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 Pi equivalent to eta v(K)/c(s), where eta v(K) 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: Pi = 0.025, 0.05, and 0.1. For each Pi 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 Pi and (2) at fixed Z, strong clumping can occur for smaller particles when Pi is smaller. Therefore, we expect planetesimals to form preferentially in regions of protoplanetary disks with a small radial pressure gradient.