A dipole anisotropy of galaxy distribution: Does the CMB rest-frame
  exist in the local universe?
  The peculiar motion of the Earth causes a dipole anisotropy modulation in the
distant galaxy distribution due to the aberration effect. However, the
amplitude and angular direction of the effect is not necessarily the same as
those of the cosmic microwave background (CMB) dipole anisotropy due to the
growth of cosmic structures. In other words exploring the aberration effect may
give us a clue to the horizon-scale physics perhaps related to the cosmic
acceleration. In this paper we develop a method to explore the dipole angular
modulation from the pixelized galaxy data on the sky properly taking into
account the covariances due to the shot noise and the intrinsic galaxy
clustering contamination as well as the partial sky coverage. We applied the
method to the galaxy catalogs constructed from the Sloan Digital Sky Survey
(SDSS) Data Release 6 data. After constructing the four galaxy catalogs that
are different in the ranges of magnitudes and photometric redshifts to study
possible systematics, we found that the most robust sample against systematics
indicates no dipole anisotropy in the galaxy distribution. This finding is
consistent with the expectation from the concordance Lambda-dominated cold dark
matter model. Finally we argue that an almost full-sky galaxy survey such as
LSST may allow for a significant detection of the aberration effect of the CMB
dipole having the precision of constraining the angular direction to ~ 20
degrees in radius. Assuming a hypothetical LSST galaxy survey, we find that
this method can confirm or reject the result implied from a stacked analysis of
the kinetic Sunyaev-Zel'dovich effect of X-ray luminous clusters in Kashlinsky
et al. (2008,2009) if the implied cosmic bulk flow is not extended out to the
horizon.
