AGN X-ray luminosity function and absorption function in the Early Universe ($3\leq z \leq 6$)

The XLF of AGN offers a robust tool to study the evolution and the growth of SMBHs over cosmic time. Owing to the limited area probed by X-ray surveys, optical surveys are routinely used to probe the accretion in the high redshift Universe $z\geq 3$. However, optical surveys may be incomplete because they are strongly affected by dust redenning. In this work, we derive the XLF and its evolution at high redshifts using a large sample of AGNs selected in different fields with various areas and depths covering a wide range of luminosities. Additionally, we put the tightest yet constraints on the absorption function in this redshift regime. In particular, we use more than 600 soft X-ray selected high-z sources in the Chandra Deep fields, the Chandra COSMOS Legacy survey and the XMM-XXL northern field. We derive the X-ray spectral properties for all sources via spectral fitting, using a consistent technique and model. For modeling the parametric form of the XLF and the absorption function, we use a Bayesian methodology allowing us to correctly propagate the uncertainties for the observed X-ray properties of our sources and also the absorption effects. The evolution of XLF is in agreement with a pure density evolution model similar to what is witnessed at optical wavelengths, although a luminosity dependent density evolution model cannot be securely ruled out. A large fraction ($60\%)$ of our sources are absorbed by column densities of $\rm N_H \geq 10^{23} cm^{-2} $, while $17$\% of the sources are CTK. Our results favor a scenario where both the ISM of the host and the AGN torus contribute to the obscuration. The derived BHAD is in agreement with the simulations, if one takes into account that the X-ray AGN are hosted by massive galaxies, while it differs from the one derived using JWST data. The latter could be due to the differences in the AGN and host-galaxy properties.