Institute of Astronomy

The discreteness-driven relaxation of collisionless gravitating systems

SpeakerTalk DateTalk Series
Beraldo e Silva (U Central Lancashire)22 February 2019Institute of Astronomy Galaxies Discussion Group


The violent relaxation of a perturbed or collapsing collisionless
gravitational system, with the fast achievement of a quasi-stationary
state, is traditionally assumed to be governed by the Vlasov equation,
in which case the entropy must be conserved. In this scenario, the
reconciliation with the 2nd law of thermodynamics is made through
coarse-graining (a subjective effect). In this talk, I will discuss
recent results obtained with entropy estimates in N-body simulations
and for orbit ensembles in fixed external potentials. In the N-body
simulations, the (slow) long-term evolution is well described as
resulting from two-body relaxation, while the early evolution
generates a fast (in a few crossing times) entropy production. The
integration of orbit ensembles in external potentials shows that this
early collisionless relaxation is due to the discreteness (finite N)
of gravitating systems in any potential, being a consequence of the
Nyquist-Shannon theorem, which precludes the development of
phase-space structures finer than a typical scale ~ N^-1/d (for a
sample of size N in d dimensions). As a result, a typical relaxation
time T/tau_cr ~ 0.1 * N^1/6 emerges in integrable potentials, with
weaker N-dependencies in the presence of chaotic orbits. Furthermore,
this scenario avoids the need for the subjective effect of
coarse-graining and indicates that the Vlasov equation does not
provide an adequate kinetic description of this fast (violent)
collisionless relaxation.


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