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Astrophysical Dynamics and Statistical Physics of Galactic Nuclei

Periodic Reporting for period 4 - GalNUC (Astrophysical Dynamics and Statistical Physics of Galactic Nuclei)

Reporting period: 2020-02-01 to 2020-07-31

We address some of the major unsolved questions of galactic nuclei using methods of condensed matter physics. Galactic nuclei host a central supermassive black hole, a dense population of stars and compact objects, and in many cases a bright gaseous disk feeding the supermassive black hole. The observed stellar distribution exhibits both spherical and counterrotating disk-like structures. Existing theoretical models cannot convincingly explain the origin of the stellar disks. Is there also a “dark cusp” or “dark disk” of stellar mass black holes? Are there intermediate mass black holes in the Galactic center? We examine the statistical physics of galactic nuclei and their long term dynamical evolution. A star orbiting a supermassive black hole on an eccentric precessing orbit covers an axisymmetric annulus. The long-term gravitational interaction between such annuli is similar to the Coulomb interaction between axisymmetric molecules constituting a liquid crystal. We apply standard methods of condensed matter physics to examine these astrophysical systems. The observed disk and spherical structures represent isotropic-nematic phase transitions. We derive the phase space distribution and time-evolution of different stellar components including a population of black holes. Further, we investigate the interaction of a stellar cluster with a gaseous disk, if present. This leads to the formation of gaps, warps, and spiral waves in the disk, the redistribution of stellar objects, and possibly the formation of intermediate mass black holes. We explore the implications for electromagnetic and gravitational wave observatories. Dark disks of black holes could provide the most frequent source of gravitational waves for LIGO and VIRGO. These detectors will open a new window on the Universe; the proposed project will open a new field in gravitational wave astrophysics to interpret the sources. We also explore implications for electromagnetic observations.
We have discovered a tantalizing connection between the statistical behavior of a stellar system and liquid crystals, and used this connection to construct state-of-the-art numerical models to understand their behavior. This connection is related to the way the orbits of stars and black holes interact gravitationally around a supermassive black hole and relax into a "thermodynamic" equilibrium. Over long timescales, these orbits represent rings, which efficiently reorient due to a process called vector resonant relaxation. The basic ingredient of this process is its Hamiltonian. We have obtained the Hamiltonian of vector resonant relaxation, which is the sum of the pairwise gravitational potential energy between the stellar orbits “smeared out over their precessing orbits”. We have shown that this Hamiltonian is algebraically very similar to the Hamiltonian of liquid crystals. This tantalizing analogy may provide great insight for understanding the behavior of stellar orbits in galactic nuclei. Using the Hamiltonian we have constructed a numerical algorithm, N-ring, to simulate the evolution as a function of time. We constructed a stochastic model to analytically understand the time-evolution during vector resonant relaxation. We derived the statistical equilibrium of vector resonant relaxation for a one-component system using mean field theory including the effect of angular momentum conservation. We showed that the system exhibits phase transitions. The system forms an ordered disk at low temperatures and a nearly isotropic disordered configuration at high temperatures. We also found stable negative absolute temperature states which are nearly isotropic. The effect of angular momentum is similar to the effect of a background magnetic field for liquid crystals. The overall implication is that stellar mass black holes are distributed in a disk in the centers of galaxies.

We have also examined the composition and distribution of objects in galactic nuclei. The gamma ray emission from the Galactic Center reveals a population of objects, magnetized rapidly spinning neutron stars, which were formed in dense stellar environments like globular clusters orbiting in the halo of the Galaxy. These clusters sank to the Galactic Center due to "dynamical friction" and facilitate the formation of the Galactic Center.

We have examined the distribution of binaries in the Galactic center as they interact with the star cluster and the central supermassive black hole. We found that a significant fraction of the binaries get destroyed within their lifetime. In active galaxies where gas falls onto the supermassive black hole to produce spectacularly luminous radiation in a disk, stars and black hole binaries get captured by the gaseous disk. These sources may be important sources of gravitational waves. We found that black holes get efficiently captured in the disk and merge due to hydodynamical interaction with gas. This produces hierarchical black hole mergers in active galactic nuclei detectable with gravitational wave instruments such as LIGO, VIRGO, and KAGRA, and may lead to the formation of intermediate mass black holes.

We constructed methods to examine the astrophysical origin of black hole mergers discovered by LIGO. In galactic nuclei we showed that the Kozai-Lidov process driven by the supermassive black hole may produce mergers observable by LIGO. We also showed that triple and quadruple systems also facilitate the mergers of black holes and lead to tidal dispruption events.

We showed that the distribution of astrophysical parameters is different for different astrophysical processes leading to a merger. The event rate distribution of gravitational wave merger events may have implications on the source environment of the observed black hole mergers with Earth-based detectors. In particular we determined the mass distribution of gravitational wave capture binaries in galactic nuclei, primoridial black hole binaries formed in the early universe, and the binaries formed dynamically in dense stellar systems without a supermassive black hole such as globular clusters.
Identifying connections between seemingly distinct fields of scientific disciplines has a great potential to advance the understanding of both fields. The link between the condensed matter physics and astrophysics found in the GALNUC project offers a new method to learn about the long-term behavior of these astrophysical systems. Previous state-of-the-art simulations could not accurately follow the evolution of galactic nuclei over extended periods with a realistic number of objects and a realistic mass distribution. We have developed numerical tools to follow the evolution of strongly interacting gravitating systems. Using methods from statistical physics we developed a new method to find the equilibrium configurations. These results may have important consequences for the theory of galaxy formation. Conversely, the study of astrophysical systems may advance the understanding of condensed matter physics.
GALNUC research group