Spatial Correlation Function of the Chandra Selected Active Galactic Nuclei

We present the spatial correlation function analysis of non-stellar X-ray point sources in the Chandra Large Area Synoptic X-ray Survey of Lockman Hole Northwest (CLASXS). Our 9 ACIS-I fields cover a contiguous solid angle of 0.4 deg^2 and reach a depth of 3x10^-15 c.g.s in the 2-8 keV band. We supplement our analysis with data from the Chandra Deep Field North (CDFN). The addition of this field allows better probe of the correlation function at small scales. A total of 233 and 252 sources with spectroscopic information are used in the study of the CLASXS and CDFN fields respectively. We calculate both redshift-space and projected correlation functions in comoving coordinates, averaged over the redshift range of 0.1<z<3.0, for both CLASXS and CDFN fields for a standard cosmology with \Omega_{\Lambda} = 0.73, \Omega_{M} = 0.27, and H_0 = 0.71. The correlation function for the CLASXS field over scales of 3 Mpc <s< 200 Mpc can be modeled as a power-law of the form \xi(s) = (s/s_0)^{-\gamma}, with \gamma = 1.6^{+0.4}_{-0.3} and s_0 = 8.0^{+1.4}_{-1.5} Mpc. The redshift-space correlation function for CDFN on scales of 1 Mpc$<s<$~100 Mpc is found to have a similar correlation length $s_0 = 8.55^{+0.75}_{-0.74}$ Mpc, but a shallower slope ($\gamma = 1.3 \pm 0.1$). The real-space correlation functions derived from the projected correlation functions, are found to be $r_0 = 8.1^{+1.2}_{-2.2}$ Mpc, and $\gamma = 2.1 \pm 0.5$ for the CLASXS field, and $r_0 = 5.8^{+1.0}_{-1.5}$ Mpc, $\gamma = 1.38^{+0.12}_{-0.14}$ for the CDFN field. By comparing the real- and redshift-space correlation functions in the combined CLASXS and CDFN samples, we are able to estimate the redshift distortion parameter $\beta = 0.4 \pm 0.2$ at an effective redshift $z = 0.94$.(abridged)