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The three-dimensional structure of the gas flow around a planet is thought toinfluence the accretion of both gas and solid materials. In particular, theoutflow in the mid-plane region may prevent the accretion of the solidmaterials and delay the formation of super-Earths' cores. However, it is notyet understood how the nature of the flow field and outflow speed change as afunction of the planetary mass. In this study, we investigate the dependence ofgas flow around a planet embedded in a protoplanetary disc on the planetarymass. Assuming an isothermal, inviscid gas disc, we perform three-dimensionalhydrodynamical simulations on the spherical polar grid, which has a planetlocated at its centre. We find that gas enters the Bondi or Hill sphere at highlatitudes and exits through the mid-plane region of the disc regardless of theassumed dimensionless planetary mass $m=R_{\rm Bondi}/H$, where $R_{\rm Bondi}$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 theplanetary mass. The outflow speed can be expressed as $|u_{\rmout}|=\sqrt{3/2}mc_{\rm s}$ $(R_{\rm Bondi}\leq R_{\rm Hill})$ or $|u_{\rmout}|=\sqrt{3/2}(m/3)^{1/3} c_{\rm s}$ ($R_{\rm Bondi}\geq R_{\rm Hill}$),where $c_{\rm s}$ is the isothermal sound speed and $R_{\rm Hill}$ is the Hillradius. The outflow around a planet may reduce the accretion of dust andpebbles onto the planet when $m\gtrsim\sqrt{\rm St}$, where St is the Stokesnumber. Our results suggest that the flow around proto-cores of super-Earthsmay delay their growth and, consequently, help them to avoid runaway gasaccretion within the lifetime of the gas disc.

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