Time-dependent injection of Oort cloud comets into Earth-crossing orbits

The effect of close stellar encounters in modulating the influx rate of Oort cloud comets is investigated. In particular, it is shown that comet showers intense enough to be reflected in crater statistics can be produced at intervals of 80 million years or so, provided we are dealing with an Oort cloud consisting of a heavy core of comets. In this case, there is found a strong predominance of incoming comets from the sky zone where the perturbing star makes its closest approach. We have also performed numerical simulations of the time evolution of comet showers or bursts. From this numerical study, a long tail of residual shower comets is found to follow the major event with an intensity (as compared with the intensity of the shower as its peak) of ∼10^-2 after 20-30 million years. Our results thus suggest that residual shower comets may be clustered mainly on certain sky areas and observable at practically any time given the lasting effects of a shower. This might explain some of the observed clustering of aphelion points of long-period comets.