Astron. Astrophys. 358, 13-29 (2000)

Lensing effects in an inhomogeneous universe

L. Bergström, M. Goliath, A. Goobar and E. Mörtsell

Stockholm University, Department of Physics, Box 6730, 113 85 Stockholm, Sweden

Received 14 December 1999 / Accepted 24 March 2000

Abstract

Recently, Holz & Wald have presented a new method for determining gravitational lensing effects on, e.g., supernova luminosity versus redshift measurements in inhomogeneous universes. In this paper, their method is generalized in several ways: First, the matter content is allowed to consist of several different types of fluids, possibly with non-vanishing pressure. Second, besides lensing by simple point masses and singular isothermal spheres, the more realistic halo dark matter distribution proposed by Navarro, Frenk & White (NFW), based on N-body simulation results, is treated. We discuss various aspects of the accuracy of the method, such as luminosity corrections, and statistics, for multiple images. We find in agreement with other recent work that a large sample of supernovae at large redshift could be used to extract gross features of the mass distribution of the lensing dark matter halos, such as the existence of a large number of point-like objects. The results for the isothermal sphere and the NFW model are, however, very similar if normalized to the observed luminosity distribution of galaxies. We give convenient analytical fitting formulas for our computed lensing probabilites as a function of magnification, for several redshifts.

Key words: cosmology: theory cosmology: gravitational lensing cosmology: dark matter galaxies: halos

Send offprint requests to: Edvard Mörtsell (edvard@physto.se)

This article contains no SIMBAD objects.

Contents

• 1. Introduction
• 2. Cosmological model
• 3. Area vs. magnification and statistical weighting
• 4. Geodesic deviation
• 5. Summary of the properties of the lensing model
• 6. The Navarro-Frenk-White distribution
• 7. Mass distribution
  • 7.1. Truncation radii for SIS-lenses
• 8. Results
• 9. Limitations of method
• 10. Multiple imaging
  • 10.1. A point-mass universe
  • 10.2. A SIS-galaxy universe
  • 10.3. One-lens approximation for point masses
  • 10.4. One-lens approximation for SIS lenses
• 11. Consistency checks
• 12. Analytical fitting formulas
• 13. Discussion
• Acknowledgements
• Appendices
  • A: for the Navarro-Frenk-White matter distribution
  • B: parameter values for mass distribution
  • C: mean area vs. luminosity
• References

© European Southern Observatory (ESO) 2000

Online publication: June 26, 2000
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