Related papers: Vector Resonant Relaxation and Statistical Closure…
We use stellar dynamics as a testbed for statistical closure theory. We focus on the process of "Vector Resonant Relaxation," a long-range, non-linear, and correlated relaxation mechanism that drives the reorientation of stellar orbital…
In the vicinity of a massive black hole, stars move on precessing Keplerian orbits. The mutual stochastic gravitational torques between the stellar orbits drive a rapid reorientation of their orbital planes, through a process called vector…
The goal of this paper is to study the statistical closures suggested by the Martin-Siggia and Rose approach to statistical turbulence. We find that the formalism leads to a Bethe-Salpeter equation for the three point correlation of the…
Stars evolving around a supermassive black hole see their orbital orientations diffuse efficiently, a process called "vector resonant relaxation". In particular, stars within the same disc, i.e. neighbors in orientations, will slowly…
Supermassive black holes dominate the gravitational potential in galactic nuclei. In these dense environments, stars follow nearly Keplerian orbits and see their orbital planes relax through the potential fluctuations generated by the…
We investigate the rate of orbital orientation dilution of young stellar clusters in the vicinity of supermassive black holes. Within the framework of vector resonant relaxation, we predict the time evolution of the two-point correlation…
Resonant relaxation has been discussed as an efficient process that changes the angular momenta of stars orbiting around a central supermassive black hole due to the fluctuating gravitational field of the stellar cluster. Other spherical…
Stars bound to a supermassive black hole interact gravitationally. Persistent torques acting between stellar orbits lead to the rapid resonant relaxation of the orbital orientation vectors ("vector" resonant relaxation) and slower…
Direct numerical integrations of the Fokker-Planck equation in energy-angular momentum space are carried out for stars orbiting a supermassive black hole (SBH) at the center of a galaxy. The algorithm, which was described in detail in an…
In nuclear star clusters, the potential is governed by the central massive black hole, so that stars move on nearly Keplerian orbits and the total potential is almost stationary in time. Yet, the deviations of the potential from the…
In this work, we apply the Martin-Siggia-Rose path integral formalism to the equations of a thin elastic plate. Using a diagrammatic technique, we obtain the direct interaction approximation (DIA) equations to describe the evolutions of the…
This paper is the third in a series presenting the results of direct numerical integrations of the Fokker-Planck equation for stars orbiting a supermassive black hole (SBH) at the center of a galaxy. The algorithm of Paper II included…
The orbits of stars close to a massive black hole are nearly Keplerian ellipses. Such orbits exert long term torques on each other, which lead to an enhanced angular momentum relaxation known as resonant relaxation. Under certain…
Vector resonant relaxation (VRR) is known to be the fastest gravitational process that shapes the geometry of stellar orbits in nuclear star clusters. This leads to the realignment of the orbital planes on the corresponding VRR time scale…
We develop the exact renormalization group approach as a way to evaluate the effective speed of propagation of a scalar wave in a medium with random inhomogeneities. We use the Martin-Siggia-Rose formalism to translate the problem into a…
Resonant relaxation (RR) of orbital angular momenta occurs near massive black holes (MBHs) where the stellar orbits are nearly Keplerian and so do not precess significantly. The resulting coherent torques efficiently change the magnitude of…
We investigate statistical properties of vorticity fluctuations in fully developed turbulence, which are known to exhibit a strong intermittent behavior. Taking as the starting point the Navier-Stokes equations with a random force term…
The coherent torques between stars on orbits near massive black holes (MBHs) lead to resonant angular momentum relaxation. Due to the fact that orbits are Keplerian to good approximation, the torques efficiently change the magnitude of the…
Spatial and momentum correlations are important in the analysis of the quantum states and different phases of trapped ultracold atom systems as a function of the strength of interatomic interactions. Identification and understanding of…
We investigate Lagrangian relative dispersion in direct numerical simulation of two-dimensional inverse cascade turbulence. The analysis is performed by using both standard fixed time statistics and an exit time approach. Our results are in…