by Cohen, Michael I. and Cutler, Curt and Vallisneri, Michele
Submitted to CQG; 28 pages, 10 figures; higher-resolution plots available at http://www.vallis.org/publications/cosmicstrings

A network of observable, macroscopic cosmic (super-)strings may have formed in the early universe. If so, the cusps that generically develop on cosmic-string loops emit bursts of gravitational radiation that could be detectable by both ground- and space-based gravitational-wave interferometers. Here we report on two versions of a LISA-oriented string-burst search pipeline that we have developed and tested within the context of the Mock LISA Data Challenges. The two versions rely on the publicly available MultiNest and PyMC software packages, respectively. To reduce the effective dimensionality of the search space, our implementations use the F-statistic to analytically maximize over the signal’s amplitude and polarization, A and psi, and use the FFT to search quickly over burst arrival times t_C. The standard F-statistic is essentially a frequentist statistic that maximizes the likelihood; we also demonstrate an approximate, Bayesian version of the F-statistic that incorporates realistic priors on A and psi. We calculate how accurately LISA can expect to measure the physical parameters of string-burst sources. To understand LISA’s angular resolution for string-burst sources, we draw maps of the waveform fitting factor [maximized over (A psi, t_C)] as a function of sky position; these maps dramatically illustrate why (for LISA) inferring the correct sky location of the emitting string loop will often be practically impossible. We also identify and elucidate several symmetries that are imbedded in this search problem, and we derive the distribution of cut-off frequencies f_max for observable bursts.

by Manca, Gian Mario and Vallisneri, Michele
RevTeX4, 21 pages, 9 PDF figures

The efficient placement of signal templates in source-parameter space is a crucial requisite for exhaustive matched-filtering searches of modeled gravitational-wave sources. Unfortunately, the current placement algorithms based on regular parameter-space meshes are difficult to generalize beyond simple signal models with few parameters. Various authors have suggested that a general, flexible, yet efficient alternative can be found in randomized placement strategies such as random placement and stochastic placement, which enhances random placement by selectively rejecting templates that are too close to others. In this article we explore several theoretical and practical issues in randomized placement: the size and performance of the resulting template banks; the effects of parameter-space boundaries; the use of quasi-random (self avoiding) number sequences; most important, the implementation of these algorithms in curved signal manifolds with and without the use of a Riemannian signal metric, which may be difficult to obtain. Specifically, we show how the metric can be replaced with a discrete triangulation-based representation of local geometry. We argue that the broad class of randomized placement algorithms offers a promising answer to many search problems, but that the specific choice of a scheme and its implementation details will still need to be fine-tuned separately for each problem.

by Adams, Matthew R. and Cornish, Neil J.
10 Pages, 10 Figures

The detection of a stochastic background of gravitational waves could significantly impact our understanding of the physical processes that shaped the early Universe. The challenge lies in separating the cosmological signal from other stochastic processes such as instrument noise and astrophysical foregrounds. One approach is to build two or more detectors and cross correlate their output, thereby enhancing the common gravitational wave signal relative to the uncorrelated instrument noise. When only one detector is available, as will likely be the case with the Laser Interferometer Space Antenna (LISA), alternative analysis techniques must be developed. Here we show that models of the noise and signal transfer functions can be used to tease apart the gravitational and instrument noise contributions. We discuss the role of gravitational wave insensitive “null channels” formed from particular combinations of the time delay interferometry, and derive a new combination that maintains this insensitivity for unequal arm length detectors. We show that, in the absence of astrophysical foregrounds, LISA could detect signals with energy densities as low as $latex \Omega_{\rm gw} = 6 \times 10^{-13}$ with just one month of data. We describe an end-to-end Bayesian analysis pipeline that is able to search for, characterize and assign confidence levels for the detection of a stochastic gravitational wave background, and demonstrate the effectiveness of this approach using simulated data from the third round of Mock LISA Data Challenges.

by Petiteau, Antoine and Shang, Yu and Babak, Stanislav and Feroz, Farhan
25 pages, 9 figures

Coalescing massive Black Hole binaries are the strongest and probably the most important gravitational wave sources in the LISA band. The spin and orbital precessions bring complexity in the waveform and make the likelihood surface richer in structure as compared to the non-spinning case. We introduce an extended multimodal genetic algorithm which utilizes the properties of the signal and the detector response function to analyze the data from the third round of mock LISA data challenge (MLDC 3.2). The performance of this method is comparable, if not better, to already existing algorithms. We have found all five sources present in MLDC 3.2 and recovered the coalescence time, chirp mass, mass ratio and sky location with reasonable accuracy. As for the orbital angular momentum and two spins of the Black Holes, we have found a large number of widely separated modes in the parameter space with similar maximum likelihood values.

by Babak, Stanislav and Baker, John G. and Benacquista, Matthew J. and Cornish, Neil J. and Larson, Shane L. and Mandel, Ilya and Petiteau, Antoine and Porter, Edward K. and Robinson, Emma L. and Vallisneri, Michele and Vecchio, Alberto and Adams, Matt and Arnaud, Keith A. and Błaut, Arkadiusz and Bridges, Michael and Cohen, Michael and Cutler, Curt and Feroz, Farhan and Gair, Jonathan R. and Graff, Philip and Hobson, Mike and Key, Joey Shapiro and Królak, Andrzej and Lasenby, Anthony and Prix, Reinhard and Shang, Yu and Trias, Miquel and Veitch, John and Whelan, John T.
11 pages, 2 figures, proceedings of the 8th Edoardo Amaldi Conference on Gravitational Waves, New York, June 21-26, 2009

The Mock LISA Data Challenges are a program to demonstrate LISA data-analysis capabilities and to encourage their development. Each round of challenges consists of one or more datasets containing simulated instrument noise and gravitational waves from sources of undisclosed parameters. Participants analyze the datasets and report best-fit solutions for the source parameters. Here we present the results of the third challenge, issued in Apr 2008, which demonstrated the positive recovery of signals from chirping Galactic binaries, from spinning supermassive–black-hole binaries (with optimal SNRs between ~ 10 and 2000), from simultaneous extreme-mass-ratio inspirals (SNRs of 10-50), from cosmic-string-cusp bursts (SNRs of 10-100), and from a relatively loud isotropic background with Omega_gw(f) ~ 10^-11, slightly below the LISA instrument noise.

by Błaut, Arkadiusz and Babak, Stanislav and Królak, Andrzej
36 pages, 13 figures

We present data analysis methods used in detection and the estimation of parameters of gravitational wave signals from the white dwarf binaries in the Mock LISA Data Challenge. Our main focus is on the analysis of Challenge 3.1, where the gravitational wave signals from more than 50 mln. Galactic binaries were added to the simulated Gaussian instrumental noise. Majority of the signals at low frequencies are not resolved individually. The confusion between the signals is strongly reduced at frequencies above 5 mHz. Our basic data analysis procedure is the maximum likelihood detection method. We filter the data through the template bank at the first step of the search, then we refine parameters using the Nelder-Mead algorithm, we remove the strongest signal found and we repeat the procedure. We detect reliably and estimate parameters accurately of more than ten thousand signals from white dwarf binaries.

by Feroz, Farhan and Gair, Jonathan R. and Graff, Philip and Hobson, Michael P and Lasenby, Anthony
21 pages, 11 figures, submitted to CQG

We consider the problem of characterisation of burst sources detected with the Laser Interferometer Space Antenna (LISA) using the multi-modal nested sampling algorithm, MultiNest. We use MultiNest as a tool to search for modelled bursts from cosmic string cusps, and compute the Bayesian evidence associated with the cosmic string model. As an alternative burst model, we consider sine-Gaussian burst signals, and show how the evidence ratio can be used to choose between these two alternatives. We present results from an application of MultiNest to the last round of the Mock LISA Data Challenge, in which we were able to successfully detect and characterise all three of the cosmic string burst sources present in the release data set. We also present results of independent trials and show that MultiNest can detect cosmic string signals with signal-to-noise ratio (SNR) as low as ~7 and sine-Gaussian signals with SNR as low as ~8. In both cases, we show that the threshold at which the sources become detectable coincides with the SNR at which the evidence ratio begins to favour the correct model over the alternative.

by Whelan, John T. and Prix, Reinhard and Khurana, Deepak
26 pages, 11 figures

We describe the application of an F-statistic search for continuous gravitational waves to the search for galactic white-dwarf binaries in the Second Mock LISA Data Challenge. The search method employs a hierarchical template-grid based exploration of the parameter space, using a coincidence step to distinguish between primary (”true”) and secondary maxima, followed by a final (multi-TDI) “zoom” stage to provide an accurate parameter estimation of 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 comparable to statistical expectations, although there is still some systematic excess above expected statistical errors due to Gaussian noise. An experimental iterative pipeline with seven rounds of subtraction and re-analysis allows us to increase the number of signals recovered, up to a total of 3419 with 29 false alarms.

by Stroeer, Alexander and Veitch, John
18 pages, 8 figures, 3 tables, submitted to PRD

The Laser Interferometer Space Antenna (LISA) defines new demands on data analysis efforts in its all-sky gravitational wave survey, recording simultaneously thousands of galactic compact object binary foreground sources and tens to hundreds of background sources like binary black hole mergers and extreme mass ratio inspirals. We approach this problem with an adaptive and fully automatic Reversible Jump Markov Chain Monte Carlo sampler, able to sample from the joint posterior density function (as established by Bayes theorem) for a given mixture of signals “out of the box”, handling the total number of signals as an additional unknown parameter beside the unknown parameters of each individual source and the noise floor. We show in examples from the LISA Mock Data Challenge implementing the full response of LISA in its TDI description that this sampler is able to extract monochromatic Double White Dwarf signals out of colored instrumental noise and additional foreground and background noise successfully in a global fitting approach. We introduce 2 examples with fixed number of signals (MCMC sampling), and 1 example with unknown number of signals (RJ-MCMC), the latter further promoting the idea behind an experimental adaptation of the model indicator proposal densities in the main sampling stage. We note that the experienced runtimes and degeneracies in parameter extraction limit the shown examples to the extraction of a low but realistic number of signals.

by Babak, Stanislav and Gair, Jonathan R. and Porter, Edward K.
14 pages, 4 figures

The gravitational wave signal from a compact object spiralling toward a massive black hole (MBH) is thought to be one of the most difficult sources to detect in the LISA data stream. Due to the large parameter space of possible signals and many orbital cycles spent in the sensitivity band of LISA, it has been estimated previously that of the order of 10^{35} templates would be required for a fully coherent search with a template grid, which is computationally impossible. Here we describe an algorithm based on a constrained Metropolis-Hastings stochastic search which allows us to find and accurately estimate parameters of isolated EMRI signals buried in Gaussian instrumental noise. We illustrate the effectiveness of the algorithm with results from searches of the Mock LISA Data Challenge round 1B data sets.