Periodicity in the crater formation rate and implications for astronomical modeling

Claim for periodicity in the crater formation rate is reinvestigated using a criterion proposed by Broadbent, and data sets of Rampino and Stothers and of Grieve are shown to satisfy the periodicity criterion (P 30 Myr).On the other hand, currently observed impactors are mainly asteroids, while long and short periodic comets whose fluxes may vary by external disturbances occupy only a small fraction. Using a Monte Carlo simulation, constraints are obtained for the dispersion Q(Myr) from an exact periodicity and for the periodic components (F_tp) in the signals for their periodicity to be detected. It is found that for = 5, 6 and 7 Myr, F_tp, would have to be 40% or greater, 60% or greater and 80% or greater, respectively. These constraints are used to discuss whether the giant molecular cloud perturbations can give rise to the periodicity in the impact events. The amplitude of the solar Z-motion need to be some 100pc for = 6 Myr, which requires the periodic component (SP and LP comets, if the former originate from the latter) to be 60%, while for = 7 Myr, the periodic component need to be 80%. The GMC perturbation model consistent with the periodicity appears to be the one where the amplitude is 100pc and the periodic component - 60% of the impactors. If SP comets mainly originate from a source such as the hypothetical Kuiper belt, the GMC perturbation would not be consistent with the periodicity.