Noise and waves: a unified kinetic theory for stellar systems
Abstract
The traditional Chandrasekhar picture of the slow relaxation of stellar systems assumes that stars' orbits are only modified by occasional, uncorrelated, twobody flyby encounters with other stars. However, the longrange nature of gravity means that in reality large numbers of stars can behave collectively. In stable systems this collective behaviour (i) amplifies the noisy fluctuations in the system's gravitational potential, effectively 'dressing' the twobody (starstar) encounters, and (ii) allows the system to support largescale density waves (a.k.a. normal modes) which decay through resonant wavestar interactions. If the relaxation of the system is dominated by effect (i) then it is described by the BalescuLenard (BL) kinetic theory. Meanwhile if (ii) dominates, one must describe relaxation using quasilinear (QL) theory, though in the stellardynamical context the full set of QL equations has never been presented. Moreover, in some systems like open clusters and galactic disks, both (i) and (ii) might be important. Here we present for the first time the equations of a unified kinetic theory of stellar systems in angleaction variables that accounts for both effects (i) and (ii) simultaneously. We derive the equations in a heuristic, physicallymotivated fashion and work in the simplest possible regime by accounting only for very weakly damped waves. This unified theory is effectively a superposition of BL and QL theories, both of which are recovered in appropriate limits. The theory is a first step towards a comprehensive description of those stellar systems for which neither the QL or BL theory will suffice.
 Publication:

arXiv eprints
 Pub Date:
 November 2020
 DOI:
 10.48550/arXiv.2011.14812
 arXiv:
 arXiv:2011.14812
 Bibcode:
 2020arXiv201114812H
 Keywords:

 Astrophysics  Astrophysics of Galaxies;
 Physics  Plasma Physics
 EPrint:
 9 pages, 2 figures. Comments welcome