Astron. Astrophys. 327, 199-206 (1997)

Centre to limb darkening of stars

New model and application to stellar interferometry

D. Hestroffer

Astrophysics Division, ESTEC, Postbus 299, 2200 AG Noordwijk, The Netherlands (e-mail: dhestrof@estec.esa.nl)

Received 19 February 1997 / Accepted 13 June 1997

Abstract

Measurement of a star's apparent diameter with an intensity interferometer yields its geometrical radius and its effective temperature when one knows or measures the specific centre to limb-darkening. This paper presents a formulation that (1) makes use of a single parameter and (2) is well suited for the interpretation and comparison of centre to limb darkening. Subsequently, this result is applied to the study of the contrast of the fringes as obtained with a stellar interferometer. A method yielding the angular diameter of the extended source together with the parameter of the law modeling its centre to limb darkening is presented. The value of such observations made by GAIA type interferometer (Lindegren & Perryman 1996) are briefly noted in the last section.

Key words: limb darkening stars: fundamental parameters of stars: atmospheres of GAIA techniques: interferometric.

Contents

• 1. Introduction
• 2. Power law for limb darkening
  • 2.1. Radius of a star
  • 2.2. Comparison to observed and calculated values
  • 2.3. Summary
• 3. Visibility function
  • 3.1. Derivation from power law parameterization
  • 3.2. Approximations
  • 3.3. Gaussian fit
• 4. Determination of limb-darkening and radius
  • 4.1. Determination from observations
    • 4.1.1. A change in the diameter
    • 4.1.2. A change in the power law parameter
  • 4.2. Least-squares solution
  • 4.3. Discussion
• 5. Observations with GAIA
• 6. Conclusion
• Acknowledgements
• References

© European Southern Observatory (ESO) 1997

Online publication: April 8, 1998
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