We present a first analysis of the clustering of SDSS galaxies using the distribution function of the sum of Fourier phases .
This statistical method was recently proposed by one of the authors as a new probe of the phase correlations of cosmological density fields .
Since the Fourier phases are statistically independent of the Fourier amplitudes , the phase statistic plays a complementary role to the conventional two-point statistics of galaxy clustering .
In particular , we focus on the distribution functions of the phase sum over three closed wavevectors as a function of the triangle configuration .
We find that the observed distribution functions of the phase sum are in good agreement with the lowest-order approximation from perturbation theory .
For a direct comparison with observations , we construct mock catalogs from N -body simulations taking account of the survey geometry , the redshift distortion , and the discreteness due to the limited number of data .
Indeed the observed phase correlations for the galaxies in 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 at k < 0.03 [ 2 \pi / ( h ^ { -1 } { Mpc } ) ] , we can constrain the ratio of the quadratic biasing parameter , b _ { 2 } , to the linear biasing parameter , b _ { 1 } , from the difference of phase correlations between observations and mock predictions .
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 .