The effect of the radial pressure gradient in protoplanetary disks on planetesimal formation

The streaming instability provides a promising mechanism for planetesimal formation because of its ability to concentrate solids into dense clumps. The degree of clumping strongly depends on the height-integrated solid to gas mass ratio Z in protoplanetary disks. In this Letter, we show that the magnitude of the radial pressure gradient that drives the streaming instability (characterized by Π = ηνK/c_s, where ηvK is the reduction of Keplerian velocity due to the radial pressure gradient and c _s is the sound speed) also strongly affects clumping. We present local two-dimensional hybrid numerical simulations of aerodynamically coupled particles and gas in the midplane of protoplanetary disks. Magnetic fields and particle self-gravity are ignored. We explore three different radial pressure gradient values appropriate for typical protoplanetary disks: Π = 0.025, 0.05, and 0.1. For each Π value, we consider four different particle size distributions ranging from submillimeter to meter sizes and run simulations with solid abundance from Z = 0.01 up to Z = 0.07. We find that a small radial pressure gradient strongly promotes particle clumping in that: (1) at fixed particle size distribution, the critical solid abundance Z_crit above which particle clumping occurs monotonically increases with Π and (2) at fixed Z, strong clumping can occur for smaller particles when Π is smaller. Therefore, we expect planetesimals to form preferentially in regions of protoplanetary disks with a small radial pressure gradient.