Mapping the real space distributions of galaxies in SDSS DR7: I. Two
  Point Correlation Functions
  Using a method to correct redshift space distortion (RSD) for individual
galaxies, we mapped the real space distributions of galaxies in the Sloan
Digital Sky Survey (SDSS) Data Release 7 (DR7). We use an ensemble of mock
catalogs to demonstrate the reliability of our method. Here as the first paper
in a series, we mainly focus on the two point correlation function (2PCF) of
galaxies. Overall the 2PCF measured in the reconstructed real space for
galaxies brighter than $^{0.1}{\rm M}_r-5\log h=-19.0$ agrees with the direct
measurement to an accuracy better than the measurement error due to cosmic
variance, if the reconstruction uses the correct cosmology. Applying the method
to the SDSS DR7, we construct a real space version of the main galaxy catalog,
which contains 396,068 galaxies in the North Galactic Cap with redshifts in the
range $0.01 \leq z \leq 0.12$. The Sloan Great Wall, the largest known
structure in the nearby Universe, is not as dominant an over-dense structure as
appears to be in redshift space. We measure the 2PCFs in reconstructed real
space for galaxies of different luminosities and colors. All of them show clear
deviations from single power-law forms, and reveal clear transitions from
1-halo to 2-halo terms. A comparison with the corresponding 2PCFs in redshift
space nicely demonstrates how RSDs boost the clustering power on large scales
(by about $40-50\%$ at scales $\sim 10 h^{-1}{\rm {Mpc}}$) and suppress it on
small scales (by about $70-80\%$ at a scale of $0.3 h^{-1}{\rm {Mpc}}$).
