Radial Pressure in the Solar Nebula as Affecting the Motions of Planetesimals

Abstract

In the classical rotating Laplacian-type nebula, pressure gradients can develop radially to the protosun because of central radiation, particle ejection, and magnetic-field expansion or because of radial temperature or total gas density gradients. Except for the last two effects, the acting central acceleration for the gas is reduced from the gravitational value; the pressure gradient in the gas caused by temperature or density gradients may either add to or subtract from the gravitational acceleration, depending on the sense of the pressure gradient. Planetesimals in the nebula may thus experience tangential accelerations (+ or —) with respect to the gas because of the differential radial accelerations acting on the particles and the gas. As a consequence, the planetesimals may spiral outward or inward with respect to the protosun. The present paper deals with growing planetesimals and a range of drag laws depending on the Reynolds number and on the ratio of particle size to mean free path.Particles spiral in the direction of positive pressure gradient, thus being concentrated toward toroidal concentrations of gas. The effect increases with decreasing rates of particle growth, i.e., with increasing time scales of planet formation by accretion. In the outer regions, where evidence suggests that comets were formed and Uranus and Neptune were so accumulated, the effect of the pressure gradient is to clear the forming comets from those regions. The large mass of Neptune may have developed because of this effect, perhaps Neptune’s solar distance was reduced from Bode’s “law,” and perhaps no comet belt exists beyond Neptune. In the asteroid belt, on a slow time scale, the effect may have spiraled planetesimals toward Mars and Jupiter, thus contributing to the lack of planet formation in this region.