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.

arXiv comment16 pages, 14 figures, Accepted for publication in Astronomy and Astrophysics (A&A)

References in corpus (32)

• The false positive rate of Kepler and the occurrence of planets
• Clouds in the atmosphere of the super-Earth exoplanet GJ 1214b
• Rapid growth of gas-giant cores by pebble accretion
• Particle Stirring in Turbulent Gas Disks: Including Orbital Oscillations
• The effect of gas drag on the growth of protoplanets -- Analytical expressions for the accretion of small bodies in laminar disks
• The Mass-Radius Relation for 65 Exoplanets Smaller than 4 Earth Radii
• The Role of Core Mass in Controlling Evaporation: the Kepler Radius Distribution and the Kepler-36 Density Dichotomy
• Separating gas-giant and ice-giant planets by halting pebble accretion
• A New Family of Planets ? "Ocean Planets"
• A Framework for Quantifying the Degeneracies of Exoplanet Interior Compositions
• Super-Earth Atmospheres: Self-Consistent Gas Accretion and Retention
• Make Super-Earths, Not Jupiters: Accreting Nebular Gas onto Solid Cores at 0.1 AU and Beyond
• Composition and fate of short-period super-Earths: The case of CoRoT-7b
• Toward a Deterministic Model of Planetary Formation VI: Dynamical Interaction and Coagulation of Multiple Rocky Embryos and Super-Earth Systems around Solar Type Stars
• Atmospheres of low-mass planets: the "boil-off"
• In-situ Accretion of Hydrogen-Rich Atmospheres on Short-Period Super-Earths: Implications for the Kepler-11 Planets
• An Extension of the Athena++ Code Framework for GRMHD Based on Advanced Riemann Solvers and Staggered-Mesh Constrained Transport
• Hydrodynamics of Embedded Planets' First Atmospheres. II. A Rapid Recycling of Atmospheric Gas
• N-body simulations of planetary accretion around M dwarf stars
• The Formation of Super-Earths and Mini-Neptunes with Giant Impacts
• Reduced gas accretion on super-Earths and ice giants
• Hydrodynamics of embedded planets' first atmospheres - III. The role of radiation transport for super-Earth planets
• The 3D Flow Field Around an Embedded Planet
• Could we identify hot Ocean-Planets with CoRoT, Kepler and Doppler velocimetry?
• Three-Dimensional Radiation-Hydrodynamics Calculations of the Envelopes of Young Planets Embedded in Protoplanetary Disks
• Hydrodynamics of Embedded Planets' First Atmospheres. I. A Centrifugal Growth Barrier for 2D Flows
• Suppression of atmospheric recycling of planets embedded in a protoplanetary disc by buoyancy barrier
• IRSF SIRIUS JHKs Simultaneous Transit Photometry of GJ1214b
• Pebble dynamics and accretion onto rocky planets. I. Adiabatic and convective models
• The maximum mass of planetary embryos formed in core-accretion models
• The steady-state flow pattern past gravitating bodies
• A limit on gas accretion onto close-in super-Earth cores from disk accretion

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