Nuclear star clusters around a central massive black hole (MBH) are expected to be abundant in stellar black hole (BH) remnants and BH-BH binaries. These binaries form a hierarchical triple system with the central MBH, and gravitational perturbations from the MBH can cause high-eccentricity excitation in the BH-BH binary orbit. During this process, the eccentricity may approach unity, and the pericenter distance may become sufficiently small so that gravitational-wave emission drives the BH-BH binary to merge. In this work, we construct asimple proof-of-concept model for this process, and specifically, we study the eccentric Kozai-Lidov mechanism in unequal-mass, soft BH-BHbinaries. Our model is based on a set of Monte Carlo simulations for BH-BH binaries in galactic nuclei, taking into account quadrupole- and octupole-level secular perturbations, general relativistic precession,and gravitational-wave emission. For a typical steady-state number of BH-BH binaries, our model predicts a total merger rate of ̃1-3 {Gpc}^-3 {yr} ^-1, depending on the assumed density profile in the nucleus. Thus, our mechanism could potentially compete with other dynamical formation processes for merging BH-BH binaries,such as the interactions of stellar BHs in globular clusters or in nuclear star clusters without an MBH.

Stars, planets and massive black holes are ubiquitous in binary and multiple configurations. In stellar systems the binary components interact through various type of mass loss and mass transfer. Mass transfer interactions in eccentric systems are in principle phase-dependent and can occur in different ways. We formulate the understanding of mass transfer interactions in binary systems and investigate how these affect their evolution and therefore their observed orbital properties. We present a theoretical framework to describe this evolution and investigate various types of mass transfer including commonly studied cases: isotropic and non-anisotropic wind mass loss; Roche-lobe-overflow; and Bondi-Hoyle accretion. We provide analytical equations of the phase-dependent and long-term (secular) evolution of mass-transferring eccentric binaries. The theoreticalf ramework provided could be implemented in future work in numerical codes widely used to study stellar binary evolution. In the planetary world giant exoplanets could be found so close to their host star that they are expected to start transferring mass to their stellar companion.We investigate the fate of roche-lobe overflowing giant exoplanets andexplore the final orbits of their remnants, trying to provide aplausible theoretical explanation to the observed systems by the planet-hunting mission "Kepler". Massive black hole binary configurations inthe nuclei of large-scale structures like galaxies are formed through galaxy mergers. We explore the evolution of massive black hole binaries in galactic nuclei as a function of the properties of the host andmerging galaxy and attempt to provide an explanation for a number ofobservations, including the puzzling discovery of multiple nuclei in thecore of the brightest galaxies.

Many giant exoplanets are found near their Roche limit and in mildlyeccentric orbits. In this study, we examine the fate of such planets through Roche-lobe overflow as a function of the physical properties ofthe binary components, including the eccentricity and the asynchronicity of the rotating planet. We use a direct three-body integrator to computethe trajectories of the lost mass in the ballistic limit and investigate the possible outcomes. We find three different outcomes for the mass transferred through the Lagrangian point L ₁: (1) self-accretion by the planet, (2) direct impact on the stellar surface, and(3) disk formation around the star. We explore the parameter space ofthe three different regimes and find that at low eccentricities, e≲ 0.2, mass overflow leads to disk formation for most systems, while, for higher eccentricities or retrograde orbits, self-accretion is the onlypossible outcome. We conclude that the assumption often made in previous work that when a planet overflows its Roche lobe it is quickly disrupted and accreted by the star is not always valid.

The supermassive black holes originally in the nuclei of two merging galaxies will form a binary in the remnant core. The early evolution of the massive binary is driven by dynamical friction before the binary becomes “hard” and eventually reaches coalescence through gravitational-wave emission. We consider the dynamical friction evolution of massive binaries consisting of a secondary hole orbiting inside a stellar cuspdominated by a more massive central black hole. In our treatment, weinclude the frictional force from stars moving faster than the inspiralling object, which is neglected in the standard Chandrasekhar reatment. We show that the binary eccentricity increases if the stellar-cusp density profile rises less steeply than ρ \propto {r}^-2.In cusps shallower than ρ \propto {r}^-1, the frictional timescale can become very long due to the deficit of stars moving slower than the massive body. Although including fast stars increases the decay rate, low mass-ratio binaries (q≲ {10}^-3) in sufficiently massive galaxies have decay timescales longer than one Hubble time. During such minor mergers, the secondary hole stalls on an eccentric orbit at a distance of order one-tenth the influence radius of the primary hole (I.e., ≈ 10{--}100 {pc} for massive ellipticals). We calculate the expected number of stalled satellites as a function of the host galaxy mass and show that the brightest cluster galaxies should have ≳ 1 of such satellites orbiting within their cores. Our results could provide an explanation for a number of observations, which include multiple nuclei in core ellipticals, off-center AGNs, and eccentric nuclear disks.

Aims: We have endeavoured to understand the formation and evolution of the black hole (BH) X-ray binary LMC X-3. We estimated the properties of the system at four evolutionary stages: (1) at the zero-age main-sequence (ZAMS); (2) immediately before the supernova (SN) explosion of the primary; (3) immediately after the SN; and (4) at the moment when Roche-lobe overflow began.
Methods: We used a hybrid approach that combined detailed calculations of the stellar structure nd binary evolution with approximate population synthesis models. This allowed us to estimate potential natal kicks and the evolution of the BH spin. We incorporated as model constraints the most up-to-date observational information throughout, which include the binary orbital properties, the companion star mass, effective temperature, surface gravity and radius, and the BH mass and spin.
Results: We find at 5% and 95% confidence, respectively, that LMC X-3 began as a ZAMS system with the mass of the primary star in the range M1,ZAMS = 22–31 solar mass and a secondary star of M2,ZAMS = 5.0−8.3 solar mass, in a wide (P_ZAMS & 2.000 days) and eccentric (e_ZAMS & 0.18) orbit. Immediately before the SN, the primary had a mass of M1,preSN = 11.1−18.0 solar mass, but the secondary star was largely unaffected. The orbital period decreased to 0.6−1.7 days and is still eccentric 0 ≤ e_preSN ≤ 0.44. We find that a symmetric SN explosion with no or small natal kicks (a few tens of km s−1 ) imparted on the BH cannot be formally excluded, but large natal kicks in excess of greater or equal than 120 km s−1 increase the estimated formation rate by an order of magnitude. Following the SN, the system has a BH MBH,postSN = 6.4−8.2 Msolar mass and is set on an eccentric orbit. At the onset of the Roche-lobe overflow, the orbit is circular and has a period of P_RLO = 0.8−1.4 days.

Selected parameters of mass transfer sequence models computed with MESAthat matches observational inferred data on the BH X-ray binary LMC X-3.Each record describes the initial configuration of the LMC X-3 binarythe moment Roche lobe overflow begins. (1 data file).

Finite eccentricities in mass-transferring eccentric binary systems can be explained by taking into account the mass loss and mass transfer processes that often occur in these systems. These processes can betreated as perturbations of the general two-body problem. The time-evolution equations for the semimajor axis and the eccentricity derivedf rom perturbative methods are generally phase-dependent. The osculating semimajor axis and eccentricity change over the orbital timescale andare not easy to implement in binary evolution codes like MESA. However, the secular orbital element evolution equations can be simplified by averaging over the rapidly varying true anomalies. In this paper, we derive the secular time-evolution equations for the semimajor axis and the eccentricity for various mass loss/transfer processes using either the adiabatic approximation or the assumption of delta-function mass loss/transfer at periastron. We begin with the cases of isotropic and anisotropic wind mass loss. We continue with conservative and non-conservative non-isotropic mass ejection/accretion (including Roche-Lobe-Overflow) for both point-masses and extended bodies. We conclude with the case of phase-dependent mass accretion. Comparison of the derived equations with similar work in the literature is included and an explanation of the existing discrepancies is provided.

Observations reveal that mass-transferring binary systems may have non-zero orbital eccentricities. The time evolution of the orbital semimajor axis and eccentricity of mass-transferring eccentric binary systems is an important part of binary evolution theory and has been widely studied. However, various different approaches to and assumptions on the subject have made the literature difficult to comprehend and comparisons between different orbital element time evolution equations not easy to make. Consequently, no self-consistent treatment of this phase has ever been included in binary population synthesis codes. In this paper, we present a general formalism to derive the time evolution equations ofthe binary orbital elements, treating mass loss and mass transfer as perturbations of the general two-body problem. We present the self-consistent form of the perturbing acceleration and phase-dependent timeevolution equations for the orbital elements under different mass loss/transfer processes. First, we study the cases of isotropic and anisotropic wind mass loss. Then, we proceed with non-isotropic ejection and accretion in a conservative as well as a non-conservative manner for both point masses and extended bodies. We compare the derived equations with similar work in the literature and explain the existing discrepancies.

We use a general relativistic approach to investigate the effects of weak cosmological magnetic fields on linear rotational perturbations during the radiation and dust epochs of the Universe. This includes ordinary kinematic vorticity, as well as vortex like inhomogeneities inthe density distribution of the matter. Our study confirms that magnetism sources both types of perturbations and that its presence helps cosmic rotation to survive longer. In agreement with previous Newtonian studies, we find that during the dust era vorticity decays slower than in nonmagnetized cosmologies. The relativistic nature of the treatment means that we can also investigate the epoch prior to equipartition. There, the magnetic effect is more pronounced, since it helps both of the above rotational distortions to maintain constant magnitude throughout the radiation era. Overall, magnetized universes not only generate vorticity but also provide a much better environment for the survival of rotational perturbations, than their magnetic-free counterparts.

We study the role of viscosity and the effects of a magnetic field on a rotating, self-gravitating fluid, using Newtonian theory and adopting the ideal magnetohydrodynamic approximation. Our results confirm that viscosity can generate vorticity in inhomogeneous environments, while the magnetic tension can produce vorticity even in the absence of fluid pressure and density gradients. Linearizing our equations around an Einstein-de Sitter cosmology, we find that viscosity adds to thediluting effect of the universal expansion. Typically, however, the dissipative viscous effects are confined to relatively small scales. We also identify the characteristic length below which the viscous dissipation is strong and beyond which viscosity is essentially negligible. In contrast, magnetism seems to favor cosmic rotation. The magnetic presence is found to slow down the standard decay rate of linear vortices, thus leading to universes with more residual rotation than generally anticipated.