Mock LISA Data Challenge Research Articles

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.

Prospects for Detecting Exoplanets around Double White Dwarfs with LISA and Taiji

Abstract Recently, Tamanini & Danielski discussed the possibility of detecting circumbinary exoplanets (CBPs) orbiting double white dwarfs (DWDs) with the Laser Interferometer Space Antenna (LISA). Extending their methods and criteria, we discuss the prospects for detecting exoplanets around DWDs not only by LISA, but also by Taiji, a Chinese space-borne gravitational-wave (GW) mission that has slightly better sensitivity at low frequencies. We first explore how different binary masses and mass ratios affect the abilities of LISA and Taiji to detect CBPs. Second, for certain known detached DWDs with high signal-to-noise ratios, we quantify the possibility of CBP detections around them. Third, based on the DWD population obtained from the Mock LISA Data Challenge, we present basic assessments of the CBP detections in our Galaxy during a 4 yr mission time for LISA and Taiji. We discuss the constraints on the detectable zone of each system, as well as the distributions of the inner/outer edge of the detectable zone. With the DWD population, we further inject two different planet distributions with an occurrence rate of 50% and constrain the total detection rates. We briefly discuss the prospects for detecting habitable CBPs around DWDs with a simplified model. These results can provide helpful inputs for upcoming exoplanetary projects and help analyze planetary systems after the common envelope phase.

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%.

Detection pipeline for Galactic binaries in LISA data

The Galaxy is suspected to contain hundreds of millions of binary white dwarf systems, a large fraction of which will have sufficiently small orbital periods to emit gravitational radiation in band for space-based gravitational wave detectors such as the Laser Interferometer Space Antenna (LISA). LISA's main science goal is the detection of cosmological events (supermassive black hole mergers, etc.) however the gravitational signal from the galaxy will be the dominant contribution to the data---including instrumental noise---over approximately two decades in frequency. The catalog of detectable binary systems will serve as an unparalleled means of studying the Galaxy. Furthermore, to maximize the scientific return from the mission, the data must be cleansed of the galactic foreground. We will present an algorithm that can accurately resolve and subtract $\ensuremath{\gtrsim}10\text{ }000$ of these sources from simulated data supplied by the Mock LISA Data Challenge Task Force. Using the time evolution of the gravitational wave frequency, we will reconstruct the position of the recovered binaries and show how LISA will sample the entire compact binary population in the Galaxy.

Detecting Double Degenerate Progenitors of SNe Ia with LISA

AbstractThe Galactic population of close white dwarf binaries is expected to provide the largest number of gravitational wave sources for low frequency detectors such as the Laser Interferometer Space Antenna (LISA). Current data analysis techniques have demonstrated the capability of resolving on the order of 104 white dwarf binaries from a 2 year observation. Resolved binaries are either at high frequencies or large amplitudes. Such systems are more likely to be high-mass binaries, a subset of which will be progenitors of SNe Ia in the double degenerate scenario. We report on results of a study of the properties of resolved binaries using a population synthesis model of the Galactic white dwarf binaries and a LISA data analysis algorithm using Mock LISA Data Challenge tools.

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.

Discriminating between a stochastic gravitational wave background and instrument noise

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 $\Omega_{\rm gw} = 6 \times 10^{-13}$ 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.

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.

Classifying LISA gravitational wave burst signals using Bayesian evidence

We consider the problem of characterization of burst sources detected by 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 characterize 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.

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.

The search for black hole binaries using a genetic algorithm

In this work, we use a genetic algorithm to search for the gravitational wave signal from the inspiralling massive black hole binaries in the simulated Laser Interferometer Space Antenna (LISA) data. We consider a single signal in the Gaussian instrumental noise. This is a first step in preparation for analysis of the third round of the mock LISA data challenge. We have extended a genetic algorithm utilizing the properties of the signal and the detector response function. The performance of this method is comparable, if not better, to already existing algorithms.

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.