Theoretical astrophysics and plasma physics at RPC

Abstract:

We derive an analytical model for the so-called phenomenon of resonant dynamical friction, where a disc of stars around a supermassive black hole interacts with a massive perturber, so as to align its inclination with the disc’s orientation. We show that it stems from a singular behaviour of the orbit-averaged equations of motion, which leads to a rapid alignment of the argument of the ascending node of each of the disc stars, with that of the perturber, p, with a phase difference of 90◦. This phenomenon occurs for all stars whose maximum possible ˙ (maximized over all values of for all the disc stars) is greater than ˙ p; this corresponds approximately to all stars whose semi-major axes are less than twice that of the perturber. The rate at which the perturber’s inclination decreases with time is proportional to its mass and is shown to be much faster than Chandrasekhar’s dynamical friction. We find that the total alignment time is inversely proportional to the root of the perturber’s mass. This persists until the perturber enters the disc. The predictions of this model agree with a suite of numerical N-body simulations, which we perform to explore this phenomenon, for a wide range of initial conditions, masses, etc., and are an instance of a general phenomenon. Similar effects could occur in the context of planetary systems, too.

Abstract:

The equations of electrostatic drift kinetics are observed to possess a symmetry associated with their intrinsic scale invariance. Under the assumptions of spatial periodicity, stationarity, and locality, this symmetry implies a particular scaling of the turbulent heat flux with the system's parallel size, from which its scaling with the equilibrium temperature gradient can be deduced under some additional assumptions. This macroscopic transport prediction is then confirmed numerically for a reduced model of electron-temperature-gradient-driven turbulence in slab geometry. The system realises this scaling through a turbulent cascade from large to small perpendicular spatial scales. The route of this cascade through wavenumber space (i.e. the relationship between parallel and perpendicular scales in the inertial range) is shown to be determined by a balance between nonlinear-decorrelation and parallel-dissipation timescales. This type of ‘critically balanced’ cascade, which maintains a constant energy flux despite the presence of parallel dissipation throughout the inertial range (as well as order-unity dissipative losses at the outer scale) is expected to be a generic feature of plasma turbulence. The outer scale of the turbulence, on which the turbulent heat flux depends, is determined by the breaking of drift-kinetic scale invariance due to the existence of large-scale parallel inhomogeneity (the parallel system size).