments. These maps could serve as templates for integral field spectroscopy observations of nearby galactic centres. The discovery of such signatures may help census the population of supermassive black hole binaries and refine signal rate predictions for future space-based low frequency gravitational wave detectors.Comment: Accepted for publication in MNRAS; 9 pages, 7 figure

Resonant relaxation in globular clusters

Resonant relaxation has been discussed as an efficient process that changes the angular momenta of stars orbiting around a central supermassive black hole due to the fluctuating gravitational field of the stellar cluster. Other spherical stellar systems, such as globular clusters, exhibit a restricted form of this effect where enhanced relaxation rate only occurs in the directions of the angular momentum vectors, but not in their magnitudes; this is called vector resonant relaxation (VRR). To explore this effect, we performed a large set of direct N-body simulations, with up to 512k particles and ~500 dynamical times. Contrasting our simulations with Spitzer-style Monte Carlo simulations, that by design only exhibit 2-body relaxation, we show that the temporal behavior of the angular momentum vectors in $N$-body simulations cannot be explained by 2-body relaxation alone. VRR operates efficiently in globular clusters with $N>10^4$. The fact that VRR operates in globular clusters may open way to use powerful tools in statistical physics for their description. In particular, since the distribution of orbital planes relaxes much more rapidly than the distribution of the magnitude of angular momentum and the radial action, the relaxation process reaches an internal statistical equilibrium in the corresponding part of phase space while the whole cluster is generally out of equilibrium, in a state of quenched disorder. We point out the need to include effects of VRR in Monte Carlo simulations of globular clusters.Comment: Submitted to Ap

Two-dimensional late-stage coarsening for nucleation and growth at high-area fractions

Numerical simulations of two-dimensional late-stage coarsening for nucleation and growth (Ostwald ripening) are performed at large-area fractions without shape restrictions. We employ efficient computational methods that allow us to study large systems. The free energy of the system we consider is composed of two different curves. Thus, the system consists of a set of isolated particles even at high-area fractions. This is totally different from the interconnected spinodal structures generated by the Cahn-Hilliard model, where the free energy is composed of a single curve. Although the domain structures are quite different, we find that the qualitative features of the structure function for both models are the same

Hypervelocity Richtmyer–Meshkov instability

The Richtmyer-Meshkov instability is numerically investigated for strong shocks, i.e., for hypervelocity cases. To model the interaction of the flow with non-equilibrium chemical effects typical of high-enthalpy flows, the Lighthill-Freeman ideal dissociating gas model is employed. Richtmyer's linear theory and the impulse model are extended to include equilibrium dissociation chemistry. Numerical simulations of the compressible Euler equations indicate no period of linear growth even for amplitude to wavelength ratios as small as one percent. For large Atwood numbers, dissociation causes significant changes in density and temperature, but the change in growth of the perturbations is small. A Mach number scaling for strong shocks is presented which holds for frozen chemistry at high Mach numbers. A local analysis is used to determine the initial baroclinic circulation generation for interfaces corresponding to both positive and negative Atwood ratios

A numerical study of Richtmyer–Meshkov instability in continuously stratified fluids

Theory and calculations are presented for the evolution of Richtmyer–Meshkov instability in two-dimensional continuously stratified fluid layers. The initial acceleration and subsequent instability of the fluid layer are induced by means of an impulsive pressure distribution. The subsequent dynamics of the fluid layer are then calculated numerically using the incompressible equations of motion. Initial conditions representing single-scale perturbations and multiple-scale random perturbations are considered. It is found that the growth rates for Richtmyer–Meshkov instability of stratified fluid layers are substantially lower than those predicted by Richtmyer for a sharp fluid interface with an equivalent jump in density. A frozen field approximation for the early-time dynamics of the instability is proposed, and shown to approximate the initial behavior of the layer over a time equivalent to the traversal of several layer thicknesses. It is observed that the nonlinear development of the instability results in the formation of plumes of penetrating fluid. Late in the process, the initial momentum deposited by the impulse is primarily used in the internal mixing of the layer rather than in the overall growth of the stratified layer. At intermediate times, some evidence for the existence of scaling behavior in the width of the mixing layer of the instability is observed for the multiple-scale random perturbations, but not for the single-scale perturbations. The time variation of the layer thickness differs from the scaling derived using ideas of self-similarity due to Barenblatt [Non-Linear Dynamics and Turbulence, edited by G. I. Barenblatt, G. Ioos, and D. D. Joseph (Pitman, Boston, 1983), p. 48] even at low Atwood ratio, presumably because of the inhomogeneity and anisotropy due to the excitation of vortical plumes

Numerical Calculation of Three-Dimensional Interfacial Potential Flows Using the Point Vortex Method

An application of the point vortex method to the singular Biot--Savart integrals used in water wave calculations is presented. The error for this approximation is shown to be a series in odd powers of h. A method for calculating the coefficients in the series is presented

Difficulties with three-dimensional weak solutions for inviscid incompressible flow

The representation of an inviscid three-dimensional incompressible flow by vortex singularities is considered and shown to lead to dynamical inconsistencies

The limited role of mergers in the black hole to bulge mass relation

We examine the intrinsic scatter in the correlation between black hole masses and their host bulge masses, and find that it cannot be accounted for by mergers alone. A simple merger scenario of small galaxies leads to a proportionality relation between the late-time black hole and bulge masses, with intrinsic scatter (in linear scale) increasing along the ridge line of the relation as the square root of the mass. By examining a sample of 86 galaxies with well measured black hole masses, we find that the intrinsic scatter increases with mass more rapidly than expected from the merger-only scenario. We discuss the possibility that the feedback mechanism that operated during galaxy formation involved the presence of a cooling flow.Comment: 6 pages, 3 figures, 2 table

The influence of mergers and ram-pressure stripping on black hole-bulge correlations

We analyse the scatter in the correlation between super-massive black hole (SMBH) mass and bulge stellar mass of the host galaxy, and infer that it cannot be accounted for by mergers alone. The merger-only scenario, where small galaxies merge to establish a proportionality relation between the SMBH and bulge masses, leads to a scatter around the linear proportionality line that increases with the square root of the SMBH (or bulge) mass. By examining a sample of 103 galaxies we find that the intrinsic scatter increases more rapidly than expected from the merger-only scenario. The correlation between SMBH masses and their host galaxy properties is therefore more likely to be determined by a negative feedback mechanism that is driven by an active galactic nucleus. We find a hint that some galaxies with missing stellar mass reside close to the centre of clusters and speculate that ram-pressure stripping of gas off the young galaxy as it moves near the cluster centre, might explain the missing stellar mass at later times.Comment: MNRAS, in pres