A radiative ionization and thermal equilibrium model for the wind from P Cygni

The statistical and thermal equilibrium of P Cygni's wind as a function of radius is discussed and calculated for a range of mass loss rates and velocity laws. The ionization balance of the most abundant heavy elements is included in the calculations, and hydrogen and helium are treated as multi-level atoms. The boundary beween the stellar core and the wind is identified with the radius, R, at which the continuum radiation field, longward of the Lyman limit, becomes optically thin. In this way, a physically plausible separation between an essentially LTE core and a wind in which non-LTE effects dominate is achieved. Because the wind is extremely opaque in the Lyman continuum and in the hydrogen and helium ground state lines, the ionization of these elements is maintained primarily by photoionization of the n=2 levels in the diluting stellar radiation field. This introduces a strong dependence upon the local wind temperature into the ionization balance of both hydrogen and helium. Outside a radius of the order of ~10 R, helium approaches neutrality in all models calculated. The wind cools mainly by hydrogen and helium free–free and bound–free emission near the base of the wind, where |Tₑ17\,000 K|⁠, but at larger radii, collisonal excitation of heavy-element semi-forbidden and auroral lines provides most of the cooling and brings the temperature down to |Tₑ 12\,000K|⁠. Increasing the mass loss rate or slowing down the velocity law is shown to produce a warmer, more highly ionized wind.