X-ray volume filling factor, f_X, as a function of log r∕R_*, for different shock distributions parameterized according to Eqs. (8) and (12) (see legend, and Table 4), and stellar and wind parameters for our ζ Pup-like model (Table 3). The vertical dotted line denotes the region where cooling and wind flow times are equal, t_c = t_f. Due to the large mass-loss rate, the ratio l_s∕r_s remains smaller than unity throughout the wind.