Distribution of long-period comets: comparison between simulations and observations

Aims. This paper is devoted to a comparison between observations and simulations of the so-called Oort spike formed by the "new" observable long-period comets. Methods. The synthetic distributions of observable comets come from the propagation of a huge sample of objects during the age of the solar system that were initially in a proto-Oort cloud, which was flattened around the ecliptic and had perihelia in the region of Uranus and Neptune. For the known new long-period comets, two samples were used, one that is assumed to be complete, and the comets of the other exclusively come from the Warsaw catalog of comets. The original orbital energy of the comets in this catalog is more reliable. Results. Considering comets with a perihelion distance smaller than 4 AU, for which one of our samples of known comets can be assumed to be complete, the comparison shows small but significant differences in the orbital energy distribution and in the proportion of retrograde comets. When we extend the limiting perihelion distance to 10 AU, the observed samples are obviously strongly incomplete. The synthetic distribution shows that the number of observable comets per year and per perihelion distance unit is proportional to q(1.09) for q < 4 AU and proportional to q(2.13) for 6 < q < 10 AU. The increase for q > 6 AU comes from comets that were already within the Jupiter-Saturn barrier (q < 15 AU) at their previous perihelion passage (which we call creepers and Kaib and Quinn creepers), with original semi-major axes generally smaller than 20 000 AU. Conclusions. To explain the small but significant differences between our synthetic sample and the known comets for a perihelion distance smaller than 4 AU, different hypotheses are proposed: a still erroneous value of the original orbital energy in the observed sample, a higher density of low-mass stars in the actual solar neighborhood, a ninth planet, and obviously the initial population of objects from which the synthetic distributions are derived.