Galactic planar tides on the comets of Oort Cloud and analogs in different reference systems. I.

Abstract

A comet cloud analog of Oort Cloud, is probably a common feature around extra solar planetary systems spread out across the Galaxy. Several external perturbations are able to change the comet orbits. The most important of them is the Galactic tide which may re-inject the comets towards the inner part of the planetary system, producing a cometary flux with possible impacts on it. To identi fy the major factors that influence the comet injection process we organi zed the work into three papers. Paper I is devoted only to Galactic tide due to mass contribution of bulge, disk and dark matter halo, for different values of parameters for central star and comets. In the present work only planar tides are preliminarly taken into account in order to focus on this component, usually disregarded, that may become no longer negligible in presence of spiral arms perturbation. To check how much the tidal outputs are system independent, their description has been done in three different reference systems: the Galactic one and two heliocentric systems with and without Hill's approximation developed for an axisymmetric potent ial in 3D-dimensions. The general consistency among the three reference systems is verified and the conditions leading to some releva nt discrepancy are highlighted. The contributions from: bulge, disk and dark matter halo are separately considered and their contri bution to the total Galactic tide is evaluated. In the other t wo of the trilogy we will treat the migration of the Sun and the dynamics of Oort Cloud comets due to the total tide and to spiral arms of the Galaxy. One of the main result reached in this paper is that the Hill's app roximation turns out to be powerful in predicting the relative importance among the Galactic components producing the tidal perturbation on the Oort Cloud and analogs around new extra solar planetary systems. The main relevance is due to the contribution to the central star circular velocity on the disk due to each Galact ic component together with their corresponding velocity logarithmic gr adients. Moreover the final results show a strong dependence of the comet perihelion variation on the combination of Galactic longitude and direction of motion. Comet orbits with the same Galactic longitude, but opposite direction of motion, have opposite signs of mean perihelion variation. This dependence is stronger as the Sun-comet system approaches the Galactic center. The harmonic trend of the mean perihelion distance as function of longitude and directions of motion is qualitatively explained on the strength of a simple application of the Lagrange Planetary Equations.