Cratering constraints on the inner Oort cloud: steady-state models

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Abstract
Observations of long-period comets and the mean terrestrial cratering rate over the past 600 Myr are used to constrain the parameters of models of the Oort cometary cloud. Steady-state models which explain the observed near-parabolic flux and the number of short-period comets generally require only a modest degree of central concentration. Although a range of possible models can satisfy the data, a typical example has a power-law distribution of orbital energies for semi-major axes greater than about 4000 AU with an energy spectral index γ=0.5. Such a model might be produced by an original source of comets in the Uranus–Neptune zone of the solar nebula. The total mass of this model, extrapolating the cometary brightness distribution to a limiting absolute magnitude H = 16 is on the order of 13.8M⊕, of which 46 per cent resides in comets with semimajor axes less than 104AU and 87 per cent is located in comets brighter than H = 7. The total number of comets to H = 16 is 9.5 × 1013. It is argued that the majority of terrestrial craters (≃98 per cent) are produced by Earth-crossing asteroids, a significant cometary contribution appearing unlikely on two counts: first, it would predict an incorrect number–diameter distribution for terrestrial craters, and secondly, it would require an extreme combination of cometary and other parameters. Apart from being improbable, this would force the total mass of the Oort cloud to be more than an order of magnitude greater.

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