We consider the formation of binary black hole mergers through the evolution of field massive triple stars. In this scenario, favorable conditions for the inspiral of a black hole 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 black hole 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 black hole mergers in our models are produced in the latter non-secular dynamical regime. We derive the properties of the merging binaries and compute a black hole merger rate in the range (0.3 − 1.3) Gpc −3 yr −1 , or up to ≈ 2.5 Gpcif the black hole orbital planes have initially random orientation. Finally, we show that black hole 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.

Field stars are frequently formed in pairs, and many of these binaries are part of triples or even higher-order systems. Even though, the principles of single stellar evolution and binary evolution, have been accepted for a long time, the long-term evolution of stellar triples is poorly understood. The presence of a third star in an orbit around a binary system can significantly alter the evolution of those stars and the binary system. The rich dynamical behaviour in three-body systems can give rise to Lidov-Kozai cycles, in which the eccentricity of the inner orbit and the inclination between the inner and outer orbit vary periodically. In turn, this can lead to an enhancement of tidal effects (tidal friction), gravitational-wave emission and stellar interactions such as mass transfer and collisions. The lack of a self-consistent treatment of triple evolution, including both three-body dynamics as well as stellar evolution, hinders the systematic study and general understanding of the long-term evolution of triple systems. In this paper, we aim to address some of these hiatus, by discussing the dominant physical processes of hierarchical triple evolution, and presenting heuristic recipes for these processes. To improve our understanding on hierarchical stellar triples, these descriptions are implemented in a public source code TrES, which combines three-body dynamics (based on the secular approach) with stellar evolution and their mutual influences. Note that modelling through a phase of stable mass transfer in an eccentric orbit is currently not implemented in TrES, but can be implemented with the appropriate methodology at a later stage.

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Binaries within the sphere of influence of a massive black hole (MBH) in galactic nuclei are susceptible to the Lidov-Kozai (LK) mechanism, which can drive orbits to high eccentricities and trigger strong interactions within the binary such as the emission of gravitational waves (GWs), and mergers of compact objects. These events are potential sources for GW detectors such as Advanced LIGO and VIRGO. The LK mechanism is only effective if the binary is highly inclined with respect to its orbit around the MBH (within a few degrees of 90 • ), implying low rates. However, close to an MBH, torques from the stellar cluster give rise to the process of vector resonant relaxation (VRR). VRR can bring a low-inclination binary into an 'active' LK regime in which high eccentricities and strong interactions are triggered in the binary. Here, we study the coupled LK-VRR dynamics, with implications for LIGO and VIRGO GW sources. We carry out Monte Carlo simulations and find that the merger fraction enhancement due to LK-VRR dynamics is up to a factor of ∼ 10 for the lower end of assumed MBH masses (M • = 10 4 M ⊙ ), and decreases sharply with increasing M • . We find that, even in our most optimistic scenario, the baseline BH-BH merger rate is small, and the enhancement by LK-VRR coupling is not large enough to increase the rate to well above the LIGO/VIRGO lower limit, 12 Gpc −3 yr −1 . For the Galactic Center, the LK-VRR-enhanced rate is ∼ 100 times lower than the LIGO/VIRGO limit, and for M • = 10 4 M ⊙ , the rate barely reaches 12 Gpc −3 yr −1 .

We study the secular gravitational dynamics of quadruple systems consisting of a hierarchical triple system orbited by a fourth body. These systems can be decomposed into three binary systems with increasing semimajor axes, binaries A, B and C. The Hamiltonian of the system is expanded in ratios of the three binary separations, and orbit averaged. Subsequently, we numerically solve the equations of motion. We study highly hierarchical systems that are well described by the lowest order terms in the Hamiltonian. We find that the qualitative behaviour is determined by the ratio R 0 of the initial Kozai-Lidov (KL) time-scales of the binary pairs AB and BC. If R 0 ≪ 1, binaries AB remain coplanar if this is initially the case, and KL eccentricity oscillations in binary B are efficiently quenched. If R 0 ≫ 1, binaries AB become inclined, even if initially coplanar. However, there are no induced KL eccentricity oscillations in binary A. Lastly, if R 0 ∼ 1, complex KL eccentricity oscillations can occur in binary A that are coupled with the KL eccentricity oscillations in B. Even if binaries A and B are initially coplanar, the induced inclination can result in very high eccentricity oscillations in binary A. These extreme eccentricities could have significant implications for strong interactions such as tidal interactions, gravitational wave dissipation, and collisions and mergers of stars and compact objects. As an example, we apply our results to a planet+moon system orbiting a central star, which in turn is orbited by a distant and inclined stellar companion or planet, and to observed stellar quadruples.

Context. Many stars do not live alone, but instead have one or more stellar companions. Observations show that these binaries, triples, and higher-order multiples are common. While the evolution of single stars and binaries have been studied extensively, the same is not true for the evolution of stellar triples. Aims. To fill in this gap in our general understanding of stellar lives, we aim to systematically explore the long-term evolution of triples and to map out the most common evolutionary pathways that triples go through. We quantitatively study how triples evolve, which processes are the most relevant, and how this differs from binary evoluion. Methods. We simulated the evolution of several large populations of triples with a population synthesis approach. We made use of the triple evolution code TRES to simulate the evolution of each triple in a consistent way, including three-body dynamics (based on the secular approach), stellar evolution, and their mutual influences. We simulated the evolution of the system up until mass transfer starts, the system becomes dynamically unstable, or a Hubble time has passed. Results. We find that stellar interactions are common in triples. Compared to a binary population, we find that the fraction of systems that can undergo mass transfer is ∼2−3 times larger in triples. Moreover, while orbits typically reach circularisation before Roche-lobe overflow in binaries, this is no longer true in triples. In our simulations, about 40% of systems retain an eccentric orbit. Additionally, we discuss various channels of triple evolution in detail, such as those where the secondary or the tertiary is the first star to initiate a mass transfer event.

Hierarchical quadruple systems arise naturally in stellar binaries and triples that harbour planets. Examples are hot Jupiters (HJs) in stellar triple systems, and planetary companions to HJs in stellar binaries. The secular dynamical evolution of these systems is generally complex, with secular chaotic motion possible in certain parameter regimes. The latter can lead to extremely high eccentricities and, therefore, strong interactions such as efficient tidal evolution. These interactions are believed to play an important role in the formation of HJs through high-eccentricity migration. Nevertheless, a deeper understanding of the secular dynamics of these systems is still lacking. Here we study in detail the secular dynamics of a special case of hierarchical quadruple systems in either the '2+2' or '3+1' configurations. We show how the equations of motion can be cast in a form representing a perturbed hierarchical three-body system, in which the outer orbital angular momentum vector is precessing steadily around a fixed axis. In this case, we show that eccentricity excitation can be significantly enhanced when the precession period is comparable to the Lidov-Kozai oscillation time-scale of the inner orbit. This arises from an induced large mutual inclination between the inner and outer orbits driven by the precession of the outer orbit, even if the initial mutual inclination is small. We present a simplified semi-analytic model that describes the latter phenomenon.

Type Ia supernovae (Ia-SNe) are thought to arise from the thermonuclear explosions of white dwarfs (WDs). The progenitors of such explosions are still highly debated; in particular the conditions leading to detonations in WDs are not well understood in most of the suggested progenitor models. Nevertheless, direct head-on collisions of two WDs were shown to give rise to detonations and produce Ia-SNe -like explosions, and were suggested as possible progenitors. The rates of such collisions in dense globular clusters are far below the observed rates of type Ia SNe, but it was suggested that quasi-secular evolution of hierarchical triples could produce a high rate of such collisions. Here we used detailed triple stellar evolution populations synthesis models coupled with dynamical secular evolution to calculate the rates of WD-WD collisions in triples and their properties. We explored a range of models with different realistic initial conditions and derived the expected SNe total mass, mass-ratio and delay time distributions for each of the models. We find that the SNe rate from WD-WD collisions is of the order of 0.1% of the observed Ia-SNe rate across all our models, and the delay-time distribution is almost uniform in time, and is inconsistent with observations. We conclude that SNe from WD-WD collisions in isolated triples can at most provide for a small fraction of Ia-SNe, and can not serve as the main progenitors of such explosions.