Surface density perturbation of $\Sigma /\overline{\Sigma }$ (left) and log(Σ) (middle), and specific torque density as a function of orbital distance (right) in run-fid for a super-Earth planet of 3 M_⊕ (upper panels, t = 4× 10⁴ P₀), a Saturn-mass planet (middle panels, t=l.4×10⁴ P₀), and a Jupiter-mass planet (lower panels, t = 3.5 × 10⁴ P₀). The location of the planet is marked by a gray circle. The data used to compute the torque density are averaged over 20 snapshots in 1 P₀, the purple crosses in the top and middle rows of panels indicate the wiggle torque positions, and the radial width between the vertical dashed lines is Δr_with = 2 max(r_H, r_hs). For visibility, the x-axes in the right panels use a linear scale up to 12 au and a logarithmic scale beyond that.