SIMBAD references

Dust at the midplane of a circumstellar disk can become gravitationally unstable and fragment into planetesimals if the local dust-to-gas ratio µ₀ ≡ ρ_d/ρ_g is sufficiently high. We simulate how dust settles in passive disks and ask how high µ₀ can become. We implement a hybrid scheme that alternates between a one-dimensional code to settle dust and a three-dimensional shearing box code to test for dynamical stability. This scheme allows us to explore the behavior of small particles having short but non-zero stopping times in gas: 0 < t_stop{Lt} the orbital period. The streaming instability is thereby filtered out. Dust settles until Kelvin-Helmholtz-type instabilities at the top and bottom faces of the dust layer threaten to overturn the entire layer. In this state of marginal stability, µ₀= 2.9 for a disk whose bulk (height-integrated) metallicity Σ_d/Σ_gis solar–thus µ₀ increases by more than two orders of magnitude from its well-mixed initial value of µ_0,init= Σ_d/Σ_g= 0.015. For a disk whose bulk metallicity is 4x solar (µ_0,init= Σ_d/Σ_g = 0.06), the marginally stable state has µ₀= 26.4. These maximum values of µ₀, which depend on the background radial pressure gradient, are so large that gravitational instability of small particles is viable in disks whose bulk metallicities are just a few ( ≲ 4) times solar. Our result supports earlier studies that assumed that dust settles until the Richardson number Ri is spatially constant. Our simulations are free of this assumption but provide evidence for it within the boundaries of the dust layer, with the proviso that Ri increases with Σ_d/Σ_g in the same way that we found in Paper I. Because increasing the dust content decreases the vertical shear and increases stability, the midplane µ₀ increases with Σ_d/Σ_g in a faster than linear way, so fast that modest enhancements in Σ_d/Σ_g can spawn planetesimals directly from small particles.