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Published December 21, 1998 | Accepted Version + Published
Journal Article Open

Theory and statistics of weak lensing from large-scale mass inhomogeneities


Weak lensing by large-scale mass inhomogeneities in the Universe induces correlations in the observed ellipticities of distant sources. We first review the harmonic analysis and statistics required of these correlations and discuss calculations for the predicted signal. We consider the ellipticity correlation function, the mean-square ellipticity, the ellipticity power spectrum and a global maximum-likelihood analysis to isolate a weak-lensing signal from the data. Estimates for the sensitivity of a survey of a given area, surface density, and mean intrinsic source ellipticity are presented. We then apply our results to the FIRST radio-source survey. We predict an rms ellipticity of roughly 0.011 in 1 × 1 deg² pixels and 0.018 in 20 × 20 arcmin² pixels if the power spectrum is normalized to σ₈Ω⁰.⁵³ = 0.6, as indicated by the cluster abundance. The signal is significantly larger in some models if the power spectrum is normalized instead to the COBE anisotropy. The uncertainty in the predictions from imprecise knowledge of the FIRST redshift distribution is about 25 per cent in the rms ellipticity. We show that FIRST should be able to make a statistically significant detection of a weak-lensing signal for cluster-abundance-normalized power spectra.

Additional Information

© 1998 RAS. Accepted 1998 August 17. Received 1997 December 8. We thank S. Brown, D. Helfand, N. Kaiser and G. Lewis for useful discussions. This work was supported at Columbia by D.O.E. contract DEFG02-92-ER 40699, NASA NAG5-3091, NSF AST94-19906, and the Alfred P. Sloan Foundation. AB gratefully acknowledges ®nancial support from New York University and University of Victoria, and through an operating grant from NSERC. AR was supported at Princeton by the MAP/MIDEX project.

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Published - 301-4-1064.pdf

Accepted Version - 9712030.pdf


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