Jeff Crowder

Beyond LISA: Exploring future gravitational wave missions

The Advanced Laser Interferometer Antenna (ALIA) and the Big Bang Observer (BBO) have been proposed as follow on missions to the Laser Interferometer Space Antenna (LISA). Here we study the capabilities of these observatories, and how they relate to the science goals of the missions. We find that the Advanced Laser Interferometer Antenna in Stereo (ALIAS), our proposed extension to the ALIA mission, will go considerably further toward meeting ALIAs main scientific goal of studying intermediate mass black holes. We also compare the capabilities of LISA to a related extension of the LISA mission, the Laser Interferometer Space Antenna in Stereo (LISAS). Additionally, we find that the initial deployment phase of the BBO would be sufficient to address the BBOs key scientific goal of detecting the Gravitational Wave Background, while still providing detailed information about foreground sources.

LISA data analysis using Markov chain Monte Carlo methods

The Laser Interferometer Space Antenna (LISA) is expected to simultaneously detect many thousands of low frequency gravitational wave signals. This presents a data analysis challenge that is very different to the one encountered in ground based gravitational wave astronomy. LISA data analysis requires the identification of individual signals from a data stream containing an unknown number of overlapping signals. Because of the signal overlaps, a global fit to all the signals has to be performed in order to avoid biasing the solution. However, performing such a global fit requires the exploration of an enormous parameter space with a dimension upwards of 50,000. Markov Chain Monte Carlo (MCMC) methods offer a very promising solution to the LISA data analysis problem. MCMC algorithms are able to efficiently explore large parameter spaces, simultaneously providing parameter estimates, error analyses and even model selection. Here we present the first application of MCMC methods to simulated LISA data and demonstrate the great potential of the MCMC approach. Our implementation uses a generalized F-statistic to evaluate the likelihoods, and simulated annealing to speed convergence of the Markov chains. As a final step we super-cool the chains to extract maximum likelihood estimates, and estimates of the Bayes factors for competing models. We find that the MCMC approach is able to correctly identify the number of signals present, extract the source parameters, and return error estimates consistent with Fisher information matrix predictions.

The Mock LISA Data Challenges: from Challenge 1B to Challenge 3

The Mock LISA Data Challenges are a programme to demonstrate and encourage the development of LISA data-analysis capabilities, tools and techniques. At the time of this workshop, three rounds of challenges had been completed, and the next was about to start. In this paper we provide a critical analysis of the entries to the latest completed round, Challenge 1B. The entries confirm the consolidation of a range of data-analysis techniques for galactic and massive-black-hole binaries, and they include the first convincing examples of detection and parameter estimation of extreme-mass-ratio inspiral sources. In this paper we also introduce the next round, Challenge 3. Its data sets feature more realistic waveform models (e.g., galactic binaries may now chirp, and massive-black-hole binaries may precess due to spin interactions), as well as new source classes (bursts from cosmic strings, isotropic stochastic backgrounds) and more complicated nonsymmetric instrument noise.

LISA data analysis using genetic algorithms

This work presents the first application of the method of genetic algorithms (GAs) to data analysis for the Laser Interferometer Space Antenna (LISA). In the low frequency regime of the LISA band there are expected to be tens of thousands of galactic binary systems that will be emitting gravitational waves detectable by LISA. The challenge of parameter extraction of such a large number of sources in the LISA data stream requires a search method that can efficiently explore the large parameter spaces involved. As signals of many of these sources will overlap, a global search method is desired. GAs represent such a global search method for parameter extraction of multiple overlapping sources in the LISA data stream. We find that GAs are able to correctly extract source parameters for overlapping sources. Several optimizations of a basic GA are presented with results derived from applications of the GA searches to simulated LISA data.

Report on the second Mock LISA data challenge

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 several data sets containing simulated instrument noise and gravitational waves from sources of undisclosed parameters. Participants are asked to analyze the data sets and report the maximum information about the source parameters. The challenges are being released in rounds of increasing complexity and realism: here we present the results of Challenge 2, issued in Jan 2007, which successfully demonstrated the recovery of signals from nonspinning supermassive-black-hole binaries with optimal SNRs between ~10 and 2000, from ~20 000 overlapping galactic white-dwarf binaries (among a realistically distributed population of 26 million), and from the extreme-mass-ratio inspirals of compact objects into central galactic black holes with optimal SNRs ~100.

Sensitivity and parameter-estimation precision for alternate LISA configurations

We describe a simple framework to assess the LISA scientific performance (more specifically, its sensitivity and expected parameter-estimation precision for prescribed gravitational-wave signals) under the assumption of failure of one or two inter-spacecraft laser measurements (links) and of one to four intra-spacecraft laser measurements. We apply the framework to the simple case of measuring the LISA sensitivity to monochromatic circular binaries, and the LISA parameter-estimation precision for the gravitational-wave polarization angle of these systems. Compared to the six-link baseline configuration, the five-link case is characterized by a small loss in signal-to-noise ratio (SNR) in the high-frequency section of the LISA band; the four-link case shows a reduction by a factor of sqrt{2} at low frequencies, and by up to ~2 at high frequencies. The uncertainty in the estimate of polarization, as computed in the Fisher-matrix formalism, also worsens when moving from six to five, and then to four links: this can be explained by the reduced SNR available in those configurations (except for observations shorter than three months, where five and six links do better than four even with the same SNR). In addition, we prove (for generic signals) that the SNR and Fisher matrix are invariant with respect to the choice of a basis of TDI observables; rather, they depend only on which inter-spacecraft and intra-spacecraft measurements are available.

Report on the first round of the Mock LISA Data Challenges

The Mock LISA Data Challenges (MLDCs) have the dual purpose of fostering the development of LISA data analysis tools and capabilities, and demonstrating the technical readiness already achieved by the gravitational-wave community in distilling a rich science payoff from the LISA data output. The first round of MLDCs has just been completed: nine challenges consisting of data sets containing simulated gravitational-wave signals produced either by galactic binaries or massive black hole binaries embedded in simulated LISA instrumental noise were released in June 2006 with deadline for submission of results at the beginning of December 2006. Ten groups have participated in this first round of challenges. All of the challenges had at least one entry which successfully characterized the signal to better than 95% when assessed via a correlation with phasing ambiguities accounted for. Here, we describe the challenges, summarize the results and provide a first critical assessment of the entries.

Extracting galactic binary signals from the first round of Mock LISA Data Challenges

We report on the performance of an end-to-end Bayesian analysis pipeline for detecting and characterizing galactic binary signals in simulated LISA data. Our principal analysis tool is the blocked-annealed Metropolis–Hasting (BAM) algorithm, which has been optimized to search for tens of thousands of overlapping signals across the LISA band. The BAM algorithm employs Bayesian model selection to determine the number of resolvable sources, and provides posterior density functions for all the model parameters. The BAM algorithm performed almost flawlessly on all the round 1 Mock LISA Data Challenge data sets, including those with many highly overlapping sources. Some misses were later traced to a particular flaw in the coding that affected high frequency sources. In addition to the BAM algorithm we also successfully tested a genetic algorithm (GA), but only on data sets with isolated signals as the GA has yet to be optimized to handle large numbers of overlapping signals.

A three-stage search for supermassive black-hole binaries in LISA data

Gravitational waves from the inspiral and coalescence of supermassive black-hole (SMBH) binaries with masses m1 ~ m2 ~ 10^6Modot are likely to be among the strongest sources for the Laser Interferometer Space Antenna (LISA). We describe a three-stage data-analysis pipeline designed to search for and measure the parameters of SMBH binaries in LISA data. The first stage uses a time–frequency track-search method to search for inspiral signals and provide a coarse estimate of the black-hole masses m1, m2 and the coalescence time of the binary tc. The second stage uses a sequence of matched-filter template banks, seeded by the first stage, to improve the measurement accuracy of the masses and coalescence time. Finally, a Markov chain Monte Carlo search is used to estimate all nine physical parameters of the binary (masses, coalescence time, distance, initial phase, sky position and orientation). Using results from the second stage substantially shortens the Markov chain burn-in time and allows us to determine the number of SMBH-binary signals in the data before starting parameter estimation. We demonstrate our analysis pipeline using simulated data from the first Mock LISA Data Challenge. We discuss our plan for improving this pipeline and the challenges that will be faced in real LISA data analysis.

LISA source confusion

The Laser Interferometer Space Antenna will detect thousands of gravitational wave sources. Many of these sources will be overlapping in the sense that their signals will have a nonzero cross correlation. Such overlaps lead to source confusion, which adversely affects how well we can extract information about the individual sources. Here we study how source confusion impacts parameter estimation for galactic compact binaries, with emphasis on the effects of the number of overlaping sources, the time of observation, the gravitational wave frequencies of the sources, and the degree of the signal correlations. Our main findings are that the parameter resolution decays exponentially with the number of overlapping sources and superexponentially with the degree of cross correlation. We also find that an extended mission lifetime is key to disentangling the source confusion as the parameter resolution for overlapping sources improves much faster than the usual square root of the observation time.