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

Comparing compact binary parameter distributions I: Methods

Being able to measure each merger's sky location, distance, component masses, and conceivably spins, ground-based gravitational-wave detectors will provide a extensive and detailed sample of coalescing compact binaries (CCBs) in the local and, with third-generation detectors, distant universe. These measurements will distinguish between competing progenitor formation models. In this paper we develop practical tools to characterize the amount of experimentally accessible information available, to distinguish between two a priori progenitor models. Using a simple time-independent model, we demonstrate the information content scales strongly with the number of observations. The exact scaling depends on how significantly mass distributions change between similar models. We develop phenomenological diagnostics to estimate how many models can be distinguished, using first-generation and future instruments. Finally, we emphasize that multi-observable distributions can be fully exploited only with very precisely calibrated detectors, search pipelines, parameter estimation, and Bayesian model inference

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

On the origin of the difference between the runaway velocities of the OB-supergiant X-ray Binaries and the Be/X-ray Binaries

The recent finding by Chevalier & Ilovaisky (1998) that OB-supergiant X-ray binaries have relatively large runaway velocities whereas Be/X-ray binaries have low runaway velocities, provides confirmation of the current models for the formation of these two types of systems. These predict a difference in runaway velocity of an order of magnitude. This difference basically results from the variation of the fractional helium core mass as a function of stellar mass, in combination with the conservation of orbital angular momentum during the mass transfer phase that preceded the formation of the compact object in the system. This combination results into: (i) Systematically narrower pre-supernova orbits in the OB-supergiant systems than in the Be-systems, and (ii) A larger fractional amount of mass ejected in the supernovae in high-mass systems relative to systems of lower mass. Regardless of possible kick velocities imparted to neutron stars at birth, this combination leads to a considerable difference in average runaway velocity between these two groups. The observed low runaway velocities of the Be/X-ray binaries confirm that in most cases not more than 1 to 2Msun was ejected in the supernovae that produced their neutron stars. This, in combination with the --on average-- large orbital eccentricities of these systems, indicates that their neutron stars must have received a velocity kick in the range 60 - 250 km/s at birth.Comment: reduced abstract, 13 pages, accepted by A&

Forming short-period Wolf-Rayet X-ray binaries and double black holes through stable mass transfer

We show that black-hole High-Mass X-ray Binaries (HMXBs) with O- or B-type donor stars and relatively short orbital periods, of order one week to several months may survive spiral in, to then form Wolf-Rayet (WR) X-ray binaries with orbital periods of order a day to a few days; while in systems where the compact star is a neutron star, HMXBs with these orbital periods never survive spiral-in. We therefore predict that WR X-ray binaries can only harbor black holes. The reason why black-hole HMXBs with these orbital periods may survive spiral in is: the combination of a radiative envelope of the donor star, and a high mass of the compact star. In this case, when the donor begins to overflow its Roche lobe, the systems are able to spiral in slowly with stable Roche-lobe overflow, as is shown by the system SS433. In this case the transferred mass is ejected from the vicinity of the compact star (so-called "isotropic re-emission" mass loss mode, or "SS433-like mass loss"), leading to gradual spiral-in. If the mass ratio of donor and black hole is $>3.5$, these systems will go into CE evolution and are less likely to survive. If they survive, they produce WR X-ray binaries with orbital periods of a few hours to one day. Several of the well-known WR+O binaries in our Galaxy and the Magellanic Clouds, with orbital periods in the range between a week and several months, are expected to evolve into close WR-Black-Hole binaries,which may later produce close double black holes. The galactic formation rate of double black holes resulting from such systems is still uncertain, as it depends on several poorly known factors in this evolutionary picture. It might possibly be as high as $\sim 10^{-5}$ per year.Comment: MNRAS in pres

The initial conditions of observed star clusters - I. Method description and validation

We have coupled a fast, parametrized star cluster evolution code to a Markov Chain Monte Carlo code to determine the distribution of probable initial conditions of observed star clusters, which may serve as a starting point for future $N$-body calculations. In this paper we validate our method by applying it to a set of star clusters which have been studied in detail numerically with $N$-body simulations and Monte Carlo methods: the Galactic globular clusters M4, 47 Tucanae, NGC 6397, M22, $\omega$ Centauri, Palomar 14 and Palomar 4, the Galactic open cluster M67, and the M31 globular cluster G1. For each cluster we derive a distribution of initial conditions that, after evolution up to the cluster's current age, evolves to the currently observed conditions. We find that there is a connection between the morphology of the distribution of initial conditions and the dynamical age of a cluster and that a degeneracy in the initial half-mass radius towards small radii is present for clusters which have undergone a core collapse during their evolution. We find that the results of our method are in agreement with $N$-body and Monte Carlo studies for the majority of clusters. We conclude that our method is able to find reliable posteriors for the determined initial mass and half-mass radius for observed star clusters, and thus forms an suitable starting point for modeling an observed cluster\rq{}s evolution.Comment: 39 pages, 28 figures, accepted for publication in MNRA