Black hole mergers in the universe

Mergers of black-hole binaries are expected to release large amounts of energy in the form of gravitational radiation. However, binary evolution models predict merger rates too low to be of observational interest. In this paper we explore the possibility that black holes become members of close binaries via dynamical interactions with other stars in dense stellar systems. In star clusters, black holes become the most massive objects within a few tens of millions of years; dynamical relaxation then causes them to sink to the cluster core, where they form binaries. These black-hole binaries become more tightly bound by superelastic encounters with other cluster members, and are ultimately ejected from the cluster. The majority of escaping black-hole binaries have orbital periods short enough and eccentricities high enough that the emission of gravitational radiation causes them to coalesce within a few billion years. We predict a black-hole merger rate of about $1.6 \times 10^{-7}$ per year per cubic megaparsec, implying gravity wave detection rates substantially greater than the corresponding rates from neutron star mergers. For the first generation Laser Interferometer Gravitational-Wave Observatory (LIGO-I), we expect about one detection during the first two years of operation. For its successor LIGO-II, the rate rises to roughly one detection per day. The uncertainties in these numbers are large. Event rates may drop by about an order of magnitude if the most massive clusters eject their black hole binaries early in their evolution.Comment: 12 pages, ApJL in pres

Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows

We develop a gradient-flow framework based on the Wasserstein metric for a parabolic moving-boundary problem that models crystal dissolution and precipitation. In doing so we derive a new weak formulation for this moving-boundary problem and we show that this formulation is well-posed. In addition, we develop a new uniqueness technique based on the framework of gradient flows with respect to the Wasserstein metric. With this uniqueness technique, the Wasserstein framework becomes a complete well-posedness setting for this parabolic moving-boundary problem.Comment: 26 page

Reconstructing the Arches I: Constraining the Initial Conditions

We have performed a series of N-body simulations to model the Arches cluster. Our aim is to find the best fitting model for the Arches cluster by comparing our simulations with observational data and to constrain the parameters for the initial conditions of the cluster. By neglecting the Galactic potential and stellar evolution, we are able to efficiently search through a large parameter space to determine e.g. the IMF, size, and mass of the cluster. We find, that the cluster's observed present-day mass function can be well explained with an initial Salpeter IMF. The lower mass-limit of the IMF cannot be well constrained from our models. In our best models, the total mass and the virial radius of the cluster are initially (5.1 +/- 0.8) 10^4 Msun and 0.76 +/- 0.12 pc, respectively. The concentration parameter of the initial King model is w0 = 3-5.Comment: 12 pages, 14 Figures, revised and accepted for publication in MNRA

The solar siblings in the Gaia era

We perform realistic simulations of the Sun's birth cluster in order to predict the current distribution of solar siblings in the Galaxy. We study the possibility of finding the solar siblings in the Gaia catalogue by using only positional and kinematic information. We find that the number of solar siblings predicted to be observed by Gaia will be around 100 in the most optimistic case, and that a phase space only search in the Gaia catalogue will be extremely difficult. It is therefore mandatory to combine the chemical tagging technique with phase space selection criteria in order to have any hope of finding the solar siblings.Comment: To be published in the proceedings of the GREAT-ITN conference "The Milky Way Unravelled by Gaia: GREAT Science from the Gaia Data Releases", 1-5 December 2014, University of Barcelona, Spain, EAS Publications Series, eds Nicholas Walton, Francesca Figueras, and Caroline Soubira

Diffusion Variational Autoencoders

A standard Variational Autoencoder, with a Euclidean latent space, is structurally incapable of capturing topological properties of certain datasets. To remove topological obstructions, we introduce Diffusion Variational Autoencoders with arbitrary manifolds as a latent space. A Diffusion Variational Autoencoder uses transition kernels of Brownian motion on the manifold. In particular, it uses properties of the Brownian motion to implement the reparametrization trick and fast approximations to the KL divergence. We show that the Diffusion Variational Autoencoder is capable of capturing topological properties of synthetic datasets. Additionally, we train MNIST on spheres, tori, projective spaces, SO(3), and a torus embedded in R3. Although a natural dataset like MNIST does not have latent variables with a clear-cut topological structure, training it on a manifold can still highlight topological and geometrical properties.Comment: 10 pages, 8 figures Added an appendix with derivation of asymptotic expansion of KL divergence for heat kernel on arbitrary Riemannian manifolds, and an appendix with new experiments on binarized MNIST. Added a previously missing factor in the asymptotic expansion of the heat kernel and corrected a coefficient in asymptotic expansion KL divergence; further minor edit

On the origin of hyperfast neutron stars

We propose an explanation for the origin of hyperfast neutron stars (e.g. PSR B1508+55, PSR B2224+65, RX J0822-4300) based on the hypothesis that they could be the remnants of a symmetric supernova explosion of a high-velocity massive star (or its helium core) which attained its peculiar velocity (similar to that of the neutron star) in the course of a strong three- or four-body dynamical encounter in the core of a young massive star cluster. This hypothesis implies that the dense cores of star clusters (located either in the Galactic disk or near the Galactic centre) could also produce the so-called hypervelocity stars -- the ordinary stars moving with a speed of ~1000 km/s.Comment: 2 pages, to appear in Dynamical Evolution of Dense Stellar Systems, Proceed. of the IAU Symp. 246 (Capri, Sept. 2007), eds. E.Vesperini, M. Giersz, and A. Sill

Monte-Carlo Simulations of Globular Cluster Evolution - I. Method and Test Calculations

We present a new parallel supercomputer implementation of the Monte-Carlo method for simulating the dynamical evolution of globular star clusters. Our method is based on a modified version of Henon's Monte-Carlo algorithm for solving the Fokker-Planck equation. Our code allows us to follow the evolution of a cluster containing up to 5x10^5 stars to core collapse in < 40 hours of computing time. In this paper we present the results of test calculations for clusters with equal-mass stars, starting from both Plummer and King model initial conditions. We consider isolated as well as tidally truncated clusters. Our results are compared to those obtained from approximate, self-similar analytic solutions, from direct numerical integrations of the Fokker-Planck equation, and from direct N-body integrations performed on a GRAPE-4 special-purpose computer with N=16384. In all cases we find excellent agreement with other methods, establishing our new code as a robust tool for the numerical study of globular cluster dynamics using a realistic number of stars.Comment: 35 pages, including 8 figures, submitted to ApJ. Revised versio