This paper explores the phenomenon of energy relaxation for stars in a galaxyembedded in a high density environment that is subjected continually toperturbations reflecting the presence of other nearby galaxies and/orincoherent internal pulsations. The analysis is similar to earlier analyses ofenergy relaxation induced by binary encounters between nearby stars and betweenstars and giant molecular clouds in that the perturbations are idealised as asum of near-random events which can be modeled as diffusion and dynamicalfriction. However, the analysis differs in one important respect: because thetime scale associated with these perturbations need not be short compared withthe characteristic dynamical time t_D for stars in the original galaxy, thediffusion process cannot be modeled as resulting from a sequence ofinstantaneous kicks, i.e., white noise. Instead, the diffusion is modeled asresulting from random kicks of finite duration, i.e., coloured noisecharacterised by a nonzero autocorrelation time t_c. A detailed analysis ofcoloured noise generated by sampling an Ornstein-Uhlenbeck process leads to asimpling scaling in terms of t_c and an effective diffusion constant D.Interpreting D and t_c following early work by Chandrasekhar (1941) (the`nearest neighbour approximation') implies that, for realistic choices ofparameter values, energy relaxation associated with an external environmentand/or internal pulsations could be important on times short compared with theage of the Universe.
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