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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:

We extend our previous work on the two-dimensional (2-D) Dimits transition in ion-scale turbulence (Ivanov et al., J. Plasma Phys., vol. 86, 2020, 855860502) to include variations along the magnetic field. We consider a three-field fluid model for the perturbations of electrostatic potential, ion temperature, and ion parallel flow in a constant-magnetic-curvature geometry without magnetic shear. It is derived in the cold-ion, long-wavelength asymptotic limit of the gyrokinetic theory. Just as in the 2-D model, a low-transport (Dimits) regime exists and is found to be dominated by a quasistatic staircase-like arrangement of strong zonal flows and zonal temperature. This zonal staircase is formed and maintained by a negative turbulent viscosity for the zonal flows. Unlike the 2-D model, the three-dimensional (3-D) one does not suffer from an unphysical blow up beyond the Dimits threshold where the staircase becomes nonlinearly unstable. Instead, a well-defined finite-amplitude saturated state is established. This qualitative difference between the 2-D and 3-D models is due to the appearance of small-scale ‘parasitic’ modes that exist only if we allow perturbations to vary along the magnetic field lines. These modes extract energy from the large-scale perturbations and provide an effective enhancement of large-scale thermal diffusion, thus aiding the energy transfer from large injection scales to small dissipative ones. We show that in our model, the parasitic modes always favour a zonal-flow-dominated state. In fact, a Dimits state with a zonal staircase is achieved regardless of the strength of the linear drive, provided the system is sufficiently extended along the magnetic field and sufficient parallel resolution is provided.