TY - JOUR

T1 - Two evolutionary paths of an axisymmetric gravitational instability in the dust layer of a protoplanetary disk

AU - Yamoto, Fumiharu

AU - Sekiya, Minoru

N1 - Funding Information:
We wish to thank Andrew Youdin for valuable comments. Numerical simulations were performed on VPP5000 at the Astronomical Data Center of the National Astronomical Observatory of Japan, and on an IBM eServer p5 595 at the Computing and Communications Center of Kyushu University. F. Y. is supported by the Research Fellowship of Japan Society for the Promotion of Science (JSPS) for Young Scientists. M. S. is supported by Grants-in-Aid from the Japanese Ministry of Education, Culture, Sports, Science, and Technology, and from JSPS (17039010 and 16340174).

PY - 2006/8/1

Y1 - 2006/8/1

N2 - We perform nonlinear numerical simulations to investigate the density evolution in the dust layer of a protoplanetary disk due to gravitational instability and dust settling toward the midplane. We restrict our study to the region where the radial pressure equilibrium is negligible so that the shear-induced instability is avoided, and we also restrict our model to an axisymmetric perturbation as a first step of nonlinear numerical simulations of the gravitational instability. We find that there are two different evolutionary paths of the gravitational instability, depending on the nondimensional gas friction time, which is defined as the product of the gas friction time and the Keplerian angular velocity. If the nondimensional gas friction time is equal to 0.01, the gravitational instability grows faster than dust settling. On the other hand, if the nondimensional gas friction time is equal to 0.1, dust aggregates settle sufficiently before the gravitational instability grows. In the latter case, an approximate analytical calculation reveals that dust settling is faster than the growth of the gravitational instability, regardless of the dust density at the midplane. Thus, the dust layer becomes extremely thin and may reach a few tenths of the material density of the dust before the gravitational instability grows, as long as there is no turbulence.

AB - We perform nonlinear numerical simulations to investigate the density evolution in the dust layer of a protoplanetary disk due to gravitational instability and dust settling toward the midplane. We restrict our study to the region where the radial pressure equilibrium is negligible so that the shear-induced instability is avoided, and we also restrict our model to an axisymmetric perturbation as a first step of nonlinear numerical simulations of the gravitational instability. We find that there are two different evolutionary paths of the gravitational instability, depending on the nondimensional gas friction time, which is defined as the product of the gas friction time and the Keplerian angular velocity. If the nondimensional gas friction time is equal to 0.01, the gravitational instability grows faster than dust settling. On the other hand, if the nondimensional gas friction time is equal to 0.1, dust aggregates settle sufficiently before the gravitational instability grows. In the latter case, an approximate analytical calculation reveals that dust settling is faster than the growth of the gravitational instability, regardless of the dust density at the midplane. Thus, the dust layer becomes extremely thin and may reach a few tenths of the material density of the dust before the gravitational instability grows, as long as there is no turbulence.

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U2 - 10.1086/507098

DO - 10.1086/507098

M3 - Article

AN - SCOPUS:33748072765

VL - 646

SP - L155-L158

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2 II

ER -