  The pebble accretion model has the potential to explain the formation of
various types of planets. A growing planet embedded in a disk induces
three-dimensional (3D) gas flow, which may influence pebble accretion. In this
study, we investigate the influence of the 3D planet-induced gas flow on pebble
accretion. Assuming a non-isothermal, inviscid gas disk, we perform 3D
hydrodynamical simulations on the spherical polar grid. Then we numerically
integrate the equation of motion of pebbles in 3D using hydrodynamical
simulations data. We find that the trajectories of pebbles in the
planet-induced gas flow differ significantly from those in the unperturbed
shear flow for a wide range of pebble sizes investigated (${\rm
St}=10^{-3}$--$10^{0}$, where ${\rm St}$ is the Stokes number). The horseshoe
flow and outflow of the gas alter the motion of the pebbles, which leads to the
reduction of the width of the accretion window, $w_{\rm acc}$, and the
accretion cross section, $A_{\rm acc}$. On the other hand, the changes in
trajectories also cause an increase in relative velocity of pebbles to the
planet, which offsets the reduction of $w_{\rm acc}$ and $A_{\rm acc}$. As a
consequence, in the Stokes regime, the accretion probability of pebbles,
$P_{\rm acc}$, in the planet-induced gas flow is comparable to that in the
unperturbed shear flow except when the Stokes number is small, ${\rm
St}\sim10^{-3}$, in 2D accretion, or when the thermal mass of the planet is
small, $m=0.03$ in 3D accretion. In contrast, in the Epstein regime, $P_{\rm
acc}$ in the planet-induced gas flow becomes smaller than that in the shear
flow in the Stokes regime in both 2D and 3D accretion, regardless of assumed
${\rm St}$ and $m$. Our results suggest that the 3D planet-induced gas flow may
be helpful to explain the distribution of exoplanets as well as the
architecture of the solar system.
