Frequency of Weak Stellar Showers of Oort Cloud Comets

Mathematics – Probability

Scientific paper

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Scientific paper

We have developed a semi-analytic model of the combined effects of tidal perturbations of the galactic force and a stellar impulse acting on the Sun and the outer Oort cloud of comets. The six dimensional phase space of near-parabolic comet orbital elements has been subdivided into cells. A mapping of the evolution of these elements from beyond the loss cylinder boundary into the inner planetary region over the course of a single orbit is possible. The time dependence of the comet flux interior to 5 AU is then obtained for a period of 5 Myr subsequent to the impulse. The peak flux and the time integrated net shower flux are obtained over a wide range of stellar impact parameters bsolar > 30 000 AU and stellar mass to relative velocity ratios, M*/Vrel, such that the peak flux enhancement is <1.5 times the background flux due to the galactic tide alone. Loci of the results for the peak flux enhancement and the time integrated net shower flux versus bsolar and M*}/V{rel are given. Using the number densities and dispersion velocities of stellar populations we also obtain the time dependent probability of a stellar impulse versus bsolar and M*}/V{rel. Finally, we employ Monte Carlo sampling to estimate the frequency of stellar encounters as functions of the peak flux enhancement and also of the time integrated net shower flux. A graph of the cumulative number of stellar impulses expected over 4 Gyr as a function of the shower strength will also be given. \em{JJM acknowledges the support of a NASA-AAS Small Research Grant and a NASA-ASEE Summer Faculty Fellowship at Ames Research Center. JJL received support from Planetary Geology and geophysics grant 334-30-50-01}

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