Noise and waves: a unified kinetic theory for stellar systems
  The traditional Chandrasekhar picture of the slow relaxation of stellar
systems assumes that stars' orbits are only modified by occasional,
uncorrelated, two-body flyby encounters with other stars. However, the
long-range 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 two-body (star-star) encounters, and (ii) allows the system to
support large-scale density waves (a.k.a. normal modes) which decay through
resonant wave-star interactions. If the relaxation of the system is dominated
by effect (i) then it is described by the Balescu-Lenard (BL) kinetic theory.
Meanwhile if (ii) dominates, one must describe relaxation using quasilinear
(QL) theory, though in the stellar-dynamical 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 angle-action variables that accounts for both effects (i) and (ii)
simultaneously. We derive the equations in a heuristic, physically-motivated
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.
