Forming Planetesimals by Gravitational Instability: I. The Role of the Richardson Number in Triggering the Kelvin-Helmholtz Instability

摘要

Gravitational instability (GI) of a dust-rich layer at the midplane of agaseous circumstellar disk is one proposed mechanism to form planetesimals, thebuilding blocks of rocky planets and gas giant cores. Self-gravity competesagainst the Kelvin-Helmholtz instability (KHI): gradients in dust content drivea vertical shear which risks overturning the dusty subdisk and forestalling GI.To understand the conditions under which the disk can resist the KHI, weperform 3D simulations of stratified subdisks in the limit that dust particlesare small and aerodynamically well coupled to gas. This limit screens out thestreaming instability and isolates the KHI. Each subdisk is assumed to have avertical density profile given by a spatially constant Richardson number Ri. Wevary Ri and the midplane dust-to-gas ratio mu and find that the criticalRichardson number dividing KH-unstable from KH-stable flows is not unique;rather Ri_crit grows nearly linearly with mu for mu=0.3-10. Only for disks ofbulk solar metallicity is Ri_crit ~ 0.2, close to the classical value. Ourresults suggest that a dusty sublayer can gravitationally fragment andpresumably spawn planetesimals if embedded within a solar metallicity gas disk~4x more massive than the minimum-mass solar nebula; or a minimum-mass diskhaving ~3x solar metallicity; or some intermediate combination of these twopossibilities. Gravitational instability seems possible without resorting tothe streaming instability or to turbulent concentration of particles.