The mean energy transfer rate to comets in the Oort cloud and implications for cometary origins

The mean energy transfer rate to comets in the Oort Cloud is calculated including both stellar and giant molecular cloud perturbations. For representative values of the parameters the clouds dominate the evolution for semi-major axes $$\text{a}\gtrsim2\times{10}^{4}$$ AU, while stars dominate if $$\text{a}\lesssim2\times{10}^{4}$$ AU. The resulting unbinding time-scales and half-lives are calculated and compared with the results of Bahcall et al. and Hut & Tremaine. Good agreement with their formulae is obtained although there are slight differences in detailed parameters. Taking the stars and clouds together we estimates the critical semi-major axis a_1/2, beyond which the majority of primordial comets are removed during the age of the solar system, is of order 10⁴AU. The implications of this work for the existence of the hypothetical solar companion star Nemesis suggests that in its present form the idea should be rejected. Finally the evolution of the Oort cloud and implications for the origins of comets are considered. A solution of the energy equation for the evolution of a massive primordial inner core of comets suggests that for every comet now in the outer Oort Cloud $$(\text{a}\gtrsim2\times{10}^{4}$$ AU) roughly 100 comets would be required initially in the Uranus–Neptune zone of the proto-planetary disc. This indicates that long-period comets may not have originated in this part of the Solar Nebula, and it is argued instead that Solar Nebula models which more readily generate a sufficiently massive inner core of comets should be investigated. The disruption of the outer Oort Cloud by the cumulative effects of stellar and giant molecular cloud perturbations over the age of the Solar System is consistent with the interstellar capture hypothesis, but places tight constraints on primordial Solar System models.