Astron. Astrophys. 326, 277-286 (1997)

Spherically symmetric model atmospheres using approximate lambda operators

III. The equations of statistical equilibrium with occupation probabilities

Jií Kubát

Astronomický ústav, Akademie vd eské republiky, 251 65 Ondejov, Czech Republic

Received 7 March 1997 / Accepted 22 April 1997

Abstract

The occupation probability formalism is implemented into the equations of statistical equilibrium. The equations and corresponding expressions for rates are presented in detail. The improved equations are used for the calculation of sample spherically symmetric NLTE model atmospheres. The difference between this formalism and standard cutoff formula is studied for pure hydrogen atmospheres. It is small for main-sequence and sdO stars. However, a larger difference is found for white dwarfs.

Key words: stars: atmospheres atomic processes methods: numerical

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Contents

• 1. Introduction
• 2. The equations of statistical equilibrium
  • 2.1. LTE ionization and excitation equilibrium
  • 2.2. NLTE ionization and excitation equilibrium (statistical equilibrium)
    • 2.2.1. Rate equations
    • 2.2.2. Closing equations
  • 2.3. Opacities with occupation probabilities
• 3. Computational details
  • 3.1. Radiative transfer
  • 3.2. Linearization of the equations of statistical equilibrium
    • 3.2.1. Explicit linearization of the b -factors
    • 3.2.2. Implicit linearization of the b -factors
    • 3.2.3. Comparison of both methods
• 4. Results and discussion
  • 4.1. Hot main sequence stars
  • 4.2. O subdwarfs
  • 4.3. White dwarfs
• 5. Conclusions
• Acknowledgements
• Appendix A
• Appendix A: details of the linearization
• A.1. Explicit linearization of the equations of statistical equilibrium
• A.2. Implicit linearization of the equations of statistical equilibrium
• A.3. The derivatives of the rate matrix
• References

© European Southern Observatory (ESO) 1997

Online publication: April 20, 1998
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