ON THE ALTERNATIVE ORIGIN OF THE DIPOLE ANISOTROPY OF MICROWAVE BACKGROUND DUE TO THE REES-SCIAMA EFFECT

摘要

Recently, Lauer & Postman discovered that the peculiar motion of Local Group with respect to the system defined by Abell clusters and the maximum of the dipole anisotropy of cosmic microwave background radiation have different directions. The standard interpretation of this phenomenon assumes that there is a bulk stream of Abell clusters themselves caused by a huge unknown mass concentration. However, in principle, it may occur also that this huge unknown mass concentration does exist, but there is no bulk stream of clusters toward this mass concentration, and the intrinsic dipole and other anisotropies of cosmic microwave background radiation are caused via the Rees-Sciama effect due to this mass concentration. In this paper, this alternative explanation of the data of Lauer & Postman is studied. The profile of the redshift of light—that crosses a spherical void and cluster—is calculated analytically. Then the obtained formula of this profile is decomposed into the sum of monopole, dipole, quadrupole, etc., terms. It is shown that the dipole and the quadrupole terms have the same order. Nevertheless, the observed dipole anisotropy of microwave background radiation is of order ～10~(-3), but the quadrupole anisotropy, if it exists, is not larger than of order ～10~(-5). Hence, we obtain the conclusion that the Rees-Sciama effect hardly can cause a dipole anisotropy of order ～10~(-3).