Fourier Phase Analysis of SDSS Galaxies

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Abstract
We present a first analysis of the clustering of SDSS galaxies using the distribution function of the sum of Fourier phases, which was recently proposed as a new probe of phase correlations of cosmological density fields. Since the Fourier phases are statistically independent of Fourier amplitudes, our phase statistic plays a complementary role to the conventional two-point statistics on the analysis of galaxy clustering. In particular, we focus on the distribution functions of phase sum over three closed wavevectors as a function of the configurations of triangle wavevectors. We find that the observed distribution functions of phase sum are in good agreement with the lowest-order approximation from perturbation theory. From direct comparison of observations with mock catalogs constructed from N-body simulations, the observed phase correlations for the galaxies agree well with those for Lambda CDM predictions with sigma8=0.9 evolved from Gaussian initial condition. Since values of phases are invariant by the homogeneous magnification of fluctuations, this agreement implies that the galaxy biasing is well approximated by the linear relation in redshift space. Assuming that the galaxy biasing is described by a quadratic deterministic function at scale larger than 30Mpc/h, we measure the ratio of the quadratic biasing parameter b2 to the linear biasing parameter b1. We find that resulting b2/b1 is mainly dependent on sigma8 assumed in mock catalogs and then their relation is well fitted by b2/b1=0.54(+-0.06)-0.62(+-0.08)sigma8 in CDM models.

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