Mock LISA Data Research Articles

GPU-accelerated semicoherent hierarchical search for stellar-mass binary inspiral signals in LISA

Searching for gravitational waves from stellar-mass binary black holes with LISA remains a challenging open problem. Conventional template-bank approaches to the search are impossible due to the prohibitive number of templates that would be required. This paper continues the development of a hierarchical semicoherent stochastic search, extending it to a full end-to-end pipeline that is then applied to multiple mock LISA data streams which include simulated noise. Particle swarm optimization is used as a stochastic search algorithm, tracking multiple maxima of a semicoherent search statistic defined over source parameter space. The pipeline is accelerated by the use of graphical processing units (GPUs). No prior information from observations by ground-based detectors is used; this is necessary in order to provide advance warning of the merger. We find that the pipeline is able to detect sources with signal-to-noise ratios as low as ρ∼17, we demonstrate that these searches can directly seed coarse parameter estimation in cases where the search trigger is loud. An example of how the false-alarm probability can be estimated for this type of GW search is also included. Published by the American Physical Society 2024

Signal identification of the stochastic gravitational wave background in the Mock LISA Data Challenge

Signal identification of the stochastic gravitational wave background in the Mock LISA Data Challenge

Search for Extreme Mass Ratio Inspirals Using Particle Swarm Optimization and Reduced Dimensionality Likelihoods

Extreme-mass-ratio inspirals (EMRIs) are significant observational targets for spaceborne gravitational wave detectors, namely, LISA, Taiji, and Tianqin, which involve the inspiral of stellar-mass compact objects into massive black holes (MBHs) with a mass range of approximately 104∼107M⊙. EMRIs are estimated to produce long-lived gravitational wave signals with more than 105 cycles before plunge, making them an ideal laboratory for exploring the strong-gravity properties of the spacetimes around the MBHs, stellar dynamics in galactic nuclei, and properties of the MBHs itself. However, the complexity of the waveform model, which involves the superposition of multiple harmonics, as well as the high-dimensional and large-volume parameter space, make the fully coherent search challenging. In our previous work, we proposed a 10-dimensional search using Particle Swarm Optimization (PSO) with local maximization over the three initial angles. In this study, we extend the search to an 8-dimensional PSO with local maximization over both the three initial angles and the angles of spin direction of the MBH, where the latter contribute a time-independent amplitude to the waveforms. Additionally, we propose a 7-dimensional PSO search by using a fiducial value for the initial orbital frequency and shifting the corresponding 8-dimensional Time Delay Interferometry responses until a certain lag returns the corresponding 8-dimensional log-likelihood ratio’s maximum. The reduced dimensionality likelihoods enable us to successfully search for EMRI signals with a duration of 0.5 years and signal-to-noise ratio of 50 within a wider search range than our previous study. However, the ranges used by both the LISA Data Challenge (LDC) and Mock LISA Data Challenge (MLDC) to generate their simulated signals are still wider than the those we currently employ in our direct searches. Consequently, we discuss further developments, such as using a hierarchical search to narrow down the search ranges of certain parameters and applying Graphics Processing Units to speed up the code. These advances aim to improve the efficiency, accuracy, and generality of the EMRI search algorithm.

Augmented kludge waveforms for detecting extreme-mass-ratio inspirals

The extreme-mass-ratio inspirals (EMRIs) of stellar-mass compact objects into massive black holes are an important class of source for the future space-based gravitational-wave detector LISA. Detecting signals from EMRIs will require waveform models that are both accurate and computationally efficient. In this paper, we present the latest implementation of an augmented analytic kludge (AAK) model, publicly available at github.com/alvincjk/EMRI_Kludge_Suite as part of an EMRI waveform software suite. This version of the AAK model has improved accuracy compared to its predecessors, with two-month waveform overlaps against a more accurate fiducial model exceeding 0.97 for a generic range of sources; it also generates waveforms 5-15 times faster than the fiducial model. The AAK model is well suited for scoping out data analysis issues in the upcoming round of mock LISA data challenges. A simple analytic argument shows that it might even be viable for detecting EMRIs with LISA through a semi-coherent template bank method, while the use of the original analytic kludge in the same approach will result in around 90% fewer detections.

Bayesian inference on EMRI signals using low frequency approximations

Extreme mass ratio inspirals (EMRIs) are thought to be one of the most exciting gravitational wave sources to be detected with LISA. Due to their complicated nature and weak amplitudes the detection and parameter estimation of such sources is a challenging task. In this paper we present a statistical methodology based on Bayesian inference in which the estimation of parameters is carried out by advanced Markov chain Monte Carlo (MCMC) algorithms such as parallel tempering MCMC. We analysed high and medium mass EMRI systems that fall well inside the low frequency range of LISA. In the context of the Mock LISA Data Challenges, our investigation and results are also the first instance in which a fully Markovian algorithm is applied for EMRI searches. Results show that our algorithm worked well in recovering EMRI signals from different (simulated) LISA data sets having single and multiple EMRI sources and holds great promise for posterior computation under more realistic conditions. The search and estimation methods presented in this paper are general in their nature, and can be applied in any other scenario such as AdLIGO, AdVIRGO and Einstein Telescope with their respective response functions.

Tackling gravity wave confusion noise with template optimizers

The Mock LISA Data Challenge 4.0 simulated the joint two-year recording of gravitational wave signals from mergers of spinning black holes, extreme mass ratio inspirals, Galactic white dwarf binaries, bursts from cosmic strings, and a stochastic background—all over LISA instrument noise. We analysed this data using a global multi-start box and bound optimization scheme, incorporating multi-dimensional Nelder Mead simplex 2 optimization. Our scheme identified 2658 binaries. Of these, 2246 were found to systematically decompose the power in a strong spinning black hole merger into a "white dwarf binary transform". The remaining 416 binaries were identified with a false alarm rate of ~ 23%.

Searches for cosmic-string gravitational-wave bursts in Mock LISA Data

A network of observable, macroscopic cosmic (super-)strings may well 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 gravitational-wave interferometers, such as the ground-based LIGO/Virgo detectors and the planned, space-based LISA detector. 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, and ψ, and use the FFT to search quickly over burst arrival times tC. 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 and ψ. We calculate how accurately LISA can expect to measure the physical parameters of string-burst sources, and compare to results based on the Fisher-matrix approximation. To understand LISA's angular resolution for string-burst sources, we draw maps of the waveform fitting factor (maximized over )) as a function of the sky position; these maps dramatically illustrate why (for LISA) inferring the correct sky location of the emitting string loop will often be practically impossible. In addition, we identify and elucidate several symmetries that are imbedded in this search problem, and we derive the distribution of cut-off frequencies fmax for observable bursts.

Search for spinning black hole binaries in mock LISA data using a genetic algorithm

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 nonspinning 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 (MLDC3.2). The performance of this method is comparable, if not better, to already existing algorithms. We have found all five sources present in MLDC3.2 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.

Nested sampling as a tool for LISA data analysis

Nested sampling is a technique for efficiently computing the probability of a data set under a particular hypothesis, also called the Bayesian Evidence or Marginal Likelihood, and for evaluating the posterior. MULTINEST is a multi-modal nested sampling algorithm which has been designed to efficiently explore and characterize posterior probability surfaces containing multiple secondary solutions. We have applied the MULTINEST algorithm to a number of problems in gravitational wave data analysis. In this article, we describe the algorithm and present results for several applications of the algorithm to analysis of mock LISA data. We summarise recently published results for a test case in which we searched for two non-spinning black hole binary merger signals in simulated LISA data. We also describe results obtained with MULTINEST in the most recent round of the Mock LISA Data Challenge (MLDC), in which the algorithm was used to search for and characterise both spinning supermassive black hole binary inspirals and bursts from cosmic string cusps. In all these applications, the algorithm found the correct number of signals and efficiently recovered the posterior probability distribution. Moreover, in most cases the waveform corresponding to the best a-posteriori parameters had an overlap in excess of 99% with the true signal.

The Mock LISA Data Challenges: from challenge 3 to challenge 4

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 April 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 Ωgw(f) ∼ 10−11, slightly below the LISA instrument noise.

Mock LISA data challenge for the Galactic white dwarf binaries

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.

Detecting white dwarf binaries in Mock LISA Data Challenge 3

We present a strategy for detecting gravitational wave signals from the Galactic white dwarf binaries in the Mock LISA Data Challenge 3 (MLDC3) and estimate their parameters. Our method is based on the matched filtering in the form of the -statistic. We perform the search on three-dimensional space (sky coordinate and frequency of gravitational wave) below 3 mHz and include the fourth parameter (frequency derivative) at high frequencies. A template bank is used to search for the strongest signal in the data, then we remove it and repeat the search until we do not have signals in the data above a preselected threshold. For the template bank, we construct an optimal grid that realizes the best lattice covering with a constraint such that the nodes of the grid coincide with the Fourier frequencies. This enables the use of the fast Fourier transform algorithm to calculate the -statistic.

An algorithm for the detection of extreme mass ratio inspirals in LISA data

The gravitational wave signal from a compact object inspiralling into a massive black hole (MBH) is considered 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 that ∼1035 templates would be required to carry out a fully coherent search using 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.

A LISA data-analysis primer

This paper is an introduction for the nonpractitioner to the ideas and issues of LISA data analysis, as reflected in the explorations and experiments of the participants in the Mock LISA Data Challenges. In particular, I discuss the methods and codes that have been developed for the detection and parameter estimation of supermassive black-hole binaries, extreme mass-ratio inspirals and galactic binaries.

Grids for efficient all sky search of white dwarf binaries in mock LISA data challenge

We present construction of the 3 and 4 dimensional grids in the parameter space for all sky-search of gravitational wave signals from white dwarf binaries with LISA data. The 3 dimensional grid is for search of frequency and the sky position of the source and the 4 dimensional grid includes the spin down parameter. The grid solves the covering problem in the parameter space with the constraint that nodes of the grid coincide with Fourier frequencies (multiples of the inverse of the observation time).This allows the use of the fast Fourier transform (FFT) in the evaluation of the optimal statistic and greatly speeds up the search.

Building a stochastic template bank for detecting massive black hole binaries

The coalescence of pairs of massive black holes are the strongest and most promising sources for LISA. In fact, the gravitational wave signal from the final inspiral and merger will be detectable throughout the universe. In this paper we describe the first step in a two-step hierarchical search for the gravitational wave signal from inspiraling massive BH binaries. It is based on a method routinely used in ground-based gravitational wave astronomy, namely filtering the data through a bank of templates. However we use a novel, Monte Carlo based (stochastic), method for laying a grid in the parameter space, and we use the likelihood maximized analytically over some parameters, known as the -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 a Metropolis–Hasting stochastic search to refine the parameter estimates. We demonstrate the performance of the method by applying it to the Mock LISA data challenge 1B (training data set).

Improved search for galactic white-dwarf binaries in Mock LISA Data Challenge 1B using an -statistic template bank

We report on our -statistic search for white-dwarf binary signals in the Mock LISA Data Challenge 1B (MLDC1B). We focus in particular on the improvements in our search pipeline since MLDC1, namely refinements in the search pipeline and the use of a more accurate detector response (rigid adiabatic approximation). 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.

A hierarchical search for gravitational waves from supermassive black hole binary mergers

We present a method to search for gravitational waves from coalescing supermassive binary black holes in LISA data. The search utilizes the -statistic to maximize over, and determine the values of, the extrinsic parameters of the binary system. The intrinsic parameters are searched over hierarchically using stochastically generated multi-dimensional template banks to recover the masses, sky location and coalescence time of the binary. We present the results of this method applied to the Mock LISA Data Challenge 1B data set.

A constrained Metropolis–Hastings search for EMRIs in the Mock LISA Data Challenge 1B

We describe a search for the extreme-mass-ratio inspiral sources in the Round 1B Mock LISA Data Challenge data sets. The search algorithm is a Monte Carlo search based on the Metropolis–Hastings algorithm, but also incorporates simulated, thermostated and time annealing, plus a harmonic identification stage designed to reduce the chance of the chain locking onto secondary maxima. In this paper, we focus on describing the algorithm that we have been developing. We give the results of the search of the Round 1B data, although parameter recovery has improved since that deadline. Finally, we describe several modifications to the search pipeline that we are currently investigating for incorporation in future searches.

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.