The structure and evolution of the Solar System comet cloud

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Abstract
The structure and evolution of a hypothetical cloud of comets surrounding the Solar System is investigated, with particular reference to showing how the derived results depend on the assumed cometary energy and velocity distribution functions. The mean energy transfer rate by stars and giant molecular clouds is calculated and it is shown that for reasonable values of the parameters the cumulative effect of the clouds is dominant. Thus it is unlikely that the loosely-bound Oort comet cloud could survive for the age of the Solar System. The equation describing the evolution of the comet cloud between close encounters with nebulae is solved in a good approximation for an initial condition where the energy spectrum is a power law. Formulae are also given which relate the energy spectrum to the velocity distribution function and density distribution, and it is shown how the current energy spectrum can be inferred from observations. Analytic results for the standard Oort model are presented and we show how this model is just one of a family of hypothetical comet clouds with power-law energy spectra. The spectral index of this standard model does not agree well with that obtained from observations, these indicating a model with flatter spectrum and higher degree of central condensation. More centrally condensed models may be easier to understand as a by-product of Solar System formation, and are more stable against disruption by encounters with nebulae.

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