Deviations in ρ, T, and p_gas for F (blue), G (black), K (green), and M-star (red) cases. The vertical axis gives the geometric deviations as a percentage relative to the hydrodynamic case. The horizontal axis is the number of pressure scale heights log₁₀(p_gas/p_gas(τ=1)), calculated for the HD cases, below the surface (dotted vertical black line). The shaded regions correspond to 1-σ standard error , N is the number of snapshots) of the mean solid curve.