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Abstract:

Close encounters between two bodies in a disc often result in a single orbital deflection. However, within their Jacobi volumes, where the gravitational forces between the two bodies and the central body become competitive, temporary captures with multiple close encounters become possible outcomes: a Jacobi capture. We perform three-body simulations in order to characterize the dynamics of Jacobi captures in the plane. We find that the phase space structure resembles a Cantor-like set with a fractal dimension of about 0.4. The lifetime distribution decreases exponentially, while the distribution of the closest separation follows a power law with index 0.5. In our first application, we consider the Jacobi capture of the Moon. We demonstrate that both tidal captures and giant impacts are possible outcomes. The impact speed is well approximated by a parabolic encounter, while the impact angles follow that of a uniform beam on a circular target. Jacobi captures at larger heliocentric distances are more likely to result in tidal captures. In our second application, we find that Jacobi captures with gravitational wave dissipation can result in the formation of binary black holes in galactic nuclei. The eccentricity distribution is approximately superthermal and includes both prograde and retrograde orientations. We conclude that dissipative Jacobi captures form an efficient channel for binary formation, which motivates further research into establishing the universality of Jacobi captures across multiple astrophysical scales.

Abstract:

We explore the dynamics of stellar discs in the close vicinity of a supermassive black hole (SMBH) by means of direct N-body simulations. We show that an isolated nuclear stellar disc exhibits anisotropic mass segregation meaning that massive stars settle to lower orbital inclinations and more circular orbits than the light stars. However, in systems in which the stellar disc is embedded in a much more massive isotropic stellar cluster, anisotropic mass segregation tends to be suppressed. In both cases, an initially thin stellar disc becomes thicker, especially in the inner parts due to the fluctuating anisotropy in the spherical component. We find that vector resonant relaxation is quenched in the disc by nodal precession, but it is still the most efficient relaxation process around SMBHs of mass 106 M⊙ and above. Two-body relaxation may dominate for less massive SMBHs found in dwarf galaxies. Stellar discs embedded in massive isotropic stellar clusters ultimately tend to become isotropic on the local two-body relaxation time-scale. Our simulations show that the dynamics of young stars at the centre of the Milky Way is mostly driven by vector resonant relaxation leading to an anticorrelation between the scatter of orbital inclinations and distance from the SMBH. If the S-stars formed in a disc less than 10 Myr ago, they may coexist with a cusp of stellar mass black holes or an intermediate mass black hole with mass up to 1000 M⊙ to reproduce the observed scatter of angular momenta.

Abstract:

The following minor errors have been found in the published article. (Equation presented). These errors do not affect any of the figures, results, or conclusions of the paper.

Abstract:

Galactic nuclei (GNs) are dense stellar environments abundant in gravitational-wave (GW) sources for the Laser Interferometer Gravitational-Wave Observatory (LIGO), Virgo, and Kamioka Gravitational Wave Detector (KAGRA). The GWs may be generated by stellar-mass black hole (BH) or neutron star mergers following gravitational bremsstrahlung, dynamical scattering encounters, Kozai–Lidov-type oscillations driven by the central supermassive black hole (SMBH), or gas-assisted mergers if present. In this paper, we examine a smoking gun signature to identify sources in GNs: the GWs scattered by the central SMBH. This produces a secondary signal, an astrophysical GW echo, which has a very similar time–frequency evolution as the primary signal but arrives after a time delay. We determine the amplitude and time-delay distribution of the GW echo as a function of source distance from the SMBH. Between ∼10 per cent and 90 per cent of the detectable echoes arrive within ∼(1--100)M₆s after the primary GW for sources between 10 and 10⁴ Schwarzschild radius, where M₆=M_SMBH,z/ (10⁶M_⊙), and M_{SMBH, z} is the observer-frame SMBH mass. The echo arrival times are systematically longer for high signal-to-noise ratio (SNR) primary GWs, where the GW echo rays are scattered at large deflection angles. In particular, ∼10 per cent--90 per cent of the distribution is shifted to ∼(5--1800)M₆s for sources, where the lower limit of echo detection is 0.02 of the primary signal amplitude. We find that ∼5 per cent--30 per cent(⁠∼1 per cent--7 per cent⁠) of GW sources have an echo amplitude larger than 0.2–0.05 times the amplitude of the primary signal if the source distance from the SMBH is 50 (200) Schwarzschild radius. Non-detections can rule out that a GW source is near an SMBH.