  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 $m=R_{\rm Bondi}/H$, 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 the
planetary mass. The outflow speed can be expressed as $|u_{\rm
out}|=\sqrt{3/2}mc_{\rm s}$ $(R_{\rm Bondi}\leq R_{\rm Hill})$ or $|u_{\rm
out}|=\sqrt{3/2}(m/3)^{1/3} c_{\rm s}$ ($R_{\rm Bondi}\geq R_{\rm Hill}$),
where $c_{\rm s}$ is the isothermal sound speed and $R_{\rm Hill}$ is the Hill
radius. The outflow around a planet may reduce the accretion of dust and
pebbles onto the planet when $m\gtrsim\sqrt{\rm St}$, 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.
