A Study of Quasar Clustering at z>2.7 from the Palomar Transit Grism Survey

The quest for structure indicators at earlier and earlier times in the evolution of the universe has led to the search for objects with ever higher redshifts. The Palomar Transit Grism Survey has produced a large sample of high redshift quasars ($z>2.7$), allowing statistical analysis of correlation between quasar positions. In this study, clustering is identified through comparison with $100 000$ Monte Carlo generated, randomly populated volumes, which are identical to the observed region in spatial coordinates, redshift distribution, and number of quasars. Three pairs have been observed with comoving separations of 11.34, 12.97, and 24.13 h_{50}^{-1}Mpc (assuming $q_0=0.5$), smaller separations than would be expected to arise by chance in an unclustered distribution. Selection effects are ruled out as a false source of clustering by scrambling the observed quasar coordinates and redshifts, which gives a pair separation distribution nearly identical to that of the Monte Carlo distribution. Tests using the distribution of pair separations and nearest neighbor distances show that the observed pairs have a probability less than 0.1% of arising in an unclustered distribution. Using a maximum likelihood technique to estimate the correlation length $r_0$, assuming $\xi(r) = (r/r_0)^{-1.8}$, we find $r_0 = 35\pm15 h_{50}^{-1}Mpc$ (comoving, $q_0=0.5$, 1$\sigma$ errors), a value much larger than the correlation length of present-day galaxies.