Analytical Modeling of the Weak Lensing of Standard Candles. I. Empirical Fitting of Numerical Simulation Results

November 1999 • 1999ApJ...525..651W

Authors • Wang, Yun

Abstract • Weak lensing leads to the non-Gaussian magnification distribution of standard candles at a given redshift z, p(μ|z). In this paper we give accurate and simple empirical fitting formulae of the weak lensing numerical simulation results with the generalized Dyer-Roeder prescription. The smoothness parameter α∼ essentially represents the amount of matter that can cause magnification of a given source. Since matter distribution in our universe is inhomogeneous, we can think of our universe as a mosaic of cones centered on the observer, each with a different value of α∼. We define the direction-dependent smoothness parameter α∼ via the Dyer-Roeder equation; there is a unique mapping between α∼ and the magnification of a source. We find that the distribution of α∼ at a given z, p(α∼|z), is well described by a modified Gaussian distribution. For the same matter distribution, i.e., the same p(α∼|z), different values of Ω_m and Ω_Λ can lead to very different magnification distributions.

Our formulae can be conveniently used to calculate the weak lensing effects for observed Type Ia supernovae at arbitrary redshifts.

Links

• PDF https://stacks.iop.org/0004-637X/525/651/pdf
• PREPRINT http://arxiv.org/abs/astro-ph/9901212
• SPIRES http://inspirehep.net/search?p=find+j+ASJOA,525,651
• ELECTR https://doi.org/10.1086%2F307922
• SPIRES http://inspirehep.net/search?p=find+eprint+astro-ph/9901212