Outflow speed at the midplane as a function of the dimensionless planetary mass and the Mach number of the headwind of the gas. The star symbols were obtained from hydrodynamical simulations, corresponding to the maximum flow speeds in the x-direction toward the outside (red) and inside (black) of the planetary orbit within the limited region, , and . The last condition avoids incorrectly sampling the large υ_x,g within the atmosphere. The solid red and black lines correspond to the analytic formulae for the x-components of the outflow speeds (Eq. (27)). The dashed lines correspond to the analytic formulae for the outflow speed in the x-direction obtained by Ormel (2013, blue; Eq. (38)), Fung et al. (2015, purple; Eq. (41)), and Kuwahara et al. (2019, yellow; Eq. (43)). The gray shading marks the region where the planetary mass exceeds the pebble isolation mass, m_iso (Eq. (12)).