Azimuthally averaged radial profiles of various hydrodynamic stability criteria in the vicinity of the planet. From top to bottom, we show the Rayleigh criterion (the left-hand side of Eq. (30)), Solberg-Høiland criterion (the left-hand side of Eq. (31)), and the generalized potential vorticity (Eq. (34)). The simulation with gap irradiation (solid black curve) and the reference non-radiative simulation (dotted blue curve) are compared. The grey rectangle shows the extent of the Hill sphere. The inflection point of the black curve at about r ≃ 1.17 r_p in the bottom panel suggests that the disk is Rossby-unstable.