The space-based detector Laser Interferometer Space Antenna (LISA) will observe inspiralling black hole binaries in the mHz band, many of which may retain orbital eccentricity. In contrast to quasicircular binaries, eccentric systems radiate through multiple orbital harmonics, while relativistic periastron precession introduces a secular phase structure in the waveform. We exploit this structure to develop a parametrized test of general relativity (GR) for eccentric bound orbits. We construct a frequency-domain eccentric waveform model in which a phenomenological deviation parameter δα modifies the GR prediction for the conservative azimuthal-to-radial frequency ratio, with δα=0 corresponding to GR. We consider two parametrizations of this deformation. In the first, δα modifies only the explicit precession-dependent sideband structures of the waveform. In the second, the secular precession phase is assigned to the dominant lower-order angular carriers and retained in resummed form. The latter produces a substantially stronger response because the dominant waveform components coherently accumulate the modified phase. We implement both models within lisabeta and perform a Bayesian analysis including the time- and frequency-dependent LISA response and associated time-delay-interferometry observables. We find that LISA can place stringent constraints on the parametrized deviation. For a binary with chirp mass 3000 M_⊙, initial eccentricity e_0=0.5 observed for four years at an SNR of 50, the second model yields a 90% credible bound of |δα|≲ 10^-4. Increasing eccentricity further sharpens the constraints by introducing additional harmonic structure and reducing degeneracies among the binary parameters. The framework developed here is general and can be extended to more complete eccentric waveform models.

Ground-based gravitational wave (GW) detectors have discovered about 200 compact object mergers. The astrophysical origins of these events are highly debated, and it is possible that at least a fraction of them originate from dynamical environments. Among these, the disks of active galactic nuclei (AGN) are particularly interesting as promising environments, as some observed properties may be more readily produced there. When compact objects merge in these environments, acceleration from the central supermassive black hole or nearby companions is inevitable. Such acceleration induces a phase shift in the observed GW waveforms, which can serve as a useful tool to distinguish the underlying merging environments for each GW event. In this paper, we investigate the expected distribution of such acceleration-induced GW phase shifts, using a semianalytical model combined with a 1D AGN population synthesis code. We find significant contributions from three-body interactions involving a nearby third object. Our results indicate that the GW phase shift is likely to be larger compared to other channels, making it distinguishable by future GW facilities such as TianQin, DECIGO, Taiji, Einstein Telescope, and Cosmic Explorer. Interestingly, a notable fraction of mergers in fact exhibit a significant GW phase shift (≳1 rad) at frequencies above 10 Hz, which could even be detectable by current GW detectors such as LIGO/Virgo/KAGRA. Additionally, if gas-hardening during three-body interactions is taken into account, the GW frequency can be boosted to ≳10 Hz, potentially further aiding in the detection of the phase shift.

We study the gravitational dynamics of quasi-hierarchical triple systems, where the outer orbital period is significantly longer than the inner one, but the outer orbit is extremely eccentric, rendering the time at pericentre comparable to the inner period. Such systems are not amenable to the standard techniques of perturbation theory and orbit-averaging. Modelling the evolution of these triples as a sequence of impulses at the outer pericentre, we show, by comparing with direct three-body integrations, that such triples lend themselves to a description as an analytical map between subsequent outer pericentre passages. This map exhibits secular oscillations, going beyond the von Zeipel-Lidov-Kozai mechanism. We show that the time to coalescence due to gravitational waves in such systems is modified. We then study the long-term evolution under this map, which lead to a random-walk-like behaviour of the inner eccentricity. While this behaviour is probably absent from isolated triples, it could exist in triples where the outer orbit is weakly coupled to a system with which it can exchange angular momentum, and we describe some properties of this random walk.

We introduce a complete model for dephasing due to line-of-sight acceleration (LOSA) in gravitational wave (GW) signals from stellar-mass binary black holes (BBHs) in three-body systems. Our prescription provides curvature- and projection-dependent phase features that are not recovered by local-expansion-based treatments. We perform parameter-space surveys and mock parameter inferences assuming the nominal sensitivity of the Einstein Telescope (ET) to identify the regime where the time-varying LOSA allows for separate constraints on the outer orbital parameters, in particular the tertiary mass and distance. We estimate that ET may detect a few to tens of such systems per year, provided that all binaries merge dynamically, and demonstrate that these constraints can be used to directly discriminate between a dynamical and AGN origin for BBHs. Finally, we reanalyse the GW190814 event and four O4a events finding no evidence for LOSA, with the previously claimed LOSA in GW190814 disappearing when a sufficiently long data segment is used.

We demonstrate that the properties of eccentric gravitational wave (GW) signals enhance the detectability of GW phase shifts caused by environmental effects (EEs): The signal-to-noise ratio (SNR) of EEs can be boosted by up to ℓ_ max^1 - n with respect to corresponding circular signals, where ℓ_ max is the highest modeled eccentric GW harmonic and n is the frequency scaling of the GW dephasing prescription associated to the EE. We investigate the impact on a population level, adopting plausible eccentricity distributions for binary sources observed by LIGO/Virgo/Kagra (A+ and A# sensitivities), as well as Cosmic Explorer (CE) and the Einstein Telescope (ET). For sources in the high eccentricity tail of a distribution (e ≳ 0.2 at 10 Hz), phase shifts can systematically be up to ℓ_ max^1 - n times smaller than in a corresponding circular signal and still be detectable. For typical EEs, such as Roemer delays and gas drag, this effect amounts to SNR enhancements that range from 10^2 up to 10^5. For CE and ET, our analysis shows that EEs will be an ubiquitous feature in the eccentric tail of merging binaries, regardless of the specific details of the formation channel. Additionally, we find that the joint analysis of eccentricity and phase shift is already plausible in current catalogs if a fraction of binaries merge in AGN migration traps.

We argue that all dynamical astrophysical black hole merger channels are expected to result in a common eccentricity distribution at gravitational wave (GW) frequencies relevant for LIGO/Virgo/KAGRA (LVK) in the high eccentricity limit. This follows from the large separation of scales between the GW regime required for creating eccentric mergers in LVK, and the underlying astrophysical formation environment. Our analytical solution shows exceptional agreement with numerical studies. This finding has important implications for both theoretical studies and ongoing searches for eccentric GW sources.

The accretion of dark matter (DM) onto compact objects and the potential gravitational collapse of neutron stars due to this accretion has become a promising indirect probe of DM properties, complementing terrestrial experiments. We show that the accretion flux of DM on stellar objects is amplified in binary systems due to the complex gravitational interaction of said particles with the binary. We perform few-body Monte Carlo simulations to show that this amplification factor is similar to 4-5 for circular binaries, small DM velocity dispersions and mass ratios q greater than or similar to 0.3. We use this factor to improve previous constraints on the scattering cross section of nonannihilating bosonic DM with baryonic matter, and derive upper bounds on this cross section from the observation of the binary NS merger associated with GW170817. We also show that the maximally accretable mass fraction of DM by binary NSs is less than or similar to 10-3, even for extreme DM densities only possible in DM spikes, due to the dynamical friction exerted by the ambient DM.

Dynamical tides can provide us vital information about the properties of neutron star (NS) matter. This is particularly true for g-modes, whose frequency and tidal coupling are highly sensitive to the composition of NSs, especially in their centers, where microphysical models are the least reliable. However, due to their weak coupling to external tidal fields, their effect on the gravitational-wave (GW) signal of binary inspirals can be difficult to observe. Here we show that the detectability of these tides can be significantly enhanced by binary NSs with moderate eccentricities. This is primarily due to higher eccentric harmonics in the early phase of the binary evolution experiencing larger phase shifts, which they transport to the sensitive band of GW detectors. In addition, g-mode tides in eccentric binaries undergo several epicyclic resonances, which also amplify the total phase shift. We demonstrate that these effects increase the detectability of g-mode dynamical tides by more than an order of magnitude for eccentricities of e10 Hz similar to 0.2-0.4, making it possible to put robust constraints on g-mode properties using current GW detectors, while all relevant models could potentially be constrained with eccentric binary NSs with the Einstein Telescope.

The discs of Active Galactic Nuclei (AGNs) provide a natural environment where stellar mass-black holes can dynamically pair, undergo repeated interactions, and eventually merge. It is commonly assumed that gas accretion will both efficiently spin-up disc-embedded black holes and align the orbits of embedded binaries with the disc plane, leading to mergers with preferentially positive effective spin parameters (chi(eff)). Such predictions have motivated the use of chi(eff) as a diagnostic for identifying candidate AGN-embedded mergers in the LIGO-Virgo-KAGRA gravitational wave catalogue. In this work, we perform post-Newtonian N-body simulations of nearly planar binary-single encounters and apply an empirically motivated gas-driven alignment prescription to characterize the expected chi(eff)-eccentricity correlations of AGN-embedded mergers. By comparing the alignment and gravitational wave inspiral time-scales, we identify the regions of parameter space, across both disc location and binary properties, where full disc-spin-orbit alignment is effective and where it is not. We find that quasi-circular binaries typically align by the time they merge, supporting the standard picture of spin-orbit aligned orientations. By contrast, eccentric binaries (with in-band eccentricity e(10Hz) greater than or similar to 0 . 1 ) typically inspiral too quickly for gas torques to act, preserving the post-encounter spin-orbit misalignments and yielding more isotropic chi(eff) distributions when disc densities and torque efficiencies are modest. This interplay naturally establishes a correlation between binary eccentricity and chi(eff) in AGN discs, highlighting a new key observable of the AGN channel and a potential explanation for massive events such as GW190521 and GW231123.

We develop a general framework to characterize non-vacuum perturbations to relativistic binaries in the gravitational-wave (GW) driven regime, for use in GW parameter estimation studies. The effect of smooth, structured and stochastic perturbations to the binary's motion is reduced to a resonant spectral projection defined on a rolling averaging window, with weights given by Hansen coefficients. This is combined with practical criteria for identifying and evaluating the corresponding dynamical response to perturbations, starting from either analytical models or numerical simulations of binaries in environments. The result is a set of coupled ODEs for the orbital elements that capture epi-cyclic, apsidal and nodal resonances, consistently incorporate feedback from radiation reaction and can be solved efficiently on a coarse time grid. We demonstrate the practical application of the framework in two representative astrophysical scenarios: a compact binary in a variable tidal field and an extreme-mass-ratio inspiral in an accretion disk. We propose the Lagrange-Fourier-Hansen framework as a unified tool for modeling environmental effects in GW templates for eccentric and precessing binary sources, and particularly for bridging the gap between phenomenological prescriptions and realistic models of binaries in environments.

The disks of active galactic nuclei (AGNs) are expected to be populated by numerous stars, either formed in the outer regions of the disk via gravitational instability or captured from the nearby nuclear star cluster. Regardless of their formation mechanism, these stars experience altered evolutionary paths, mostly shaped by the accretion of dense disk material. In this study, through the comparison of different timescales, we chart the evolutionary outcomes of these AGN stars as a function of disk radius and across a range of supermassive black hole masses, spanning from 10 6 to 10 9 M ⊙ , for two popular AGN disk models. We find that in the outer regions of the disk, stars evolve similarly to those in the interstellar medium, but in the inner and denser regions, accretion quickly turns low-mass stars into massive stars, and their fate depends on just how quickly they accrete. If accretion occurs at a faster rate than nuclear burning, they can reach a quasi-steady “immortal” state. If stars accrete faster than they can thermally adjust, runaway accretion occurs, potentially preventing a quasi-steady state and altering the disk structure. During the AGN lifetime, in the regions of the disk that produce massive stars, supernovae (SNe) and gamma-ray bursts (GRBs) may occur within the disk over a wide range of optical depths and ambient densities. Subsequently, in the final phase of the AGN, as the disk becomes depleted, formerly immortal stars will be unable to replenish their fuel, leading to additional SNe and GRBs.

We model the effect of resonances between time-varying perturbative forces and the epicyclical motion of eccentric binaries in the gravitational wave (GW) driven regime. These induce secular drifts in the orbital elements, which are reflected in a dephasing of the binary's GW signal, derived here systematically. The resulting dephasing prescriptions showcase a much richer phenomenology with respect to typically adopted models and are better able to model realistic environmental effects. The most important consequences are for gas embedded binaries, which we analyze in detail with a series of analytical calculations, numerical experiments, and a curated set of hydrodynamical simulations for equal masses. Even in these simplified tests, we find the surprising result that dephasing caused by epicyclical resonances dominate over expectations based on smoothed or orbit averaged gas drag models in GW signals that retain mild eccentricity in the detector band (e > 0.05). We discuss how dissecting GW dephasing in its component Fourier modes can be used to probe the coupling of binaries with their surrounding environment in unprecedented detail.

We here quantify the gravitational-wave (GW) phase shift appearing in the waveform of eccentric binary black hole (BBH) mergers formed dynamically in 3-body systems. For this, we have developed a novel numerical method where we construct a reference binary, by evolving the post-Newtonian ( PN ) evolution equations backwards from a point near merger without the inclusion of the third object, that can be compared to the perturbed binary that evolves under the influence from the third BH. From this, we quantify how the interplay between dynamical tides, PN -effects, and the time-dependent Doppler shift of the eccentric GW source results in unique observable GW phase shifts that can be used to probe the dynamical assembly mechanism of individual GW sources. We further find an analytical expression for the GW phase shift, which has a universal functional form that only depends on the time-evolving BBH eccentricity. The normalization scales with the BH masses and initial separation, which can be linked to the underlying astrophysical environment. GW phase shifts from a chaotic 3-body BH scattering taking place in a cluster, and from a BBH inspiraling in a disk migration trap near a supermassive BH, are also shown for illustration.

In the first part of this work, we provide a curated overview of the theoretical framework necessary for incorporating dephasing due to environmental effects (EEs) in gravitational wave (GW) templates. We focus in particular on the relationship between orbital perturbations in the time-domain and the resulting dephasing in both time and frequency domain, elucidating and resolving some inconsistencies present in the literature. We discuss how commonly studied binary environments often result in several sources of dephasing that affect the GW signal at the same time. This work synthesizes insights from two decades of literature, offering a unified conceptual narrative alongside a curated reference of key formulas, illustrative examples and methodological prescriptions. It can serve both as a reference for researchers in the field as well as a modern introduction for those who wish to enter it. In the second part, we derive novel aspects of dephasing for eccentric GW sources and lay the foundations for consistently treating the full problem. Importantly, we demonstrate that the detectability of EEs can be significantly enhanced in the presence of eccentricity, even for e10Hz less than or similar to 0.2, substantially increasing the prospects for detection in ground based detectors. Our results highlight the unique potential of modeling and searching for EE in eccentric binary sources of GWs.

This study explores the formation and implications of mini-active galactic nuclei (mAGN) disks around intermediate-mass black holes (IMBHs) embedded in gas-rich globular/nuclear clusters (GCs). We examine the parameter space for stable mAGN disks, considering the influence of IMBH mass, disk radius, and gas density on disk stability. The dynamics of stars and black holes within the mAGN disk are modeled, with a focus on gas-induced migration and gas dynamical friction. These dynamical processes can lead to several potentially observable phenomena, including the alignment of stellar orbits into the disk plane, the enhancement of gravitational wave mergers (particularly IMRIs and EMRIs), and the occurrence of mili/centi-tidal disruption events (mTDEs/cTDEs) with unique observational signatures. We find that gas hardening can significantly accelerate the inspiral of binaries within the disk, potentially leading to a frequency shift in the emitted gravitational waves. Additionally, we explore the possibility of forming accreting IMBH systems from captured binaries within the mAGN disk, potentially resulting in the formation of ultraluminous X-ray sources (ULXs). The observational implications of such accreting systems, including X-ray emission, optical signatures, and transient phenomena, are discussed. Furthermore, we investigate the possibility of large-scale jets emanating from gas-embedded IMBHs in GCs. While several caveats and uncertainties exist, our work highlights the potential for mAGN disks to provide unique insights into IMBH demographics, accretion physics, and the dynamics of GCs.

We study the gravitational-wave (GW) phase shift arising from center-of-mass accelerations of binary black hole (BBH) mergers formed dynamically in three-body systems, where both the inner orbit of the merging binary and the outer orbit are eccentric. We provide a semi-analytical model and several analytical approximations that allow for fast evaluation of both the temporal evolution and the maximum value of the phase shift. The highest phase shifts occur when the binary merges close to the pericenter of the outer orbit, and can in this case be orders of magnitude larger compared to the circular limit. At high outer-orbit eccentricities, the orbital curvature leaves distinct imprints on the phase shift if the binary passes the outer pericenter during its inspiral. By comparing with phase shifts measured in numerical chaotic three-body scatterings, we show that our model accurately describes the observed phase of dynamically assembled binary systems in realistic astrophysical scenarios, providing a way to directly determine their formation channel via single GW observations. Phase shifts produced in such environments may receive additional amplifications due to the tidal pull from the perturber on the BBH.

Strong lensing of gravitational wave (GW) sources allows the observer to see the GW source from different lines-of-sight (LOS) through the corresponding images, which provides a way for constraining the relative proper motion of the GW source. This is possible as the GW signals received from each image will have slightly different projected velocity components, from which one can `Doppler-Triangulate' for the GW source velocity vector. The difference in projected velocity between the different images can be observationally inferred through pairwise GW phase measurements that accumulate over the time-of-observation. In this paper we study lensed eccentric GW sources and explore how the observable GW phase shift between images evolve as a function of time, eccentricity, lens- and binary parameters. Next generation GW observatories, including the Einstein Telescope and Cosmic Explorer, will see ∼hundreds/year of lensed GW sources, where a significant fraction of these are expected to be eccentric. We discuss the expected unique observables for such eccentric lensed GW sources, and the relation to their observable relative linear motion, which otherwise is exceedingly difficult to constrain in general.

Strongly lensed binary neutron star (NS–NS) mergers are expected to be observed once LIGO/Virgo/Kagra reaches the planned A+ or proposed A# sensitivity. We demonstrate that the relative transverse velocity of the source-lens system can be constrained by comparing the phase of the two associated gravitational wave (GW) images, using both semianalytical and numerical Bayesian methods. For A+ sensitivity, a 1 σ NS–NS merger signal in magnification ( μ = 200) and redshift ( z _S = 1) will carry a marginally detectable dephasing signature for a source transverse velocity of ∼1800 km s ^−1 . This is comparable to the velocity dispersion of large galaxy clusters. Assuming the same population distribution, the most likely source parameters of μ = 100 and z _S = 1.4 are always expected to showcase detectable dephasing imprints for A# sensitivity, provided they are moving with transverse velocities larger than ∼ 2000 km s ^−1 . We conclude that a first measurement of the relative transverse velocity of a source via GW dephasing methods is likely only a few years away.

The observation of multiple images from a strongly lensed gravitational wave (GW) source provides the observer with a stereoscopic view of the source. This allows for a measure of its relative proper motion by comparing the induced GW Doppler shifts between the different images. In addition, if the GW source is in a dynamical environment it will be subject to an acceleration, which will show up as a time dependent Doppler shift in each individual image. In this work we quantify for the first time how a joint detection of these effects can be used to constrain the underlying dynamics and environment of the lensed GW source. We consider a range of different astrophysical environments, from massive clusters to stellar triples, and find that binary black hole (BBH) mergers in Active Galactic Nuclei disks (AGN-disks) are particularly likely to have orbital parameters that can be constrained through our considered lensing setup. Applying these methods to the upcoming catalog of cosmologically strongly lensed GW sources will open up new possibilities for probing their origin and underlying formation mechanisms.