Radial entropy profiles for a halo of 10¹⁵ M_⊙ at z = 0. The black filled line shows the profile in the case of single shock at the virial radius. The blue filled line shows a profile modified with a sigmoid of the from reported in Eq. (22) and parameters shown in the figure. The vertical dotted and dashed lines mark the position of R₅₀₀ and R₂₀₀ respectively. The slope of the profiles can be gauged by comparison with the power laws plotted as dashed lines.