Astron. Astrophys. 358, 956-992 (2000)

2-D non-LTE models of radiation driven winds from rotating early-type stars

I. Winds with an optically thin continuum

P. Petrenz and J. Puls

Universitäts-Sternwarte München, Scheinerstrasse 1, 81679 München, Germany

Received 2 February 2000 / Accepted 26 April 2000

Abstract

We extend previous 2-D models of line-driven winds from rotating hot stars by accounting for the dependence of ionization structure and occupation numbers on local physical properties (density, velocity field) and the non-local stellar radiation field.

For this purpose, we formulate for the first time an approximate non-LTE description of 2-D winds. We propose the concept of a "mean irradiating atmosphere", which allows one, in a computationally effective way and for all locations in the stellar wind, to consider the frequency dependence of the incident photospheric radiation field, which decisively determines the local ionization equilibrium.

Employing 2-D NLTE occupation numbers, force-multipliers and according force-multiplier parameters as functions of (), our hydrodynamic models are entirely self-consistent.

To estimate maximum effects arising from rotation and a consistent non-LTE approach, we concentrate on rapidly rotating B-star winds, since for this spectral regime the ionization structure is most sensitive to local conditions and variations of the radiation field. In order to avoid any contamination by the bi-stability effect (Lamers & Pauldrach 1991), we further restrict ourselves to winds with an optically thin Lyman continuum.

For all considered models, we find a prolate wind structure if gravity darkening and non-radial line forces are accounted for. Thus, the "-effect" suggested by Maeder (1999), aiming at the possibility to obtain an oblate wind morphology, is actually not present for winds with an optically thin continuum. This result should be valid at least in the OB-star range, excluding B-supergiant winds close to the bi-stability jump.

The density contrast between the polar and the equatorial flow grows with rotation rate and decreases from thin winds (: ) to denser ones (: ). The latter values are valid for winds rotating at 85 % of the break-up velocity. The variation of terminal velocity as function of latitude, however, is only small.

In comparison to simplified models with global averages for the force-multiplier parameters, the selfconsistent calculation results in a density contrast larger by roughly a factor of two, with a moderately enhanced concentration of wind material over the poles and a significant reduction in the equatorial plane. This difference is shown to be the consequence of ionization effects, related to the specific radial dependence of the mean radiation temperature over the poles and about the equatorial plane, respectively.

We conclude that a quantitatively correct description of line-driven winds from rapidly rotating hot stars requires a self-consistent approach if the variation of at the stellar surface can induce a (significantly) stratified ionization equilibrium and should be included especially for B-stars with lower luminosities and thinner winds.

Our most important finding with regard to the influence of rotation on global wind properties is that the total mass-loss rate deviates from its 1-D value (for ) by at most 10... 20 %, even for very high rotation rates (), except for winds from supergiants close to the Eddington-limit, where differences up to a factor of 2 become possible. We explain this remarkable coincidence by appropriate scaling relations and finally discuss our results with special emphasis regarding the wind-momentum luminosity relation of rapidly rotating stars.

Key words: hydrodynamics methods: numerical stars: circumstellar matter stars: early-type stars: mass-loss stars: rotation

Send offprint requests to: J. Puls (uh101aw@usm.uni-muenchen.de)

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Contents

• 1. Introduction
• 2. The model
  • 2.1. Physical processes
  • 2.2. Physical approximations
  • 2.3. Geometry and co-ordinate systems
  • 2.4. The hydrodynamic equations
  • 2.5. Numerical specifications
• 3. The radiative acceleration
  • 3.1. The continuum acceleration
  • 3.2. The line acceleration
  • 3.3. Impact of non-radial line forces and gravity darkening on the wind dynamics
• 4. Ionization equilibrium and occupation numbers
• 5. Properties of the force-multiplier
• 6. The line force parameterization
  • 6.1. Minor simplifications
  • 6.2. Quantities of the radiation field
    • 6.2.1. Radiation temperatures for black-body irradiation
    • 6.2.2. Mean effective temperatures
    • 6.2.3. The dilution factor
  • 6.3. Depth-dependent force-multiplier parameterization
  • 6.4. Local line force parameterization in 2-D winds
  • 6.5. Synopsis: calculation of a consistent 2-D line force by means of the force-multiplier concept
• 7. Self-consistent models
  • 7.1. Numerical aspects and tests for 1-D models
  • 7.2. 2-D models
    • 7.2.1. 2-D reference model for a B-supergiant wind
    • 7.2.2. Gravity darkening alone
    • 7.2.3. Irradiation by Planck flux distributions
    • 7.2.4. Dependence of wind properties on rotation rate
    • 7.2.5. Dependence of wind properties on stellar luminosity
• 8. Summary, conclusions and future work
• Acknowledgements
• References

© European Southern Observatory (ESO) 2000

Online publication: June 20, 2000
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