No Arabic abstract
We derive the probability for a newly formed binary black hole (BBH) to undergo an eccentric gravitational wave (GW) merger during binary-single interactions inside a stellar cluster. By integrating over the hardening interactions such a BBH must undergo before ejection, we find that the observable rate of BBH mergers with eccentricity $>0.1$ at $10 rm{Hz}$ relative to the rate of circular mergers can be as high as $sim 5%$ for a typical globular cluster (GC). This further suggests that BBH mergers forming through GW captures in binary-single interactions, eccentric or not, are likely to constitute $sim 10%$ of the total BBH merger rate from GCs. Such GW capture mergers can only be probed with an $N$-body code that includes General Relativistic corrections, which explains why recent Newtonian cluster studies not have been able to resolve this population. Finally, we show that the relative rate of eccentric BBH mergers depends on the compactness of their host cluster, suggesting that an observed eccentricity distribution can be used to probe the origin of BBH mergers.
The astrophysical origin of gravitational wave (GW) transients is a timely open question in the wake of discoveries by LIGO/Virgo. In active galactic nuclei (AGNs), binaries form and evolve efficiently by interaction with a dense population of stars and the gaseous AGN disk. Previous studies have shown that stellar-mass black hole (BH) mergers in such environments can explain the merger rate and the number of suspected hierarchical mergers observed by LIGO/Virgo. The binary eccentricity distribution can provide further information to distinguish between astrophysical models. Here we derive the eccentricity distribution of BH mergers in AGN disks. We find that eccentricity is mainly due to binary-single (BS) interactions, which lead to most BH mergers in AGN disks having a significant eccentricity at $0.01,mathrm{Hz}$, detectable by LISA. If BS interactions occur in isotropic-3D directions, then $8$--$30%$ of the mergers in AGN disks will have eccentricities at $10,mathrm{Hz}$ above $e_{10,rm Hz}gtrsim 0.03$, detectable by LIGO/Virgo/KAGRA, while $5$--$17%$ of mergers have $e_{10,rm Hz}geq 0.3$. On the other hand, if BS interactions are confined to the AGN-disk plane due to torques from the disk, with 1-20 intermediate binary states during each interaction, or if BHs can migrate to $lesssim10^{-3},mathrm{pc}$ from the central supermassive black hole, then $10$--$70%$ of the mergers will be highly eccentric ($e_{10,rm Hz} geq 0.3$), consistent with the possible high eccentricity in GW190521.
We show that nearly half of all binary black hole (BBH) mergers dynamically assembled in globular clusters have measurable eccentricities ($e>0.01$) in the LISA band ($10^{-2}$ Hz), when General Relativistic corrections are properly included in the $N$-body evolution. If only Newtonian gravity is included, the derived fraction of eccentric LISA sources is significantly lower, which explains why recent studies all have greatly underestimated this fraction. Our findings have major implications for how to observationally distinguish between BBH formation channels using eccentricity with LISA, which is one of the key science goals of the mission. We illustrate that the relatively large population of eccentric LISA sources reported here originates from BBHs that merge between hardening binary-single interactions inside their globular cluster. These results indicate a bright future for using LISA to probe the origin of BBH mergers.
We present the first systematic study of strong binary-single and binary-binary black hole interactions with the inclusion of general relativity. When including general relativistic effects in strong encounters, dissipation of orbital energy from gravitational waves (GWs) can lead to captures and subsequent inspirals with appreciable eccentricities when entering the sensitive frequency ranges of the LIGO and Virgo GW detectors. In this study, we perform binary-binary and binary-single scattering experiments with general relativistic dynamics up through the 2.5 post-Newtonian order included, both in a controlled setting to gauge the importance of non-dissipative post-Newtonian terms and derive scaling relations for the cross-section of GW captures, as well as experiments tuned to the strong interactions from state-of-the art globular cluster models to assess the relative importance of the binary-binary channel at facilitating GW captures and the resultant eccentricity distributions of inspiral from channel. Although binary-binary interactions are 10-100 times less frequent in globular clusters than binary-single interactions, their longer lifetime and more complex dynamics leads to a higher probability for GW captures to occur during the encounter. We find that binary-binary interactions contribute 25-45% of the eccentric mergers which occur during strong black hole encounters in globular clusters, regardless of the properties of the cluster environment. The inclusion of higher multiplicity encounters in dense star clusters therefore have major implications on the predicted rates of highly eccentric binaries potentially detectable by the LIGO/Virgo network. As gravitational waveforms of eccentric inspirals are distinct from those generated by merging binaries which have circularized, measurements of eccentricity in such systems would highly constrain their formation scenario.
Black hole mergers detected by LIGO and Virgo continue delivering transformational discoveries. The most recent example is the merger GW190521, which is the first detected with component masses exceeding the limit predicted by stellar models, and the first with non-zero orbital eccentricity. The large masses can be explained by build up through successive mergers, which has been suggested to occur efficiently in the gas disks of active galactic nuclei (AGN). The eccentricity, however, is a major puzzle. Here we show that AGN-disk environments naturally lead to a very high fraction of highly eccentric mergers, if interactions between binaries and singles are frequent, and the interactions are constrained to a plane representing the AGN-disk. By deriving a statistical solution to the chaotic 3-body problem with the inclusion of General Relativistic corrections, we find in our fiducial AGN-disk model that up to $sim 70%$ of all black hole mergers could appear with an eccentricity $>0.1$ in LIGO/Virgo. Besides representing the most effective mechanism for producing eccentric mergers presented to date, our results have also profound implications for the origin of GW190521, and open up new lines of research on black hole scatterings in disk environments with far-reaching implications for gravitational wave astrophysics.
Hierarchical mergers are one of the distinctive signatures of binary black hole (BBH) formation through dynamical evolution. Here, we present a fast semi-analytic approach to simulate hierarchical mergers in nuclear star clusters (NSCs), globular clusters (GCs) and young star clusters (YSCs). Hierarchical mergers are more common in NSCs than they are in both GCs and YSCs, because of the different escape velocity. The mass distribution of hierarchical BBHs strongly depends on the properties of first-generation BBHs, such as their progenitors metallicity. In our fiducial model, we form black holes (BHs) with masses up to $sim{}10^3$ M$_odot$ in NSCs and up to $sim{}10^2$ M$_odot$ in both GCs and YSCs. When escape velocities in excess of 100 km~s$^{-1}$ are considered, BHs with mass $>10^3$ M$_odot$ are allowed to form in NSCs. Hierarchical mergers lead to the formation of BHs in the pair instability mass gap and intermediate-mass BHs, but only in metal-poor environments. The local BBH merger rate in our models ranges from $sim{}10$ to $sim{} 60$ Gpc$^{-3}$ yr$^{-1}$; hierarchical BBHs in NSCs account for $sim{}10^{-2}- 0.2$ Gpc$^{-3}$ yr$^{-1}$, with a strong upper limit of $sim{}10$ Gpc$^{-3}$ yr$^{-1}$. When comparing our models with the second gravitational-wave transient catalog, we find that multiple formation channels are favored to reproduce the observed BBH population.