The planned Laser Interferometer Space Antenna (LISA) is expected to detect gravitational wave signals from ~100 extreme-mass-ratio inspirals (EMRIs) of stellar-mass compact objects into massive black holes. The long duration and large parameter space of EMRI signals makes data analysis for these signals a challenging problem. One approach to EMRI data analysis is to use time-frequency methods. This consists of two steps: (i) searching for tracks from EMRI sources in a time-frequency spectrogram, and (ii) extracting parameter estimates from the tracks. In this paper we discuss the results of applying these techniques to the latest round of the Mock LISA Data Challenge, Round 1B. This analysis included three new techniques not used in previous analyses: (i) a new Chirp-based Algorithm for Track Search for track detection; (ii) estimation of the inclination of the source to the line of sight; (iii) a Metropolis-Hastings Monte Carlo over the parameter space in order to find the best fit to the tracks.
In this paper we describe a Bayesian inference framework for analysis of data obtained by LISA. We set up a model for binary inspiral signals as defined for the Mock LISA Data Challenge 1.2 (MLDC), and implemented a Markov chain Monte Carlo (MCMC) algorithm to facilitate exploration and integration of the posterior distribution over the 9-dimensional parameter space. Here we present intermediate results showing how, using this method, information about the 9 parameters can be extracted from the data.
The LISA International Science Team Working Group on Data Analysis (LIST-WG1B) is sponsoring several rounds of mock data challenges, with the purposeof fostering the development of LISA data analysis capabilities, and of demonstrating technical readiness for the maximum science exploitation of the LISA data. The first round of challenge data sets were released at the Sixth LISA Symposium. We briefly describe the objectives, structure, and time-line of this programme.
The LISA International Science Team Working Group on Data Analysis (LIST-WG1B) is sponsoring several rounds of mock data challenges, with the purpose of fostering development of LISA data-analysis capabilities, and of demonstrating technical readiness for the maximum science exploitation of the LISA data. The first round of challenge data sets were released at this Symposium. We describe the models and conventions (for LISA and for gravitational-wave sources) used to prepare the data sets, the file format used to encode them, and the tools and resources available to support challenge participa…
We study parameter estimation of supermassive black hole binary systems in the final stage of inspiral using the full post-Newtonian gravitational waveforms. We restrict our analysis to systems in circular orbit with negligible spins, in the mass range $10^8\Ms-10^5\Ms$, and compare the results with those arising from the commonly used restricted post-Newtonian approximation. The conclusions of this work are particularly important with regard to the astrophysical reach of future LISA measurements. Our analysis clearly shows that modeling the inspiral with the full post-Newtonian waveform, not …
Extreme-mass-ratio inspirals (EMRIs) of ~ 1-10 solar-mass compact objects into ~ million solar-mass massive black holes can serve as excellent probes of strong-field general relativity. The Laser Interferometer Space Antenna (LISA) is expected to detect gravitational wave signals from apprxomiately one hundred EMRIs per year, but the data analysis of EMRI signals poses a unique set of challenges due to their long duration and the extensive parameter space of possible signals. One possible approach is to carry out a search for EMRI tracks in the time-frequency domain. We have applied a time-fre…
We report on our F-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 f…
The F-statistic is an optimal detection statistic for continuous gravitational waves, i.e., long-duration (quasi-)monochromatic signals with slowly-varying 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 F-statistic 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 first Mock LISA Data Challenge. Somewhat surprisingly, the …
The future space mission LISA will observe a wealth of gravitational-wave sources at millihertz frequencies. Of these, the extreme-mass-ratio inspirals of compact objects into massive black holes are the only sources that combine the challenges of strong-field complexity with that of long-lived signals. Such signals are found and characterized by comparing them against a large number of accurate waveform templates during data analysis, but the rapid generation of such templates is hindered by computing the $\sim10^3$-$10^5$ harmonic modes in a fully relativistic waveform. We use order-reductio…
The inspirals of compact objects into massive black holes are some of the most exciting of the potential sources of gravitational waves for the planned Laser Interferometer Space Antenna (LISA). Observations of such extreme mass ratio inspirals (EMRIs) will not only reveal to us the properties of black holes in the Universe, but will allow us to verify that the space-time structure around massive compact objects agrees with the predictions of relativity. Detection of EMRI signals via matched filtering and interpretation of the observations will require models of the gravitational waveforms. Th…
We are developing a Bayesian approach based on Markov chain Monte Carlo techniques to search for and extract information about white dwarf binary systems with the Laser Interferometer Space Antenna (LISA). Here we present results obtained by applying an initial implementation of this method to some of the data sets released in Round 1B of the Mock LISA Data Challenges. For Challenges 1B.1.1a and 1b the signals were recovered with parameters lying within the 95.5% posterior probability interval and the correlation between the true and recovered waveform is in excess of 99%. Results were not sub…
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 distribution functions for all the model parameters. The BAM algorithm performed almost flawlessly on all the Round 1 Mock LISA Data Ch…
Captures of compact objects (COs) by massive black holes in galactic nuclei (aka ``extreme-mass-ratio inspirals'') will be an important source for LISA. However, a large fraction of captures will not be individually resolvable, and so will constitute a source of ``confusion noise,'' obscuring other types of sources. Here we estimate the shape and overall magnitude of the spectrum of confusion noise from CO captures. The overall magnitude depends on the capture rates, which are rather uncertain, so we present results for a plausible range of rates. We show that the impact of capture confusion n…
The Mock LISA Data Challenge is a worldwide effort to solve the LISA data analysis problem. We present here our results for the Massive Black Hole Binary (BBH) section of Round 1. Our results cover Challenge 1.2.1, where the coalescence of the binary is seen, and Challenge 1.2.2, where the coalescence occurs after the simulated observational period. The data stream is composed of Gaussian instrumental noise plus an unknown BBH waveform. Our search algorithm is based on a variant of the Markov Chain Monte Carlo method that uses Metropolis-Hastings sampling and thermostated frequency annealing. …
Results are presented from high-precision computations of the orbital evolution and emitted gravitational waves for a stellar-mass object spiraling into a massive black hole in a slowly shrinking, circular, equatorial orbit. The focus of these computations is inspiral near the innermost stable circular orbit (isco)---more particularly, on orbits for which the angular velocity Omega is 0.03 < Omega/Omega_{isco} < 1. The computations are based on the Teukolsky-Sasaki-Nakamura formalism, and the results are tabulated in a set of functions that are of order unity and represent relativistic correct…
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 …
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 descr…
A binary compact object early in its inspiral phase will be picked up by its nearly monochromatic gravitational radiation by LISA. But even this innocuous appearing candidate poses interesting detection challenges. The data that will be scanned for such sources will be a set of three functions of LISA's twelve data streams obtained through time-delay interferometry, which is necessary to cancel the noise contributions from laser-frequency fluctuations and optical-bench motions to these data streams. We call these three functions pseudo-detectors. The sensitivity of any pseudo-detector to a giv…
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…
The Mock Data Challenges (MLDCs) have the dual purpose of fostering the development of LISA data-analysis tools and capabilities and of demonstrating the technical readiness already achieved by the gravitational-wave community in distilling a rich science payoff from the LISA data. The first round of MLDCs has just been completed and the second-round data sets are being released shortly after this workshop. The second-round data sets contain radiation from an entire Galactic population of stellar-mass binary systems, from massive--black-hole binaries, and from extreme--mass-ratio inspirals. Th…
The inspirals of stellar-mass compact objects into supermassive black holes are some of the most important sources for LISA. Detection techniques based on fully coherent matched filtering have been shown to be computationally intractable. We describe an efficient and robust detection method that utilizes the time-frequency evolution of such systems. We show that a typical extreme mass ratio inspiral (EMRI) source could possibly be detected at distances of up to ~2 Gpc, which would mean ~10s of EMRI sources can be detected per year using this technique. We discuss the feasibility of using this …
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 SNR…
One of the most exciting prospects for the Laser Interferometer Space Antenna (LISA) is the detection of gravitational waves from the inspirals of stellar-mass compact objects into supermassive black holes. Detection of these sources is an extremely challenging computational problem due to the large parameter space and low amplitude of the signals. However, recent work has suggested that the nearest extreme mass ratio inspiral (EMRI) events will be sufficiently loud that they might be detected using computationally cheap, template-free techniques, such as a time-frequency analysis. In this pap…
In this review article I attempt to summarise past and present-ongoing-work on the problem of the inspiral of a small body in the gravitational field of a much more massive Kerr black hole. Such extreme mass ratio systems, expected to occur in galactic nuclei, will constitute prime sources of gravitational radiation for the future LISA gravitational radiation detector. The article's main goal is to provide a survey of basic celestial mechanics in Kerr spacetime and calculations of gravitational waveforms and backreaction on the small body's orbital motion, based on the traditional `flux-balanc…
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 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 beginn…
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…
Probing Kerr symmetry breaking with LISA extreme-mass-ratio inspirals
Institut de Ciències de l’Espai (ICE, CSIC)（空间科学研究所）；Institut d’Estudis Espacials de Catalunya (IEEC)（加泰罗尼亚空间研究学院）；Department of Physics, Universitat Autònoma de Barcelona（巴塞罗那自治大学物理系）
Ori and Thorne have discussed the duration and observability (with LISA) of the transition from circular, equatorial inspiral to plunge for stellar-mass objects into supermassive ($10^{5}-10^{8}M_{\odot}$) Kerr black holes. We extend their computation to eccentric Kerr equatorial orbits. Even with orbital parameters near-exactly determined, we find that there is no universal length for the transition; rather, the length of the transition depends sensitively -- essentially randomly -- on initial conditions. Still, Ori and Thorne's zero-eccentricity results are essentially an upper bound on the …
The inspirals of stellar-mass compact objects into supermassive black holes constitute some of the most important sources for LISA. Detection of these sources using fully coherent matched filtering is computationally intractable, so alternative approaches are required. In a previous paper (Wen and Gair 2005, gr-qc/0502100), we outlined a detection method based on looking for excess power in a time-frequency spectrogram of the LISA data. The performance of the algorithm was assessed using a single `typical' trial waveform and approximations to the noise statistics. In this paper we present resu…
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-wave sources of undisclosed parameters. Participants are asked to analyze the data sets and report the maximum information about source parameters. The challenges are being released in rounds of increasing complexity and realism: in this proceeding we present the results of Challenge 2, issued in January 2007, which successfully demonstrated the recovery of si…
The Laser Interferometer Space Antenna, LISA, will detect gravitational wave signals from Extreme Mass Ratio Inspirals, where a stellar mass compact object orbits a supermassive black hole and eventually plunges into it. Here we report on LISA's capability to detect whether the smaller compact object in an Extreme Mass Ratio Inspiral is endowed with a scalar field, and to measure its scalar charge -- a dimensionless quantity that acts as a measure of how much scalar field the object carries. By direct comparison of signals, we show that LISA will be able to detect and measure the scalar charge…
The planned Laser Interferometer Space Antenna (LISA) is expected to detect the inspiral and merger of massive black hole binaries (MBHBs) at z <~ 5 with signal-to-noise ratios (SNRs) of hundreds to thousands. Because of these high SNRs, and because these SNRs accrete over periods of weeks to months, it should be possible to extract the physical parameters of these systems with high accuracy; for instance, for a ~ 10^6 Msun MBHBs at z = 1 it should be possible to determine the two masses to ~ 0.1% and the sky location to ~ 1 degree. However, those are just the errors due to noise: there will b…
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 accur…
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 article we provide a critical analysis of 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 inspir…
We describe a hybrid evolutionary algorithm that can simultaneously search for multiple supermassive black hole binary (SMBHB) inspirals in LISA data. The algorithm mixes evolutionary computation, Metropolis-Hastings methods and Nested Sampling. The inspiral of SMBHBs presents an interesting problem for gravitational wave data analysis since, due to the LISA response function, the sources have a bi-modal sky solution. We show here that it is possible not only to detect multiple SMBHBs in the data stream, but also to investigate simultaneously all the various modes of the global solution. In al…
One of the sources of gravitational waves for the proposed space-based gravitational wave detector, the Laser Interferometer Space Antenna (LISA), are the inspirals of compact objects into supermassive black holes in the centres of galaxies - extreme-mass-ratio inspirals (EMRIs). Using LISA observations, we will be able to measure the parameters of each EMRI system detected to very high precision. However, the statistics of the set of EMRI events observed by LISA will be more important in constraining astrophysical models than extremely precise measurements for individual systems. The black ho…
One of the most exciting prospects for the LISA gravitational wave observatory is the detection of gravitational radiation from the inspiral of a compact object into a supermassive black hole. The large inspiral parameter space and low amplitude of the signal makes detection of these sources computationally challenging. We outline here a first cut data analysis scheme that assumes realistic computational resources. In the context of this scheme, we estimate the signal-to-noise ratio that a source requires to pass our thresholds and be detected. Combining this with an estimate of the population…
The inspiral of stellar compact objects into massive black holes, usually known as extreme-mass-ratio inspirals (EMRIs), is one of the most important sources of gravitational-waves for the future Laser Interferometer Space Antenna (LISA). Intermediate-mass-ratio inspirals (IMRIs are also of interest to advance ground-based gravitational-wave observatories. We discuss here how modifications to the gravitational interaction can affect the signals emitted by these systems and their detectability by LISA. We concentrate in particular on Chern-Simons modified gravity, a theory that emerges in diffe…
We open the discussion into how the Laser Interferometer Space Antenna (LISA) observations of supermassive black-hole (SMBH) mergers (in the mass range ~10^6-10^8 Msun) may be complementary to pulsar timing-based gravitational wave searches. We consider the toy model of determining pulsar distances by exploiting the fact that LISA SMBH inspiral observations can place tight parameter constraints on the signal present in pulsar timing observations. We also suggest, as a future path of research, the use of LISA ring-down observations from the most massive (>~ a few 10^7 Msun) black-hole mergers, …
One of the key astrophysical sources for the Laser Interferometer Space Antenna (LISA) are the inspirals of stellar-origin compact objects into massive black holes in the centres of galaxies. These extreme-mass-ratio inspirals (EMRIs) have great potential for astrophysics, cosmology and fundamental physics. In this paper we describe the likely numbers and properties of EMRI events that LISA will observe. We present the first results computed for the 2.5 Gm interferometer that was the new baseline mission submitted in January 2017 in response to the ESA L3 mission call. In addition, we attempt …
One of the most exciting potential sources of gravitational waves for the Laser Interferometer Space Antenna (LISA) are the inspirals of approximately solar mass compact objects into massive black holes in the centres of galaxies - extreme mass ratio inspirals (EMRIs). LISA should observe between a few tens and a few hundred EMRIs over the mission lifetime, mostly at low redshifts (z < 1). Each observation will provide a measurement of the parameters of the host system to unprecendented precision. LISA EMRI observations will thus offer a new and unique way to probe black holes at low redshift.…
Primordial black holes possibly formed in the early universe could provide a significant fraction of the dark matter and would be unique probes of inflation. A smoking gun for their discovery would be the detection of a subsolar mass compact object. We argue that extreme mass-ratio inspirals will be ideal to search for subsolar-mass black holes not only with LISA but also with third-generation ground-based detectors such as Cosmic Explorer and the Einstein Telescope. These sources can provide unparalleled measurements of the mass of the secondary object at subpercent level for primordial black…
A main scientific output of the LISA Pathfinder mission is to provide a noise model that can be extended to the future gravitational wave observatory, LISA. The success of the mission depends thus upon a deep understanding of the instrument, especially the ability to correctly determine the parameters of the underlying noise model. In this work we estimate the parameters of a simplified model of the LISA Technology Package (LTP) instrument. We describe the LTP by means of a closed-loop model that is used to generate the data, both injected signals and noise. Then, parameters are estimated usin…
We review the contribution of extra galactic inspiralling double neutron stars, to the LISA astrophysical gravitational wave foreground. Using recent fits of the star formation rate, we show that sources beyond $z_*=0.005$ contribute to a truly continuous background, which may dominate the LISA instrumental noise in the range $3 \simeq 10^{-4}$ - $1 \times 10^{-2}$ Hz and overwhelm the galactic WD-WD confusion noise at frequencies larger than $ν_o \simeq 2\times 10^{-3}$.
Extreme-mass-ratio inspirals (EMRIs), stellar-mass compact objects (SCOs) inspiralling into a massive black hole, are one of the main sources of gravitational waves expected for the Laser Interferometer Space Antenna (LISA). To extract the EMRI signals from the expected LISA data stream, which will also contain the instrumental noise as well as other signals, we need very accurate theoretical templates of the gravitational waves that they produce. In order to construct those templates we need to account for the gravitational backreaction, that is, how the gravitational field of the SCO affects…
Extreme mass ratio inspirals (EMRIs), the inspirals of compact objects into supermassive black holes, are important gravitational wave sources for the Laser Interferometer Space Antenna (LISA). We study the performance of various post-Newtonian (PN) template families relative to the high precision numerical waveforms in the context of EMRI parameter estimation with LISA. Expressions for the time domain waveforms TaylorT1, TaylorT2, TaylorT3, TaylorT4 and TaylorEt are derived up to 22PN order, i.e $\mathcal{O}(v^{44})$ ($v$ is the characteristic velocity of the binary) beyond the Newtonian term…
We report on the analysis of selected single source data sets from the first round of the Mock LISA Data Challenges (MLDC) for white dwarf binaries. We implemented an end-to-end pipeline consisting of a grid-based coherent pre-processing unit for signal detection, and an automatic Markov Chain Monte Carlo post-processing unit for signal evaluation. We demonstrate that signal detection with our coherent approach is secure and accurate, and is increased in accuracy and supplemented with additional information on the signal parameters by our Markov Chain Monte Carlo approach. We also demonstrate …
This article 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.
We investigate the capability of LISA to measure the sky position of equal-mass, nonspinning black hole binaries, combining for the first time the entire inspiral-merger-ringdown signal, the effect of the LISA orbits, and the complete three-channel LISA response. We consider an ensemble of systems near the peak of LISA's sensitivity band, with total rest mass of 2\times10^6 M\odot, a redshift of z = 1, and randomly chosen orientations and sky positions. We find median sky localization errors of approximately \sim3 arcminutes. This is comparable to the field of view of powerful electromagnetic …
An extreme mass ratio inspiral takes place when a compact stellar object is inspiraling into a supermassive black hole due to gravitational radiation reaction. Gravitational waves (GWs) from this system can be calculated using the Teukolsky equation (TE). In our case, we compute the asymptotic GW fluxes of a spinning body orbiting a Kerr black hole by solving numerically the TE both in time and frequency domain. Our ultimate goal is to produce GW templates for space-based detectors such as LISA.
LISA will be able to detect gravitational waves from inspiralling massive black hole (MBH) binaries out to redshifts z > 10. If the binary masses and luminosity distances can be extracted from the LISA data stream, this information can be used to reveal the merger history of MBH binaries and their host galaxies in the evolving universe. Since this parameter extraction generally requires that LISA observe the inspiral for a significant fraction of its yearly orbit, carrying out this program requires adequate sensitivity at low frequencies, f < 10^{-4} Hz. Using several candidate low frequency s…
The analysis method currently proposed to search for isotropic stochastic radiation of primordial or astrophysical origin with the Laser Interferometer Space Antenna (LISA) relies on the combined use of two LISA channels, one of which is insensitive to gravitational waves, such as the symmetrised Sagnac. For this method to work, it is essential to know how the instrumental noise power in the two channels are related to one another; however, no quantitative estimates of this key information are available to date. The purpose of our study is to assess the performance of the symmetrised Sagnac me…
