Upper panel: changes in the position of the critical (R_crit; dark gray diamonds), sonic (R_sonίc; light gray squares), and photospheric (R_2/3; colored stars connected by the blue line) radii as a function of different values of the clumping volume filling factor, f_⊙ The bold black symbols indicate the best-fit model. Lower panel: same as the upper panel but showing the sonic and critical points in terms of the Rosseland-mean optical depth, τ. The blue horizontal line indicates the photosphere, where τ = 2/3.