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Register a new userBlack Hole Mergers from Globular Clusters Observable by LISA and LIGO: Results from post-Newtonian Binary-Single Scatterings
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We study the gravitational wave (GW) frequency and chirp mass distribution of binary black hole (BBH) mergers assembled through three-body interactions in globular clusters (GCs), when GW emission at the 2.5 post-Newtonian (PN) level is included in the $N$-body equation-of-motion (EOM). From performing $sim 2.5times10^{6}$ PN binary-single interactions based on GC data from the `MOCCA-Survey Database I project, and by the use of analytical methods, we find that $5-10%$ of all the three-body assembled GC BBH mergers have a GW frequency at formation that is $gtrsim 10^{-1}$ Hz, implying they enter the LIGO band without having drifted through the LISA band first. If PN terms are not included in the EOM, one finds instead that all BBH mergers drifts through both LISA and LIGO. As the fraction of BBH mergers that only show up in LIGO is expected to be $sim 0%$ for standard field binary BBH mergers, future joint measurements with LISA and LIGO can be used to gain insight into the formation of BBH mergers.
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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 derive the observable gravitational wave (GW) peak frequency ($f$) distribution of binary black holes (BBHs) that currently reside inside their globular clusters (GCs), with and without 2.5 Post-Newtonian (2.5PN) effects included in the dynamical evolution of the BBHs. Recent Newtonian studies have reported that a notable number of nearby non-merging BBHs, i.e. those BBHs that are expected to undergo further dynamical interactions before merger, in GCs are likely to be observable by LISA. However, our 2.5PN calculations show that the distribution of $log f$ for the non-merging BBH population above $sim 10^{-3.5}$ Hz scales as $f^{-34/9}$ instead of the $f^{-2/3}$ scaling found in the Newtonian case. This leads to an approximately two-orders-of-magnitude reduction in the expected number of GW sources at $sim 10^{-3}$ Hz, which lead us to conclude that observing nearby BBHs with LISA is not as likely as has been claimed in the recent literature. In fact, our results suggest that it might be more likely that LISA detects the population of BBHs that will merge before undergoing further interactions. This interestingly suggests that the BBH merger rate derived from LIGO can be used to forecast the number of nearby LISA sources, as well as providing insight into the fraction of BBH mergers forming in GCs.
Since the first signal in 2015, the gravitational-wave detections of merging binary black holes (BBHs) by the LIGO and Virgo collaborations (LVC) have completely transformed our understanding of the lives and deaths of compact object binaries, and have motivated an enormous amount of theoretical work on the astrophysical origin of these objects. We show that the phenomenological fit to the redshift-dependent merger rate of BBHs from Abbott et al. (2020) is consistent with a purely dynamical origin for these objects, and that the current merger rate of BBHs from the LVC could be explained entirely with globular clusters alone. While this does not prove that globular clusters are the dominant formation channel, we emphasize that many formation scenarios could contribute a significant fraction of the current LVC rate, and that any analysis that assumes a single (or dominant) mechanism for producing BBH mergers is implicitly using a specious astrophysical prior.
A transient gravitational-wave signal, GW150914, was identified in the twin Advanced LIGO detectors on September 14, 2015 at 09:50:45 UTC. To assess the implications of this discovery, the detectors remained in operation with unchanged configurations over a period of 39 d around the time of the signal. At the detection statistic threshold corresponding to that observed for GW150914, our search of the 16 days of simultaneous two-detector observational data is estimated to have a false alarm rate (FAR) of $< 4.9 times 10^{-6} , mathrm{yr}^{-1}$, yielding a $p$-value for GW150914 of $< 2 times 10^{-7}$. Parameter estimation followup on this trigger identifies its source as a binary black hole (BBH) merger with component masses $(m_1, m_2) = left(36^{+5}_{-4},29^{+4}_{-4}right) , M_odot$ at redshift $z = 0.09^{+0.03}_{-0.04}$ (median and 90% credible range). Here we report on the constraints these observations place on the rate of BBH coalescences. Considering only GW150914, assuming that all BBHs in the Universe have the same masses and spins as this event, imposing a search FAR threshold of 1 per 100 years, and assuming that the BBH merger rate is constant in the comoving frame, we infer a 90% credible range of merger rates between $2$--$53 , mathrm{Gpc}^{-3} mathrm{yr}^{-1}$ (comoving frame). Incorporating all search triggers that pass a much lower threshold while accounting for the uncertainty in the astrophysical origin of each trigger, we estimate a higher rate, ranging from $13$--$600 , mathrm{Gpc}^{-3} mathrm{yr}^{-1}$ depending on assumptions about the BBH mass distribution. All together, our various rate estimates fall in the conservative range $2$--$600 , mathrm{Gpc}^{-3} mathrm{yr}^{-1}$.
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.
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