We study parameter estimation of supermassive black holes in the range $10^5-10^8\Ms$ by LISA using the inspiral full post-Newtonian gravitational waveforms, and we compare the results with those arising from the commonly used restricted post-Newtonian approximation. The analysis shows that for observations of the last year before merger, the inclusion of the higher harmonics clearly improves the parameter estimation. We pay special attention to the source location errors and we study the improvement on the percentage of sources for which we could potentially identify electromagnetic counterparts. We also show how the additional harmonics can help to mitigate the impact of losing laser links during the mission.
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…
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 …
Gravitational waves from the inspiral and coalescence of supermassive black-hole (SMBH) binaries with masses ~10^6 Msun are likely to be among the strongest sources for the Laser Interferometer Space Antenna (LISA). We describe a three-stage data-analysis pipeline designed to search for and measure the parameters of SMBH binaries in LISA data. The first stage uses a time-frequency track-search method to search for inspiral signals and provide a coarse estimate of the black-hole masses m_1, m_2 and of the coalescence time of the binary t_c. The second stage uses a sequence of matched-filter tem…
Spin induced precessional modulations of gravitational wave signals from supermassive black hole binaries can improve the estimation of luminosity distance to the source by space based gravitational wave missions like the Laser Interferometer Space Antenna (LISA). We study how this impacts the ablity of LISA to do cosmology, specifically, to measure the dark energy equation of state (EOS) parameter $w$. Using the $Λ$CDM model of cosmology, we show that observations of precessing binaries by LISA, combined with a redshift measurement, can improve the determination of $w$ up to an order of magni…
Current expectations on the signal to noise ratios and masses of supermassive black holes which the Laser Interferometer Space Antenna (LISA) can observe are based on using in matched filtering only the dominant harmonic of the inspiral waveform at twice the orbital frequency. Other harmonics will affect the signal-to-noise ratio of systems currently believed to be observable by LISA. More significantly, inclusion of other harmonics in our matched filters would mean that more massive systems that were previously thought to be {\it not} visible in LISA should be detectable with reasonable SNRs.…
Current simulations of the rate at which stellar-mass compact objects merge with supermassive black holes (called extreme mass ratio inspirals, or EMRIs) focus on two-body capture by emission of gravitational radiation. The gravitational wave signal of such events will likely involve a significant eccentricity in the sensitivity range of the Laser Interferometer Space Antenna (LISA). We show that tidal separation of stellar-mass compact object binaries by supermassive black holes will instead produce events whose eccentricity is nearly zero in the LISA band. Compared to two-body capture events…
We present a method to search for gravitational waves from coalescing supermassive binary black holes in LISA data. The search utilizes the $\mathcal{F}$-statistic to maximize over, and determine the values of, the extrinsic parameters of the binary system. The intrinsic parameters are searched over hierarchically using stochastically generated multi-dimensional template banks to recover the masses and sky locations of the binary. We present the results of this method applied to the mock LISA data Challenge 1B data set.
Stellar-mass black hole binaries (BHBs) near supermassive black holes (SMBH) in galactic nuclei undergo eccentricity oscillations due to gravitational perturbations from the SMBH. Previous works have shown that this channel can contribute to the overall BHB merger rate detected by the Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo Interferometer. Significantly, the SMBH gravitational perturbations on the binary's orbit may produce eccentric BHBs which are expected to be visible using the upcoming Laser Interferometer Space Antenna (LISA) for a large fraction of their life…
The gravitational wave measurements of spin-induced multipole moment coefficients of a binary black hole system can be used to distinguish black holes from other compact objects [N. V. Krishnendu et al., PRL 119, 091101 (2017)]. Here, we apply the idea proposed in [N. V. Krishnendu et al., PRL 119, 091101 (2017)] to binary systems composed of intermediate-mass and supermassive black holes and derive the expected bounds on their Kerr nature using future space-based gravitational wave detectors. Using astrophysical models of binary black hole population, we study the measurability of the spin-in…
One of the central goals of LISA is the detection of gravitational waves from the merger of supermassive black holes. Contrary to stellar-mass black hole mergers, such events are expected to be rich X-ray sources due to the accretion of material from the circumbinary disks onto the black holes. The orbital dynamics before merger is also expected to modulate the resulting X-ray emission via Doppler boosting in a quasi-periodic way, and in a simple phase relation with the gravitational wave from the inspiral of the black holes. Detecting the X-ray source would enable a precise and early localiza…
The coalescence history of massive black holes has been derived from cosmological simulations, in which the evolution of those objects and that of the host galaxies are followed in a consistent way. The present study indicates that supermassive black holes having masses greater than $\sim 10^{9} M_{\odot}$ underwent up to 500 merger events along their history. The derived coalescence rate per comoving volume and per mass interval permitted to obtain an estimate of the expected detection rate distribution of gravitational wave signals ("ring-down") along frequencies accessible by the planned in…
Laser Interferometer Space Antenna (LISA) will routinely observe coalescences of supermassive black hole (BH) binaries up to very high redshifts. LISA can measure mass parameters of such coalescences to a relative accuracy of $10^{-4}-10^{-6}$, for sources at a distance of 3 Gpc. The problem of parameter estimation of massive nonspinning binary black holes using post-Newtonian (PN) phasing formula is studied in the context of LISA. Specifically, the performance of the 3.5PN templates is contrasted against its 2PN counterpart using a waveform which is averaged over the LISA pattern functions. T…
Massive black hole binary systems are among the most interesting sources for the Laser Interferometer Space Antenna (LISA); gravitational radiation emitted during the last year of in-spiral could be detectable with a very large signal-to-noise ratio for sources at cosmological distance. Here we discuss the impact of LISA for astronomy and cosmology; we review our present understanding of the relevant issues, and highlight open problems that deserve further investigations.
Gravitational lensing of gravitational waves (GWs) is a powerful probe of the matter distribution in the universe. Here we revisit the wave-optics effects induced by dark matter (DM) halos on the GW signals of merging massive black hole binaries (MBHBs), and we study the possibility of discerning these effects using the Laser Interferometer Space Antenna (LISA). In particular, we include the halos in the low-mass range of $\rm 10^5-10^8\, M_\odot$ since they are the most numerous according to the cold DM model. We simulate the lensed signals corresponding to a wide range of impact parameters, …
In this work, we discuss the improvement that the joint network of LISA and Taiji could provide on exploring two kinds of black hole formation mechanisms. For astrophysical origin, we consider light seed and heavy seed scenarios, and generate populations accordingly. We find that the joint network has the potential to observe growing light seeds in the range 15 < z < 20, while single detector can hardly see, which would shed light on the light seeding mechanism. For the heavy seeds, the joint network only improves the signal-to-noise ratio. For primordial origin, we calculate the event rate at…
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.…
We conduct an analysis of the measurement abilities of distinctive LISA detector designs, examining the influence of LISA's low-frequency performance on the detection and characterization of massive black hole binaries. We are particularly interested in LISA's ability to measure massive black holes merging at frequencies near the low-frequency band edge, with masses in the range of $\sim 10^6-10^{10}M_\odot$. We examine the signal-to-noise ratio (SNR) using phenomenological waveforms for inspiral, merger, and ringdown over a wide range of massive black hole binary parameters. We employ a broad…
We consider LISA observations of in-spiral signals emitted by massive black hole binary systems in circular orbit and with negligible spins. We study the accuracy with which the source parameters can be extracted from the data stream. We show that the use of waveforms retaining post-Newtonian corrections not only to the phase but also the amplitude can drastically improve the estimation of some parameters.
While recent gravitational wave observations by LIGO and Virgo allow for tests of general relativity in the extreme gravity regime, these observations are still blind to a large swath of phenomena outside these instruments' sensitivity curves. Future gravitational-wave detectors, such as LISA, will enable probes of longer-duration and lower-frequency events. In particular, LISA will enable the characterization of the non-linear dynamics of extreme mass-ratio inspirals, when a small compact object falls into a supermassive black hole. In this paper, we study the motion of test particles around …
Recently Fuller & Shi proposed that the gravitational collapse of supermassive objects ($M \gtrsim 10^4M_\odot$) could be a cosmological source of $γ$-ray bursts (GRBs). The major advantage of their model is that supermassive object collapses are far more energetic than solar mass-scale compact mergers. Also, in their proposal the seeds of supermassive black holes (SMBHs) thus formed could give rise to the SMBHs observed at the center of many galaxies. We argue here that, besides the generation of GRBs, there could well occur a strong generation of gravitational waves (GWs) during the formatio…
One of the major assumptions in the search for gravitational wave signatures from massive and supermassive black hole binaries with LISA, is that these systems will have circularized before entering the LISA bandwidth. Current astrophysical simulations now suggest that systems could have a non-negligible eccentricity in the LISA band, and an important level of eccentricity in the Pulsar Timing regime. In this work, we use a set of source catalogues from astrophysically motivated models of massive black hole binary formation and assume a one year LISA mission lifetime. Depending on the model in…
For a successful detection of gravitational waves by LISA, it is essential to construct theoretical waveforms in a reliable manner. We discuss gravitational waves from an extreme mass ratio binary system which is expected to be a promising target of the LISA project. The extreme mass ratio binary is a binary system of a supermassive black hole and a stellar mass compact object. As the supermassive black hole dominates the gravitational field of the system, we suppose that the system might be well approximated by a metric perturbation of a Kerr black hole. We discuss a recent theoretical progre…
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 …
The development of search algorithms for gravitational wave sources in the LISA data stream is currently a very active area of research. It has become clear that not only does difficulty lie in searching for the individual sources, but in the case of galactic binaries, evaluating the fidelity of resolved sources also turns out to be a major challenge in itself. In this article we review the current status of developed algorithms for galactic binary, non-spinning supermassive black hole binary and extreme mass ratio inspiral sources. While covering the vast majority of algorithms, we will highl…
Massive black hole binaries are key targets for the space based gravitational wave interferometer LISA. Several studies have investigated how LISA observations could be used to constrain the parameters of these systems. Until recently, most of these studies have ignored the higher harmonic corrections to the waveforms. Here we analyze the effects of the higher harmonics in more detail by performing extensive Monte Carlo simulations. We pay particular attention to how the higher harmonics impact parameter correlations, and show that the additional harmonics help mitigate the impact of having tw…
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. …
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…
The Laser Interferometer Space Antenna (LISA) will be able to detect massive black hole mergers throughout the visible Universe. These observations will provide unique information about black hole formation and growth, and the role black holes play in galaxy evolution. Here we develop several key building blocks for detecting and characterizing black hole binary mergers with LISA, including fast heterodyned likelihood evaluations, and efficient stochastic search techniques.
The noise produced by the inspiral of millions of white dwarf binaries in the Milky Way may pose a threat to one of the main goals of the space-based LISA mission: the detection of massive black hole binary mergers. We present a novel study for reconstruction of merger waveforms in the presence of Galactic confusion noise using dictionary learning. We discuss the limitations of untangling signals from binaries with total mass from $10^2 M_{\odot}$ to $10^4 M_{\odot}$. Our method proves extremely successful for binaries with total mass greater than $\sim 3\times 10^3$ $ M_{\odot}$ up to redshif…
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 infe…
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 wi…
LISA should detect gravitational waves from tens to hundreds of systems containing black holes with mass in the range from 10 thousand to 10 million solar masses. Black holes in this mass range are not well constrained by current electromagnetic observations, so LISA could significantly enhance our understanding of the astrophysics of such systems. In this paper, we describe a framework for combining LISA observations to make statements about massive black hole populations. We summarise the constraints that LISA observations of extreme-mass-ratio inspirals might be able to place on the mass fu…
Binary black hole coalescences emit gravitational waves that will be measurable by the space-based detector it LISA to large redshifts. This suggests that LISA may be able to observe black holes grow and evolve as the universe evolves, mapping the distribution of black hole masses as a function of redshift. An immediate difficulty with this idea is that LISA measures certain redshifted combinations of masses with good accuracy: if a system has some mass parameter m, then LISA measures (1+z)m. This mass-redshift degeneracy makes it difficult to follow the mass evolution. In many cases, LISA wil…
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…
Idealized models are used to illustrate the potential of the Laser Interferometer Space Antenna (LISA) as a probe of the largely unknown population of cosmologically-distant Massive Black Holes (MBHs) and as a tool to measure their masses with unprecedented accuracy. The models suggest that LISA will most efficiently probe a MBH population of lower mass than the one found in bright quasars and nearby galactic nuclei. The mass spectrum of these MBHs could constrain formation scenarios for high-redshift, low-mass galaxies.
The signal-to-noise ratio (SNR) for black hole quasinormal mode sources of low-frequency gravitational waves is estimated using a Monte Carlo approach that replaces the all-sky average approximation. We consider an eleven dimensional parameter space that includes both source and detector parameters. We find that in the black-hole mass range $M\sim 4$-$7\times 10^6M_{\odot}$ the SNR is significantly higher than the SNR for the all-sky average case, as a result of the variation of the spin parameter of the sources. This increased SNR may translate to a higher event rate for the Laser Interferome…
We study how the angular resolution of LISA for merging massive black-hole binaries would be improved if we observe multiple gravitational wave ``images'' due to strong gravitational lensing. The correlation between fitting parameters is reduced by the additional information of the second image which significantly reduces the error box on the sky. This improvement would be very helpful for identifying the host galaxy of a binary. The angular resolution expected with multiple detectors is also discussed.
We study the angular resolution of the gravitational wave detector LISA and show that numerical relativity can drastically improve the accuracy of position location for coalescing Super Massive Black Hole (SMBH) binaries. For systems with total redshifted mass above $10^7 M_{\odot}$, LISA will mainly see the merger and ring-down of the gravitational wave (GW) signal, which can now be computed numerically using the full Einstein equations. Using numerical waveforms that also include about ten GW cycles of inspiral, we improve inspiral-only position estimates by an order of magnitude. We show th…
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…
Stellar-mass binary black holes will sweep through the frequency band of the Laser Interferometer Space Antenna (LISA) for months to years before appearing in the audio-band of ground-based gravitational-wave detectors. One can expect several tens of these events up to a distance of $500 \,\mathrm{Mpc}$ each year. The LISA signal-to-noise ratio for such sources even at these close distances will be too small for a blind search to confidently detect them. However, next generation ground-based gravitational-wave detectors, expected to be operational at the time of LISA, will observe them with si…
We study the gravitational wave background produced from the formation and assembly of supermassive black holes within the cosmological paradigm of hierarchical structure formation. In particular, we focus on a supermassive black hole formation scenario in which the present-day population of supermassive black holes is built from high-mass seed black holes and we compute the concomitant spectrum of gravitational radiation produced by mergers of the seed black holes. We find that this scenario predicts a large, gravitational wave background that should be resolved into individual sources with s…
A number of scenarios have been proposed for the origin of the supermassive black holes (SMBHs) that are found in the centres of most galaxies. Many such scenarios predict a high-redshift population of massive black holes (MBHs), with masses in the range 100 to 100000 times that of the Sun. When the Laser Interferometer Space Antenna (LISA) is finally operational, it is likely that it will detect on the order of 100 of these MBH binaries as they merge. The differences between proposed population models produce appreciable effects in the portion of the population which is detectable by LISA, so…
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, …
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 Laser Interferometer Space Antenna (LISA) is designed to detect gravitational wave signals from astrophysical sources, including those from coalescing binary systems of compact objects such as black holes. Colliding galaxies have central black holes that sink to the center of the merged galaxy and begin to orbit one another and emit gravitational waves. Some galaxy evolution models predict that the binary black hole system will enter the LISA band with significant orbital eccentricity, while other models suggest that the orbits will already have circularized. Using a full seventeen paramet…
The Laser Interferometer Space Antenna (LISA) will observe black hole binaries of stellar origin during their gravitational wave inspiral, months to years before coalescence. Due to the long duration of the signal in the LISA band, a faithful waveform is necessary in order to keep track of the binary phase. This is crucial to extract the signal from the data and to perform an unbiased estimation of the source parameters. We consider Post-Newtonian (PN) waveforms, and analyze the PN order needed to keep the bias caused by the PN approximation negligible relative to the statistical parameter est…
The observability of gravitational waves from supermassive and intermediate-mass black holes by the forecoming Laser Interferometer Space Antenna (LISA), and the physics we can learn from the observations, will depend on two basic factors: the event rates for massive black hole mergers occurring in the LISA best sensitivity window, and our theoretical knowledge of the gravitational waveforms. We first provide a concise review of the literature on LISA event rates for massive black hole mergers, as predicted by different formation scenarios. Then we discuss what (in our view) are the most urgen…
The tidal force from a third body near a binary system could introduce long-term oscillations in the binary's eccentricity, known as Kozai-Lidov oscillations. We show that the Kozai-Lidov oscillations of stellar-mass black hole binaries have the potential to be observed by LISA. Detections of such binaries will give insights into binary formation channels and also provide an important benchmark of observing Kozai-Lidov oscillations directly.
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 …
A space-based gravitational-wave detector, LISA, consists of a triangle of three spacecrafts with a separation distance of 2.5 million kilometers in a heliocentric orbit behind the Earth. Like LISA, Taiji is compose of a triangle of three spacecrafts with a separation distance of 3 million kilometers in a heliocentric orbit ahead of the Earth. They are expected to launch in 2030-2035. Assuming a one-year overlap, we propose the LISA-Taiji network in space to fast and accurately localize the gravitational-wave sources. We use the Fisher information matrix approach to analyze the sky localizatio…
