Anisotropy of Long-period Comets Explained by Their Formation Process

Long-period comets coming from the Oort cloud are thought to be planetesimals formed in the planetary region on the ecliptic plane. We have investigated the orbital evolution of these bodies due to the Galactic tide. We extended Higuchi et al. (2007) and derived the analytical solutions to the Galactic longitude and latitude of the direction of aphelion, $L$ and $B$. Using the analytical solutions, we show that the ratio of the periods of the evolution of $L$ and $B$ is very close to either 2 or $\infty$ for initial eccentricities $e_i\simeq 1$, as is true for the Oort cloud comets. From the relation between $L$ and $B$, we predict that Oort cloud comets returning to the planetary region are concentrated on the ecliptic plane and a second plane, which we call the "empty ecliptic." This consists in a rotation of the ecliptic around the Galactic pole by 180$^\circ$. Our numerical integrations confirm that the radial component of the Galactic tide, which is neglected in the derivation of the analytical solutions, is not strong enough to break the relation between $L$ and $B$ derived analytically. Brief examination of observational data shows that there are concentrations near both the ecliptic and the empty ecliptic. We also show that the anomalies of the distribution of $B$ of long-period comets mentioned by several authors are explained by the concentrations on the two planes more consistently than by previous explanations.