Exponential Growth of Distance between Nearby Rays Due to Multiple Gravitational Scatterings
Abstract
We give an estimate of the relative error in the angular measurement of observations for highredshift objects induced by gravitational scatterings (lensing). Gunn concluded in 1967 that the gravitational scatterings by galaxies induce a relative error of a few percent in observations for objects at z = 1. This estimate has been considered as a fundamental limitation of accuracy of the angular measurements in observational cosmology, In multiple gravitational scatterings, the bending angle of a single ray grows through the random work process. Gunn assumed that the difference of nearby rays also grows through the random walk process. However, the distance between nearby photons grows exponentially because the two rays suffer coherent scatterings by the same scattering object. This exponential growth continues as long as the scattering is coherent. In the case of scattering by individual galaxies, the exponential growth continues until the angular distance reaches 1' or so. The relative error of the angular measurements under 1' due to the exponential growth is ~30% at z = 1 and exceeds 100% at z = 3, when the density parameter of galaxies is 0.2. The effects of clusters of galaxies or superclusters are more difficult to estimate accurately but might be significant. In the case of superclusters, the angular measurements up to a few degrees could be affected.
 Publication:

The Astrophysical Journal
 Pub Date:
 December 1994
 DOI:
 10.1086/187645
 arXiv:
 arXiv:astroph/9409070
 Bibcode:
 1994ApJ...436L.111F
 Keywords:

 Background Radiation;
 Big Bang Cosmology;
 Error Analysis;
 Gravitational Lenses;
 Halos;
 Anisotropy;
 Brightness Temperature;
 Gravitational Constant;
 Red Shift;
 Astrophysics;
 COSMOLOGY: GRAVITATIONAL LENSING;
 COSMOLOGY: OBSERVATIONS;
 Astrophysics
 EPrint:
 compressed uuencoded postscript, 8 pages including 5 figures, APJL accepted