Astronomy and Astrophysics – Astronomy
Scientific paper
May 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008dda....39.1510t&link_type=abstract
American Astronomical Society, DDA meeting #39, #15.10
Astronomy and Astrophysics
Astronomy
Scientific paper
When the mass of a protoplanet growing in the nebular gas is large enough and it has an atmosphere around it, the gas drag by the atmosphere is expected to enhance the accretion rate of planetesimals by the protoplanet and can reduce its growth timescale. We study the effect of gas drag on the accretion rate of planetesimals by a protoplanet that has a spherical symmetric atmosphere, by analytic calculation and three-body orbital integration.
In the orbital integration, the motion of planetesimals motion is solved on Hill's coordinate using 8th-order Runge-Kutta method. We numerically integrated the motion of planetesimals with a wide range of initial random velocities.
Planetesimals experience strong gas drag when they pass close to the planet, where the gas density in higher. For an assumed spherical gas density distribution, we obtain an analytic expression for a planetesimal's energy dissipation in a single passage through the atmosphere, and confirmed agreement with orbital integration. Using results of numerical integration of a large number of orbits, where the Rayleigh distribution of planetesimals' orbital eccentricities and inclinations are taken into account, we obtain capture rates of planetesimals for various values of the strength of gas drag.
We also obtained an analytical formula to describe the capture rates for the high random velocity regime, which agree well with the results obtained by our numerical integration. We derived an empirical formula for the capture rate which can describe the dependence of the accretion rate on random velocity, which was not considered by previous studies.
This work was supported by NASA's Origins of Solar Systems Program (NNG05GH87G) and Outer Planets Research Program (NNG05GH42G).
Ohtsuki Keiji
Tanigawa Takayuki
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