Distance, R_{H II}, to the radial molecular cloud filament within which the gas is ionised in dependence of the number of ionising photons, γ_ion, whereby one O5V star emits γ_ion = 10^49.49 ionising photons s⁻¹ according to Sternberg et al. (2003). Bottom panel: histograms show the range of values obtained for the random sampling case (10 000 realisations), and the thick vertical lines refer to the optimal sampling cases which have no Poisson spread. The ionising flux from all stars in a co-eval population is summed to obtain γ_ion. The maximum value of the histogram is proportional to the mass of the population. The colour code is the same as in Table 1. Thin gray vertical lines are presented for better orientation in the figure. Top panel: dotted lines are R_S, which are the initial radii of the UCHII regions (Eq. (1)) for different values of the density of the cloud, n_H, assuming no change in density within the UCHII region compared to the surrounding molecular cloud. The solid lines are expanded HII regions (Eq. (2)) for the same set of n_H values as for the dotted lines. The dashed lines indicate R_HII assuming the density of the ionised gas is zero up until the ionisation front. This front expands with 10 km s⁻¹ such that at 10⁵ yr R_HII ≈ 1 pc for γ_ion < 10^49.49 photons s⁻¹, being progressively larger for larger photon fluxes. For example, the first (oldest, blue) population, if it by chance were to contain 10 O5V stars, would have produced an UCHII region with R_HII ≈ 10⁻¹ pc. If this UCHII region can break out as a champagner flow, it expands within about 0.1 Myr to R_HII ≈ 1 pc (note that 10⁵ cm⁻³ = 2500 M_⊙ pc⁻³ is about thebest vacuum achievable on Earth). The present-day size of the observed HII region in the ONC, the green asterisk (Felli et al. 1993), is consistent with our estimates.