Search

Pulsar Timing Array (PTA) observations hinted towards the existence of a stochastic gravitational wave background (SGWB) in the nHz frequency band. Still, the nature of the SGWB signal cannot be confidently inferred from current data, and the leading explanation invokes mergers of supermassive black holes. If confirmed, such discovery would not only represent a turning point in our understanding of astrophysics, but it may severely limit the capability of searching for additional cosmological sources in the nHz frequency range. In this work, we build a simple framework to forecast the sensitivity of future PTA configurations and assess the parameter estimation of SGWB, which could consist of several contributions. We release the python code fastPTA implementing this framework and ready to use., Comment: 16 pages, 9 figures

The future space based gravitational wave detector LISA (Laser Interferometer Space Antenna) will observe millions of Galactic binaries constantly present in the data stream. A small fraction of this population (of the order of several thousand) will be individually resolved. One of the challenging tasks from the data analysis point of view will be to estimate the parameters of resolvable galactic binaries while disentangling them from each other and from other gravitational wave sources present in the data. This problem is quite often referred to as a global fit in the field of LISA data analysis. A Bayesian framework is often used to infer the parameters of the sources and their number. The efficiency of the sampling techniques strongly depends on the proposals, especially in the multi-dimensional parameter space. In this paper we demonstrate how we can use neural density estimators, and in particular Normalising flows, in order to build proposals which significantly improve the convergence of sampling. We also demonstrate how these methods could help in building priors based on physical models and provide an alternative way to represent the catalogue of identified gravitational wave sources.

The Laser Interferometer Space Antenna (LISA) is the first scientific endeavour to detect and study gravitational waves from space. LISA will survey the sky for Gravitational Waves in the 0.1 mHz to 1 Hz frequency band which will enable the study of a vast number of objects ranging from Galactic binaries and stellar mass black holes in the Milky Way, to distant massive black-hole mergers and the expansion of the Universe. This definition study report, or Red Book, presents a summary of the very large body of work that has been undertaken on the LISA mission over the LISA definition phase., Comment: 155 pages, with executive summary and table of contents

We search for a stochastic gravitational wave background (SGWB) generated by a network of cosmic strings using six millisecond pulsars from Data Release 2 (DR2) of the European Pulsar Timing Array (EPTA). We perform a Bayesian analysis considering two models for the network of cosmic string loops, and compare it to a simple power-law model which is expected from the population of supermassive black hole binaries. Our main strong assumption is that the previously reported common red noise process is a SGWB. We find that the one-parameter cosmic string model is slightly favored over a power-law model thanks to its simplicity. If we assume a two-component stochastic signal in the data (supermassive black hole binary population and the signal from cosmic strings), we get a $95\%$ upper limit on the string tension of $\log_{10}(G\mu) < -9.9$ ($-10.5$) for the two cosmic string models we consider. In extended two-parameter string models, we were unable to constrain the number of kinks. We test two approximate and fast Bayesian data analysis methods against the most rigorous analysis and find consistent results. These two fast and efficient methods are applicable to all SGWBs, independent of their source, and will be crucial for analysis of extended data sets., Comment: 14 pages, 6 figures; typo corrected in (5)

Cosmic string cusps are sources of short-lived, linearly polarised gravitational wave bursts which can be searched for in gravitational wave detectors. We assess the capability of LISA to detect these bursts using the latest LISA configuration and operational assumptions. For such short bursts, we verify that LISA can be considered as ``frozen", namely that one can neglect LISA's orbital motion. We consider two models for the network of cosmic string loops, and estimate that LISA should be able to detect 4-30 bursts per year assuming a string tension $G\mu \approx 10^{-10.6} - 10^{-10.1}$ and detection threshold $\rm{SNR} \ge 20$. Non-detection of these bursts would constrain the string tension to $G\mu\lesssim 10^{-11}$ for both models., Comment: 7 pages, 4 figures

We use the latest constraints on the population of stellar origin binary black holes (SOBBH) from LIGO/Virgo/KAGRA (LVK) observations, to estimate the stochastic gravitational wave background (SGWB) they generate in the frequency band of LISA. We account for the faint and distant binaries, which contribute the most to the SGWB, by extending the merger rate at high redshift assuming it tracks the star formation rate. We adopt different methods to compute the SGWB signal: an analytical evaluation, Monte Carlo sums over SOBBH population realisations, and a method that accounts for the role of the detector by simulating LISA data and iteratively removing resolvable signals until only the confusion noise is left, allowing for the extraction of both the expected SGWB and the number of resolvable SOBBHs. Since the latter are few for SNR thresholds larger than five, we confirm that the spectral shape of the SGWB in the LISA band follows the analytical prediction of a power law. We infer the probability distribution of the SGWB amplitude from the LVK GWTC-3 posterior of the binary population model; its interquartile range of $h^2\Omega_\mathrm{GW}(f=3\times10^{-3}\,\mathrm{Hz}) \in [5.65,\,11.5]\times10^{-13}$ is in agreement with most previous estimates. We perform a MC analysis to assess LISA's capability to detect and characterise this signal. Accounting for both the instrumental noise and the galactic binaries foreground, with four years of data, LISA will be able to detect the SOBBH SGWB with percent accuracy, narrowing down the uncertainty on the amplitude by one order of magnitude with respect to the range of possible amplitudes inferred from the population model. A measurement of this signal by LISA will help to break the degeneracy among some of the population parameters, and provide interesting constraints, in particular on the redshift evolution of the SOBBH merger rate., Comment: 39 pages, 15 figures. Prepared for submission to JCAP

Galactic compact binaries with orbital periods shorter than a few hours emit detectable gravitational waves at low frequencies. Their gravitational wave signals can be detected with the future Laser Interferometer Space Antenna (LISA). Crucially, they may be useful in the early months of the mission operation in helping to validate LISA's performance in comparison to pre-launch expectations. We present an updated list of 55 candidate LISA binaries with measured properties, for which we derive distances based on Gaia Data release 3 astrometry. Based on the known properties from electromagnetic observations, we predict the LISA detectability after 1, 3, 6, and 48 months with state-of-the-art Bayesian analysis methods. We distinguish between verification and detectable binaries as being detectable after 3 and 48 months respectively. We find 18 verification binaries and 22 detectable sources, which triples the number of known LISA binaries over the last few years. These include detached double white dwarfs, AM CVn binaries, one ultracompact X-ray binary and two hot subdwarf binaries. We find that across this sample the gravitational wave amplitude is expected to be measured to $\approx10\%$ on average, while the inclination is expected to be determined with $\approx15^\circ$ precision. For detectable binaries these average errors increase to $\approx50\%$ and to $\approx40^\circ$ respectively., Comment: accepted for publication in ApJ, 19 pages, 7 figures, 2 table

Extreme mass ratio inspirals (EMRIs) are among the primary targets for the Laser Interferometer Space Antenna (LISA). The extreme mass ratios of these systems result in relatively weak GW signals, that can be individually resolved only for cosmologically nearby sources (up to $z\approx2$). The incoherent piling up of the signal emitted by unresolved EMRIs generate a confusion noise, that can be formally treated as a stochastic GW background (GWB). In this paper, we estimate the level of this background considering a collection of astrophysically motivated EMRI models, spanning the range of uncertainties affecting EMRI formation. To this end, we employed the innovative Augmented Analytic Kludge waveforms and used the full LISA response function. For each model, we compute the GWB SNR and the number of resolvable sources. Compared to simplified computations of the EMRI signals from the literature, we find that for a given model the GWB SNR is lower by a factor of $\approx 2$ whereas the number of resolvable sources drops by a factor 3-to-5. Nonetheless, the vast majority of the models result in potentially detectable GWB which can also significantly contribute to the overall LISA noise budget in the 1-10 mHz frequency range.

Markov Chain Monte Carlo approach is frequently used within Bayesian framework to sample the target posterior distribution. Its efficiency strongly depends on the proposal used to build the chain. The best jump proposal is the one that closely resembles the unknown target distribution, therefore we suggest an adaptive proposal based on Kernel Density Estimation (KDE). We group parameters of the model according to their correlation and build KDE based on the already accepted points for each group. We adapt the KDE-based proposal until it stabilizes. We argue that such a proposal could be helpful in applications where the data volume is increasing and in the hyper-model sampling. We tested it on several astrophysical datasets (IPTA and LISA) and have shown that in some cases KDE-based proposal also helps to reduce the autocorrelation length of the chains. The efficiency of this proposal is reduces in case of the strong correlations between a large group of parameters., Comment: 12 pages, 11 figures

Gravitational-wave observations of extreme mass ratio inspirals (EMRIs) offer the opportunity to probe the environments of active galactic nuclei (AGN) through the torques that accretion disks induce on the binary. Within a Bayesian framework, we study how well such environmental effects can be measured using gravitational wave observations from the Laser Interferometer Space Antenna (LISA). We focus on the torque induced by planetary-type migration on quasicircular inspirals, and use different prescriptions for geometrically thin and radiatively efficient disks. We find that LISA could detect migration for a wide range of disk viscosities and accretion rates, for both $\alpha$ and $\beta$ disk prescriptions. For a typical EMRI with masses $50M_\odot+10^6M_\odot$, we find that LISA could distinguish between migration in $\alpha$ and $\beta$ disks and measure the torque amplitude with $\sim 20\%$ relative precision. Provided an accurate torque model, we also show how to turn gravitational-wave measurements of the torque into constraints on the disk properties. Furthermore, we show that, if an electromagnetic counterpart is identified, the multimessenger observations of the AGN EMRI system will yield direct measurements of the disk viscosity. Finally, we investigate the impact of neglecting environmental effects in the analysis of the gravitational-wave signal, finding 3$\sigma$ biases in the primary mass and spin, and showing that ignoring such effects can lead to false detection of a deviation from general relativity. This work demonstrates the scientific potential of gravitational observations as probes of accretion-disk physics, accessible so far through electromagnetic observations only.

Multiband observations of coalescing stellar-mass black holes binaries could deliver valuable information on the formation of those sources and potential deviations from General Relativity. Some of these binaries might be first detected by the space-based detector LISA and, then, several years later, observed with ground-based detectors. Due to large uncertainties in astrophysical models, it is hard to predict the population of such binaries that LISA could observe. In this work, we assess the ability of LISA to detect the events of the third catalogue of gravitational wave sources released by the LIGO/Virgo/KAGRA collaboration. We consider the possibility of directly detecting the source with LISA and performing archival searches in the LISA data stream, after the event has been observed with ground-based detectors. We also assess how much could LISA improve the determination of source parameters. We find that it is not guaranteed that any event other than GW150914 would have been detected. Nevertheless, if any event is detected by LISA, even with a very low signal-to-noise ratio, the measurement of source parameters would improve by combining observations of LISA and ground based detectors, in particular for the chirp mass., Comment: 10 pages, 11 figures

Binaries of relatively massive black holes like GW190521 have been proposed to form in dense gas environments, such as the disks of Active Galactic Nuclei (AGNs), and they might be associated with transient electromagnetic counterparts. The interactions of this putative environment with the binary could leave a significant imprint at the low gravitational wave frequencies observable with the Laser Interferometer Space Antenna (LISA). We show that LISA will be able to detect up to ten GW190521-like black hole binaries, with sky position errors $\lesssim1$ deg$^2$. Moreover, it will measure directly various effects due to the orbital motion around the supermassive black hole at the center of the AGN, especially the Doppler modulation and the Shapiro time delay. Thanks to a careful treatment of their frequency domain signal, we were able to perform the full parameter estimation of Doppler and Shapiro-modulated binaries as seen by LISA. We find that the Doppler and Shapiro effects will allow for measuring the AGN parameters (radius and inclination of the orbit around the AGN, central black hole mass) with up to percent-level precision. Properly modeling these low-frequency environmental effects is crucial to determine the binary formation history, as well as to avoid biases in the reconstruction of the source parameters and in tests of general relativity with gravitational waves., Comment: 13+4 pages, 7+1 figures v3: corrected typo in Fig 5

The primary scientific results of the future space-based gravitational wave interferometer LISA will come from the parameter inference of a large variety of gravitational wave sources. However, the presence of calibration errors could potentially degrade the measurement precision of the system parameters. Here, we assess the impact of calibration uncertainties on parameter estimation for individual sources, focusing on massive black holes, extreme-mass-ratio inspirals (EMRIs), galactic binaries, and stellar origin black hole binaries. Using a Fisher matrix formalism, we investigate how the measurement precision of source parameters degrades as a function of the size of the assumed calibration uncertainties. If we require that parameter measurements are degraded by no more than a factor of two relative to their value in the absence of calibration error, we find that calibration errors should be smaller than a few tenths of a percent in amplitude and $10^{-3}$ in phase. We also investigate the possibility of using verification binaries and EMRIs to constrain calibration uncertainties. Verification binaries can constrain amplitude calibration uncertainties at the level of a few percent, while both source types can provide constrain phase calibration at the level of a few$\times10^{-2}$., Comment: 25 pages, 15 figures

This Technical Note (LISA reference LISA-LCST-SGS-TN-001) describes the computation of the noise power spectral density, the sensitivity curve and the signal-to-noise ratio for LISA (Laser Interferometer Antenna). It is an applicable document for ESA (European Space Agency) and the reference for the LISA Science Requirement Document., Comment: 41 pages, 20 figures, Technical Noite of the LISA Consortium. Applicable document for ESA: reference for the LISA Science Requirement Document

The science objectives of the LISA mission have been defined under the implicit assumption of a 4 yr continuous data stream. Based on the performance of LISA Pathfinder, it is now expected that LISA will have a duty cycle of $\approx 0.75$, which would reduce the effective span of usable data to 3 yr. This paper reports the results of a study by the LISA Science Group, which was charged with assessing the additional science return of increasing the mission lifetime. We explore various observational scenarios to assess the impact of mission duration on the main science objectives of the mission. We find that the science investigations most affected by mission duration concern the search for seed black holes at cosmic dawn, as well as the study of stellar-origin black holes and of their formation channels via multi-band and multi-messenger observations. We conclude that an extension to 6 yr of mission operations is recommended., Comment: 50 pages, 19 figures, 5 tables. Matches version published in GERG

Electromagnetic observations have provided strong evidence for the existence of massive black holes in the center of galaxies, but their origin is still poorly known. Different scenarios for the formation and evolution of massive black holes lead to different predictions for their properties and merger rates. LISA observations of coalescing massive black hole binaries could be used to reverse engineer the problem and shed light on these mechanisms. In this paper, we introduce a pipeline based on hierarchical Bayesian inference to infer the mixing fraction between different theoretical models by comparing them to LISA observations of massive black hole mergers. By testing this pipeline against simulated LISA data, we show that it allows us to accurately infer the properties of the massive black hole population as long as our theoretical models provide a reliable description of the Universe. We also show that measurement errors, including both instrumental noise and weak lensing errors, have little impact on the inference., Comment: Matches PRD version, minor changes

Time-delay interferometry (TDI) is a processing step essential for the scientific exploitation of LISA, as it reduces the otherwise overwhelming laser noise in the interferometric measurements. The fundamental idea is to define new laser-noise-free observables by combining appropriately time-shifted measurements. First- and second-generation TDI combinations cancel laser noise under the assumption that the LISA armlengths are constant or evolve linearly with time, respectively. We recently extended TDI by solving for the laser-noise-free combinations implicitly, writing the likelihood of the data directly in terms of the basic measurements, and using a discretized representation of the delays that can accommodate any time dependence of the armlengths. We named the resulting formalism "TDI-infinity'' [PRD 103, 082001 (2021)]. According to Tinto, Dhurandhar, and Joshi [arXiv/2105.02054], our matrix-based approach is invalidated by the simplified start-up conditions assumed for the design matrix that connects the time series of laser-noise fluctuations to the time series of interferometric measurements along the LISA arms. Here we respond that, if those boundary conditions are indeed unrealistic, they do not invalidate the algorithm, since one can simply truncate the design matrix to exclude "incomplete'' measurements, or set them to zero. Our formalism then proceeds unmodified, except that the length of the laser-noise canceling time series is reduced by the number of excluded measurements. Tinto and colleagues further claim that the matrix formulation is merely a finite representation of the polynomial ring of delay operators introduced by Dhurandar, Nayak, and Vinet to formalize TDI. We show that this is only true if all interferometric delays are exact multiples of the sampling interval, which will not be possible in practical contexts such as LISA., Comment: Response to arXiv/2105.02054, 2 pages, no figures

The Laser Interferometer Space Antenna (LISA) mission, scheduled for launch in the early 2030s, is a gravitational wave observatory in space designed to detect sources emitting in the milli-Hertz band. In contrast to the present ground based detectors, the LISA data are expected to be a signaldominated, with strong and weak gravitational wave signals overlapping in time and in frequency. Astrophysical population models predict a sufficient number of signals in the LISA band to blend together and form an irresolvable foreground noise. In this work, we present a generic method for characterizing the foreground signals originating from a given astrophysical population of coalescing compact binaries. Assuming idealized detector conditions and perfect data analysis technique capable of identifying and removing the bright sources, we apply an iterative procedure which allows us to predict the different levels of foreground noise.

The Laser Interferometer Space Antenna (LISA) will open the mHz frequency window of the gravitational wave (GW) landscape. Among all the new GW sources expected to emit in this frequency band, extreme mass-ratio inspirals (EMRIs) constitute a unique laboratory for astrophysics and fundamental physics. Here we show that EMRIs can also be used to extract relevant cosmological information, complementary to both electromagnetic (EM) and other GW observations. By using the loudest EMRIs (SNR$>$100) detected by LISA as dark standard sirens, statistically matching their sky localisation region with mock galaxy catalogs, we find that constraints on $H_0$ can reach $\sim$1.1% ($\sim$3.6%) accuracy, at the 90% credible level, in our best (worst) case scenario. By considering a dynamical dark energy (DE) cosmological model, with $\Lambda$CDM parameters fixed by other observations, we further show that in our best (worst) case scenario $\sim$5.9% ($\sim$12.3%) relative uncertainties at the 90% credible level can be obtained on $w_0$, the DE equation of state parameter. Besides being relevant in their own right, EMRI measurements will be affected by different systematics compared to both EM and ground-based GW observations. Cross validation with complementary cosmological measurements will therefore be of paramount importance, especially if convincing evidence of physics beyond $\Lambda$CDM emerges from future observations., Comment: 22 pages, 9 figures. v2: new author in author list, new sub-Appendix with additional results, new Fig. A1; some explicative paragraphs added, Fig. 3 updated. Matches the journal version

Exotic compact objects can be difficult to distinguish from black holes in the inspiral phase of the binaries observed by gravitational-wave detectors, but significant differences may be present in the merger and post-merger signal. We introduce a toy model capturing the salient features of binaries of exotic compact objects with compactness below $0.2$, which do not collapse promptly following the merger. We use it to assess their detectability with current and future detectors, and whether they can be distinguished from black hole binaries. We find that the Einstein Telescope (LISA) could observe exotic binaries with total mass $\mathcal{O}(10^2) \ M_{\odot}$ ($10^4-10^6 \ M_{\odot}$), and potentially distinguish them from black hole binaries, throughout the observable Universe, as compared to $z\lesssim 1$ for Advanced LIGO. Moreover, we show that using standard black hole templates for detection could lead to a loss of up to $60\%$ in the signal-to-noise ratio, greatly reducing our chances of observing these signals. Finally, we estimate that if the loudest events in the O1/O2 catalog released by the LIGO/Virgo collaboration were ECO binaries as the ones considered in this paper, they would have left a post-merger signal detectable with model-agnostic searches, making this hypothesis unlikely., Comment: 11 pages (13 with appendix) Matches the version published in PRD

GW190521 is the compact binary with the largest masses observed to date, with at least one in the pair-instability gap. This event has also been claimed to be associated with an optical flare observed by the Zwicky Transient Facility in an Active Galactic Nucleus (AGN), possibly due to the post-merger motion of the merger remnant in the AGN gaseous disk. We show that the Laser Interferometer Space Antenna (LISA) will detect up to ten of such gas-rich black hole binaries months to years before their detection by LIGO/Virgo-like interferometers, localizing them in the sky within $\approx1$ deg$^2$. LISA will also measure directly deviations from purely vacuum and stationary waveforms, arising from gas accretion, dynamical friction, and orbital motion around the AGN's massive black hole (acceleration, strong lensing, and Doppler modulation). LISA will therefore be crucial to alert and point electromagnetic telescopes ahead of time on this novel class of gas-rich sources, to gain direct insight on their physics, and to disentangle environmental effects from corrections to General Relativity that may also appear in the waveforms at low frequencies., Comment: 6 pages, 4 figures. Matches published version

The space-based gravitational-wave observatory LISA relies on a form of synthetic interferometry (time-delay interferometry, or TDI) where the otherwise overwhelming laser phase noise is canceled by linear combinations of appropriately delayed phase measurements. These observables grow in length and complexity as the realistic features of the LISA orbits are taken into account. In this paper we outline an implicit formulation of TDI where we write the LISA likelihood directly in terms of the basic phase measurements, and we marginalize over the laser phase noises in the limit of infinite laser-noise variance. Equivalently, we rely on TDI observables that are defined numerically (rather than algebraically) from a discrete-filter representation of the laser propagation delays. Our method generalizes to any time dependence of the armlengths; it simplifies the modeling of gravitational-wave signals; and it allows a straightforward treatment of data gaps and missing measurements., Comment: 7 pages, 3 figures

Stellar-mass black hole binaries (SBHBs), like those currently being detected with the ground-based gravitational-wave (GW) observatories LIGO and Virgo, are also an anticipated GW source for LISA. LISA will observe them during the early inspiral stage of evolution; some of them will chirp through the LISA band and reappear some time later in the band of $3^{rd}$ generation ground-based detectors. SBHBs could serve as laboratories for testing the theory of General Relativity and inferring the astrophysical properties of the underlying population. In this study, we assess LISA's ability to infer the parameters of those systems, a crucial first step in understanding and interpreting the observation of those binaries and their use in fundamental physics and astrophysics. We simulate LISA observations for several fiducial sources and perform a full Bayesian analysis. We demonstrate and explain degeneracies in the parameters of some systems. We show that the redshifted chirp mass and the sky location are always very well determined, with typical errors below $10^{-4}$ (fractional) and $0.4 \ {\rm deg^2}$. The luminosity distance to the source is typically measured within $40-60\%$, resulting in a measurement of the chirp mass in the source frame of $\mathcal{O}(1 \%)$. The error on the time to coalescence improves from $\mathcal{O}(1 \ {\rm day})$ to $\mathcal{O}(30 \ {\rm s})$ as we observe the systems closer to their merger. We introduce an augmented Fisher-matrix analysis which gives reliable predictions for the intrinsic parameters compared to the full Bayesian analysis. Finally, we show that combining the use of the long-wavelength approximation for the LISA instrumental response together with the introduction of a degradation function at high frequencies yields reliable results for the posterior distribution when used self-consistently, but not in the analysis of real LISA data., Comment: Some additions and reshaping, matches PRD version

Massive black hole binaries (MBHBs) of $10^5 \, \rm M_\odot - 3 \times 10^7 \, \rm M_\odot $ merging in low redshift galaxies ($z\le4$) are sufficiently loud to be detected weeks before coalescence with the Laser Interferometer Space Antenna (LISA). This allows us to perform the parameter estimation $on$ $the$ $fly$, i.e. as a function of the time to coalescence during the inspiral phase, relevant for early warning of the planned LISA protected periods and for searches of electromagnetic signals. In this work, we study the evolution of the sky position, luminosity distance, chirp mass and mass ratio uncertainties as function of time left before merger. Overall, light systems with total intrinsic mass $\rm M_{\rm tot} = 3 \times 10^5 \, \rm M_\odot$ are characterized by smaller uncertainties than heavy ones ($\rm M_{\rm tot} = 10^7 \, \rm M_\odot$) during the inspiral. Luminosity distance, chirp mass and mass ratio are well constrained at the end of the inspiral. Concerning sky position, at $z=1$, MBHBs with $\rm M_{\rm tot} = 3 \times 10^5 \, \rm M_\odot$ can be localized with a median precision of $\simeq 10^2 \, \rm deg^2 (\simeq 1 \, \rm deg^2)$ at 1 month (1 hour) from merger, while the sky position of heavy MBHBs can be determined to $10 \, \rm deg^2$ only 1 hour before merger. However the uncertainty around the median values broadens with time, ranging in between 0.04 -- 20 $\rm deg^2$ (0.3 -- 3 $\times 10^3 \, \rm deg^2$) for light (heavy) systems at 1 hour before merger. At merger the sky localization improves down to $\simeq 10^{-1} \, \rm deg^2$ for all masses. For the benefit of the observer community, we provide the full set of data from our simulations and simple and ready-to-use analytical fits to describe the time evolution of uncertainties in the aforementioned parameters, valid for systems with total mass between $10^5$--$10^7 \, \rm M_\odot$ and redshift $0.3$--$3$., Comment: 31 pages, 24 figures and 6 tables. Accepted for publication in Physical Review D

The Laser Interferometer Space Antenna (LISA) is slated for launch in the early 2030s. A main target of the mission is massive black hole binaries that have an expected detection rate of $\sim20$ yr$^{-1}$. We present a parameter estimation analysis for a variety of massive black hole binaries. This analysis is performed with a graphics processing unit (GPU) implementation comprising the phenomhm waveform with higher-order harmonic modes and aligned spins; a fast frequency-domain LISA detector response function; and a GPU-native likelihood computation. The computational performance achieved with the GPU is shown to be 500 times greater than with a similar CPU implementation, which allows us to analyze full noise-infused injections at a realistic Fourier bin width for the LISA mission in a tractable and efficient amount of time. With these fast likelihood computations, we study the effect of adding aligned spins to an analysis with higher-order modes by testing different configurations of spins in the injection, as well as the effect of varied and fixed spins during sampling. Within these tests, we examine three different binaries with varying mass ratios, redshifts, sky locations, and detector-frame total masses ranging over three orders of magnitude. We discuss varied correlations between the total masses and mass ratios; unique spin posteriors for the larger mass binaries; and the constraints on parameters when fixing spins during sampling, allowing us to compare to previous analyses that did not include aligned spins., Comment: 27 pages, 13 figures

As gravitational-wave detectors become more sensitive, we will access a greater variety of signals emitted by compact binary systems, shedding light on their astrophysical origin and environment. A key physical effect that can distinguish among formation scenarios is the misalignment of the spins with the orbital angular momentum, causing the spins and the binary's orbital plane to precess. To accurately model such systems, it is crucial to include multipoles beyond the dominant quadrupole. Here, we develop the first multipolar precessing waveform model in the effective-one-body (EOB) formalism for the inspiral, merger and ringdown (IMR) of binary black holes: SEOBNRv4PHM. In the nonprecessing limit, the model reduces to SEOBNRv4HM, which was calibrated to numerical-relativity (NR) simulations, and waveforms from perturbation theory. We validate SEOBNRv4PHM by comparing it to the public catalog of 1405 precessing NR waveforms of the Simulating eXtreme Spacetimes (SXS) collaboration, and also to new 118 precessing NR waveforms, which span mass ratios 1-4 and spins up to 0.9. We stress that SEOBNRv4PHM is not calibrated to NR simulations in the precessing sector. We compute the unfaithfulness against the 1523 SXS precessing NR waveforms, and find that, for $94\%$ ($57\%$) of the cases, the maximum value, in the total mass range $20-200 M_\odot$, is below $3\%$ ($1\%$). Those numbers become $83\%$ ($20\%$) when using the IMR, multipolar, precessing phenomenological model IMRPhenomPv3HM. We investigate the impact of such unfaithfulness values with two parameter-estimation studies on synthetic signals. We also compute the unfaithfulness between those waveform models and identify in which part of the parameter space they differ the most. We validate them also against the multipolar, precessing NR surrogate model NRSur7dq4, and find that the SEOBNRv4PHM model outperforms IMRPhenomPv3HM., Comment: 24 pages, 18 figures. Abstract abridged

We consider the observation of stellar-mass black holes binaries with the Laser Interferometer Space Antenna (LISA). Preliminary results based on Fisher information matrix analyses have suggested that gravitational waves from those sources could be very sensitive to possible deviations from the theory of general relativity and from the strong equivalence principle during the low-frequency binary inspiral. We perform a full Markov Chain Monte Carlo Bayesian analysis to quantify the sensitivity of these signals to two phenomenological modifications of general relativity, namely a putative gravitational dipole emission and a non-zero mass for the graviton, properly accounting for the detector's response. Moreover, we consider a scenario where those sources could be observed also with Earth-based detectors, which should measure the coalescence time with precision better than $1 \ {\rm ms}$. This constraint on the coalescence time further improves the bounds that we can set on those phenomenological deviations from general relativity. We show that tests of dipole radiation and the graviton's mass should improve respectively by seven and half an order(s) of magnitude over current bounds. Finally, we discuss under which conditions one may claim the detection of a modification to general relativity., Comment: Update references

We study the impact of gas accretion on the orbital evolution of black-hole binaries initially at large separation in the band of the planned Laser Interferometer Space Antenna (LISA). We focus on two sources: (i)~stellar-origin black-hole binaries~(SOBHBs) that can migrate from the LISA band to the band of ground-based gravitational-wave observatories within weeks/months; and (ii) intermediate-mass black-hole binaries~(IMBHBs) in the LISA band only. Because of the large number of observable gravitational-wave cycles, the phase evolution of these systems needs to be modeled to great accuracy to avoid biasing the estimation of the source parameters. Accretion affects the gravitational-wave phase at negative ($-4$) post-Newtonian order, and is therefore dominant for binaries at large separations. If accretion takes place at the Eddington or at super-Eddington rate, it will leave a detectable imprint on the dynamics of SOBHBs. In optimistic astrophysical scenarios, a multiwavelength strategy with LISA and a ground-based interferometer can detect about $10$ (a few) SOBHB events for which the accretion rate can be measured at $50\%$ ($10\%$) level. In all cases the sky position can be identified within much less than $0.4\,{\rm deg}^2$ uncertainty. Likewise, accretion at $\gtrsim 10\%$ ($\gtrsim 100\%$) of the Eddington rate can be measured in IMBHBs up to redshift $z\approx 0.1$ ($z\approx 0.5$), and the position of these sources can be identified within less than $0.01\,{\rm deg}^2$ uncertainty. Altogether, a detection of SOBHBs or IMBHBs would allow for targeted searches of electromagnetic counterparts to black-hole mergers in gas-rich environments with future X-ray detectors (such as Athena) and radio observatories (such as SKA)., Comment: 14 pages, 8 figures; v2: references and comments added to match the final version published in ApJ

A number of open problems hinder our present ability to extract scientific information from data that will be gathered by the near-future gravitational-wave mission LISA. Many of these relate to the modeling, detection and characterization of signals from binary inspirals with an extreme component-mass ratio of $\lesssim10^{-4}$. In this paper, we draw attention to the issue of systematic error in parameter estimation due to the use of fast but approximate waveform models; this is found to be relevant for extreme-mass-ratio inspirals even in the case of waveforms with $\gtrsim90\%$ overlap accuracy and moderate ($\gtrsim30$) signal-to-noise ratios. A scheme that uses Gaussian processes to interpolate and marginalize over waveform error is adapted and investigated as a possible precursor solution to this problem. Several new methodological results are obtained, and the viability of the technique is successfully demonstrated on a three-parameter example in the setting of the LISA Data Challenge., Comment: Published version

We present a detailed investigation into the properties of GW170729, the gravitational wave with the most massive and distant source confirmed to date. We employ an extensive set of waveform models, including new improved models that incorporate the effect of higher-order waveform modes which are particularly important for massive systems. We find no indication of spin-precession, but the inclusion of higher-order modes in the models results in an improved estimate for the mass ratio of $(0.3-0.8)$ at the 90\% credible level. Our updated measurement excludes equal masses at that level. We also find that models with higher-order modes lead to the data being more consistent with a smaller effective spin, with the probability that the effective spin is greater than zero being reduced from $99\%$ to $94\%$. The 90\% credible interval for the effective spin parameter is now $(-0.01-0.50)$. Additionally, the recovered signal-to-noise ratio increases by $\sim0.3$ units compared to analyses without higher-order modes. We study the effect of common spin priors on the derived spin and mass measurements, and observe small shifts in the spins, while the masses remain unaffected. We argue that our conclusions are robust against systematic errors in the waveform models. We also compare the above waveform-based analysis which employs compact-binary waveform models to a more flexible wavelet- and chirplet-based analysis. We find consistency between the two, with overlaps of $\sim 0.9$, typical of what is expected from simulations of signals similar to GW170729, confirming that the data are well-described by the existing waveform models. Finally, we study the possibility that the primary component of GW170729 was the remnant of a past merger of two black holes and find this scenario to be indistinguishable from the standard formation scenario., Comment: 14 pages, 8 figures, final published version, samples available at https://git.ligo.org/katerina.chatziioannou/gw170729hm_datarelease

We present TEOBResumS, a new effective-one-body (EOB) waveform model for nonprecessing (spin-aligned) and tidally interacting compact binaries.Spin-orbit and spin-spin effects are blended together by making use of the concept of centrifugal EOB radius. The point-mass sector through merger and ringdown is informed by numerical relativity (NR) simulations of binary black holes (BBH) computed with the SpEC and BAM codes. An improved, NR-based phenomenological description of the postmerger waveform is developed.The tidal sector of TEOBResumS describes the dynamics of neutron star binaries up to merger and incorporates a resummed attractive potential motivated by recent advances in the post-Newtonian and gravitational self-force description of relativistic tidal interactions. Equation-of-state dependent self-spin interactions (monopole-quadrupole effects) are incorporated in the model using leading-order post-Newtonian results in a new expression of the centrifugal radius. TEOBResumS is compared to 135 SpEC and 19 BAM BBH waveforms. The maximum unfaithfulness to SpEC data $\bar{F}$ -- at design Advanced-LIGO sensitivity and evaluated with total mass $M$ varying between $10M_\odot \leq M \leq 200 M_\odot$ --is always below $2.5 \times 10^{-3}$ except for a single outlier that grazes the $7.1 \times 10^{-3}$ level. When compared to BAM data, $\bar{F}$ is smaller than $0.01$ except for a single outlier in one of the corners of the NR-covered parameter space, that reaches the $0.052$ level.TEOBResumS is also compatible, up to merger, to high end NR waveforms from binary neutron stars with spin effects and reduced initial eccentricity computed with the BAM and THC codes. The model is designed to generate accurate templates for the analysis of LIGO-Virgo data through merger and ringdown. We demonstrate its use by analyzing the publicly available data for GW150914., Comment: 39 pages, 36 figures. Extended appendix with discussion of the postmerger fits. Version accepted for publication in Phys. Rev. D

We develop the foundations of an effective-one-body (EOB) model for eccentric binary coalescences that includes the conservative dynamics, radiation reaction, and gravitational waveform modes from the inspiral and the merger-ringdown signals. We use the same approach as is commonly employed in black-hole perturbation theory by introducing a relativistic parameterization of the dynamics that is defined by the orbital geometry and consists of a set of phase variables and quantities that evolve only due to gravitational radiation reaction. Specializing to nonspinning binaries, we derive the EOB evolution equations and compute the binary's radiative multipole moments that determine the gravitational waves through a decomposition into the fundamental frequencies of the motion. The major differences between our treatment and the quasi-Keplerian approach often used in post-Newtonian (PN) calculations are that the orbital parameters describe strong-field dynamics, and that expressing the multipole moments in terms of the frequencies simplifies the calculations and also results in an unambiguous orbit-averaging operation. While our description of the conservative dynamics is fully relativistic, we limit explicit derivations in the radiative sector to 1.5PN order for simplicity. This already enables us to establish methods for computing both instantaneous and hereditary contributions to the gravitational radiation in EOB coordinates that have straightforward extensions to higher PN order. The weak-field, small eccentricity limit of our results for the orbit-averaged fluxes of energy and angular momentum agrees with known PN results when expressed in terms of gauge-invariant quantities. We further address considerations for the numerical implementation of the model and the completion of the waveforms to include the merger and ringdown signals, and provide illustrative results., Comment: 25 pages, 8 figures, small changes to match published version

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 to quantify the astrophysical uncertainties in EMRI event rate estimates by considering a range of different models for the astrophysical population. We present both likely event rates and estimates for the precision with which the parameters of the observed sources could be measured. We finish by discussing the implications of these results for science using EMRIs., Comment: 12 pages, 3 figures, 5 tables. These proceedings are a summary of the results presented in arXiv:1703.09722

The space-based Laser Interferometer Space Antenna (LISA) will be able to observe the gravitational-wave signals from systems comprised of a massive black hole and a stellar-mass compact object. These systems are known as extreme-mass-ratio inspirals (EMRIs) and are expected to complete $\sim 10^4$-$10^5$ cycles in band, thus allowing exquisite measurements of their parameters. In this work, we attempt to quantify the astrophysical uncertainties affecting the predictions for the number of EMRIs detectable by LISA, and find that competing astrophysical assumptions produce a variance of about three orders of magnitude in the expected intrinsic EMRI rate. However, we find that irrespective of the astrophysical model, at least a few EMRIs per year should be detectable by the LISA mission, with up to a few thousands per year under the most optimistic astrophysical assumptions. We also investigate the precision with which LISA will be able to extract the parameters of these sources. We find that typical fractional statistical errors with which the intrinsic parameters (redshifted masses, massive black hole spin and orbital eccentricity) can be recovered are $\sim 10^{-6}$-$10^{-4}$. Luminosity distance (which is required to infer true masses) is inferred to about $10\%$ precision and sky position is localized to a few square degrees, while tests of the multipolar structure of the Kerr metric can be performed to percent-level precision or better., Comment: 13 figures, 22 pages; updated to match published version

Following the selection of The Gravitational Universe by ESA, and the successful flight of LISA Pathfinder, the LISA Consortium now proposes a 4 year mission in response to ESA's call for missions for L3. The observatory will be based on three arms with six active laser links, between three identical spacecraft in a triangular formation separated by 2.5 million km. LISA is an all-sky monitor and will offer a wide view of a dynamic cosmos using Gravitational Waves as new and unique messengers to unveil The Gravitational Universe. It provides the closest ever view of the infant Universe at TeV energy scales, has known sources in the form of verification binaries in the Milky Way, and can probe the entire Universe, from its smallest scales near the horizons of black holes, all the way to cosmological scales. The LISA mission will scan the entire sky as it follows behind the Earth in its orbit, obtaining both polarisations of the Gravitational Waves simultaneously, and will measure source parameters with astrophysically relevant sensitivity in a band from below $10^{-4}\,$Hz to above $10^{-1}\,$Hz., Comment: Submitted to ESA on January 13th in response to the call for missions for the L3 slot in the Cosmic Vision Programme

We improve the accuracy of the effective-one-body (EOB) waveforms that were employed during the first observing run of Advanced LIGO for binaries of spinning, nonprecessing black holes by calibrating them to a set of 141 numerical-relativity (NR) waveforms. The NR simulations expand the domain of calibration towards larger mass ratios and spins, as compared to the previous EOBNR model. Merger-ringdown waveforms computed in black-hole perturbation theory for Kerr spins close to extremal provide additional inputs to the calibration. For the inspiral-plunge phase, we use a Markov-chain Monte Carlo algorithm to efficiently explore the calibration space. For the merger-ringdown phase, we fit the NR signals with phenomenological formulae. After extrapolation of the calibrated model to arbitrary mass ratios and spins, the (dominant-mode) EOBNR waveforms have faithfulness --- at design Advanced-LIGO sensitivity --- above $99\%$ against all the NR waveforms, including 16 additional waveforms used for validation, when maximizing only on initial phase and time. This implies a negligible loss in event rate due to modeling for these binary configurations. We find that future NR simulations at mass ratios $\gtrsim 4$ and double spin $\gtrsim 0.8$ will be crucial to resolve discrepancies between different ways of extrapolating waveform models. We also find that some of the NR simulations that already exist in such region of parameter space are too short to constrain the low-frequency portion of the models. Finally, we build a reduced-order version of the EOBNR model to speed up waveform generation by orders of magnitude, thus enabling intensive data-analysis applications during the upcoming observation runs of Advanced LIGO., Comment: 27 pages, 15 figures

In Ref. [1], the properties of the first gravitational wave detected by LIGO, GW150914, were measured by employing an effective-one-body (EOB) model of precessing binary black holes whose underlying dynamics and waveforms were calibrated to numerical-relativity (NR) simulations. Here, we perform the first extensive comparison of such EOBNR model to 70 precessing NR waveforms that span mass ratios from 1 to 5, dimensionless spin magnitudes up to 0.5, generic spin orientations, and length of about 20 orbits. We work in the observer's inertial frame and include all $\ell=2$ modes in the gravitational-wave polarizations. We introduce new prescriptions for the EOB ringdown signal concerning its spectrum and time of onset. For total masses between 10Msun and 200Msun, we find that precessing EOBNR waveforms have unfaithfulness within about 3% to NR waveforms when considering the Advanced-LIGO design noise curve. This result is obtained without recalibration of the inspiral-plunge of the underlying nonprecessing EOBNR model. The unfaithfulness is computed with maximization over time and phase of arrival, sky location and polarization of the EOBNR waveform and it is averaged over sky location and polarization of the NR signal. We also present comparisons between NR and EOBNR waveforms in a frame that tracks the orbital precession., Comment: 16 pages, 8 figures

We compare the science capabilities of different eLISA mission designs, including four-link (two-arm) and six-link (three-arm) configurations with different arm lengths, low-frequency noise sensitivities and mission durations. For each of these configurations we consider a few representative massive black hole formation scenarios. These scenarios are chosen to explore two physical mechanisms that greatly affect eLISA rates, namely (i) black hole seeding, and (ii) the delays between the merger of two galaxies and the merger of the black holes hosted by those galaxies. We assess the eLISA parameter estimation accuracy using a Fisher matrix analysis with spin-precessing, inspiral-only waveforms. We quantify the information present in the merger and ringdown by rescaling the inspiral-only Fisher matrix estimates using the signal-to-noise ratio from non-precessing inspiral-merger-ringdown phenomenological waveforms, and from a reduced set of precessing numerical relativity/post-Newtonian hybrid waveforms. We find that all of the eLISA configurations considered in our study should detect some massive black hole binaries. However, configurations with six links and better low-frequency noise will provide much more information on the origin of black holes at high redshifts and on their accretion history, and they may allow the identification of electromagnetic counterparts to massive black hole mergers., Comment: 28 pages, 13 figures, 7 tables

We have searched for continuous gravitational wave (CGW) signals produced by individually resolvable, circular supermassive black hole binaries (SMBHBs) in the latest EPTA dataset, which consists of ultra-precise timing data on 41 millisecond pulsars. We develop frequentist and Bayesian detection algorithms to search both for monochromatic and frequency-evolving systems. None of the adopted algorithms show evidence for the presence of such a CGW signal, indicating that the data are best described by pulsar and radiometer noise only. Depending on the adopted detection algorithm, the 95\% upper limit on the sky-averaged strain amplitude lies in the range $6\times 10^{-15}10^9$M$_\odot$ out to a distance of about 25Mpc, and with $\cal{M}_c>10^{10}$M$_\odot$ out to a distance of about 1Gpc ($z\approx0.2$). We show that state-of-the-art SMBHB population models predict $<1\%$ probability of detecting a CGW with the current EPTA dataset, consistent with the reported non-detection. We stress, however, that PTA limits on individual CGW have improved by almost an order of magnitude in the last five years. The continuing advances in pulsar timing data acquisition and analysis techniques will allow for strong astrophysical constraints on the population of nearby SMBHBs in the coming years., Comment: 16 pages, 11 figures, accepted for publication in MNRAS

We present new limits on an isotropic stochastic gravitational-wave background (GWB) using a six pulsar dataset spanning 18 yr of observations from the 2015 European Pulsar Timing Array data release. Performing a Bayesian analysis, we fit simultaneously for the intrinsic noise parameters for each pulsar, along with common correlated signals including clock, and Solar System ephemeris errors, obtaining a robust 95$\%$ upper limit on the dimensionless strain amplitude $A$ of the background of $A<3.0\times 10^{-15}$ at a reference frequency of $1\mathrm{yr^{-1}}$ and a spectral index of $13/3$, corresponding to a background from inspiralling super-massive black hole binaries, constraining the GW energy density to $\Omega_\mathrm{gw}(f)h^2 < 1.1\times10^{-9}$ at 2.8 nHz. We also present limits on the correlated power spectrum at a series of discrete frequencies, and show that our sensitivity to a fiducial isotropic GWB is highest at a frequency of $\sim 5\times10^{-9}$~Hz. Finally we discuss the implications of our analysis for the astrophysics of supermassive black hole binaries, and present 95$\%$ upper limits on the string tension, $G\mu/c^2$, characterising a background produced by a cosmic string network for a set of possible scenarios, and for a stochastic relic GWB. For a Nambu-Goto field theory cosmic string network, we set a limit $G\mu/c^2<1.3\times10^{-7}$, identical to that set by the {\it Planck} Collaboration, when combining {\it Planck} and high-$\ell$ Cosmic Microwave Background data from other experiments. For a stochastic relic background we set a limit of $\Omega^\mathrm{relic}_\mathrm{gw}(f)h^2<1.2 \times10^{-9}$, a factor of 9 improvement over the most stringent limits previously set by a pulsar timing array., Comment: 24 pages, 5 tables, 17 figures

In this article we consider prospects for detecting extreme mass ratio inspirals (EMRIs) using gravitational wave (GW) observations by a future space borne interferometric observatory eLISA. We start with a description of EMRI formation channels. Different formation scenarios lead to variations in the expected event rate and predict different distributions of the orbital parameters when the GW signal enters the eLISA sensitivity band. Then we will briefly overview the available theoretical models describing the GW signal from EMRIs and describe proposed methods for their detection., Comment: 39 pages, 4 figures, to appear in proceedings of EOM 2013 "Equations of Motion in Relativistic Gravity"

We study for the first time a three-dimensional octahedron constellation for a space-based gravitational wave detector, which we call the Octahedral Gravitational Observatory (OGO). With six spacecraft the constellation is able to remove laser frequency noise and acceleration disturbances from the gravitational wave signal without needing LISA-like drag-free control, thereby simplifying the payloads and placing less stringent demands on the thrusters. We generalize LISA's time-delay interferometry to displacement-noise free interferometry (DFI) by deriving a set of generators for those combinations of the data streams that cancel laser and acceleration noise. However, the three-dimensional configuration makes orbit selection complicated. So far, only a halo orbit near the Lagrangian point L1 has been found to be stable enough, and this allows only short arms up to 1400 km. We derive the sensitivity curve of OGO with this arm length, resulting in a peak sensitivity of about $2\times10^{-23}\,\mathrm{Hz}^{-1/2}$ near 100 Hz. We compare this version of OGO to the present generation of ground-based detectors and to some future detectors. We also investigate the scientific potentials of such a detector, which include observing gravitational waves from compact binary coalescences, the stochastic background and pulsars as well as the possibility to test alternative theories of gravity. We find a mediocre performance level for this short-arm-length detector, between those of initial and advanced ground-based detectors. Thus, actually building a space-based detector of this specific configuration does not seem very efficient. However, when alternative orbits that allow for longer detector arms can be found, a detector with much improved science output could be constructed using the octahedron configuration and DFI solutions demonstrated in this paper. (abridged), Comment: 17 pages, 5 figures, revtex4-1, matches version accepted by PRD

Pulsar timing arrays (PTAs) might detect gravitational waves (GWs) from massive black hole (MBH) binaries within this decade. The signal is expected to be an incoherent superposition of several nearly-monochromatic waves of different strength. The brightest sources might be individually resolved, and the overall deconvolved, at least partially, in its individual components. In this paper we extend the maximum-likelihood based method developed in Babak & Sesana 2012, to search for individual MBH binaries in PTA data. We model the signal as a collection of circular monochromatic binaries, each characterized by three free parameters: two angles defining the sky location, and the frequency. We marginalize over all other source parameters and we apply an efficient multi-search genetic algorithm to maximize the likelihood function and look for sources in synthetic datasets. On datasets characterized by white Gaussian noise plus few injected sources with signal-to-noise ratio (SNR) in the range 10-60, our search algorithm performs well, recovering all the injections with no false positives. Individual source SNRs are estimated within few % of the injected values, sky locations are recovered within few degrees, and frequencies are determined with sub-Fourier bin precision., Comment: 12 pages, 4 figures, 1 table; submitted to Physical Review D