Stationary structure of relativistic superfluid neutron stars

We describe recent progress in the numerical study of the structure of rapidly rotating superfluid neutron star models in full general relativity. The superfluid neutron star is described by a model of two interpenetrating and interacting fluids, one representing the superfluid neutrons and the second consisting of the remaining charged particles (protons, electrons, muons). We consider general stationary configurations where the two fluids can have different rotation rates around a common rotation axis. The previously discovered existence of configurations with one fluid in a prolate shape is confirmed.Comment: 5 pages, 2 figures. Conference proceedings for the 26th Spanish Relativity Meeting (ERE 2002), Menorca, Spain, 22-24 Sept. 200

Searching for Galactic White Dwarf Binaries in Mock LISA Data using an F-Statistic Template Bank

We describe an F-statistic search for continuous gravitational waves from galactic white-dwarf binaries in simulated LISA Data. Our search method employs a hierarchical template-grid based exploration of the parameter space. In the first stage, candidate sources are identified in searches using different simulated laser signal combinations (known as TDI variables). Since each source generates a primary maximum near its true "Doppler parameters" (intrinsic frequency and sky position) as well as numerous secondary maxima of the F-statistic in Doppler parameter space, a search for multiple sources needs to distinguish between true signals and secondary maxima associated with other, "louder" signals. Our method does this by applying a coincidence test to reject candidates which are not found at nearby parameter space positions in searches using each of the three TDI variables. For signals surviving the coincidence test, we perform a fully coherent search over a refined parameter grid to provide an accurate parameter estimation for the final candidates. Suitably tuned, the pipeline is able to extract 1989 true signals with only 5 false alarms. The use of the rigid adiabatic approximation allows recovery of signal parameters with errors comparable to statistical expectations, although there is still some systematic excess with respect to statistical errors expected from Gaussian noise. An experimental iterative pipeline with seven rounds of signal subtraction and re-analysis of the residuals allows us to increase the number of signals recovered to a total of 3419 with 29 false alarms.Comment: 29 pages, 11 figures; submitted to Classical and Quantum Gravit

New Coordinates for the Amplitude Parameter Space of Continuous Gravitational Waves

The parameter space for continuous gravitational waves (GWs) can be divided into amplitude parameters (signal amplitude, inclination and polarization angles describing the orientation of the source, and an initial phase) and phase-evolution parameters. The division is useful in part because the Jaranowski-Krolak-Schutz (JKS) coordinates on the four-dimensional amplitude parameter space allow the GW signal to be written as a linear combination of four template waveforms with the JKS coordinates as coefficients. We define a new set of coordinates on the amplitude parameter space, with the same properties, which is more closely connected to the physical amplitude parameters. These naturally divide into two pairs of Cartesian-like coordinates on two-dimensional subspaces, one corresponding to left- and the other to right-circular polarization. We thus refer to these as CPF (circular polarization factored) coordinates. The corresponding two sets of polar coordinates (known as CPF-polar) can be related in a simple way to the physical parameters. We illustrate some simplifying applications for these various coordinate systems, such as: a calculation of Jacobians between various coordinate systems; an illustration of the signal coordinate singularities associated with left- and right-circular polarization, which correspond to the origins of the two two-dimensional subspaces; and an elucidation of the form of the log-likelihood ratio between hypotheses of Gaussian noise with and without a continuous GW signal. These are used to illustrate some of the prospects for approximate evaluation of a Bayesian detection statistic defined by marginalization over the physical parameter space. Additionally, in the presence of simplifying assumptions about the observing geometry, we are able to explicitly evaluate the integral for the Bayesian detection statistic, and compare it to the approximate results.Comment: REVTeX, 18 pages, 8 image files included in 7 figure

F-statistic search for white-dwarf binaries in the first Mock LISA Data Challenge

The F-statistic is an optimal detection statistic for continuous gravitational waves, i.e. long-duration (quasi-)monochromatic signals with slowlyvarying intrinsic frequency. This method was originally developed in the context of ground-based detectors, but it is equally applicable to LISA where many signals fall into this class of signals. We report on the application of a LIGO/GEO Fstatistic code to LISA data-analysis using the long-wavelength limit (LWL), and we present results of our search for white-dwarf binary signals in the ¯rst Mock LISA Data Challenge. Somewhat surprisingly, the LWL is found to be su±cient { even at high frequencies { for detection of signals and their accurate localization on the sky and in frequency, while a more accurate modelling of the TDI response only seems necessary to correctly estimate the four amplitude parameters

Random template banks and relaxed lattice coverings

Template-based searches for gravitational waves are often limited by the computational cost associated with searching large parameter spaces. The study of efficient template banks, in the sense of using the smallest number of templates, is therefore of great practical interest. The "traditional" approach to template-bank construction requires every point in parameter space to be covered by at least one template, which rapidly becomes inefficient at higher dimensions. Here we study an alternative approach, where any point in parameter space is covered only with a given probability < 1. We find that by giving up complete coverage in this way, large reductions in the number of templates are possible, especially at higher dimensions. The prime examples studied here are "random template banks", in which templates are placed randomly with uniform probability over the parameter space. In addition to its obvious simplicity, this method turns out to be surprisingly efficient. We analyze the statistical properties of such random template banks, and compare their efficiency to traditional lattice coverings. We further study "relaxed" lattice coverings (using Zn and An* lattices), which similarly cover any signal location only with probability < 1. The relaxed An* lattice is found to yield the most efficient template banks at low dimensions (n < 10), while random template banks increasingly outperform any other method at higher dimensions.Comment: 13 pages, 10 figures, submitted to PR

Targeted search for continuous gravitational waves: Bayesian versus maximum-likelihood statistics

We investigate the Bayesian framework for detection of continuous gravitational waves (GWs) in the context of targeted searches, where the phase evolution of the GW signal is assumed to be known, while the four amplitude parameters are unknown. We show that the orthodox maximum-likelihood statistic (known as F-statistic) can be rediscovered as a Bayes factor with an unphysical prior in amplitude parameter space. We introduce an alternative detection statistic ("B-statistic") using the Bayes factor with a more natural amplitude prior, namely an isotropic probability distribution for the orientation of GW sources. Monte-Carlo simulations of targeted searches show that the resulting Bayesian B-statistic is more powerful in the Neyman-Pearson sense (i.e. has a higher expected detection probability at equal false-alarm probability) than the frequentist F-statistic.Comment: 12 pages, presented at GWDAW13, to appear in CQ

Building a stochastic template bank for detecting massive black hole binaries

Coalescence of two massive black holes is the strongest and most promising source for LISA. In fact, gravitational signal from the end of inspiral and merger will be detectable throughout the Universe. In this article we describe the first step in the two-step hierarchical search for gravitational wave signal from the inspiraling massive BH binaries. It is based on the routinely used in the ground base gravitational wave astronomy method of filtering the data through the bank of templates. However we use a novel Monte-Carlo based (stochastic) method to lay a grid in the parameter space, and we use the likelihood maximized analytically over some parameters, known as F-statistic, as a detection statistic. We build a coarse template bank to detect gravitational wave signals and to make preliminary parameter estimation. The best candidates will be followed up using Metropolis-Hasting stochastic search to refine the parameter estimation. We demonstrate the performance of the method by applying it to the Mock LISA data challenge 1B (training data set).Comment: revtex4, 8 figure

Template-based searches for gravitational waves: efficient lattice covering of flat parameter spaces

The construction of optimal template banks for matched-filtering searches is an example of the sphere covering problem. For parameter spaces with constant-coefficient metrics a (near-) optimal template bank is achieved by the A_n* lattice, which is the best lattice-covering in dimensions n <= 5, and is close to the best covering known for dimensions n <= 16. Generally this provides a substantially more efficient covering than the simpler hyper-cubic lattice. We present an algorithm for generating lattice template banks for constant-coefficient metrics and we illustrate its implementation by generating A_n* template banks in n=2,3,4 dimensions.Comment: 10 pages, submitted to CQG for proceedings of GWDAW1