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Pebble accretion is one of the major theories in planet formation.Aerodynamically small particles, called pebbles, are highly affected by the gasflow. A growing planet embedded in a protoplanetary disk inducesthree-dimensional (3D) gas flow. In our previous study, Paper I, we focused onthe shear regime of pebble accretion, and investigated the influence ofplanet-induced gas flow on pebble accretion. In Paper I, we found that pebbleaccretion is inefficient in the planet-induced gas flow compared to that in theunperturbed flow, in particular when ${\rm St}\lesssim10^{-3}$, where St is theStokes number. Following Paper I, we investigate the influence ofplanet-induced gas flow on pebble accretion. We consider the headwind of thegas, which is not included in Paper I. We extend our study to the headwindregime of pebble accretion in this study. Assuming a nonisothermal, inviscidsub-Keplerian gas disk, we perform 3D hydrodynamical simulations on thespherical polar grid which has a planet with the dimensionless mass, $m=R_{\rmBondi}/H$, located at its center, where $R_{\rm Bondi}$ and $H$ are the Bondiradius and the disk scale height. We then numerically integrate the equation ofmotion of pebbles in 3D using hydrodynamical simulation data. Combining ourresults with the spacial variety of turbulence strength and pebble size in adisk, we conclude that the planet-induced gas flow still allows for pebbleaccretion in the early stage of planet formation. Suppression of pebbleaccretion due to the planet-induced gas flow occurs only in the late stage ofplanet formation, in particular in the inner region of the disk. This may behelpful to explain the distribution of exoplanets and the architecture of theSolar System, both of which have small inner and large outer planets.

Influences of protoplanet-induced three-dimensional gas flow on pebble accretion $\rm\,I\hspace{-.1em}I\,$. Headwind regime