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The Effect of the Radial Pressure Gradient in Protoplanetary Disks on Planetesimal Formation

The streaming instability (SI) 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 (PPDs). In this letter, we show that the magnitude of the radial pressure gradient (RPG) which drives the SI (characterized by $q\equivηv_K/c_s$, where $ηv_K$ is the reduction of Keplerian velocity due to the RPG 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 PPDs. Magnetic fields and particle self-gravity are ignored. We explore three different RPG values appropriate for typical PPDs: $q=0.025, 0.05$ and 0.1. For each $q$ value, we consider four different particle size distributions ranging from sub millimeter to meter sizes and run simulations with solid abundance from Z=0.01 up to Z=0.07. We find that a small RPG strongly promotes particle clumping in that: 1) At fixed particle size distribution, the critical solid abundance $Z_{\rm crit}$ above which particle clumping occurs monotonically increases with $q$; 2) At fixed Z, strong clumping can occur for smaller particles when $q$ is smaller. Therefore, we expect planetesimals to form preferentially in regions of PPDs with a small RPG.