3. Unified stark broadening theories
Due to its importance in later analysis and discussions, we first make a brief summary of the situation for the Stark broadening, which includes the effects of the ion field and the electrons. Stark broadening of hydrogen lines has received considerable attention. The most used of the treatments are those of Vidal et al. (1970, 1971, 1973), and more recently Stehlé (1994). The theory of Vidal et al. (1970) was the first "unified theory" of electron and ion collisional broadening of hydrogen lines. This theory was for the first time capable of computing the line profile over the whole line, from the impact limit at line centre to the quasistatic limit in the line wings, including the transition region. The calculations of Stehlé (1994) are based on the theory of Frisch & Brissaud (1971a, 1971b), the so called Model Microfield Method (MMM). The major advantage of these calculations, over the Vidal et al. (1973) calculations, is the modelling of the dynamics of ions and non-Markovian effects (overlapping collisions). As stated by Stehlé & Jacquemot (1993), "MMM can be seen as an interpolating formalism between well described asymptotic `static' and `impact' limits". By comparison the Vidal et al. (1970) theory is simply a unified treatment of the two limits.
The Vidal et al. (1973) and Stehlé (1994) calculations are in reasonable agreement, mostly showing differences in the line core due to ion dynamics. In cool stars the ions are produced by the ionisation of heavy metals like iron which move relatively slowly so the effects of ion motion will be very small. The Stehlé calculations show quite good agreement with experiment (Stehlé 1994), noticeably better than Vidal et al. (1973) in the line core. However, this difference is often lost in astrophysical applications when the profiles are folded with Doppler profiles (Lemke 1997). Both theories show reasonable agreement in the wings.
© European Southern Observatory (ESO) 2000
Online publication: December 5, 2000