The Chandra COSMOS Legacy Survey: Clustering of X-ray selected AGN at 2.9<z<5.5 using photometric redshift Probability Distribution Functions

We present the measurement of the projected and redshift space 2-point correlation function (2pcf) of the new catalog of Chandra COSMOS-Legacy AGN at 2.9$\leq$z$\leq$5.5 ($\langle L_{bol} \rangle \sim$10$^{46}$ erg/s) using the generalized clustering estimator based on phot-z probability distribution functions (Pdfs) in addition to any available spec-z. We model the projected 2pcf estimated using $\pi_{max}$ = 200 h$^{-1}$ Mpc with the 2-halo term and we derive a bias at z$\sim$3.4 equal to b = 6.6$^{+0.60}_{-0.55}$, which corresponds to a typical mass of the hosting halos of log M$_h$ = 12.83$^{+0.12}_{-0.11}$ h$^{-1}$ M$_{\odot}$. A similar bias is derived using the redshift-space 2pcf, modelled including the typical phot-z error $\sigma_z$ = 0.052 of our sample at z$\geq$2.9. Once we integrate the projected 2pcf up to $\pi_{max}$ = 200 h$^{-1}$ Mpc, the bias of XMM and \textit{Chandra} COSMOS at z=2.8 used in Allevato et al. (2014) is consistent with our results at higher redshift. The results suggest only a slight increase of the bias factor of COSMOS AGN at z$\gtrsim$3 with the typical hosting halo mass of moderate luminosity AGN almost constant with redshift and equal to logM$_h$ = 12.92$^{+0.13}_{-0.18}$ at z=2.8 and log M$_h$ = 12.83$^{+0.12}_{-0.11}$ at z$\sim$3.4, respectively. The observed redshift evolution of the bias of COSMOS AGN implies that moderate luminosity AGN still inhabit group-sized halos at z$\gtrsim$3, but slightly less massive than observed in different independent studies using X-ray AGN at z$\leq2$.