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.
We report a study of cloud cover over Indonesia based on meteorological satellite data spanning 15 years (from 1996 to 2010) to aid in the selection of a new astronomical site capable of hosting a multi-wavelength astronomical observatory. High-spatial-resolution meteorological satellite data acquired from Geostationary Meteorological Satellite 5 (GMS 5), Geostationary Operational Environmental Satellite 9 (GOES 9) and Multi-functional Transport Satellite-1R (MTSAT-1R) are used to derive yearly average clear fractions over various regions of Indonesia. This parameter is determined from temperature measurements in the IR3 channel (water vapour, 6.7 µm) for high-altitude clouds (cirrus), and from the IR1 channel (10.7 µm) for lower-altitude clouds. An algorithm is developed to detect the corresponding clouds. The results of this study were used to select the best possible sites in Indonesia, which will be analysed further by performing in situ measurements in the future. The results suggest that regions of East Nusa Tenggara, located in southeastern Indonesia, are the most promising candidates for such an astronomical site. The yearly clear sky fraction of this region may reach better than 70 per cent, with an uncertainty of 10 per cent.
Using a multiple-lens plane algorithm, we study light propagation in inhomogeneous universes, for 43 different COBE-normalized Cold Dark Matter models, with various values of the density parameter Ω 0 , cosmological constant λ 0 , Hubble constant H 0 , and rms density fluctuation σ 8 . This is the largest cosmological parameter survey ever done in this field. We performed a total of 3,798 experiments, each experiment consisting of propagating a square beam of angular size 21.9 ′′ × 21.9 ′′ composed of 116,281 light rays from the observer up to redshift z = 3. These experiments provide statistics of the magnification, shear, and multiple imaging of distant sources. The results of these experiments can be compared with observations, and eventually help constraining the possible values of the cosmological parameters. Additionally, they provide insight into the gravitational lensing process and its complex relationship with the various cosmological parameters.Our main results are the following: (1) The magnification distribution depends mostly upon λ 0 and σ 8 . As σ 8 increases, the low-tail of the magnification distribution shifts toward lower magnifications, while the high-tail is hardly affected. The magnification distribution also becomes wider as λ 0 increases. This effect is particularly large for models with λ 0 = 0.8. (2) The magnification probability P m is almost independent of σ 8 , for any combination of Ω 0 , λ 0 , H 0 , indicating that P m does not depend strongly on the amount of largescale structure. (3) The shear distribution, like the magnification distribution, depends mostly upon λ 0 and σ 8 . The shear distribution becomes wider with increasing σ 8 and increasing λ 0 . The similarities between the properties of the magnification and shear distributions suggests that both phenomena are caused by weak lensing. (4) About 0.3% of sources have multiple images. The double-image probability P 2 increases strongly with λ 0 and is independent of Ω 0 , H 0 , and σ 8 . ( 5) The distribution of image separations depends strongly upon λ 0 , and is independent of σ 8 . Summarizing these results, we find that (1) The properties of gravitational lensing, both weak and strong, depend much more strongly upon λ 0 than any other cosmological parameter, (2) magnification and shear are examples of weak lensing caused primarily by the distribution of background matter, with negligible contribution form galaxies, while multiple images and rings are examples of strong lensing, caused by direct interaction with galaxies, with negligible contribution from the background matter. Observations of weak lensing can be used to determine the cosmological constant and the density structure of the universe, while observations of strong lensing can be used to determine the cosmological constant and the internal structure of galaxies and clusters. Gravitational lensing depends much more weakly upon Ω 0 and H 0 than σ 8 and λ 0 , making a determination of these parameters from observations more difficult.
Using an analytical model, we compute the distribution of image separations resulting from gravitational lensing of distant sources, for 7 COBE-normalized CDM models with various combinations of Ω 0 and λ 0 . Our model assumes that multiple imaging results from strong lensing by individual galaxies. We model galaxies as nonsingular isothermal spheres whose parameters are functions of the luminosity and morphological type, and take into account the finite angular size of the sources. Our model neglects the contribution of the background matter distribution to lensing, and assumes that lensing is entirely caused by galaxies. To test the validity of this assumption, we performed a series of ray-tracing experiments to study the effect of the background matter on the distribution of image separations. Our results are the following: (1) The presence of the background matter tends to increase the image separations produced by lensing galaxies, making the distributions of image separations wider. However, this effect is rather small, and independent of the cosmological model. (2) Simulations with galaxies and background matter often produce a secondary peak in the distribution of image separations at large separations. This peak does not appear when the background matter is excluded from the simulations. (3) The effect of the background matter on the magnification distribution is negligible in low density universes (Ω 0 = 0.2) with small density contrast (σ 8 = 0.4), but becomes very important as Ω 0 and σ 8 increase, resulting in a significant widening of the distribution. (4) Multiple imaging is caused primarily by early-type galaxies (elliptical and S0's), with a negligible contribution from spiral galaxies. (5) Our analytical model, which has only 2 free parameters, is in good agreement with the results of ray-tracing experiments, successfully reproducing the distributions of image separations, and also the multiple-imaging probability, for all cosmological models considered. (6) The analytical model predicts that the distributions of image separations are virtually indistinguishable for flat, cosmological constant models with different values of Ω 0 . (7) For models with no cosmological constant, the distributions of image separations do depend upon Ω 0 , but this dependence is weak. We conclude that while the number of multiple-imaged sources can put strong constraints on the cosmological parameters, the distribution of image separations does not constrain the cosmological models in any significant way, and mostly provides constraints on the structure of the galaxies responsible for lensing.Accepted for publication in The Astrophysical Journal
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