2007ApJS..172..396M

We present the first results of the measurements of angular auto-correlation functions (ACFs) of X-ray point sources detected in the XMM-Newton observations of the ∼2 deg² COSMOS field (COSMOS XMM-Newton). Significant positive signals have been detected in the 0.5-2 (SFT) band, in the angle range of 0.5'-24', while the positive signals were at the ∼2 and ∼3 σ levels in the 2-4.5 (MED) and 4.5-10 (UHD) keV bands, respectively. Correctly taking integral constraints into account is a major limitation in interpreting our results. With power-law fits to the ACFs without the integral constraint term, we find correlation lengths of θ_c=1.9"±0.3", 0.8"^+0.5"_–0.4", and 6"±2" for the SFT, MED, and UHD bands, respectively, for γ=1.8. The inferred comoving correlation lengths, also taking into account the bias by the source merging due to XMM-Newton PSF, are r_c~9.8±0.7, 5.8^+1.4_–1.7, and 12±2 h^–1 Mpc at the effective redshifts of z{d1}_eff~1.1, 0.9, and 0.6 for the SFT, MED, and UHD bands, respectively. If we include the integral constraint term in the fitting process, assuming that the power law extends to the scale length of the entire COSMOS XMM-Newton field, the correlation lengths become larger by ∼20%-90%. Comparing the inferred rms fluctuations of the spatial distribution of AGNs σ_8,AGNwith those of the underlying mass, the bias parameters of the X-ray source clustering at these effective redshifts are in the range b_AGN=1.5-4.