Two-dimensional distributions of (upper panels) gas and (middle panels) particles in a radius–azimuthal angle plane. Lower panels: azimuthally-averaged radial profiles of gas (solid black lines) and dust (solid gray lines) surface density. The black dashed curves present the initial gas surface density profile, while the black dotted lines present the radial location of the planet. In the isothermal model, the red and blue arrows indicate the location of the shocks due to the primary (red) and secondary (blue) spiral arms. From left to right: (left) isothermal model, (middle) β = 1 model, and (right) β = 100 model. The planet is located at (R, ϕ) = (70 au, 0°). The disk rotation is upward in the upper and middle panels.