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The pebble accretion model has the potential to explain the formation ofvarious types of planets. A growing planet embedded in a disk inducesthree-dimensional (3D) gas flow, which may influence pebble accretion. In thisstudy, we investigate the influence of the 3D planet-induced gas flow on pebbleaccretion. Assuming a non-isothermal, inviscid gas disk, we perform 3Dhydrodynamical simulations on the spherical polar grid. Then we numericallyintegrate the equation of motion of pebbles in 3D using hydrodynamicalsimulations data. We find that the trajectories of pebbles in theplanet-induced gas flow differ significantly from those in the unperturbedshear flow for a wide range of pebble sizes investigated (${\rmSt}=10^{-3}$--$10^{0}$, where ${\rm St}$ is the Stokes number). The horseshoeflow and outflow of the gas alter the motion of the pebbles, which leads to thereduction of the width of the accretion window, $w_{\rm acc}$, and theaccretion cross section, $A_{\rm acc}$. On the other hand, the changes intrajectories also cause an increase in relative velocity of pebbles to theplanet, which offsets the reduction of $w_{\rm acc}$ and $A_{\rm acc}$. As aconsequence, in the Stokes regime, the accretion probability of pebbles,$P_{\rm acc}$, in the planet-induced gas flow is comparable to that in theunperturbed shear flow except when the Stokes number is small, ${\rmSt}\sim10^{-3}$, in 2D accretion, or when the thermal mass of the planet issmall, $m=0.03$ in 3D accretion. In contrast, in the Epstein regime, $P_{\rmacc}$ in the planet-induced gas flow becomes smaller than that in the shearflow 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 maybe helpful to explain the distribution of exoplanets as well as thearchitecture of the solar system.

Influences of three-dimensional gas flow induced by protoplanets on pebble accretion --$\rm\,I\,$. shear regime