Dynamics of Core Accretion

Abstract

(shortened) We perform 3D hydrodynamic simulations of gas flowing around a planetary core of mass \mplan=10\me embedded in a near Keplerian background flow, using a modified shearing box approximation. We employ a nested grid hydrodynamic code with as many as six nested grids, providing spatial resolution on the finest grid comparable to the present day diameters of Neptune and Uranus. We find that a strongly dynamically active flow develops such that no static envelope can form. The activity is not sensitive to plausible variations in the rotation curve of the underlying disk. It is sensitive to the thermodynamic treatment of the gas, as modeled by prescribed equations of state (either `locally isothermal' or `locally isentropic') and the temperature of the background disk material. The activity is also sensitive to the shape and depth of the core's gravitational potential, through its mass and gravitational softening coefficient. The varying flow pattern gives rise to large, irregular eruptions of matter from the region around the core which return matter to the background flow: mass in the envelope at one time may not be found in the envelope at any later time. The angular momentum of material in the envelope, relative to the core, varies both in magnitude and in sign on time scales of days to months near the core and on time scales a few years at distances comparable to the Hill radius. We show that material entering the dynamically active environment may suffer intense heating and cooling events the durations of which are as short as a few hours to a few days. Peak temperatures in these events range from $T \sim 1000$ K to as high as $T \sim 3-4000$ K, with densities $\rho\sim 10^{-9}-10^{-8}$ g/cm$^3$. These time scales, densities and temperatures span a range consistent with those required for chondrule formation in the nebular shock model.