Astronomy and Astrophysics – Astrophysics
Scientific paper
Dec 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977apj...218..406k&link_type=abstract
Astrophysical Journal, Part 1, vol. 218, Dec. 1, 1977, p. 406-414.
Astronomy and Astrophysics
Astrophysics
3
Astrophysics, Star Clusters, Stochastic Processes, Autocorrelation, Differential Equations, Markov Processes, Tides
Scientific paper
It is assumed that the tidal encounters which disrupt star clusters can be described by a stochastic equation with a given autocorrelation function, and the problem of the tidal disruption of clusters is formulated in terms of a stochastic differential equation. The rate of increase of the total energy of a test star encountering a spherically symmetric cluster of uniform mean density is calculated directly (to second order) in terms of the autocorrelation function of the stochastic process by using the mean-field approximation. This approximation is found to be in agreement with Spitzer's (1958) result for a uniform spherical cluster, and the autocorrelation function is computed for the case where the perturbers move in straight lines with a constant velocity. The asymptotic form of the autocorrelation function for large times is shown to follow simply from the form of the tidal force and, consequently, to be independent of the specific cluster model. It is concluded that Spitzer's (1958) results are a reasonable approximation even for nonuniform clusters in cases where mass loss is negligible.
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