A.1. Extent of the Ionized Region

The size of the H II region has been calculated by considering photoionization and recombination of hydrogen, along with the absorption due to the dust grains. The presence of the dust component reduces the size of the ionized region, (R_HII), compared to that of pure gas Stromgren sphere considerably, depending on the density and the gas to dust ratio. The dust grains can exist in principle, only beyond a radial distance, say r_subl, depending on its sublimation temperature and the local radiation field. In practice, the actual distance beyond which the dust exists, say r_fit, is determined by the model fitting of the observed SED, by radiative transport calculations through the dust. The r_fit is often much larger than r_subl.

Hence, whether one encounters a dusty Stromgren sphere or not, is determined by the type of the star / integrated spectrum of the cluster; radial density distribution around the central star; and r_fit. We call it a Case A, if the ionized region extends into the region where the gas the and dust co-exist. The other case of entire ionized region devoid of any dust grains is termed Case B. So for Case B, the extent of the H II region can be obtained by solving the equation,

(A1)

where, N(r) is the Lyman continuum photon flux, ₂ is the recombination coefficient for hydrogen (for recombinations to all states except the ground state) and n_e is the number density of electrons or H⁺ ions (for a pure H II region), which in our case is the gas number density (n_g) and may be given by,

(A2)

For m = 0, 1, 2 equation(A1) can be solved easily by using the boundary condition

(A3)

where, N_Lyc is the total number of Lyman continuum photons emitted per second by the embedded exciting star / star cluster and r_* is an effective stellar radius (with volume equal to the sum of that of all the stars of the embedded cluster; as it turns out, results are extremely insensitive to r_*).

In case A however, the ionizing (Lyman continuum) photons experience further attenuation due to direct absorption by the dust, so the modified radiation transfer equation would be,

(A4)

where _Lyc refers to the optical depth of dust at < 912 Å. We solve the above equation, using the boundary conditions,

(A5)

where N₁ is determined by using equation (A1) and

(A6)