Fourier Phase Analysis of SDSS Galaxies

We present a first analysis of the clustering of SDSS galaxies using the distribution function of the sum of Fourier phases over three closed wavevectors. Since the Fourier phases are statistically independent of the Fourier amplitudes, the phase statistics plays a complementary role to the conventional two-point statistics of galaxy clustering. We find that the observed distribution functions of the phase sum are in good agreement with the lowest-order approximation from perturbation theory. From comparison of observations with mock catalogs constructed from $$N$$-body simulations, we find that the observed phase correlations for the galaxies within the range of the absolute magnitude, $$-22 < M_r <-18$$, agree well with those for $$\Lambda$$-dominated spatially flat cold dark matter predictions with $$\sigma_8 = 0.9$$ evolved from the Gaussian initial condition. This agreement implies that the galaxy biasing is approximately linear in redshift space. Instead, assuming that the galaxy biasing is described by a quadratic deterministic function $$\delta_{\mathrm{g}} = b_1 \delta_{\mathrm{m}} + (b_2/2)(\delta_{\mathrm{m}}^2-\langle \delta_{\mathrm{m}}^2 \rangle)$$ at scale larger than $$30 \, h^{-1} \,\mathrm{Mpc}$$, we find that the resulting $$b_2/b_1$$ is well fitted by $$b_2/b_1 = 0.54(\pm 0.06)-0.62(\pm 0.08) \,\sigma_8$$ and is almost insensitive to the cosmology and luminosity in those ranges. Indeed, $$b_2/b_1$$ is nearly zero when $$\sigma_8 = 0.9$$.