The Problem of the 1/a-Distribution and Cometary Fading

Abstract

The background to the problem of explaining the frequency distribution of cometary 1/a-values is briefly reviewed and it is emphasised that the explanation in terms of the Oort Cloud model relies on an ad hoc fitting function — the fading/disruption probability per revolution. Assuming an underlying steady-state Oort Cloud and the integral equation formalism developed by Oort and Yabushita to predict the 1/a-distribution for an arbitrary fading probability, we have been able to constrain the unknown fading function by comparison with observations. In agreement with previous work we find that the tendency for fading or disruption should be strong at small 1/a-values and weak at large 1/a-values. The mean fading probability per revolution, k(x), is found to lie within a factor roughly of order 2 about k(x) ≈ 0.3(1+(x/4 x 10^-3)₂)^-3/2, where x is 1/a in units AU^-1. A physical model for fading which might qualitatively account for this behaviour is tentatively proposed. This depends on the thermal shock experienced by a long-period comet nucleus around perihelion passage. It is emphasised that until a viable model for fading has been found, the validity of the steady-state primordial hypothesis remains unresolved.