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

Expected Coalescence Rate of Double Neutron Stars for Ground Based Interferometers

In this paper we present new estimates of the coalescence rate of neutron star binaries in the local universe and we discuss its consequences for the first generations of ground based interferometers. Our approach based on both evolutionary and statistical methods gives a galactic merging rate of 1.7 10$^{-5}$ yr$^{-1}$, in the range of previous estimates 10$^{-6}$ - 10$^{-4}$ yr$^{-1}$. The local rate which includes the contribution of elliptical galaxies is two times higher, in the order of 3.4 10$^{-5}$ yr$^{-1}$. We predict one detection every 148 and 125 years with initial VIRGO and LIGO, and up to 6 events per year with their advanced configuration. Our recent detection rate estimates from investigations on VIRGO future improvements are quoted.Comment: talk given at the GWDAW9 (Annecy, 2004) to be published in CQ

Demand for wool by grade

The aims of the project were to examine the relationships between auction prices of different types of wool, to identify categories of wool and to investigate substitution effects amongst wools. A modelling framework was developed which enabled these relationships to be analysed. While there are some clear avenues for further research, this study makes some useful first steps towards a conceptualisation of wool markets

The Sandwich algorithm for spatial equilibrium analysis

Recent advances in mathematical programming techniques have made it possible to provide more realistic solutions to applied economic problems. Although mathematical programming techniques are widely used, the economic content of the solutions is often limited by the assumptions imposed by the algorithms available. This report is designed to demonstrate the increased flexibility which is currently available for the solution of a wide range of spatial economic problems. Transportation and transhipment models have been widely used in the analysis of the impact of policy changes on spatial activity, Borrell & Zwart [l]; Beck, Rathbun and Abbott [2]. One of the major shortcomings of such models has been an inability to model the impact of more flexible pricing policies on regional supply and demand, while maintaining the realistic non linearities which are associated with processing and transportation costs. In this paper a simplified version of the transhipment model developed by Borrell & Zwart [l] is modified to incorporate regional supply response while at the same time retaining complex processing and handling cost relationships. This report outlines the general form of the spatial equilibrium problem and some of the solution techniques available, in a format easily understood by readers not conversant with operational research techniques. Initially the problem is defined and solution methods used in the past are then briefly described. The advantages and disadvantages of these methods are outlined before showing how a relatively new solution technique may be able to improve both the scope and flexibility of the problems being solved

A runaway collision in a young star cluster as the origin of the brightest supernova

Supernova 2006gy in the galaxy NGC 1260 is the most luminous one recorded \cite{2006CBET..644....1Q, 2006CBET..647....1H, 2006CBET..648....1P, 2006CBET..695....1F}. Its progenitor might have been a very massive ($>100$ \msun) star \cite{2006astro.ph.12617S}, but that is incompatible with hydrogen in the spectrum of the supernova, because stars $>40$ \msun are believed to have shed their hydrogen envelopes several hundred thousand years before the explosion \cite{2005A&A...429..581M}. Alternatively, the progenitor might have arisen from the merger of two massive stars \cite{2007ApJ...659L..13O}. Here we show that the collision frequency of massive stars in a dense and young cluster (of the kind to be expected near the center of a galaxy) is sufficient to provide a reasonable chance that SN 2006gy resulted from such a bombardment. If this is the correct explanation, then we predict that when the supernova fades (in a year or so) a dense cluster of massive stars becomes visible at the site of the explosion

A pilgrimage to gravity on GPUs

In this short review we present the developments over the last 5 decades that have led to the use of Graphics Processing Units (GPUs) for astrophysical simulations. Since the introduction of NVIDIA's Compute Unified Device Architecture (CUDA) in 2007 the GPU has become a valuable tool for N-body simulations and is so popular these days that almost all papers about high precision N-body simulations use methods that are accelerated by GPUs. With the GPU hardware becoming more advanced and being used for more advanced algorithms like gravitational tree-codes we see a bright future for GPU like hardware in computational astrophysics.Comment: To appear in: European Physical Journal "Special Topics" : "Computer Simulations on Graphics Processing Units" . 18 pages, 8 figure

Modelling Collision Products of Triple-Star Mergers

In dense stellar clusters, binary-single and binary-binary encounters can ultimately lead to collisions involving two or more stars. A comprehensive survey of multi-star collisions would need to explore an enormous amount of parameter space, but here we focus on a number of representative cases involving low-mass main-sequence stars. Using both Smoothed Particle Hydrodynamics (SPH) calculations and a much faster fluid sorting software package (MMAS), we study scenarios in which a newly formed product from an initial collision collides with a third parent star. By varying the order in which the parent stars collide, as well as the orbital parameters of the collision trajectories, we investigate how factors such as shock heating affect the chemical composition and structure profiles of the collision product. Our simulations and models indicate that the distribution of most chemical elements within the final product is not significantly affected by the order in which the stars collide, the direction of approach of the third parent star, or the periastron separations of the collisions. We find that the sizes of the products, and hence their collisional cross sections for subsequent encounters, are sensitive to the order and geometry of the collisions. For the cases that we consider, the radius of the product formed in the first (single-single star) collision ranges anywhere from roughly 2 to 30 times the sum of the radii of its parent stars. The final product formed in our triple-star collisions can easily be as large or larger than a typical red giant. We therefore expect the collisional cross section of a newly formed product to be greatly enhanced over that of a thermally relaxed star of the same mass.Comment: 20 pages, submitted to MNRA

Gravitational-wave confusion background from cosmological compact binaries: Implications for future terrestrial detectors

Increasing the sensitivity of a gravitational-wave (GW) detector improves our ability to measure the characteristics of detected sources. It also increases the number of weak signals that contribute to the data. Because GW detectors have nearly all-sky sensitivity, they can be subject to a confusion limit: Many sources which cannot be distinguished may be measured simultaneously, defining a stochastic noise floor to the sensitivity. For GW detectors operating at present and for their planned upgrades, the projected event rate is sufficiently low that we are far from the confusion-limited regime. However, some detectors currently under discussion may have large enough reach to binary inspiral that they enter the confusion-limited regime. In this paper, we examine the binary inspiral confusion limit for terrestrial detectors. We consider a broad range of inspiral rates in the literature, several planned advanced gravitational-wave detectors, and the highly advanced "Einstein Telescope" design. Though most advanced detectors will not be impacted by this limit, the Einstein Telescope with a very low frequency "seismic wall" may be subject to confusion noise. At a minimum, careful data analysis will be require to separate signals which will appear confused. This result should be borne in mind when designing highly advanced future instruments.Comment: 19 pages, 6 figures and 3 tables; accepted for publication in Phys. Rev.