There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

We present the results from three gravitational-wave searches for coalescing compact binaries with component masses above 1 Ma™ during the first and second observing runs of the advanced gravitational-wave detector network. During the first observing run (O1), from September 12, 2015 to January 19, 2016, gravitational waves from three binary black hole mergers were detected. The second observing run (O2), which ran from November 30, 2016 to August 25, 2017, saw the first detection of gravitational waves from a binary neutron star inspiral, in addition to the observation of gravitational waves from a total of seven binary black hole mergers, four of which we report here for the first time: GW170729, GW170809, GW170818, and GW170823. For all significant gravitational-wave events, we provide estimates of the source properties. The detected binary black holes have total masses between 18.6-0.7+3.2 Mâ™ and 84.4-11.1+15.8 Mâ™ and range in distance between 320-110+120 and 2840-1360+1400 Mpc. No neutron star-black hole mergers were detected. In addition to highly significant gravitational-wave events, we also provide a list of marginal event candidates with an estimated false-alarm rate less than 1 per 30 days. From these results over the first two observing runs, which include approximately one gravitational-wave detection per 15 days of data searched, we infer merger rates at the 90% confidence intervals of 110-3840 Gpc-3 y-1 for binary neutron stars and 9.7-101 Gpc-3 y-1 for binary black holes assuming fixed population distributions and determine a neutron star-black hole merger rate 90% upper limit of 610 Gpc-3 y-1.

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GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs

Monthly Notices is one of the three largest general primary astronomical research publications. It is an international journal, published by the Royal Astronomical Society. This article 1 describes its publication policy and practice.

Monthly Notices of the Royal Astronomical Society

Many problems in the experimental estimation of parameters for models can be solved through use of the likelihood ratio test. Applications of the likelihood ratio, with particular attention to photon counting experiments, are discussed. The procedures presented solve a greater range of problems than those currently in use, yet are no more difficult to apply. The procedures are proved analytically, and examples from current problems in astronomy are discussed.

Parameter estimation in astronomy through application of the likelihood ratio. [satellite data analysis techniques

The environment near supermassive black holes (SMBHs) in galactic nuclei contains a large number of stars and compact objects. A fraction of these are likely to be members of binaries. Here we discuss the binary population of stellar black holes and neutron stars near SMBHs and focus on the secular evolution of such binaries, due to the perturbation by the SMBH. Binaries with highly inclined orbits with respect to their orbit around the SMBH are strongly affected by secular Kozai processes, which periodically change their eccentricities and inclinations (Kozai cycles). During periapsis approach, at the highest eccentricities during the Kozai cycles, gravitational wave (GW) emission becomes highly efficient. Some binaries in this environment can inspiral and coalesce at timescales much shorter than a Hubble time and much shorter than similar binaries that do not reside near an SMBH. The close environment of SMBHs could therefore serve as a catalyst for the inspiral and coalescence of binaries and strongly affect their orbital properties. Such compact binaries would be detectable as GW sources by the next generation of GW detectors (e.g., advanced-LIGO). Our analysis shows that ~0.5% of such nuclear merging binaries will enter the LIGO observational window while on orbits that are still very eccentric (e 0.5). The efficient GW analysis for such systems would therefore require the use of eccentric templates. We also find that binaries very close to the SMBH could evolve through a complex dynamical (non-secular) evolution, leading to emission of several GW pulses during only a few years (though these are likely to be rare). Finally, we note that the formation of close stellar binaries, X-ray binaries, and their merger products could be induced by similar secular processes, combined with tidal friction rather than GW emission as in the case of compact object binaries.

https://iopscience.iop.org/article/10.1088/0004-637X/757/1/27/pdf

Secular evolution of compact binaries near massive black holes: gravitational wave sources and other exotica

Motivated by the recent detection of gravitational waves from the black hole binary merger GW150914, we study the dynamical evolution of (stellar-mass) black holes in galactic nuclei, where massive star clusters reside. With masses of and sizes of only a few parsecs, nuclear star clusters (NSCs) are the densest stellar systems observed in the local universe and represent a robust environment where black hole binaries can dynamically form, harden, and merge. We show that due to their large escape speeds, NSCs can retain a large fraction of their merger remnants. Successive mergers can then lead to significant growth and produce black hole mergers of several tens of solar masses similar to GW150914 and up to a few hundreds of solar masses, without the need to invoke extremely low metallicity environments. We use a semi-analytical approach to describe the dynamics of black holes in massive star clusters. Our models give a black hole binary merger rate of from NSCs, implying up to a few tens of possible detections per year with Advanced LIGO. Moreover, we find a local merger rate of for high mass black hole binaries similar to GW150914; a merger rate comparable to or higher than that of similar binaries assembled dynamically in globular clusters (GCs). Finally, we show that if all black holes receive high natal kicks, , then NSCs will dominate the local merger rate of binary black holes compared to either GCs or isolated binary evolution.

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Merging black hole binaries in galactic nuclei: implications for advanced-LIGO detections

We consider the formation of binary black hole (BH) mergers through the evolution of field massive triple stars. In this scenario, favorable conditions for the inspiral of a BH binary are initiated by its gravitational interaction with a distant companion, rather than by a common-envelope phase invoked in standard binary evolution models. We use a code that follows self-consistently the evolution of massive triple stars, combining the secular triple dynamics (Lidov–Kozai cycles) with stellar evolution. After a BH triple is formed, its dynamical evolution is computed using either the orbit-averaged equations of motion, or a high-precision direct integrator for triples with weaker hierarchies for which the secular perturbation theory breaks down. Most BH mergers in our models are produced in the latter non-secular dynamical regime. We derive the properties of the merging binaries and compute a BH merger rate in the range (0.3–1.3) Gpc(−)(3) yr(−)(1), or up to ≈2.5 Gpc(−)(3) yr(−)(1) if the BH orbital planes have initially random orientation. Finally, we show that BH mergers from the triple channel have significantly higher eccentricities than those formed through the evolution of massive binaries or in dense star clusters. Measured eccentricities could therefore be used to uniquely identify binary mergers formed through the evolution of triple stars. While our results suggest up to ≈10 detections per year with Advanced-LIGO, the high eccentricities could render the merging binaries harder to detect with planned space based interferometers such as LISA.

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Binary Black Hole Mergers from Field Triples: Properties, Rates, and the Impact of Stellar Evolution

Coalescing black hole (BH) binaries forming in the dense core of globular clusters (GCs) are expected to be one of the brightest sources of gravitational wave (GW) radiation for the next generation of ground-based laser interferometers. Favorable conditions for a merger are initiated by the Kozai resonance in which the gravitational interaction with a third distant object, typically another BH, induces quasi-periodic variations of the inner BH binary eccentricity. In this article we perform high precision three-body simulations of the long-term evolution of hierarchical BH triples and investigate the conditions that lead to the merging of the BH binary and the way it might become an observable source of GW radiation. We find that the secular orbit average treatment, which was adopted in previous works, does not reliably describe the dynamics of these systems if the binary is orbited by the outer BH on a highly inclined orbit at a moderate distance. We show that 50% of coalescing BH binaries driven by the Kozai mechanism in GCs will have eccentricities larger than 0.1, with 10% of them being extremely eccentric, (1 – e) ≲ 10{sup –4}, when they first chirp in the frequency band of ground-based laser interferometers. This impliesmore » that a large fraction of such GW sources could be missed if conventional quasi-circular templates are used for analysis of GW detector data. The efficient detection of all coalescing BH binaries in GCs will therefore require template banks of eccentric inspiral waveforms for matched-filtering and dedicated search strategies.« less

http://iopscience.iop.org/article/10.1088/0004-637X/781/1/45/pdf

Black hole triple dynamics: a breakdown of the orbit average approximation and implications for gravitational wave detections

In one widely discussed model for the formation of nuclear star clusters (NSCs), massive globular clusters spiral into the center of a galaxy and merge to form the nucleus. It is now known that at least some NSCs coexist with supermassive black holes (SMBHs); this is the case, for instance, in the Milky Way. In this paper, we investigate how the presence of an SMBH at the center of the Milky Way impacts the merger hypothesis for the formation of its NSC. Starting from a model consisting of a low-density nuclear stellar disk and the SMBH, we use direct N-body simulations to follow the successive inspiral and merger of globular clusters. The clusters are started on circular orbits of radius 20 pc, and their initial masses and radii are set up in such a way as to be consistent with the galactic tidal field at that radius. These clusters, decayed orbitally in the central region due to their large mass, were followed in their inspiral events; as a result, the total accumulated mass by ≈10 clusters is about 1.5 × 107 M ☉. Each cluster is disrupted by the SMBH at a distance of roughly 1 pc. The density profile that results after the final inspiral event is characterized by a core of roughly this radius and an envelope with density that falls off ρ ~ r –2. These properties are similar to those of the Milky Way NSC, with the exception of the core size, which in the Milky Way is somewhat smaller. But by continuing the evolution of the model after the final inspiral event, we find that the core shrinks substantially via gravitational encounters in a time (when scaled to the Milky Way) of 10 Gyr as the stellar distribution evolves toward a Bahcall-Wolf cusp. We also show that the luminosity function of the Milky Way NSC is consistent with the hypothesis that 1/2 of the mass comes from old (~10 Gyr) stars, brought in by globular clusters, with the other half due to continuous star formation. We conclude that a model in which a large fraction of the mass of the Milky Way NSC is due to infalling globular clusters is consistent with existing observational constraints.

https://iopscience.iop.org/article/10.1088/0004-637X/750/2/111/pdf

Fabio Antonini

Papers

Secular evolution of compact binaries near massive black holes: gravitational wave sources and other exotica

Merging black hole binaries in galactic nuclei: implications for advanced-LIGO detections

Binary Black Hole Mergers from Field Triples: Properties, Rates, and the Impact of Stellar Evolution

Black hole triple dynamics: a breakdown of the orbit average approximation and implications for gravitational wave detections

Dissipationless Formation and Evolution of the Milky Way Nuclear Star Cluster