Abstract

Gravitational systems surrounded by a large number of substructures experience fluctuations of the external tidal field that inject energy into their internal motions. In this talk I will show that “tidal heating” can be statistically modelled as a random walk in velocity space, and compute the Green’s propagators from the number density and velocity distribution of substructures with known mass & size functions. In addition, a Monte-Carlo Markov-chain technique will be introduced which mimics the effects of an fluctuating tidal field by sampling velocity ’kicks’ from a probability function. Tests against direct-force N-body models show that (i) the new technique is extremely CPU effective, and (ii) it provides an accurate description of the response of gravitationally-bound particles to repeated tidal fluctuations in both impulsive and adiabatic regimes. For illustration, I will present idealized models that follow the dynamical evolution of planetary discs in a clumpy environment. The results indicate that the presence of a stochastic tidal field necessarily leads to the formation, and subsequent “evaporation” of Oort-like clouds, as well as to a sizeable population of comets on retrograde orbits.