On the fairness of the main galaxy sample of SDSS

Flux-limited and volume-limited galaxy samples are constructed from SDSS data releases DR4, DR6 and DR7 for statistical analysis. The two-point correlation functions $\xi(s)$, monopole of three-point correlation functions $\zeta_0$, projected two-point correlation function $w_p$ and pairwise velocity dispersion $\sigma_{12}$ are measured to test if galaxy samples are fair for these statistics. We find that with increment of sky coverage of SDSS, $\xi(s)$ of flux-limited sample is extremely robust and insensitive to local structures at low redshift. But for volume-limited samples fainter than $L^*$ at large scales $s>\sim 10\hmpc$, deviation of $\xi(s)$ and $\zeta_0$ of DR7 to those of DR4 and DR6 increases with larger absolute magnitude. In the weakly nonlinear regime, there is no agreement between $\zeta_0$ of different data releases in all luminosity bins. Furthermore, $w_p$ of volume-limited samples of DR7 in luminosity bins fainter than $-M_{r,0.1}=[18.5,19.5]$ are significantly larger, and $\sigma_{12}$ of the two faintest volume-limited samples of DR7 display very different scale dependence than results of DR4 and DR6. Our findings call for cautions in understanding clustering analysis results of SDSS faint galaxy samples, and higher order statistics of SDSS volume-limited samples in the weakly nonlinear regime. The first zero-crossing points of $\xi(s)$ of volume-limited samples are also investigated and discussed.