MODERN COSMOLOGY
The lens equation in cosmology 407 We recall that the expression for the time delay in an almost Newtonian situation is given by ...
408 Gravitational lensing events at redshiftsz 1 andz 2 (z 1 <z 2 ),isgivenby D(z 1 ,z 2 )= 2 c √ 1 + 0 z 1 ( 2 − 0 + 0 z ...
Galaxy clusters as lenses 409 14.5.1 Hubble constant from time delays As first noted by Refsdal in 1964 [59], time delay measure ...
410 Gravitational lensing Figure 14.8. Light curves of the two images of the gravitationally lensed quasar Q0957+561. Note the s ...
Galaxy clusters as lenses 411 Figure 14.9.The light curve of image A of figure 14.3 is advanced by the optimal value of the time ...
412 Gravitational lensing Figure 14.10.Wavefronts in the presence of a cluster perturbation. Inside the so defined circle the su ...
Galaxy clusters as lenses 413 Figure 14.11. Hubble Space Telescope image of the cluster Abell 2218. Beside arcs around the two c ...
414 Gravitational lensing formulation of lensing theory (see, for instance, [65]). In the following we will, however, not use it ...
Galaxy clusters as lenses 415 whereλis a real constant. This is the so-calledmass-sheet degeneracy(a homogeneous mass sheet does ...
416 Gravitational lensing ellipticity allowsγ, to be determined and, making use of equation (14.130) one can get the surface mas ...
References 417 Figure 14.12.The radial mass profiles determined from the x-ray and lensing analysis for Abell 2163. The triangle ...
418 Gravitational lensing [4] Schneider P, Ehlers J and Falco E E 1992Gravitational Lensing(Berlin: Springer) [5] Refsdal S and ...
References 419 [45] Grenacher L, Jetzer Ph, Str ̈assle M and De Paolis F 1999Astron. Astrophys. 351775 [46] Crotts A P 1992Astro ...
Chapter 15 Numerical simulations in cosmology Anatoly Klypin Astronomy Department, New Mexico State University, Las Cruces, USA ...
Methods 421 functions, (2) density and velocity profiles and (3) concentration of halos. The results are not sensitive to the pa ...
422 Numerical simulations in cosmology particles with different masses. It was shown that if one distributes the mass of a clust ...
Methods 423 therein). The Press–Schechter approximation is also difficult to justify without numerical simulations. It operates ...
424 Numerical simulations in cosmology Herea=( 1 +z)−^1 is the expansion parameter,p=a^2 x ̇is the momentum,dm is the contribut ...
Methods 425 φorφ′. At early stages of evolution perturbations still grow almost linearly. In this case we expect thatδdm∝ a,φ≈ c ...
426 Numerical simulations in cosmology In order to set the initial conditions, we choose the size of the computational boxLand t ...
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