FORMING PLANETESIMALS BY GRAVITATIONAL INSTABILITY. II. HOW DUST SETTLES TO ITS MARGINALLY STABLE STATE

Journal Article · Mon Dec 20 00:00:00 EST 2010 · Astrophysical Journal

DOI:https://doi.org/10.1088/0004-637X/725/2/1938· OSTI ID:21476653

Lee, Aaron T; Chiang, Eugene ^[1]; Asay-Davis, Xylar ^[2]; Barranco, Joseph ^[3]

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1. Department of Astronomy, University of California Berkeley, Berkeley, CA 94720 (United States)
2. Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)
3. Department of Physics and Astronomy, San Francisco State University, San Francisco, CA 94132 (United States)

Dust at the midplane of a circumstellar disk can become gravitationally unstable and fragment into planetesimals if the local dust-to-gas ratio {mu}{sub 0} {identical_to} {rho}{sub d}/{rho}{sub g} is sufficiently high. We simulate how dust settles in passive disks and ask how high {mu}{sub 0} 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{sub stop}<< 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, {mu}{sub 0} = 2.9 for a disk whose bulk (height-integrated) metallicity {Sigma}{sub d}/{Sigma}{sub g} is solar-thus {mu}{sub 0} increases by more than two orders of magnitude from its well-mixed initial value of {mu}{sub 0,init} = {Sigma}{sub d}/{Sigma}{sub g} = 0.015. For a disk whose bulk metallicity is 4x solar ({mu}{sub 0,init} = {Sigma}{sub d}/{Sigma}{sub g} = 0.06), the marginally stable state has {mu}{sub 0} = 26.4. These maximum values of {mu}{sub 0}, 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 ({approx}<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 {Sigma}{sub d}/{Sigma}{sub 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 {mu}{sub 0} increases with {Sigma}{sub d}/{Sigma}{sub g} in a faster than linear way, so fast that modest enhancements in {Sigma}{sub d}/{Sigma}{sub g} can spawn planetesimals directly from small particles.

• OSTI ID: 21476653
• Journal Information: Astrophysical Journal, Vol. 725, Issue 2; Other Information: DOI: 10.1088/0004-637X/725/2/1938; ISSN 0004-637X
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
DUSTS
GRAVITATIONAL INSTABILITY
HYDRODYNAMICS
ONE-DIMENSIONAL CALCULATIONS
PLANETS
PRESSURE GRADIENTS
PROTOPLANETS
RICHARDSON NUMBER
STAR EVOLUTION
THREE-DIMENSIONAL CALCULATIONS
DIMENSIONLESS NUMBERS
EVOLUTION
FLUID MECHANICS
INSTABILITY
MECHANICS
PLASMA INSTABILITY