Population dependence of early relaxation

Details Population dependence of early relaxation Population dependence of early relaxation

Feb 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phrve..51..884r&link_type=abstract

Physical Review E (Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics), Volume 51, Issue 2, February 199

Nonlinear Sciences

Chaotic Dynamics

13

Celestial Mechanics, Chaotic Dynamics

Scientific paper

The general view of galactic evolution suggests an early period of ``violent'' relaxation followed by the establishment of a long-lived quasiequilibrium state which is associated with a stationary or steady-state solution of the Vlasov equation. The predicted time scale for the initial violent period, which has been supported by a number of simulations, is of the order of a few galactic crossing times. However, the formation of stellar clusters may constrain the early mixing to a slower diffusion which precedes the violent phase. To explore this possibility, we report on a recent study of the relaxation of a highly virialized (large ratio of kinetic to potential energy) model of a one-dimensional ``galaxy'' consisting of N parallel mass sheets interacting solely through their mutual gravitational attraction. We show that (1) relaxation consists of a long diffusive phase which can be of the order of a thousand crossing times and depends sensitively on the system population, followed by a short-lived ``violent'' period lasting less than 100 crossing times, and (2) the overall relaxation time has a minimum for a system consisting of about 30 sheets, suggesting that dynamics is most ``chaotic'' for this population. However, regardless of the population, the ultimate stationary state exhibits the expected core-halo structure in μ (position, velocity) space. Possible implications of the study for both nonlinear dynamics and astrophysics are considered.

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