Detailed numerical modelling involving radiative transfer with realistic assumptions needs to be performed, in order to achieve similar (or even better) accuracy in predicting (i) the emergent continuum and line spectrum, and (ii) the structural details as a function of wavelength, as expected from instruments onboard ISO.
With the above aim in mind, a simple model, considering a compact H II region as a spherically symmetric cloud (made of typical interstellar gas-dust material), powered by a centrally embedded zero age main sequence star, is considered. This cloud is assumed to be immersed in an isotropic radiation field (typical Interstellar Radiation Field, ISRF). The interstellar gas and the dust is assumed to follow the same radial density distribution law, but with the following difference - whereas the gas exists throughout the cloud (i.e. right from the stellar surface upto the outer boundary of the cloud, Rmax; see Figure 1), there is a natural lower limit to the inner boundary, Rmin, for the dust distribution (i.e. a cavity in the dust cloud). This is because the dust grains are destroyed when exposed to excessive radiative heating. The gas to dust ratio, where they co-exist ( Rmin < r < Rmax), is assumed to be constant. As a simplistic approach, the interstellar gas is assumed to be consisting of hydrogen only. The position of the ionization front (RHII, refer to Figure 1) depends on the effective temperature and luminosity of the exciting star, as well as the gas density. The case, RHII < Rmin is also possible, if either the star is not hot enough and / or the gas density in the vicinity of the star is quite high. The gas component is assumed to have a uniform elemental abundance throughout the cloud, though the ionization structure and the various level populations depend on several physical parameters including the local radiation field.
Figure 1. Schematic diagram of the spherical compact H II region surrounded by a dusty molecular cloud. The region with r Rmin consists of only gas, ionized and/or neutral, the region between Rmin and RHII contains ionized gas and dust and the region between RHII and Rmax contains neutral gas and dust (if RHII > Rmin; as in the figure). In general RHII could also be < Rmin.
Families of models have been constructed to cover three primary parameters, viz., (1) the radial density distribution; (2) the spectral type of the embedded ZAMS star (determining the luminosity and the shape of the input spectrum); and (3) the total radial optical depth at a fiducial wavelength. All other relevant variables are either determined self-consistently by the primary parameters or chosen to be fixed at some reasonable values.
This modelling scheme involves the use of a modified version of the code CSDUST3 (Egan et al., 1988). This code takes into account the effects of multiple scattering, absorption and re-emission on the temperature of dust grains and the internal radiation field. In addition, the radiation field anisotropy, linear anisotropic scattering and multi grain components are also considered. This code has been modified by us and the main modification has been in terms of incorporating gas and dust self-consistently, in order to calculate emission from both. More details of this modification are presented in Mookerjea & Ghosh (1999) and also in Appendix A. This scheme considers photo-ionization and recombination, along with absorption due to the grains. Self-absorption of the radio emission within the cloud has also been considered in this scheme, but the gas-dust coupling has been neglected. Details about the considerations regarding energetics of this scheme have been presented in Mookerjea et al. (1999). Additional numerical details about the code are presented in Appendix B.