The Mass and Size Distribution of Planetesimals Formed by the Streaming Instability. II. The Effect of the Radial Gas Pressure Gradient

The streaming instability concentrates solid particles in protoplanetary disks, leading to gravitational collapse into planetesimals. Despite its key role in producing particle clumping and determining critical length scales in the instability's linear regime, the influence of the disk's radial pressure gradient on planetesimal properties has not been examined in detail. Here, we use streaming instability simulations that include particle self-gravity to study how the planetesimal initial mass function depends on the radial pressure gradient. Fitting our results to a power-law, ${\rm d}N / {\rm d}M_p \propto M_p^{-p}$, we find a single value $p \approx 1.6$ describes simulations in which the pressure gradient varies by $\gtrsim 2$. An exponentially truncated power-law provides a significantly better fit, with a low mass slope of $p^\prime \approx 1.3$ that weakly depends on the pressure gradient. The characteristic truncation mass is found to be $\sim M_G = 4 \pi^5 G^2 \Sigma_p^3 / \Omega^4$. We exclude the cubic dependence of the characteristic mass with pressure gradient suggested by linear considerations, finding instead a linear scaling. These results strengthen the case for a streaming-derived initial mass function that depends at most weakly on the aerodynamic properties of the disk and participating solids. A simulation initialized with zero pressure gradient---which is {\em not} subject to the streaming instability---also yields a top-heavy mass function but with modest evidence for a different shape. We discuss the consistency of the theoretically predicted mass function with observations of Kuiper Belt planetesimals, and describe implications for models of early stage planet formation..