The effect of the solar motion on the flux of long-period comets

ABSTRACT The long-term dynamics of Oort cloud comets are studied under the influence of boththe radial and the vertical components of the Galactic tidal field. Sporadic dynamicalperturbation processes are ignored, such as passing stars, since we aim to study theinfluence of just the axisymmetric Galactic tidal field on the cometary motion andhow it changes in time. We use a model of the Galaxy with a disc, bulge and darkhalo, and a local disc density, and disc scale length constrained to fit the best availableobservational constraints. By integrating a few million of cometary orbits over 1 Gyr,we calculate the time variable flux of Oort cloud comets that enter the inner SolarSystem, for the cases of a constant Galactic tidal field, and a realistically varyingtidal field which is a function of the Sun’s orbit. The applied method calculates theevolution of the comets by using first-order averaged mean elements. We find that theperiodicity in the cometary flux is complicated and quasi-periodic. The amplitude ofthe variations in the flux are of order 30 %. The radial motion of the Sun is the chiefcause of this behaviour, and should be taken into account when the Galactic influenceon the Oort cloud comets is studied.Key words: methods: numerical – celestial mechanics – comets: general – Solarsystem : general – stars: kinematics and dynamics.