We present results for the cooling and heating that arise from cyclotron resonant and nonresonant scattering by photons injected into a planar slab plasma of thickness Ne electrons cm-2 that is threaded by a superstrong field (B) oriented parallel to the slab normal. From a balance of the cooling and heating, we calculate the equilibrium temperature TC as a function of field strength B and column depth through the slab. We obtain analytic expressions for TC for both beamed and isotropic photon injection in the optically thin limit. For the optically thick case, we use Monte Carlo simulations to study the values of TC resulting from isotropic photon injection into the slab plasma. We find that when TC is determined by the cooling/heating balance due solely to cyclotron resonant scattering TC/B remains fairly constant for Ne up to ∼6 × 1021 electrons cm-2 in the optically thick regime. This line-dominated region comes to an end when the extra heating from the hard continuum photons (>100 keV) becomes competitive with the line processes and drives the equilibrium temperature well above the pure line value. With parameters characteristic of GB 880205, we determine the thickness of the line-dominated region to be ≃1021-1022 electrons cm-2. Using the pure line cooling/heating model for the line-forming region, Wang et al. computed theoretical line spectra and compared these spectra with the data from GB 880205. They found good fits to the data for line-forming regions with column depths ≈(0.6-1.8) × 1021 electrons cm-2. This qualitative agreement between the best-fit thickness of the line-forming layer demanded by the data and the thickness of the line-dominated layer determined in this paper strongly suggests that the line-dominated layer plays an important, if not central, role in the line formation process. Requiring that the line-enhanced radiation force exerted on the scattering layer be less than the gravitational force binding this layer to the surface of, for example, a neutron star, gives a limiting magnetic Eddington luminosity. Strictly speaking, we can find a limit on the spectral flux at the cyclotron lines. Applying this limit to GB 880205 constrains the distance to this burst to be ≲200 pc (3 σ upper bound) and implies that the total luminosity L ≲ 0.3LE, where LE ≈ 1.26 × 1038 M/M⊙ (ergs s-1) is the nonmagnetic Eddington limit for an electron-proton plasma. A pair-dominated scattering layer cannot easily be accommodated in our model since the corresponding distance limit would be far smaller, ≲5 pc, which is highly unlikely. Both the cyclotron interpretation of line features seen in GB 880205 and the distance limit strongly suggest that this burst originates from a strongly magnetized neutron star in the Galactic disk.
