The connection between comet p/machholz and the quadrantid meteor stream

Abstract

The parent comet of the Quadrantid meteors was not observed until, perhaps, quite recently. Comet P/Machholz (1986 VIII) currently has orbital elements that differ drastically from those of the meteor stream, but its secular perturbations involve large-scale oscillations in inclination and perihelion distance similar to those earlier found for the Quadrantids. Whether there may have been an epoch in the past, when the Quadrantids were shed by comet P/Machholz depends upon whether or not there has been enough time since that epoch for differential Jovian perturbations to cause the 180° discrepancy in nodal longitudes presently observed. We have investigated the variation of the period of q-i oscillation between different meteor particles in relation to the hypothesis that the shedding of meteors occurred nearly 4000 yr ago, when comet P/Machholz last had a very small perihelion distance. We show that this hypothesis is viable in view of the ejection velocities typically expected and the resulting spread in the period of q-i oscillations. The most promising range of semimajor axes is just inside the 2/1 resonance, and detailed study reveals many cases of chaotic behaviour due to close encounters with Jupiter. The dynamics of the Quadrantid stream thus appears even more complex than earlier studies have indicated.