Reduced Convergence and the Local Smoothness Parameter: Bridging Two Different Descriptions of Weak-lensing Amplification

May 2005 • 2005ApJ...624...46W

Authors • Wang, Yun • Tenbarge, Jason • Fleshman, Bobby

Abstract • Weak gravitational lensing due to the inhomogeneous matter distribution in the universe is an important systematic uncertainty in the use of standard candles in cosmology. There are two different descriptions of weak-lensing amplification: one uses a local smoothness parameter α∼, and the other uses reduced convergence η=1+κ/|κ_min| (where κ is convergence). The α∼ description involves Dyer-Roeder distance D_A(α∼|z) (α∼=1 corresponds to a smooth universe); it is simple and convenient and has been used by the community to illustrate the effect of weak lensing on point sources such as Type Ia supernovae. Wang has previously shown that the α∼ description can be made realistic by allowing α∼ to be a local variable, the local smoothness parameter. The η description has been used by Wang et al. to derive a universal probability distribution for weak-lensing amplification. In this paper, we bridge the two different descriptions of weak-lensing amplification by relating the reduced convergence η and the local smoothness parameter α∼. We give the variance of α∼ in terms of the matter power spectrum, thus providing a quantitative guidance to the use of Dyer-Roeder distances in illustrating the effect of weak lensing. The by-products of this work include a corrected definition of the reduced convergence and simple and accurate analytical expressions for D_A(α∼|z). Our results should be very useful in studying the weak lensing of standard candles.

Links

• PDF https://stacks.iop.org/0004-637X/624/46/pdf
• PREPRINT http://arxiv.org/abs/astro-ph/0307415
• ELECTR https://doi.org/10.1086%2F428892
• SPIRES http://inspirehep.net/search?p=find+eprint+astro-ph/0307415