On Secular Gravitational Instability in Vertically Stratified Disks

Abstract

Secular gravitational instability (GI) is one promising mechanism for explaining planetesimal formation. Previous studies of secular GI utilized a razor-thin disk model and derived the growth condition in terms of vertically integrated physical values such as dust-to-gas surface density ratio. However, in weakly turbulent disks where secular GI can operate, a dust disk can be orders of magnitude thinner than a gas disk, and analyses treating the vertical structures are necessary to clarify the interplay of the midplane dust motion and the upper gas motion. In this work, we perform vertically global linear analyses of secular GI with a vertical domain size of a few gas scale heights. We find that dust grains accumulate radially around the midplane while gas circulates over the whole vertical region. We obtain well-converged growth rates when the outer gas boundary is above two gas scale heights. The growth rates are underestimated if we assume the upper gas to be steady and regard it just as the source of external pressure to the dusty lower layer. Therefore, treating the upper gas motion is important even when the dust disk is much thinner than the gas disk. Conducting a parameter survey, we represent the growth condition in terms of the Toomre Q value for dust and dust-to-gas surface density ratio. The critical dust disk mass for secular GI is ∼10 ^−4 M _* for a dust-to-gas surface density ratio of 0.01, a Stokes number of 0.1, and a radial dust diffusivity of 10 ^−4 c _s H , where c _s is the gas sound speed, and H is the gas scale height.

Keywords

• Protoplanetary disks
• Hydrodynamics
• Astrophysical fluid dynamics