Light Propagation in Inhomogeneous Universes. I. Methodology and Preliminary Results

Abstract

We describe a numerical algorithm which simulates the propagation of light in inhomogeneous universes. This algorithm computes the trajectories of light rays between the observer, located at redshift z = 0, and distant sources located at high redshift, using the multiple lens-plane method. The deformation and deflection of light beams as they interact with each lens plane are computed using the filled-beam approximation.We use a Particle-Particle/Particle-Mesh (P 3 M) N-body numerical code to simulate the formation of large scale structure in the universe. We extend the length resolution of the simulations to sub-Megaparsec scales by using a Monte-Carlo method for locating galaxies inside the computational volume according to the underlying distribution of background matter. The observed galaxy 2-point correlation function is reproduced. This algorithm constitutes a major improvement over previous methods, which either neglected the presence of large-scale structure, neglected the presence of galaxies, neglected the contribution of distant matter (matter located far from the beam), or used the Zel'dovich approximation for simulating the formation of largescale structure. In addition, we take into account the observed morphology-density relation when assigning morphological types to galaxies, something that was ignored in all previous studies.To test this algorithm, we perform 1981 simulations, for three different cosmological models: an Einstein-de Sitter model with density parameter Ω 0 = 1, an open model with Ω 0 = 0.2, and a flat, low density model with Ω 0 = 0.2 and a cosmological constant λ 0 = 0.8. In all models, the initial density fluctuations correspond to a Cold Dark Matter power spectrum normalized to COBE. In each simulation, we compute the shear and magnification resulting from the presence of inhomogeneities. Our results are the following: (1) The magnification is totally dominated by the convergence, with the shear contributing less than one part in 10 4 . (2) Most of the cumulative shear and magnification is contributed by matter located at intermediate redshifts z = 1 − 2.(3) The actual value of the redshift where the largest contribution to shear and magnification occurs depends on the cosmological model. In particular, the lens planes contributing the most are located at larger redshift for models with smaller Ω 0 . (4) The number of galaxies directly hit by the beam increases with redshift, while the contribution of lens planes to the shear and magnification decrease with increasing lens-plane redshift for z > 2, indicating that the bulk of the shear and magnification does not originate from direct hits, but rather from the tidal influence of nearby and more distant galaxies, and background matter. (5) The average contributions of background matter and nearby galaxies to the shear is comparable for models with small Ω 0 . For the Einstein-de Sitter model, the contribution of the background matter exceeds the one of nearby galaxies by nearly one order of magnitude.

Testing the reliability of weak lensing cluster detections

“…Using finite-differencing schemes, we finally obtain maps of the deflection angles on each plane, α i lm (Premadi et al 1998).…”

Various Approaches to Cosmological Gravitational Lensing in Inhomogeneous Models

“…Recently Premadi et al 16) have improved the work of Jaroszyński et al by adopting an N -body simulation (P 3 M code) and considering the spatial distribution of galaxies with the mass spectrum and morphological types (due to the morphological type-density relation). They adopted Jaroszyński's assumption that the main lens objects are galaxies and the background matter outside galaxies has smooth distribution with radii ≈ 1h −1 Mpc.…”

“…13) can be performed along the unperturbed path to first order, k · (x − x ′ ) in the exponent is written as k ⊥ · θD(χ) + k (χ − χ ′ ) where k ⊥ (or k ) is the wavenumber perpendicular (or parallel) to the line of sight. When θ ≪ 1 we can approximate k ≪ k ⊥ and obtain 16) where …”

Magnification Probability Distribution Functions of Standard Candles in a Clumpy Universe

“…In this sense, the (de)magnification is often defined asμ := D 2 F L /D 2 A in weak lensing analyses and ray shooting calculations. 42)- 44) In their works, the surface mass density of each lens plane is not positive definite, namely, the under dense regions have negative mass density. The relation between μ andμ is given as…”