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

Marketing strategies to utilise Central Otago's resources

Paper presented at the 48th New Zealand Grassland Association Conference, 3-6 November 1986, Alexandra.This paper provides an overview of trends in marketing at the national level and in regions such as Central Otago. The movement away from centrally co-ordinated marketing strategies and ihe increased sophistication of marketing and processing are highlighted. Such developments have implications for the structure of the agricultural and horticultural marketing systems. It is suggested that there is a requirement for improved strategy development and planning by individual firms. This can best be aided at the national level, by considering ways in which the planning by individual firms can be improved. Several specific areas in which improvements could be made are discussed

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

The evolution of the Sun's birth cluster and the search for the solar siblings with Gaia

We use self-consistent numerical simulations of the evolution and disruption of the Sun's birth cluster in the Milky Way potential to investigate the present-day phase space distribution of the Sun's siblings. The simulations include the gravitational N-body forces within the cluster and the effects of stellar evolution on the cluster population. In addition the gravitational forces due to the Milky Way potential are accounted for in a self-consistent manner. Our aim is to understand how the astrometric and radial velocity data from the Gaia mission can be used to pre-select solar sibling candidates. We vary the initial conditions of the Sun's birth cluster, as well as the parameters of the Galactic potential. We show that the disruption time-scales of the cluster are insensitive to the details of the non-axisymmetric components of the Milky Way model and we make predictions, averaged over the different simulated possibilities, about the number of solar siblings that should appear in surveys such as Gaia or GALAH. We find a large variety of present-day phase space distributions of solar siblings, which depend on the cluster initial conditions and the Milky Way model parameters. We show that nevertheless robust predictions can be made about the location of the solar siblings in the space of parallaxes ($\varpi$), proper motions ($\mu$) and radial velocities ($V_\mathrm{r}$). By calculating the ratio of the number of simulated solar siblings to that of the number of stars in a model Galactic disk, we find that this ratio is above 0.5 in the region given by: $\varpi \geq 5$mas, $4 \leq \mu \leq 6$masyr$^{-1}$, and $-2\leq V_\mathrm{r} \leq 0$kms$^{-1}$. Selecting stars from this region should increase the probability of success in identifying solar siblings through follow up observations [Abridged].Comment: 13 pages, 7 figures. Accepted for publication in MNRA

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

Planets in triple star systems--the case of HD188753

We consider the formation of the recently discovered ``hot Jupiter'' planet orbiting the primary component of the triple star system HD188753. Although the current outer orbit of the triple is too tight for a Jupiter-like planet to have formed and migrated to its current location, the binary may have been much wider in the past. We assume here that the planetary system formed in an open star cluster, the dynamical evolution of which subsequently led to changes in the system's orbital parameters and binary configuration. We calculate cross sections for various scenarios that could have led to the multiple system currently observed, and conclude that component A of HD188753 with its planet were most likely formed in isolation to be swapped in a triple star system by a dynamical encounter in an open star cluster. We estimate that within 500pc of the Sun there are about 1200 planetary systems which, like Hd188753, have orbital parameters unfavorable for forming planets but still having a planet, making it quite possible that the HD188753 system was indeed formed by a dynamical encounter in an open star cluster.Comment: ApJ Letters in pres

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