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 3 \times 10 ^ { -15 } { \thinspace erg } { \thinspace cm } ^ { -2 } { \thinspace s } ^ { -1 } 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 = 0.71 ( H _ { 0 } = 100 h km s ^ { -1 } Mpc ^ { -1 } ) .
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 .
We compare the correlation functions for hard and soft spectra sources in the CLASXS field and find no significant difference between the two groups .
We have also found that the correlation between X-ray luminosity and clustering amplitude is weak , which , however , is fully consistent with the expectation using the simplest relations between X-ray luminosity , blackhole mass , and dark halo mass .

We study the evolution of the AGN clustering by dividing the samples into 4 redshift bins over 0.1 Mpc < z < 3.0 Mpc .
We find a very mild evolution in the clustering amplitude , which show the same evolution trend found in optically selected quasars in the 2dF survey .
We estimate the evolution of the bias , and find that the bias increases rapidly with redshift ( b ( z = 0.45 ) = 0.95 \pm 0.15 and b ( z = 2.07 ) = 3.03 \pm 0.83 ) .
The typical mass of the dark matter halo derived from the bias estimates show little change with redshift .
The average halo mass is found to be \log~ { } ( M _ { halo } / M _ { \sun } ) \sim 12.1 .