The generation of a Gaussian random process in a position parameter

Analog computer method for approximating stationary Gaussian random process depending only on position paramete

Binary inspiral, gravitational radiation, and cosmology

Observations of binary inspiral in a single interferometric gravitational wave detector can be cataloged according to signal-to-noise ratio $\rho$ and chirp mass $\cal M$. The distribution of events in a catalog composed of observations with $\rho$ greater than a threshold $\rho_0$ depends on the Hubble expansion, deceleration parameter, and cosmological constant, as well as the distribution of component masses in binary systems and evolutionary effects. In this paper I find general expressions, valid in any homogeneous and isotropic cosmological model, for the distribution with $\rho$ and $\cal M$ of cataloged events; I also evaluate these distributions explicitly for relevant matter-dominated Friedmann-Robertson-Walker models and simple models of the neutron star mass distribution. In matter dominated Friedmann-Robertson-Walker cosmological models advanced LIGO detectors will observe binary neutron star inspiral events with $\rho>8$ from distances not exceeding approximately $2\,\text{Gpc}$, corresponding to redshifts of $0.48$ (0.26) for $h=0.8$ ($0.5$), at an estimated rate of 1 per week. As the binary system mass increases so does the distance it can be seen, up to a limit: in a matter dominated Einstein-deSitter cosmological model with $h=0.8$ ($0.5$) that limit is approximately $z=2.7$ (1.7) for binaries consisting of two $10\,\text{M}_\odot$ black holes. Cosmological tests based on catalogs of the kind discussed here depend on the distribution of cataloged events with $\rho$ and $\cal M$. The distributions found here will play a pivotal role in testing cosmological models against our own universe and in constructing templates for the detection of cosmological inspiraling binary neutron stars and black holes.Comment: REVTeX, 38 pages, 9 (encapsulated) postscript figures, uses epsf.st

Optimization of graded multilayer designs for astronomical x-ray telescopes

We developed a systematic method for optimizing the design of depth-graded multilayers for astronomical hard-x-ray and soft-γ-ray telescopes based on the instrument’s bandpass and the field of view. We apply these methods to the design of the conical-approximation Wolter I optics employed by the balloon-borne High Energy Focusing Telescope, using W/Si as the multilayer materials. In addition, we present optimized performance calculations of mirrors, using other material pairs that are capable of extending performance to photon energies above the W K-absorption edge (69.5 keV), including Pt/C, Ni/C, Cu/Si, and Mo/Si

Gravitational Wave Hotspots: Ranking Potential Locations of Single-Source Gravitational Wave Emission

The steadily improving sensitivity of pulsar timing arrays (PTAs) suggests that gravitational waves (GWs) from supermassive black hole binary (SMBHB) systems in the nearby universe will be de- tectable sometime during the next decade. Currently, PTAs assume an equal probability of detection from every sky position, but as evidence grows for a non-isotropic distribution of sources, is there a most likely sky position for a detectable single source of GWs? In this paper, a collection of galactic catalogs is used to calculate various metrics related to the detectability of a single GW source resolv- able above a GW background, assuming that every galaxy has the same probability of containing a SMBHB. Our analyses of these data reveal small probabilities that one of these sources is currently in the PTA band, but as sensitivity is improved regions of consistent probability density are found in predictable locations, specifically around local galaxy clusters.Comment: 9 pages, 9 figures, accepted for submission in Ap

Methodological tests of the use of trace elements as tracers to assess root activity

peer-reviewedN.J.H. was funded by the Irish Research Council, co-funded by Marie Curie Actions under FP7. The field experiments A, B and G were supported by the European Community's Seventh Framework Programme (FP7/2007-2013) under the grant agreements FP7-266018 (AnimalChange) and FP7- 244983 (MultiSward). Experiment F was supported by the German Science Foundation (FOR 456).Background and aims There is increasing interest in how resource utilisation in grassland ecosystems is affected by changes in plant diversity and abiotic conditions. Research to date has mainly focussed on aboveground responses and there is limited insight into belowground processes. The aim of this study was to test a number of assumptions for the valid use of the trace elements caesium, lithium, rubidium and strontium as tracers to assess the root activity of several grassland species. Methods We carried out a series of experiments addressing the reliability of soil labelling, injection density, incubation time, application rate and the comparability of different tracers in a multiple tracer method. Results The results indicate that it is possible to achieve a reliable labelling of soil depths. Tracer injection density affected the variability but not the mean level of plant tracer concentrations. Tracer application rates should be based on pilot studies, because of site- and species-specific responses. The trace elements did not meet prerequisites to be used in a multiple tracer method. Conclusions The use of trace elements as tracers is potentially a very useful tool to give insight into plant root activity at different soil depths. This work highlights some of the main benefits and pitfalls of the method and provides specific recommendations to assist the design of tracer experiments and interpretation of the results.N.J.H. was funded by the Irish Research Council, co-funded by Marie Curie Actions under FP7. The field experiments A, B and G were supported by the European Community's Seventh Framework Programme (FP7/2007-2013) under the grant agreements FP7-266018 (AnimalChange) and FP7- 244983 (MultiSward). Experiment F was supported by the German Science Foundation (FOR 456).European Unio

Gravitational Waves from coalescing binaries: Estimation of parameters

The paper presents a statistical model which reproduces the results of Monte Carlo simulations to estimate the parameters of the gravitational wave signal from a coalesing binary system. The model however is quite general and would be useful in other parameter estimation problems.Comment: LaTeX with RevTeX macros, 4 figure

A First Comparison of SLOPE and Other LIGO Burst Event Trigger Generators

A number of different methods have been proposed to identify unanticipated burst sources of gravitational waves in data arising from LIGO and other gravitational wave detectors. When confronted with such a wide variety of methods one is moved to ask if they are all necessary, i.e. given detector data that is assumed to have no gravitational wave signals present, do they generally identify the same events with the same efficiency, or do they each 'see' different things in the detector? Here we consider three different methods, which have been used within the LIGO Scientific Collaboration as part of its search for unanticipated gravitational wave bursts. We find that each of these three different methods developed for identifying candidate gravitational wave burst sources are, in fact, attuned to significantly different features in detector data, suggesting that they may provide largely independent lists of candidate gravitational wave burst events.Comment: 10 Pages, 5 Figures, Presented at the 10th Gravitational Wave Data Analysis Workshop (GWDAW-10), 14-17 December 2005 at the University of Texas, Brownsvill

Templates for stellar mass black holes falling into supermassive black holes

The spin modulated gravitational wave signals, which we shall call smirches, emitted by stellar mass black holes tumbling and inspiralling into massive black holes have extremely complicated shapes. Tracking these signals with the aid of pattern matching techniques, such as Wiener filtering, is likely to be computationally an impossible exercise. In this article we propose using a mixture of optimal and non-optimal methods to create a search hierarchy to ease the computational burden. Furthermore, by employing the method of principal components (also known as singular value decomposition) we explicitly demonstrate that the effective dimensionality of the search parameter space of smirches is likely to be just three or four, much smaller than what has hitherto been thought to be about nine or ten. This result, based on a limited study of the parameter space, should be confirmed by a more exhaustive study over the parameter space as well as Monte-Carlo simulations to test the predictions made in this paper.Comment: 12 pages, 4 Tables, 4th LISA symposium, submitted to CQ

Orbital evolution of a test particle around a black hole: higher-order corrections

We study the orbital evolution of a radiation-damped binary in the extreme mass ratio limit, and the resulting waveforms, to one order beyond what can be obtained using the conservation laws approach. The equations of motion are solved perturbatively in the mass ratio (or the corresponding parameter in the scalar field toy model), using the self force, for quasi-circular orbits around a Schwarzschild black hole. This approach is applied for the scalar model. Higher-order corrections yield a phase shift which, if included, may make gravitational-wave astronomy potentially highly accurate.Comment: 4 pages, 3 Encapsulated PostScript figure

Crustal Oscillations of Slowly Rotating Relativistic Stars

We study low-amplitude crustal oscillations of slowly rotating relativistic stars consisting of a central fluid core and an outer thin solid crust. We estimate the effect of rotation on the torsional toroidal modes and on the interfacial and shear spheroidal modes. The results compared against the Newtonian ones for wide range of neutron star models and equations of state.Comment: 15 page