Upcoming space-based gravitational wave detectors such as LISA, the Laser Interferometer Space Antenna, will be sensitive to extreme- and intermediate-mass-ratio inspirals (EMRIs and IMRIs). These binaries are comprised of a supermassive black hole and a stellar-mass object or intermediate-mass black hole. Their detection will probe the structure of galactic nuclei and enable tests of general relativity. As these events will be observed over thousands of orbital cycles, they will be extremely sensitive to both the underlying spacetime and astrophysical environment, demanding exquisite theoretical models on both fronts to avoid biased or even erroneous results. In particular, many (E/)IMRIs are expected to occur within accretion discs around supermassive black holes, and the nonlinearities present when modeling these systems require numerical simulations. In preparation for future modeling of LISA sources, we have conducted a comparison between eight different hydrodynamical codes and applied them to the problem of a q = 10^-4 mass ratio binary interacting with an accretion disc. Thicker discs appear more lenient, and all codes at sufficiently high resolutions are in good agreement with each other and analytical predictions. For thinner discs, beyond the reach of analytical models, we find substantial disagreement between 2D and 3D simulations and between different codes, including both the magnitude and sign of the torque. With time and energy efficiency in mind, codes that leverage moving meshes or grid-based Lagrangian remapping seem preferable, as do codes that can leverage graphical processing units and other energy-efficient hardware.

Over the past 15 yr, the evidence has clearly demonstrated that massive black hole (MBH) binary merger timescales depend strongly on the structural and kinematic properties of their host galaxy. Stellar density, gas content, shape, and kinematics all play a role, combining in nonlinear ways to affect the evolution of the binary. The binary properties themselves—such as the eccentricity, mass ratio, and orbital plane—all matter as well. This makes it nontrivial to estimate accurate cosmological MBH binary merger rates or to generate merger-rate ranges that reflect the distribution of galaxy hosts and orbits. We seek to accurately model the few-body stellar scattering phase, as this is the least well understood part of the journey from black holes in separate galaxies to a merged black hole. Using an extensive set of high-resolution, gas-free, direct N -body simulations, in which the shape, structure, and kinematics of each galaxy host are directly informed by observations, we map out MBH binary merger timescales over a range of galaxy hosts and MBH binary orbits. This yields a convenient set of scaling relations to determine MBH binary merger timescales—and the range of merger timescales—as functions of basic observables. Such scaling relations can be readily employed as a subgrid model in cosmological or semianalytic studies—for example, to model event rates for LISA or pulsar timing.

The Lunar Gravitational-wave Antenna (LGWA) is a proposed array of next-generation inertial sensors to monitor the response of the Moon to gravitational waves (GWs). Given the size of the Moon and the expected noise produced by the lunar seismic background, the LGWA would be able to observe GWs from about 1 mHz to 1 Hz. This would make the LGWA the missing link between space-borne detectors like LISA with peak sensitivities around a few millihertz and proposed future terrestrial detectors like Einstein Telescope or Cosmic Explorer. In this article, we provide a first comprehensive analysis of the LGWA science case including its multi-messenger aspects and lunar science with LGWA data. We also describe the scientific analyses of the Moon required to plan the LGWA mission.

With the recent announcement by NASA's Planetary Science and Astrobiology Decadal Survey 2023-2032, a priority flagship mission to the planet Uranus is anticipated. Here, we explore the prospects of using the mission's radio Doppler tracking equipment to detect gravitational waves (GWs) and other analogous signals related to dark matter (DM) over the duration of its interplanetary cruise. We develop a methodology to stack tracking data and account for time varying detector geometry, thereby constructing the sensitivity of the mission to GWs over the wide frequency range of 3 x 10-9 Hz to 10-4 Hz. We find that the mission has the potential to fill the gap between pulsar timing and space-based-interferometry GW observatories. If improvements in reducing Cassini era noise by a factor of O(10) are implemented, we forecast the detection of O(few) individual massive black hole binaries using two independent population models. Additionally, we determine the mission's sensitivity to both astrophysical and primordial stochastic gravitational wave backgrounds, as well as its capacity to test, or even confirm via detection, ultralight DM models. In all these cases, the tracking of the spacecraft over its interplanetary cruise would enable coverage of unexplored regions of parameter space, where signals from new phenomena in our Universe may be lurking.

The opening of the gravitational wave window has significantly enhanced our capacity to explore the Universe's most extreme and dynamic sector. In the mHz frequency range, a diverse range of compact objects, from the most massive black holes at the farthest reaches of the Universe to the lightest white dwarfs in our cosmic backyard, generate a complex and dynamic symphony of gravitational wave signals. Once recorded by gravitational wave detectors, these unique fingerprints have the potential to decipher the birth and growth of cosmic structures over a wide range of scales, from stellar binaries and stellar clusters to galaxies and large-scale structures. The TianQin space-borne gravitational wave mission is scheduled for launch in the 2030s, with an operational lifespan of five years. It will facilitate pivotal insights into the history of our Universe. This document presents a concise overview of the detectable sources of TianQin, outlining their characteristics, the challenges they present, and the expected impact of the TianQin observatory on our understanding of them.

Gravitational waves from asymmetric mass-ratio black-hole binaries carry unique information about their astrophysical environment. For instance, the Laser Interferometer Space Antenna (LISA) could potentially measure the amplitude and slope of gas torques in binaries embedded in the accretion disks of Active Galactic Nuclei, helping differentiate competing accretion disk models. However, this relies on simplified analytic models, which do not account for the stochastic variability of torques seen in hydrodynamic simulations. In this work, we use hydrodynamic simulations to create gravitational waveforms for extreme and intermediate mass-ratio inspirals in the LISA band. We then analyze these simulated waveforms using simpler templates that assume analytic torques, without stochastic time variability. By performing realistic Bayesian parameter estimation, we find no bias at 90% confidence in the binary parameters; however, estimates of accretion disk parameters, such as torque amplitude and slope, may be biased. Typically, the posterior distribution is centered around the average value of the torques, but when stochastic variability is large, the posterior can indicate no torques, even though they are present in the simulation. Our results suggest that while simplified analytic torque models work well for estimating binary parameters, caution is needed when using them to infer properties of the accretion disk. This work moves towards a more realistic assessment of one of the LISA science objectives, i.e., probing the properties of the astrophysical environments of black holes.

ABSTRACT We explore the eccentricity measurement threshold of Laser Interferometer Space Antenna (LISA) for gravitational waves radiated by massive black hole binaries (MBHBs) with redshifted BH masses Mz in the range 104.5–107.5 M⊙ at redshift z = 1. The eccentricity can be an important tracer of the environment where MBHBs evolve to reach the merger phase. To consider LISA’s motion and apply the time delay interferometry, we employ the lisabeta software and produce year-long eccentric waveforms using the inspiral-only post-Newtonian model taylorf2ecc. We study the minimum measurable eccentricity (emin, defined one year before the merger) analytically by computing matches and Fisher matrices, and numerically via Bayesian inference by varying both intrinsic and extrinsic parameters. We find that emin strongly depends on Mz and weakly on mass ratio and extrinsic parameters. Match-based signal-to-noise ratio criterion suggest that LISA will be able to detect emin ∼ 10−2.5 for lighter systems (Mz ≲ 105.5 M⊙) and ∼10−1.5 for heavier MBHBs with a 90 per cent confidence. Bayesian inference with Fisher initialization and a zero noise realization pushes this limit to emin ∼ 10−2.75 for lower-mass binaries, assuming a <50 per cent relative error. Bayesian inference can recover injected eccentricities of 0.1 and 10−2.75 for a 105 M⊙ system with an ∼10−2 per cent and an ∼10 per cent relative errors, respectively. Stringent Bayesian odds criterion ($\ln {\mathcal {B}}\gt 8$) provides nearly the same inference. Both analytical and numerical methodologies provide almost consistent results for our systems of interest. LISA will launch in a decade, making this study valuable and timely for unlocking the mysteries of the MBHB evolution.

GWnext 2024 was a meeting held in the Kavli Institute for Astronomy and Astrophysics at Peking University in March $4^\text{th} - 8^\text{th}$, 2024. In the meeting researchers at different career stages -- with a particular focus on early career scientists -- working on the different aspects of gravitational wave (GW) astronomy gathered to discuss the current status as well as prospects of the field. The meeting was divided into three core sessions: Astrophysics, GW Theory, and Detection. Each session consisted of introductory talks and extended discussion sessions. Moreover, there was a poster session where students could present their results. In this paper, we summarize the results presented during the meeting and present the most important outcomes.

ABSTRACT We assess the possibility of detecting both eccentricity and gas effects (migration and accretion) in the gravitational wave (GW) signal from LISA massive black hole binaries at redshift $z=1$. Gas induces a phase correction to the GW signal with an effective amplitude ($C_{\rm g}$) and a semimajor axis dependence (assumed to follow a power-law with slope $n_{\rm g}$). We use a complete model of the LISA response and employ a gas-corrected post-Newtonian inspiral-only waveform model TaylorF2Ecc. By using the Fisher formalism and Bayesian inference, we constrain $C_{\rm g}$ together with the initial eccentricity $e_0$, the total redshifted mass $M_z$, the primary-to-secondary mass ratio q, the dimensionless spins $\chi _{1,2}$ of both component BHs, and the time of coalescence $t_c$. We find that simultaneously constraining $C_{\rm g}$ and $e_0$ leads to worse constraints on both parameters with respect to when considered individually. For a standard thin viscous accretion disc around $M_z=10^5~{\rm M}_{\odot }$, $q=8$, $\chi _{1,2}=0.9$, and $t_c=4$ years MBHB, we can confidently measure (with a relative error of $\lt 50$ per cent) an Eddington ratio ${\rm f}_{\rm Edd}\sim 0.1$ for a circular binary and ${\rm f}_{\rm Edd}\sim 1$ for an eccentric system assuming $\mathcal {O}(10)$ stronger gas torque near-merger than at the currently explored much-wider binary separations. The minimum measurable eccentricity is $e_0\gtrsim 10^{-2.75}$ in vacuum and $e_0\gtrsim 10^{-2}$ in gas. A weak environmental perturbation (${\rm f}_{\rm Edd}\lesssim 1$) to a circular binary can be mimicked by an orbital eccentricity during inspiral, implying that an electromagnetic counterpart would be required to confirm the presence of an accretion disc.

We study the gravitational wave (GW) emission of sources perturbed by periodic dynamical forces which do not cause secular evolution in the orbital elements. We construct a corresponding post-Newtonian waveform model and provide estimates for the detectability of the resulting GW phase perturbations, for both space-based and future ground-based detectors. We validate our results by performing a set of Bayesian parameter recovery experiments with post-Newtonian waveforms. We find that, in stark contrast to the more commonly studied secular dephasing, periodic phase perturbations do not suffer from degeneracies with any of the tested vacuum binary parameters. We discuss the applications of our findings to a range of possible astrophysical scenarios, finding that such periodic perturbations may be detectable for massive black hole binaries embedded in circum-binary discs, extreme mass-ratio inspirals in accretion discs, as well as stellar-mass compact objects perturbed by tidal fields. We argue that modelling conservative sub-orbital dynamics opens up a promising new avenue to detect environmental effects in binary sources of GWs that should be included in state-of-the-art waveform templates.

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.

GW190521, the most massive binary black hole merger confidently detected by the LIGO-Virgo-KAGRA collaboration, is the first gravitational-wave observation of an intermediate-mass black hole. The signal was followed approximately 34 days later by flare ZTF19abanrhr, detected in AGN J124942.3+344929 by the Zwicky Transient Facility at the 78% spatial contour for GW190521s sky localization. Using the GWTC-2.1 data release, we find that the association between GW190521 and flare ZTF19abanrhr as its electromagnetic counterpart is preferred over a random coincidence of the two transients with a log Bayes factor of 8.6, corresponding to an odds ratio of $\sim$ 5400 to 1 for equal prior odds and $\sim$ 400 to 1 assuming an astrophysical prior odds of 1/13. Given the association, the multi-messenger signal allows for an estimation of the Hubble constant, finding $H_0 = 102^{+27}_{-25}\mathrm{\ km \ s^{-1} \ Mpc^{-1}}$ when solely analyzing GW190521 and $79.2^{+17.6}_{-9.6}\mathrm{\ km \ s^{-1} \ Mpc^{-1}}$ assuming prior information from the binary neutron star merger GW170817, both consistent with the existing literature.

ABSTRACT We investigate the properties of stars born via gravitational instability in accretion discs around supermassive black holes (SMBHs) in active galactic nuclei (AGNs), and how this varies with the SMBH mass, accretion rate, or viscosity. We show with geometrically thin, steady-state disc solutions that fragmentation results in different populations of stars when one considers the initial conditions (e.g. density and temperature of the gravitationally unstable regions). We find that opacity gaps in discs around $10^6 \, {\rm M}_{\odot }$ SMBHs can trigger fragmentation at radii ≲ 10−2 pc, although the conditions lead to the formation of initially low stellar masses primarily at $0.1\!-\!0.5 \, {\rm M}_{\odot }$. Discs around more massive SMBHs ($M_{\rm BH} =10^{7-8} \, {\rm M}_{\odot }$) form moderately massive or supermassive stars (the majority at $10^{0-2} \, {\rm M}_{\odot }$). Using linear migration estimates, we discuss three outcomes: stars migrate till they are tidally destroyed, accreted as extreme mass ratio inspirals (EMRIs), or leftover after disc dispersal. For a single-AGN activity cycle, we find a lower limit for the EMRI rate $R_{\rm emri}\sim 0\!-\!10^{-4} \, \rm yr^{-1}$ per AGN assuming a star formation efficiency $\epsilon =1\!-\!30{{\ \rm per\ cent}}$. In cases where EMRIs occur, this implies a volumetric rate up to $0.5\!-\!10 \, \rm yr^{-1}\, Gpc^{-3}$ in the local Universe. The rates are particularly sensitive to model parameters for $M_{\rm BH}=10^6 \, {\rm M}_{\odot }$, for which EMRIs only occur if stars can accrete to 10s of solar masses. Our results provide further evidence that gas-embedded EMRIs can contribute a substantial fraction of events detectable by milliHz gravitational wave detectors such as the Laser Interferometer Space Antenna (LISA). Our disc solutions suggest the presence of migration traps, as has been found for more massive SMBH discs. Finally, the surviving population of stars after the disc lifetime leaves implications for stellar discs in galactic nuclei.

This text will appear as Section II of Chapter 5 of the book "Black Holes in the Era of Gravitational-Wave Astronomy". As a stand alone text, it serves as a brief overview of astrophysics and gravitational wave radiation of extreme mass ratio inspirals, or EMRIs. Topics covered consist of: dynamical and gas-assisted formation channels, basics of EMRI dynamics and gravitational radiation, and science potential for both astrophysics and fundamental physics.

We analyse the effect of stochastic torque fluctuations on the orbital evolution and the gravitational wave (GW)emission of gas-embedded sources with intermediate and extreme mass ratios. We show that gas-driven fluctuations imprint additional harmonic content in the GWs of the binary system, which we dub dirty waveforms(DWs). We find three interesting observational prospects for DWs, provided that torque fluctuations do indeed persist beyond the resolution limit of current hydrodynamical simulations. Firstly, DWs can produce a significant stochastic GW background, comparable to other GW noise sources. Secondly, the energy flux implied by the additional harmonics can cause a detectable secular phase shift in Laser Interferometer Space Antenna (LISA) sources, even if the net torque fluctuations vanish when averaged over orbital time-scales. Lastly, the DWs of moderate-redshift nHz supermassive binaries detectable by pulsar timing arrays (PTAs) could be detectable in the mHz range, producing a new type of PTA-LISA multiband gravitational source. Our results suggest that searching for DWs and their effects can potentially be a novel way to probe the heaviest of black holes and the physics of the accretion discs surrounding them. We find these results to be a further confirmation of the many exciting prospects of actively searching for environmental effects within the data stream of future GW detectors.

ABSTRACT We study the effect of torques on circular inspirals of intermediate-mass black hole binaries (IMBHBs) embedded in gas discs, wherein both BH masses are in the range 102–105 M⊙, up to redshift z = 10. We focus on how torques impact the detected gravitational wave (GW) waveform in the LISA frequency band when the binary separation is within a few hundred Schwarzschild radii. For a sub-Eddington accretion disc with a viscosity coefficient α = 0.01, surface density Σ ≈ 105 g cm−2, and Mach number $\mathcal {M}_{\rm {a}}\approx 80$, a gap, or a cavity, opens when the binary is in the LISA band. Depending on the torque’s strength, LISA will observe dephasing in the IMBHB’s GW signal up to either z ∼ 5 for high mass ratios (q ≈ 0.1) or to z ∼ 7 for q ≈ 10−3. We study the dependence of the measurable dephasing on variations of BH masses, redshift, and accretion rates. Our results suggest that phase shift is detectable even in high-redshift (z = 10) binaries if they experience super-Eddington accretion episodes. We investigate if the disc-driven torques can result in an observable ‘time-dependent’ chirp mass with a simplified Fisher formalism, finding that, at the expected signal-to-noise ratio, the gas-induced variation of the chirp mass is too small to be detected. This work shows how gas-induced perturbations of vacuum waveforms should be strong enough to be detected by LISA for the IMBHB in the early inspiral phase. These perturbations encode precious information on accretion discs and galactic nuclei astrophysics. High-accuracy waveform models which incorporate these effects will be needed to extract such information.

ABSTRACTAmong the potential milliHz gravitational wave (GW) sources for the upcoming space-based interferometer LISA are extreme- or intermediate-mass ratio inspirals (EMRI/IMRIs). These events involve the coalescence of supermassive black holes in the mass range 105M⊙ ≲ M ≲ 107M⊙ with companion BHs of much lower masses. A subset of E/IMRIs are expected to occur in the accretion discs of active galactic nuclei (AGNs), where torques exerted by the disc can interfere with the inspiral and cause a phase shift in the GW waveform. Here we use a suite of 2D hydrodynamical simulations with the moving-mesh code disco to present a systematic study of disc torques. We measure torques on an inspiralling BH and compute the corresponding waveform deviations as a function of the binary mass ratio q ≡ M2/M1, the disc viscosity (α), and gas temperature (or equivalently Mach number; $\mathcal {M}$). We find that the absolute value of the gas torques is within an order of magnitude of previously determined planetary migration torques, but their precise value and sign depends non-trivially on the combination of these parameters. The gas imprint is detectable by LISA for binaries embedded in AGN discs with surface densities above $\Sigma _0\ge 10^{4-6} \rm \, g cm^{-2}$, depending on q, α, and $\mathcal {M}$. Deviations are most pronounced in discs with higher viscosities, and for E/IMRIs detected at frequencies where LISA is most sensitive. Torques in colder discs exhibit a noticeable dependence on the GW-driven inspiral rate as well as strong fluctuations at late stages of the inspiral. Our results further suggest that LISA may be able to place constraints on AGN disc parameters and the physics of disc–satellite interaction.

Using numerical hydrodynamics calculations and a novel method for densely sampling parameter space, we measure the accretion and torque on a binary system from a circumbinary disk. In agreement with previous studies, we find that the net torque on the binary is positive for mass ratios close to unity, and that accretion always drives the binary towards equal mass. Accretion variability depends sensitively on the numerical sink prescription, but the torque and relative accretion onto each component do not depend on the sink timescale. Positive torque and highly variable accretion occurs only for mass ratios greater than around $0.05$. This means that for mass ratios below $0.05$, the binary would migrate inward until the secondary accreted sufficient mass, after which it would execute a U-turn and migrate outward. We explore a range of viscosities, from $\alpha = 0.03$ to $\alpha = 0.15$, and find that this outward torque is proportional to the viscous torque, simply proportional to viscosity in this range. Dependence of accretion and torque on mass ratio is explored in detail, densely sampling mass ratios between $0.01$ and unity. For mass ratio $q > 0.6$, accretion variability is found to exhibit a distinct sawtooth pattern, typically with a five-orbit cycle that provides a "smoking gun" prediction for variable quasars observed over long periods, as a potential means to confirm the presence of a binary.