In this section we describe the computational procedure, assumptions, free parameters, and the quantities which are calculated. Chief among the assumptions is that each model consists of a spherical gas cloud with a point source of continuum radiation at the center. Therefore it implicitly assumes spherical symmetry and radially beamed incident radiation. In principle, more complicated geometries can be mimiced by adding the local emission from various spherical sections with appropriately chosen conditions. Also important is the assumption that all physical processes affecting the state of the gas are in a steady-state, i.e. that the the timescales for variation in the gas density and illuminating radiation are long compared with timescales affecting all atomic processes and propogation of radiation within the gas. The validity of this assumption in any given situation depends on the conditions there, such as the gas density, temperature, and degree of ionization, and can be evaluated by using a model assuming steady-state and then calculating atomic rates which can (hopefully) justify the steady-state assumption a posteriori.
The primary difference between these models and atmospheric models lies in the treatment of the radiation field. In an optically thick atmosphere the state of the gas at any point in the cloud is coupled to the state of the gas in a large part of the rest of the cloud by the continuum radiation field and, in the limit of very large optical depth, can affect the excitation and ionization by suppressing radiative free-bound (recombination) transitions. We attempt to mimic some of these effects by assigning to each recombination event an escape probability, using an expression given in the following section. We also calculate the transfer of radiation by assuming that diffuse radiation emitted at each radius is directed radially outward or inward. These assumptions will be described in more detail later in this section.
A further assumption governs the treatment of the transport of radiation in spectral lines. Over a wide range of plausible situations large optical depths occur in the cores of lines of abundant ions, which may be important in cooling the gas. In treating the transfer of these photons we make the (conventional) assumption of complete redistribution in the scattering, which assumes that the transfer of the line photons occurs in a spatial region very close to the point where the photons are emitted. Therefore the line emission rates are multiplied by an escape probability using an expression given in the following section. This factor is intended to simulate the line scattering in the immediate vicinity of the emission region, and it assumes that escape from this region occurs when the photon scatters into a frequency where the optical depth is less than unity. Following escape from the local region, the line photon is assumed to be subject to absorption by continuum processes which are treated using the same 2-stream transfer equation as for the continuum.