A fundamental aspect of the three-body problem is its stability. Most stability studies have focused on the co-planar three-body problem, deriving analytic criteria for the dynamical stability of such pro/retrograde systems. Numerical studies of inclined systems phenomenologically mapped their stability regions, but neither complement it by theoretical framework, nor provided satisfactory fit for their dependence on mutual inclinations. Here we present a novel approach to study the stability of hierarchical three-body systems at arbitrary inclinations, which accounts not only for the instantaneous stability of such systems, but also for the secular stability and evolution through Lidov-Kozai cycles and evection. We generalize the Hill-stability criteria to arbitrarily inclined triple systems, explain the existence of quasistable regimes and characterize the inclination dependence of their stability. We complement the analytic treatment with an extensive numerical study, to test our analytic results. We find excellent correspondence up to high inclinations (∼ 120• ), beyond which the agreement is marginal. At such high inclinations the stability radius is larger, the ratio between the outer and inner periods becomes comparable, and our secular averaging approach is no longer strictly valid. We therefore combine our analytic results with polynomial fits to the numerical results to obtain a generalized stability formula for triple systems at arbitrary inclinations. Besides providing a generalized secular-based physical explanation for the stability of non co-planar systems, our results have direct implications for any triple systems, and in particular binary planets and moon/satellite systems; we briefly discuss the latter as a test case for our models.
Recent studies have shown that secular evolution of triple systems can play a major role in the evolution and interaction of their inner binaries. Very few studies explored the stellar evolution of triple systems, and in particular the mass loss phase of the evolving stellar components. Here we study the dynamical secular evolution of hierarchical triple systems undergoing mass loss. We use the secular evolution equations and include the effects of mass-loss and mass-transfer, as well as general relativistic effects. We present various evolutionary channels taking place in such evolving triples, and discuss both the effects of mass-loss and mass-transfer in the inner binary system, as well as the effects of mass-loss/transfer from an outer third companion. We discuss several distinct types/regimes of triple secular evolution, where the specific behavior of a triple system can sensitively depend on its hierarchy and the relative importance of classical and general relativistic effects. We show that the orbital changes due to mass-loss and/or mass-transfer processes can effectively transfer a triple system from one dynamical regime to another. In particular, mass loss/transfer can both induce and quench high amplitude (Lidov-Kozai) variations in the eccentricity and inclination of the inner binaries of evolving triples. They can also change the system dynamics from an orderly periodic behavior to a chaotic one, and vice versa.
Context. The mergers of neutron stars (NSs) and white dwarfs (WDs) could give rise to explosive transients, potentially observable with current and future transient surveys. However, the expected properties and distribution of such events is not well understood. Aims. Here we characterise the rates of such events, their delay-time distributions, their progenitors, and the distribution of their properties. Methods. We use binary population synthesis models and consider a wide range of initial conditions and physical processes. In particular we consider different common-envelope evolution models and different NS natal kick distributions. We provide detailed predictions arising from each of the models considered.Results. We find that the majority of NS-WD mergers are born in systems in which mass-transfer played an important role, and the WD formed before the NS. For the majority of the mergers the WDs have a carbon-oxygen composition (60−80%) and most of the rest are with oxygen-neon WDs. The time-integrated rates of NS-WD mergers are in the range of 3−15% of the type Ia supernovae (SNe) rate. Their delay-time distribution is very similar to that of type Ia SNe, but is slightly biased towards earlier times. They typically explode in young 100 Myr < τ < 1 Gyr environments, but have a tail distribution extending to long, gigayear-timescales. Models including significant kicks give rise to relatively wide offset distribution extending to hundreds of kiloparsecs. Conclusions. The demographic and physical properties of NS-WD mergers suggest they are likely to be peculiar type Ic-like SNe, mostly exploding in late-type galaxies. Their overall properties could be related to a class of recently observed rapidly evolving SNe, while they are less likely to be related to the class of Ca-rich SNe.
Several scenarios were suggested for the origins of gravitational-wave (GW) sources from mergers of stellar binary black holes (BBHs). Here we propose a novel origin through catalyzed formation of GW-sources from ultra-wide binaries in the field. Such binaries experience perturbations from random stellar fly-bys which excite their eccentricities. Once a wide-binary is driven to a sufficiently small peri-center approach, GW-emission becomes significant, and the binary inspirals and merges. We derive an analytic model and verify it with numerical calculation to compute the merger rate to be ∼ 10×f wide Gpc −3 yr −1 (f wide is the fraction of wide BH-binaries), which is comparable to the observationally inferred rate. The observational signatures from this channel include spin-orbit misalignment; preference for high mass-ratio BBH; preference for high velocity-dispersion hostgalaxies; and a uniform delay-time distribution.
We present a potentially efficient dynamical formation scenario for Low Mass X-ray Binaries (LMXBs) in the field, focusing on black-hole (BH) LMXBs. In this formation channel LMXBs are formed from wide binaries (> 1000 AU) with a BH component and a stellar companion. The wide binary is perturbed by fly-by's of field stars and its orbit random-walks and changes over time. This diffusion process can drive the binary into a sufficiently eccentric orbit such that the binary components tidally interact at pericenter and the binary evolves to become a short period binary, which eventually evolves into an LMXB. The formation rate of LMXBs through this channel mostly depends on the number of such BH wide binaries progenitors, which in turn depends on the velocity kicks imparted to BHs (or NSs) at birth. We consider several models for the formation and survival of such wide binaries, and calculate the LMXB formation rates for each model. We find that models where BHs form through direct collapse with no/little natal kicks can give rise to high formation rates comparable with those inferred from observations. This formation scenario had several observational signatures: (1) the number density of LMXBs generally follows the background stellar density and (2) the mass function of the BH stellar companion should be comparable to the mass function of the background stellar population, likely peaking at 0.4 − 0.6 M ⊙ . The latter aspect, in particular, is unique to this model compared with previously suggested LMXB formation models following common envelope binary stellar evolution. We note that NS LMXBs can similarly form from wide binaries, but their formation rate through this channel is likely significantly smaller due to their much higher natal kicks.
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