How Efficient Is the Streaming Instability in Viscous Protoplanetary Disks?

Abstract

Abstract The streaming instability is a popular candidate for planetesimal formation by concentrating dust particles to trigger gravitational collapse. However, its robustness against the physical conditions expected in protoplanetary disks is unclear. In particular, particle stirring by turbulence may impede the instability. To quantify this effect, we develop the linear theory of the streaming instability with external turbulence modeled by gas viscosity and particle diffusion. We find the streaming instability is sensitive to turbulence, with growth rates becoming negligible for alpha viscosity parameters , where is the particle Stokes number. We explore the effect of nonlinear drag laws, which may be applicable to porous dust particles, and find growth rates are modestly reduced. We also find that gas compressibility increases growth rates by reducing the effect of diffusion. We then apply the linear theory to global models of viscous protoplanetary disks. For minimum-mass solar nebula disk models, we find the streaming instability only grows within disk lifetimes beyond tens of astronomical units, even for centimeter-sized particles and weak turbulence ( ). Our results suggest it is rather difficult to trigger the streaming instability in nonlaminar protoplanetary disks, especially for small particles.