Runaway planetary growth with collision rate in the solar gravitational field

Abstract

The effect of collision rate between planetesimals in the solar gravitational field on runaway planetary growth is intensively examined. First, the characteristics of the collision rate in the solar gravitational field, which were obtained recently by a large number of orbital calculations (S. Ida and K. Nakazawa, 1989, Astron. Astrophys. 224, 303–315) , are investigated through comparison with those in the two-body approximation neglecting the Sun. They are qualitatively explained with the aid of two-body approximation neglecting the sun. They are qualitatively explained with the aid of two-body collision rates in three-dimensional space in a high-velocity region and in two-dimensional space in a low-velocity region; however, there still remains a particular feature which cannot be explained by analogy of the two-body approximation and is closely related to the occurrence of runaway growth. Next, competitive growth of several protoplanets is numerically simulated with a simple model. The results show that the collision rate in the solar gravitational field enhances the possibility of occurrence of runaway growth in a certain low-velocity region (but suppresses it in a very low-velocity region), compared with that in the two-body approximation. However, whether runaway growth occurs or not sensitively depends on the random velocity of planetesimals: its magnitude, the ratio of eccentricity to inclination, mass dependence, and distribution around its mean value, all of which should be also determined including the effect of the solar gravitational field.