http://arxiv.org/abs/1801.07707
We present nested-grid, high-resolution hydrodynamic simulations of gas and particle dynamics in the vicinity of Mars- to Earth-mass planetary embryos. The simulations extend from the surface of the planetary embryo to a few vertical disk scale heights, with a vertical dynamic range of $L_z/\Delta z$ of $\sim! 1.4\times 10^5$. Our results confirm that “pebble”-sized particles can be easily accreted, with accretion rates continuing to increase to meter size for our nominal 10\% MMSN surface density model. The gas mass flux in and out through the Hill sphere is consistent with the Hill rate, $\Sigma\Omega R_{\rm H}^2$. While smaller size particles mainly follow the gas flow out again, a net accretion rate of $\approx 7 \ 10^{-5}$ M$_{\oplus}$ yr$^{-1}$ is reached for 0.3 — 1 cm particles, with still a significant fraction leaving the Hill sphere again. Effectively all pebble-sized particles that cross the Bondi sphere are accreted. The resolution of these simulations is sufficient to resolve accretion-driven convection. Convection driven by a nominal accretion of $10^{-6}$ \ME yr$^{-1}$ does not significantly alter the pebble accretion rate. We find that, because of cancellation effects, accretion rates of pebble sized particles are nearly independent of disk surface density. Because of this we can estimate accurate growth times for specified particle sizes. For particles of size 0.3 — 1 cm, the growth time would be about 0.4 million years for a 1 earth mass planet at 1 AU, with about 1.2 million years for an 0.1 earth mass planet at 1.5 AU.
A. Popovas, %7B. Nordlund, J. Ramsey, et. al.
Wed, 24 Jan 18
30/73
Comments: 20 pages, 23 figures; submitted to MNRAS. Comments welcome