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 identify the major factors that influence the comet injection process we organized 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 potential in 3D-dimensions. The general consistency among the three reference systems is verified and the conditions leading to some relevant discrepancy are highlighted. The contributions from: bulge, disk and dark matter halo are separately considered and their contribution to the total Galactic tide is evaluated. In the other two 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 approximation 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 Galactic component together with their corresponding velocity logarithmic gradients. 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.

Habitability on local, Galactic and cosmological scales

“…24 Distribution of comet orbits in an inertial frame on the Galactic plane with the same perihelion and increasing aphelions at different Galactic longitudes (see text) before switching on the Galactic tides (Masi et al, 2003;Masi et al, 2009). The initial not perturbed orbits here considered are similar to those taken into account by De Biasi et al (2015).…”

“…Moreover they will certainly be non negligible in presence of spiral arm perturbations, as also Kaib et al (2011) have already pointed out and it has been confirmed in the preliminary results of De Biasi ( 2014). An interesting contribution to this problem comes out by the work of De Biasi et al (2015). They consider only the effects of Galactic planar tides but at two different distances from the Galactic center: 4 kpc and 8 kpc, assuming the last one as the current solar position.…”

“…The main contributions to Galactic tide have their origin from the gravitational potential of the bulge Φ BG (r), of the disk Φ D (R, z) and of the dark matter halo Φ DH (r) respectively given by (De Biasi et al, 2015):…”

“…with ρ 0 the central dark halo density. The values of the constants a n , b, M n , according with Flynn et al(1996), and the parameter values for each Galactic components are listed in Tab.1 of De Biasi et al (2015).…”

“…Because these contributions vary with the location of the Sun Fig. 26 The different contributions to the circular velocity vs the distance from the center are here plotted for Galaxy assuming a MPI density profile for DM halo (Spano et al, 2008) (De Biasi et al, 2015.…”