Population dependence of early relaxation

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Abstract
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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