Post-Newtonian waveforms from spinning scattering amplitudes

We revisit the phases of the pairing and sinking of black holes (BHs) in galaxy mergers and circumnuclear discs in light of the results of recent simulations with massive BHs embedded in predominantly gaseous backgrounds. After a general overview we highlight for the first time the existence of a clear transition, for unequal mass BHs, between the regime in which the orbital decay is dominated by the conventional dynamical friction wake and one in which global disc torques associated with density waves launched by the secondary BH as well as co-orbital torques arising from gas gravitationally captured by the BH dominate and lead to faster decay. The new regime intervenes at BH binary separations of a few tens of parsecs and below, following a phase of orbital circularization driven dynamical friction. It bears some resemblance with planet migration in protoplanetary discs. While the orbital timescale is reasonably matched by the migration rate for the Type-I regime, the dominant negative torque arises near the co-rotation resonance, which is qualitatively similar to what is found in the so-called Type-III migration, the fastest migration regime identified so far for planets. This fast decay rate brings the BHs to separations of order 10−1 pc, the resolution limit of our simulations, in less than ∼107 yr in a smooth disc, while the decay timescale can increase to >108 yr in clumpy discs due to gravitational scattering with molecular clouds. Eventual gap opening at sub-pc scale separations will slow down the orbital decay subsequently. How fast the binary BH can reach the separation at which gravitational waves take over will be determined by the nature of the interaction with the circumbinary disc and the complex torques exerted the gas flowing through the edge of such disc, the subject of many recent studies. We also present a new intriguing connection between the conditions required for rapid orbital decay of massive BH binaries and those required for prominent gas inflows in gas-rich galaxies undergoing major mergers. We derive a condition for the maximum inflow rate that a circumnuclear disc can host while still maintaining a sufficiently high gas density at large radii to sustain the decay of a BH binary. We find that gas inflows rates exceeding 10 M⊙ yr−1, postulated to form massive BH seeds in some direct collapse models, would stifle the sinking of massive BH binaries in gas-dominated galactic nuclei. Vice-versa, lower inflow rates, below a solar mass per year, as required to feed typical active galactic nuclei (AGNs), are compatible with a fast orbital decay of BH binaries across a wide range of masses.

Studying the formation and evolution of black hole binaries (BHBs) is essential for the interpretation of current and forthcoming gravitational wave (GW) detections. We investigate the statistics of BHBs that form from isolated binaries, by means of a new version of the SEVN population-synthesis code. SEVN integrates stellar evolution by interpolation over a grid of stellar evolution tracks. We upgraded SEVN to include binary stellar evolution processes and we used it to evolve a sample of $1.5\times{}10^8$ binary systems, with metallicity in the range $\left[10^{-4};4\times 10^{-2}\right]$. From our simulations, we find that the mass distribution of black holes (BHs) in double compact-object binaries is remarkably similar to the one obtained considering only single stellar evolution. The maximum BH mass we obtain is $\sim 30$, $45$ and $55\, \mathrm{M}_\odot$ at metallicity $Z=2\times 10^{-2}$, $6\times 10^{-3}$, and $10^{-4}$, respectively. A few massive single BHs may also form ($\lesssim 0.1\%$ of the total number of BHs), with mass up to $\sim 65$, $90$ and $145\, \mathrm{M}_\odot$ at $Z=2\times 10^{-2}$, $6\times 10^{-3}$, and $10^{-4}$, respectively. These BHs fall in the mass gap predicted from pair-instability supernovae. We also show that the most massive BHBs are unlikely to merge within a Hubble time. In our simulations, merging BHs like GW151226 and GW170608, form at all metallicities, the high-mass systems (like GW150914, GW170814 and GW170104) originate from metal poor ($Z\lesssim{}6\times 10^{-3}$) progenitors, whereas GW170729-like systems are hard to form, even at $Z = 10^{-4}$. The BHB merger rate in the local Universe obtained from our simulations is $\sim 90 \mathrm{Gpc}^{-3}\mathrm{yr}^{-1}$, consistent with the rate inferred from LIGO-Virgo data.

It is still unknown how a binary black hole (BBH) evolves after its semi-major axis has reached the sub-parsec scale, where dynamical friction with neighboring stars is no longer effective (the so-called final-parsec problem). In this paper, we propose a new mechanism by which a massive BBH can naturally coalesce within a Hubble time. We consider the evolution of a BBH with a triple disk composed of an accretion disk around each black hole and one circumbinary disk surrounding them. While the circumbinary disk removes the orbital angular momentum of the BBH via a binary-disk resonant interaction, the mass transfer from the circumbinary disk to each black hole adds some fraction of its angular momentum to the orbital angular momentum of the BBH. We find that there is a critical value of the mass-transfer rate where extraction of the orbital angular momentum from the BBH is balanced with the addition of orbital angular momentum to the BBH. The semi-major axis of the BBH decays with time, whereas the orbital eccentricity of the BBH grows with time, if the mass-transfer rate is smaller than the critical one, and vice versa. Its evolutionary timescale is characterized by the product of the viscous timescale of the circumbinary disk and the ratio of the total black-hole mass to the mass of the circumbinary disk. Most massive BBHs are able to merge within a Hubble time by the proposed mechanism, which helps to solve the final parsec problem.

Monday, 5th of September 2016Chair: M. ColpiS. VitaleThe LTP experiment on LISA Pathfinder and its first resultsK. DooleyAdvanced LIGO: news from the dark universeB. SchutzLIGOs Black Holes and Science in the LISA EraP. McNamaraLISA Pathfinder: First steps to observing gravitational waves from spaceM. HewitsonIn-flight Performance of the Optical Metrology System on LISA PathfinderW. WeberPhysical model of the LISA Pathfinder differential acceleration measurement and its application to LISAK. DanzmannThe Status of LISAChair: O. JennrichJ. MartinoOn-flight characterization of Coldgas micro-Newton thrusters for Lisa PathfinderM. NofrariasMagnetic force noise in LISA PathfinderL. FerraioliThe LISA Pathfinder GRS Front-End ElectronicsD. VetrugnoThe Δg workflow: from measured displacements to the differential external acceleration.A. WittchenCoupling of relative intensity noise and pathlength noise to the length measurement in the optical metrology system of LISA PathfinderS. PaczkowskiLaser frequency stabilisation and interferometer path length differences on LISA PathfinderR. GiusteriThe free-fall mode experiment on LISA Pathfinder: first resultsP. WassElectrostatic test-mass force-noise disturbances as measured by LISA PathfinderR. DolesiThe contribution of Brownian noise from viscous gas damping to the differential acceleration noise measured in LISA Pathfinder between two nominally free falling test massesC. TrenkelThe engineering of LISA Pathfinder – the quietest laboratory ever flown in spaceW. KlipsteinLISA-derived Flight Phasemeter on the GRACE Follow-On MissionP. LauferMEMS Ion Thruster Chips to Significantly Enhance Cold Gas Thruster Lifetime for LISAM. TintoEnhanced Gravitational Wave Science with LISA and gLISATuesday, 6th of September 2016Chair: P. McNamaraF. RicciAdvanced VIRGO: State of the ArtC. BelczynskiEvolutionary predictions in the advanced LIGO/Virgo eraA. SesanaThe promise of multi-band gravitational wave astronomyB. SathyaprakashExploring the Universe with third generation interferometersS. SatoThe status of DECIGOG. HeinzelSatellite interferometry from LTP and GRACE Follow-On to LISAP. BinetruyCosmology with LISAChair: S. VitaleA. Giménez CañeteBeyond LISA PathfinderP. HertzNASA Astrophysics Program: Present and FutureF. SafaESA activities towards the Gravitation Waves Space ObservatoryH. WardLPF Interferometry and route to LISAJ. CampDevelopment of a US Laser System for the Gravitational Wave Mission LISAT. SchwarzePerformance of an optical three-signal test for the LISA metrologyM. LaporteStatus of the eLISA on table (LOT) electro-optical simulator for space based gravitational waves observatoriesS. AppleUF Torsion Pendulum and GRS Technology DevelopmentJ. LivaseLISA Telescope In-field Pointing and Scattered Light StudyK. IsleifThe LISA backlink – comparing optical phase reference systemsWednesday, 7th of September 2016Chair: C. SopuertaT. AlexanderEMRIs and the relativistic loss coneR. SchoedelThe stellar cusp around the Milky Way’s central black holeJ. GairImpact of eLISA design on EMRI ScienceM. van de MeentModelling spinning EMRIs with Self-ForceA. GianninasA Progress Report on the Search for the Most Extreme Binary White DwarfsI. ThorpeInitial Results from ST7-Disturbance Reduction System on LISA PathfinderG. JinOngoing development of detection of gravitational waves in space in ChinaThursday, 8th of September 2016Chair: P. BinetruyR. BlandfordThe Future of Black Hole Astrophysics in the LISA-VIRGO-LPF EraC. MooreObserving black hole merger kicks directly with gravitational wavesN. TamaniniLate time cosmology with eLISAI. DvorkinA synthetic model of the gravitational wave background from evolving binary compact objectsA. PetiteauLISA science performance in the context of LISAPathfinder first results and simulation for LISAN. CornishFast, fully precessing frequency domain waveforms for analyzing black hole mergers with LISAA. KleinSupermassive Black Hole Observations with eLISAS. HughesMeasuring EMRIs: A reality checkChair: Ch. CapriniL. MayerMassive black hole mergers and their timescales: connecting galaxy formation with gravitational wave scienceS. BabakEnchilada: analysis of simulated eLISA data setA. RicciardonePrimordial Gravitational Waves and eLISAS. SanidasCan eLISA save the day? Hunting for cosmic strings in the SKA era.G. ServantProbing cosmological phase transitions with eLISAD. WeirAcoustic waves and the detectability of first-order phase transitions by eLISAM. BonettiPost-Newtonian Dynamics of Massive Black Holes TripletsJ. Garcia-BellidoGravitational waves from primordial black holes as dark matterT. RegimbauSearching for the stochastic gravitational-wave background with Advanced LIGO and Advanced VirgoM. PieroniPrimordial GW from universality classes of pseudo-scalar inflationFriday, 9th of September 2016Chair: G. MuellerK. Holley-BockelmannThe Known Unknowns: predicting the landscape of LISA black hole sourcesE. RossiSupermassive black hole seeds: updates on the quasi star modelC. MingarelliThe Gravitational-Wave Universe seen by Pulsar Timing ArraysS. SmarttSearching for the electromagnetic counterparts to gravitational wave sourcesJ. BergéMICROSCOPE: the first few months in orbitO. JennrichThe preparation for L3 – building on LISA Pathfinder

Massive black hole binaries (MBHBs) could be the loudest gravitational-wave (GW) sources in the millihertz (mHz) GW band, but their dynamical evolution may stall when the black holes reach the innermost parsec of a galaxy. Such a “final-parsec problem” could be solved if an MBHB forms in a gas-rich environment, such as an active galactic nucleus (AGN), but other solutions not involving AGNs also exist. Testing the correlation between these mHz GW sources and AGNs is difficult in real observation because AGNs are ubiquitous. To overcome this difficulty, we use a statistical method, first designed to constrain the host galaxies of stellar-mass binary black holes, to search for the MBHB–AGN correlation in different astrophysical scenarios. We find that by detecting only one MBHB at z ≲ 0.5, a mHz GW detector, such as the Laser Interferometer Space Antenna, can already distinguish different merger scenarios thanks to the precise localization of the source. Future detector networks and deeper AGNs surveys can further testify to the MBHB–AGN correlation up to a redshift of z ∼ 2 even if only a small fraction of MBHBs merge inside AGNs. These constraints will help settle the long-standing debate on the possible solutions to the final-parsec problem.

Stellar black hole (BH) binaries are one of the most promising gravitational wave (GW) sources for GW detection by the ground-based detectors. Nuclear star clusters (NCs) located at the centre of galaxies are known to harbour massive black holes (MBHs) and to be bounded by a gravitational potential by other galactic components such as the galactic bulge. Such an environment of NCs provides a favourable conditions for the BH–BH binary formation by the gravitational radiation capture due to the high BH number density and velocity dispersion. We carried out detailed numerical study of the formation of BH binaries in the NCs using a series of N-body simulations for equal-mass cases. There is no mass segregation introduced. We have derived scaling relations of the binary formation rate with the velocity dispersion of the stellar system beyond the radius of influence and made estimates of the rate of formation of BH binaries per unit comoving volume and thus expected detection rate by integrating the binary formation rate over galaxy population within the detection distance of the advanced detectors. We find that the overall formation rates for BH–BH binaries per NC is ∼10−10 yr−1 for the Milky Way-like galaxies and weakly dependent on the mass of MBH as Γ ∝ |$M_{\rm MBH}^{3/28}$|⁠. We estimate the detection rate of 0.02–14 yr−1 for advanced LIGO/Virgo considering several factors such as the dynamical evolution of NCs, the variance of the number density of stars and the mass range of MBH giving uncertainties.

Advanced LIGO and Advanced Virgo are detecting a large number of binary stellar origin black hole (BH) mergers. A promising channel for accelerated BH merger lies in active galactic nucleus (AGN) discs of gas around supermasssive BHs. Here, we investigate the relative number of compact object (CO) mergers in AGN disc models, including BH, neutron stars (NS), and white dwarfs, via Monte Carlo simulations. We find the number of all merger types in the bulk disc grows ∝ t1/3 which is driven by the Hill sphere of the more massive merger component. Median mass ratios of NS–BH mergers in AGN discs are $\tilde{q}=0.07\pm 0.06(0.14\pm 0.07)$ for mass functions (MF) M−1(− 2). If a fraction fAGN of the observed rate of BH–BH mergers (RBH–BH) come from AGN, the rate of NS–BH (NS–NS) mergers in the AGN channel is ${R}_{\mathrm{ BH}\!-\!\mathrm{ NS}} \sim f_{\mathrm{ AGN}}[10,300]\, \rm {Gpc}^{-3}\, \rm {yr}^{-1},({\mathit{ R}}_{NS\!-\!NS} \le \mathit{ f}_{AGN}400\, \rm {Gpc}^{-3}\, \rm {yr}^{-1}$). Given the ratio of NS–NS/BH–BH LIGO search volumes, from preliminary O3 results the AGN channel is not the dominant contribution to observed NS–NS mergers. The number of lower mass gap events expected is a strong function of the nuclear MF and mass segregation efficiency. CO merger ratios derived from LIGO can restrict models of MF, mass segregation, and populations embedded in AGN discs. The expected number of electromagnetic (EM) counterparts to NS–BH mergers in AGN discs at z < 1 is $\sim [30,900]\, {\rm {yr}}^{-1}(f_{\mathrm{ AGN}}/0.1)$. EM searches for flaring events in large AGN surveys will complement LIGO constraints on AGN models and the embedded populations that must live in them.

Extending the electromagnetic and gravitational radiations from binary black holes with electric and magnetic charges in circular orbits in Liu et al. (Phys. Rev. D 102:103520, 2020), we calculate the total emission rates of energy and angular momentum due to gravitational and electromagnetic radiations from dyonic binary black holes in precessing elliptical orbits. It is shown that the emission rates of energy and angular momentum due to gravitational and electromagnetic radiations have the same dependence on the conic angle for different orbits. Moreover, we obtain the evolutions of orbits and find that a circular orbit remains circular while an elliptic orbit becomes quasi-circular due to electromagnetic and gravitational radiations. Using the evolution of orbits, we derive the waveform models for dyonic binary black hole inspirals and show the amplitudes of the gravitational waves for dyonic binary black hole inspirals differ from those for Schwarzschild binary black hole inspirals, which can be used to test electric and magnetic charges of black holes.

The astrophysical origin of gravitational-wave (GW) events is one of the most timely problems in the wake of the LIGO/Virgo discoveries. In active galactic nuclei (AGNs), binaries form and evolve efficiently by dynamical interactions and gaseous dissipation. Previous studies have suggested that binary black hole (BBH) mergers in AGN disks can contribute significantly to BBH mergers observed by GW interferometers. Here we examine the distribution of the effective spin parameter χ eff of this GW source population. We extend our semi-analytical model of binary formation and evolution in AGN disks by following the evolution of the binary orbital angular momenta and black hole (BH) spins. BH spins change due to gas accretion and BH mergers, while the binary orbital angular momenta evolve due to gas accretion and binary–single interactions. We find that the distribution of χ eff predicted by our AGN model is similar to the distribution observed during LIGO/Virgo O1 and O2. On the other hand, if radial migration of BHs is inefficient, χ eff is skewed toward higher values than the observed distribution, because of the paucity of scattering events that would randomize spin directions relative to the orbital plane. We suggest that high binary masses and the positive correlation between binary mass and the standard deviation of χ eff for chirp masses up to can be possible signatures for mergers originating in AGN disks. Finally, hierarchical mergers in AGN disks naturally produce properties of the recent GW event GW190412, including a low mass ratio, a high primary BH spin, and a significant spin component in the orbital plane.

We study the compact binary population in star clusters, focusing on binaries containing black holes, using a self-consistent Monte Carlo treatment of dynamics and full stellar evolution. We find that the black holes experience strong mass segregation and become centrally concentrated. In the core the black holes interact strongly with each other and black hole-black hole binaries are formed very efficiently. The strong interactions, however, also destroy or eject the black hole-black hole binaries. We find no black hole-black hole mergers within our simulations but produce many hard escapers that will merge in the galactic field within a Hubble time. We also find several highly eccentric black hole-black hole binaries that are potential LISA sources, suggesting that star clusters are interesting targets for space-based detectors. We conclude that star clusters must be taken into account when predicting compact binary population statistics.

We report on the population properties of compact binary mergers inferred from gravitational-wave observations of these systems during the first three LIGO-Virgo observing runs. The Gravitational-Wave Transient Catalog 3 (GWTC-3) contains signals consistent with three classes of binary mergers: binary black hole, binary neutron star, and neutron star–black hole mergers. We infer the binary neutron star merger rate to be between 10 and 1700 Gpc−3 yr−1 and the neutron star–black hole merger rate to be between 7.8 and 140 Gpc−3 yr−1, assuming a constant rate density in the comoving frame and taking the union of 90% credible intervals for methods used in this work. We infer the binary black hole merger rate, allowing for evolution with redshift, to be between 17.9 and 44 Gpc−3 yr−1 at a fiducial redshift (z=0.2). The rate of binary black hole mergers is observed to increase with redshift at a rate proportional to (1+z)κ with κ=2.9−1.8+1.7 for z≲1. Using both binary neutron star and neutron star–black hole binaries, we obtain a broad, relatively flat neutron star mass distribution extending from 1.2−0.2+0.1 to 2.0−0.3+0.3M⊙. We confidently determine that the merger rate as a function of mass sharply declines after the expected maximum neutron star mass, but cannot yet confirm or rule out the existence of a lower mass gap between neutron stars and black holes. We also find the binary black hole mass distribution has localized over- and underdensities relative to a power-law distribution, with peaks emerging at chirp masses of 8.3−0.5+0.3 and 27.9−1.8+1.9M⊙. While we continue to find that the mass distribution of a binary’s more massive component strongly decreases as a function of primary mass, we observe no evidence of a strongly suppressed merger rate above approximately 60M⊙, which would indicate the presence of a upper mass gap. Observed black hole spins are small, with half of spin magnitudes below χi≈0.25. While the majority of spins are preferentially aligned with the orbital angular momentum, we infer evidence of antialigned spins among the binary population. We observe an increase in spin magnitude for systems with more unequal-mass ratio. We also observe evidence of misalignment of spins relative to the orbital angular momentum. Published by the American Physical Society 2023

Expressions for the gravitational wave (GW) energy flux and center-of-mass energy of a compact binary are integral building blocks of post-Newtonian (PN) waveforms. In this paper, we compute the GW energy flux and GW frequency derivative from a highly accurate numerical simulation of an equal-mass, non-spinning black hole binary. We also estimate the (derivative of the) center- of-mass energy from the simulation by assuming energy balance. We compare these quantities with the predictions of various PN approximants (adiabatic Taylor and Pade models; non-adiabatic effective-one-body (EOB) models). We find that Pade summation of the energy flux does not accelerate the convergence of the flux series; nevertheless, the Pade flux is markedly closer to the numerical result for the whole range of the simulation (about 30 GW cycles). Taylor and Pade models overestimate the increase in flux and frequency derivative close to merger, whereas EOB models reproduce more faithfully the shape of and are closer to the numerical flux, frequency derivative and derivative of energy. We also compare the GW phase of the numerical simulation with Pade and EOB models. Matching numerical and untuned 3.5 PN order waveforms, we find that the phase difference accumulated until Mω = 0.1 is -0.12 radians for Pade approximants, and 0.50 (0.45) radians for an EOB approximant with Keplerian (non-Keplerian) flux. We fit free parameters within the EOB models to minimize the phase difference, and confirm the presence of degeneracies among these parameters. By tuning the pseudo 4PN order coefficients in the radial potential or in the flux, or, if present, the location of the pole in the flux, we find that the accumulated phase difference at Mω = 0.1 can be reduced—if desired—to much less than the estimated numerical phase error (0.02 radians).

Nearly 150 massive black hole binary (MBHB) candidates at sub-pc orbital separations have been reported in recent literature. Nevertheless, the definitive detection of even a single such object remains elusive. If at least one of the black holes is accreting, the light emitted from its accretion disc will be lensed by the other black hole for binary orbital inclinations near to the line of sight. This binary self-lensing could provide a unique signature of compact MBHB systems. We show that, for MBHBs with masses in the range 10^6 - 10^10 solar masses and with orbital periods less than ~10 yr, strong lensing events should occur in one to 10s of percent of MBHB systems that are monitored for an entire orbit. Lensing events will last from days for the less massive, shorter period MBHBs up to a year for the most massive ~10 year orbital period MBHBs. At small inclinations of the binary orbit to the line of sight, lensing must occur and will be accompanied by periodicity due to the relativistic Doppler boost. Flares at the same phase as the otherwise average flux of the Doppler modulation would be a smoking gun signature of self-lensing and can be used to constrain binary parameters. For MBHBs with separation >100 Schwarzschild radii, we show that finite-sized source effects could serve as a probe of MBH accretion disc structure. Finally, we stress that our lensing probability estimate implies that ~10 of the known MBHB candidates identified through quasar periodicity should exhibit strong lensing flares.

Using a one-dimensional height integrated model, we calculate the evolution\nof an unequal mass binary black hole with a coplanar gas disk that contains a\ngap due to the presence of the secondary black hole. Viscous evolution of the\nouter circumbinary disk initially hardens the binary, while the inner disk\ndrains onto the primary (central) black hole. As long as the inner disk remains\ncool and thin at low $\\dot{M}_{\\rm ext}$ (rather than becoming hot and\ngeometrically thick), the mass of the inner disk reaches an asymptotic mass\ntypically $\\sim 10^{-3}-10^{-4}\\Msun$. Once the semimajor axis shrinks below a\ncritical value, angular momentum losses from gravitational waves dominate over\nviscous transport in hardening the binary. The inner disk then no longer\nresponds viscously to the inspiraling black holes. Instead, tidal interactions\nwith the secondary rapidly drive the inner disk into the primary. Tidal and\nviscous dissipation in the inner disk lead to a late time brightening in\nluminosity $L\\propto t_{\\rm minus}^{5/4}$, where $t_{\\rm minus}$ is the time\nprior to the final merger. This late time brightening peaks $\\sim 1$ day prior\nto the final merger at $\\sim 0.1 L_{\\rm Edd}$. This behavior is relatively\nrobust because of self regulation in the coupled viscous-gravitational\nevolution of such binary systems. It constitutes a unique electromagnetic\nsignature of a binary supermassive black hole merger and may allow the host\ngalaxy to be identified if used in conjunction with the Laser Interferometric\nSpace Antenna (LISA) localization.\n

In a recent paper, we determined the measurement accuracy of physical parameters for eccentric, precessing, non-spinning, inspiraling, stellar-mass black hole - black hole (BH–BH) binaries for the upcoming second-generation LIGO/VIRGO/KAGRA detector network at design sensitivity using the Fisher matrix method. Here we extend that study to a wide range of binary masses including neutron star - neutron star (NS–NS), NS–BH, and BH–BH binaries with BH masses up to 110 . The measurement error of eccentricity at a gravitational-wave (GW) frequency of 10 Hz is in the range for NS–NS, NS–BH, and BH–BH binaries at a luminosity distance of D L if . For events with masses and distances similar to the detected 10 GW transients, we show that nonzero orbital eccentricities may be detected if . Consequently, the LIGO/VIRGO/KAGRA detector network at design sensitivity will have the capability to distinguish between eccentric waveforms and circular waveforms. In comparison to circular inspirals, we find that the chirp mass measurement precision can improve by up to a factor of ∼20 and ∼50–100 for NS–NS and NS–BH binaries with BH companion masses ≲40 , respectively. The identification of eccentric sources may give information on their astrophysical origin; it would indicate merging binaries in triple or higher multiplicity systems or dynamically formed binaries in dense stellar systems such as globular clusters or galactic nuclei.