The hierarchical three-body problem has many applications in relativistic astrophysics, and can play an important role in the formation of the binary black hole mergers detected by LIGO/Virgo. However, many studies have only included relativistic corrections responsible for the precession of pericenter of the inner and outer binaries, neglecting relativistic interactions between the three bodies. We revisit this problem and develop a fully consistent derivation of the secular three-body problem to first post-Newtonian order. We start with the Einstein-Infeld-Hoffman equations for a three-body system and expand the accelerations as a power series in the ratio of the semi-major axes of the inner ($a_1$) and outer ($a_2$) binary. We then perform a post-Keplerian, two-parameter expansion of the single-orbit-averaged Lagrange planetary equations in $δ= v^2/c^2$ and $ε= a_1/a_2$ using the method of multiple scales. Using this method, we derive previously-indentified secular effects at $δε^{5/2}$ order that arise directly from the equations of motion. We also calculate new secular effects through $δε^4$ order that can lead to eccentricity growth over many Lidov-Kozai cycles when the tertiary is much more massive than the inner binary. In such cases, inclusion of these effects can substantially alter the evolution of three-body systems as compared to an analysis in which they are neglected. Careful analysis of post-Newtonian three-body effects will be important to understand the formation and properties of coalescing binaries that form via three-body dynamical processes.
We study gravitational wave (GW) emission in the strong-field regime by a hierarchical triple system composed of a binary system placed in the vicinity of a supermassive black hole (SMBH). The LIGO-Virgo collaboration recently reported evidence for coalescences with this dynamical origin. These systems are common in galactic centers and thus are a target for the space-based LISA mission as well as other advanced detectors. Doppler shifts, aberration, lensing and strong amplitude modulations are features present in the GW signal from these systems, built into our framework and with no need for …
We describe a new kind of resonance occuring in relativistic three-body hierarchical systems: the precession resonance, occuring when the relativistic precession timescale of a binary equals the period of a distant perturber. We find that, contrary to what most previous studies assume, it can lead to an exponential increase of eccentricity of the binary even when relativistic precession dominates the quadrupolar perturbation. The resonance may happen in the observation band of LISA or change the eccentricity distribution of triples. We discuss the physics of the resonance, showing that it main…
We consider binary black holes (BBHs) in a hierarchical triple system where a more compact, less-massive binary is emitting detectable gravitational waves (GWs), and the tertiary is a supermassive BH at the center of a nuclear star cluster. As previous works have shown, the orbital motion of the outer binary can generate a detectable relativistic Doppler boost of the GWs emitted by the orbiting inner binary. We show here that for outer-binary orbits with a period of order one year, there can be a non-negligible probability for repeated gravitational lensing of the GWs emitted by the inner bina…
We study the general relativitic (GR) effects induced by a spinning supermassive black hole on the orbital and spin evolution of a merging black hole binary (BHB) in a hierarchical triple system. A sufficiently inclined outer orbit can excite Lidov-Kozai eccentricity oscillations in the BHB and induce its merger. These GR effects generate extra precessions on the BHB orbits and spins, significantly increasing the inclination window for mergers and producing a wide range of spin orientations when the BHB enters LIGO band. This "GR-enhanced" channel may play an important role in BHB mergers.
With better statistics and precision, eccentricity could prove to be a useful tool for understanding the origin and environment of binary black holes. Hierarchical triples in particular, which might be abundant in globular clusters and galactic nuclei, could generate observably large eccentricity at LIGO and future gravitational wave detectors. Measuring the eccentricity distribution accurately could help us probe the background and the formation of the mergers. In this paper we continue our previous investigation and improve our semi-analytical description of the eccentricity distribution of …
Kozai-Lidov (KL) oscillations can accelerate compact object mergers via gravitational wave (GW) radiation by driving the inner binaries of hierarchical triples to high eccentricities. We perform direct three-body integrations of high mass ratio compact object triple systems using Fewbody including post-Newtonian terms. We find that the inner binary undergoes rapid eccentricity oscillations (REOs) on the timescale of the outer orbital period which drive it to higher eccentricities than secular theory would otherwise predict, resulting in substantially reduced merger times. For a uniform distrib…
Neutron star mergers have been proposed as the main source of heavy $r$-process nucleosynthesis in the Universe. However, the mergers' significant expected delay after binary formation is in tension with observed very early $r$-process enrichment, e.g., in the dwarf galaxy Reticulum II. The LIGO and Virgo gravitational-wave observatories discovered two binary mergers with lighter companion masses ($\sim 2.6$ M$_\odot$) similar to the total mass of many binary neutron star systems in the Galaxy. The progenitor of such mergers could be a neutron star binary orbiting a black hole. Here we show th…
We study the secular dynamics of compact binaries (consisting of white dwarfs, neutron stars or black holes) with tertiary companions in hierarchical triple systems. As the inner binary (with initially negligible eccentricity) undergoes orbital decay due to gravitational radiation, its eccentricity can be excited by gravitational forcing from the tertiary. This excitation occurs when the triple system passes through an "apsidal precession resonance", when the precession rate of the inner binary, driven by the gravitational perturbation of the external companion and general relativity, matches …
A promising channel for producing binary black hole mergers is the Lidov-Kozai orbital resonance in hierarchical triple systems. While this mechanism has been studied in isolation, the distribution of such mergers in time and across star-forming environments is not well characterized. In this work, we explore Lidov-Kozai-induced black hole mergers in open clusters, combining semi-analytic and Monte Carlo methods to calculate merger rates and delay times for eight different population models. We predict a merger rate density of $\sim$1--10\,Gpc$^{-3}$\,yr$^{-1}$ for the Lidov-Kozai channel in t…
The Roche lobe formalism describes mass transfer from one star to another. We develop an extension to hierarchical triples, considering the case in which a star donates mass to a companion which is itself a binary. The L1 point moves as the inner binary rotates, and the Roche lobe pulsates with the period of the inner binary. Signatures of mass transfer may therefore be imprinted with the orbital period of the inner binary. For some system parameters, the pulsing Roche lobe can drive mass transfer at high rates. Systems undergoing this type of mass transfer include those with inner binaries co…
The 559 Hz black-widow pulsar PSR J1555-2908, originally discovered in radio, is also a bright gamma-ray pulsar. Timing its pulsations using 12 yr of Fermi-LAT gamma-ray data reveals long-term variations in its spin frequency that are much larger than is observed from other millisecond pulsars. While this variability in the pulsar rotation rate could be intrinsic "timing noise", here we consider an alternative explanation: the variations arise from the presence of a very-low-mass third object in a wide multi-year orbit around the neutron star and its low-mass companion. With current data, this…
A binary star orbited by an outer companion constitutes a hierarchical triple system. The outer body may excite the eccentricity of the inner binary through the von~Zeipel-Lidov-Kozai (ZLK) mechanism, triggering the gravitational wave (GW) coalescence of the inner binary when its members are compact objects. Here, we study a sample of hierarchical triples with an inner black hole (BH) -- BH binary, BH -- neutron star (NS) binary, and BH -- white dwarf (WD) binary, formed via dynamical interactions in low-mass young star clusters. Our sample of triples was obtained self-consistently from direct…
Binary interactions in relativistic plasma, such as Coulomb and Compton scattering as well as pair creation and annihilation are well known and studied in details. Triple interactions, namely relativistic bremsstrahlung, double Compton scattering, radiative pair production, triple pair production/annihilation and their inverse processes, are usually considered as emission processes in astrophysical problems, as well as in laboratory plasmas. Their role in plasma kinetics is fundamental [1]. We present a new conservative scheme for computation of Uehling-Uhlenbeck collision integral for all tri…
Dynamical scattering of binaries and triple systems of stars, planets, and compact objects may produce highly inclined triple systems subject to Kozai-Lidov (KL) oscillations, potentially leading to collisions, mergers, Type Ia supernovae, and other phenomena. We present the results of more than 400 million gravitational scattering experiments of binary-binary, triple-single, and triple-binary scattering. We compute the cross sections for all possible outcomes and explore their dependencies on incoming velocity, mass, semi-major axis, and eccentricity, including analytic fits and discussion of…
The isolated binary evolution model for merging neutron stars (NSs) involves processes such as mass transfer, common-envelope evolution, and natal kicks, all of which are poorly understood. Also, the predicted NS-NS merger rates are typically lower than the rates inferred from the LIGO GW170817 event. Here, we investigate merger rates of NS and black hole (BH)-NS binaries in hierarchical triple-star systems. In such systems, the tertiary can induce Lidov-Kozai (LK) oscillations in the inner binary, accelerating its coalescence, and potentially enhancing compact object merger rates. However, si…
The formation of Black Hole (BH) Low-Mass X-ray Binaries (LMXB) poses a theoretical challenge, as low-mass companions are not expected to survive the common-envelope scenario with the BH progenitor. Here we propose a formation mechanism that skips the common-envelope scenario and relies on triple-body dynamics. We study the evolution of hierarchical triples, following the secular dynamical evolution up to the octupole-level of approximation, including general relativity, tidal effects and post-main-sequence evolution, such as mass loss, changes to stellar radii and supernovae. During the dynam…
Close-orbit binaries consisting of two compact objects are a center of attention because of the detection of gravitational-radiation-induced mergers. The creation of close, compact-object binaries involves physical processes that are not yet well understood; there are open questions about the manner in which two compact objects come to be close enough to merge within a Hubble time. Here we explore an important, and likely common physical process: mass transfer from a third star in a wider, hierarchical orbit. Mass added to the close binary's components can reduce the time to merger and can eve…
Mergers of compact object binaries are one of the most powerful sources of gravitational waves (GWs) in the frequency range of second-generation ground-based gravitational wave detectors (Advanced LIGO and Virgo). Dynamical simulations of young dense star clusters (SCs) indicate that ~27 per cent of all double compact object binaries are members of hierarchical triple systems (HTs). In this paper, we consider 570 HTs composed of three compact objects (black holes or neutron stars) that formed dynamically in N-body simulations of young dense SCs. We simulate them for a Hubble time with a new co…
Most massive stars, if not all, are in binary configuration or higher multiples. These massive stars undergo supernova explosions and end their lives as either black holes or neutron stars. Recent observations have suggested that neutron stars and perhaps even black holes receive large velocity kicks at birth. Such natal kicks and the sudden mass loss can significantly alter the orbital configuration of the system. Here we derive general analytical expressions that describe the effects of natal kicks in binaries on hierarchical triple systems. We explore several proof-of-concept applications s…
The non-equilibrium electron-positron-photon plasma thermalization process is studied using relativistic Boltzmann solver, taking into account quantum corrections both in non-relativistic and relativistic cases. Collision integrals are computed from exact QED matrix elements for all binary and triple interactions in the plasma. It is shown that in non-relativistic case (temperatures $k_B T\leq 0.3 m_e c^2$) binary interaction rates dominate over triple ones, resulting in establishment of the kinetic equilibrium prior to final relaxation towards the thermal equilibrium, in agreement with the pr…
In hierarchical triple systems, the inner binary is perturbed by a distant companion. For large mutual inclinations, the Lidov-Kozai mechanism secularly excites large eccentricity and inclination oscillations of the inner binary. The maximal eccentricity attained, $e_{\rm max}$ is simply derived and widely used. However, for mildly hierarchical systems (i.e. the companion is relatively close and massive), non-secular perturbations affect the evolution. Here we account for fast non-secular variations and find new analytic formula for $e_{\rm max}$, in terms of the system's hierarchy level, corr…
Discovery of a compact hierarchical triple main-sequence star system while searching for binary stars with compact objects
Fukui Prefectural University（福井县立大学）；Subaru Telescope Okayama Branch, National Astronomical Observatory of Japan（日本国立天文台 Subaru 望远镜冈山分部）；Nishi-Harima Astronomical Observatory, Center for Astronomy, University of Hyogo（兵库大学天文学中心西播磨天文台）；Department of Earth and Planetary Sciences, Institute of Science Tokyo（东京科学大学地球行星科学系）；Department of Earth and Space Science, Graduate School of Science, Osaka University（大阪大学理学研究科地球宇宙科学系）；Astrobiology Center（天体生物学中心）
Over a dozen millisecond pulsars are ablating low-mass companions in close binary systems. In the original "black widow", the 8-hour orbital period eclipsing pulsar PSR J1959+2048 (PSR B1957+20), high energy emission originating from the pulsar is irradiating and may eventually destroy a low-mass companion. These systems are not only physical laboratories that reveal the dramatic result of exposing a close companion star to the relativistic energy output of a pulsar, but are also believed to harbour some of the most massive neutron stars, allowing for robust tests of the neutron star equation …
Recent radio VLBI observations of the relativistic jet in M87 radio galaxy have shown a triple-ridge structure that consists of the conventional limb-brightened feature and a central narrow ridge. Motivated by these observations, we examine a steady axisymmetric force-free model of a jet driven by the central black hole (BH) with its electromagnetic structure being consistent with general relativistic magnetohydrodynamic simulations, and find that it can produce triple-ridge images even if we assume a simple Gaussian distribution of emitting electrons at the base of the jet. We show that the f…
