Gas flow around a planet embedded in a protoplanetary disc: the dependence on the planetary mass

Abstract

The three-dimensional structure of the gas flow around a planet is thought to influence the accretion of both gas and solid materials. In particular, the outflow in the mid-plane region may prevent the accretion of the solid materials and delay the formation of super-Earths' cores. However, it is not yet understood how the nature of the flow field and outflow speed change as a function of the planetary mass. In this study, we investigate the dependence of gas flow around a planet embedded in a protoplanetary disc on the planetary mass. Assuming an isothermal, inviscid gas disc, we perform three-dimensional hydrodynamical simulations on the spherical polar grid, which has a planet located at its centre. We find that gas enters the Bondi or Hill sphere at high latitudes and exits through the mid-plane region of the disc regardless of the assumed dimensionless planetary mass $m=R_{\mathrm{Bondi}}/H$, where $R_{\mathrm{Bondi}}$ and $H$ are the Bondi radius of the planet and disc scale height, respectively. The altitude from where gas predominantly enters the envelope varies with the planetary mass. The outflow speed can be expressed as $|u_{\mathrm{out}}|=\sqrt{3/2}m{c}_{\mathrm{s}}$ $(R_{\mathrm{Bondi}}\le R_{\mathrm{Hill}})$ or $|u_{\mathrm{out}}|=\sqrt{3/2}(m/3{)}^{1/3}{c}_{\mathrm{s}}$ ($R_{\mathrm{Bondi}}\ge R_{\mathrm{Hill}}$), where $c_{\mathrm{s}}$ is the isothermal sound speed and $R_{\mathrm{Hill}}$ is the Hill radius. The outflow around a planet may reduce the accretion of dust and pebbles onto the planet when $m\gtrsim \sqrt{\mathrm{St}}$, where St is the Stokes number. Our results suggest that the flow around proto-cores of super-Earths may delay their growth and, consequently, help them to avoid runaway gas accretion within the lifetime of the gas disc.

16 pages, 14 figures, Accepted for publication in Astronomy and Astrophysics (A&A)

References in corpus (9)

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• Unified simulations of planetary formation and atmospheric evolution II: Rapid disk clearing by photoevaporation yields low-mass super-Earth atmospheres
• The Growth of Protoplanets via the Accretion of Small Bodies in Disks Perturbed by the Planetary Gravity
• Three-Dimensional Dust Stirring by a Giant Planet Embedded in a Protoplanetary Disk
• Mars' atmospheric neon suggests volatile-rich primitive mantle
• The Dynamic Proto-atmospheres around Low-Mass Planets with Eccentric Orbits
• Delivery of gas onto the circumplanetary disk of giant planets: Planetary-mass dependence of the source region of accreting gas and mass accretion rate
• Dust ring and gap formation by gas flow induced by low-mass planets embedded in protoplanetary disks $\mathrm{I}$. Steady-state model