On the Rees-Sciama effect: maps and statistics

Abstract

Small maps of the Rees-Sciama (RS) effect are simulated by using an appropriate N-body code and a certain ray-tracing procedure. A method designed for the statistical analysis of cosmic microwave background (CMB) maps is applied to study the resulting simulations. These techniques, recently proposed --by our team-- to consider lens deformations of the CMB, are adapted to deal with the RS effect. This effect and the deviations from Gaussianity associated to it seem to be too small to be detected in the near future. This conclusion follows from our estimation of both the RS angular power spectrum and the RS reduced n-direction correlation functions for n<7.Comment: 11 pages, 13 figures, to appear in MNRA

Some remarks on new numerical estimations of the Rees-Sciama effect

“…The angular size of this image is close to ∼ 5 • × 5 • . Scales greater than 42h −1 Mpc are linear and the integrated Sachs-Wolfe effect they produce can be independently calculated (without N-body simulations), see [8]. Hereafter, n is the unit vector corresponding to the observation direction, ∆T /T is the relative temperature contrast, φ is the peculiar gravitational potential, a is the scale factor, and whatever quantity B may be, B 0 and B e stand for the B values at present (observation) and emission (decoupling) times, respectively.…”

“…The peculiar gravitational potential -necessary to estimate the RS anisotropy-is calculated and used at every time step of the N-body simulation, and CMB photons evolve under the action of this potential. Some advantages due to the use of an AP3M code -against the PM code of [8]-are pointed out. A more exhaustive study of the RS anisotropy -based on these advantages-is being performed and it will be presented elsewhere.…”

“…Here, the RS effect is studied again by using an AP3M N-body Hydra code, which may lead to resolutions better than those reachable with the simple PM code of reference [8]. The peculiar gravitational potential -necessary to estimate the RS anisotropy-is calculated and used at every time step of the N-body simulation, and CMB photons evolve under the action of this potential.…”

“…An appropriate ray-tracing procedure, through Particle-Mesh (PM) N-body simulations, was used in [8] to compute the Rees-Sciama (RS) contribution to the cosmic microwave background (CMB) anisotropy. Related talks -presented by the authors in previous FFP Symposium editionswere summarized in [1] and [2].…”

“…The use of a parallel AP3M code led to more accurate computations [6,7], but further research is necessary. Almost a decade ago, we computed the RS effect by using a PM N-body code [8]. Here, some preliminary estimations of the RS effect, obtained with a parallel AP3M Hydra code, are presented.…”