Covering factor in AGNs: evolution versus selection

In every proposed unification scheme for Active Galactic Nuclei (AGN), an integral element is the presence of circumnuclear dust arranged in torus-like structures. A crucial model parameter in this context is the covering factor (CF), defined as the ratio between the infrared luminosity of the dusty torus $L_{\rm IR}$, and the accretion disk bolometric luminosity $L_{\rm agn}$. Our study aims to determine whether CF evolution is genuine or if selection effects significantly influence it. Based on cross-matched multiwavelength photometrical data from the five major surveys (SDSS, GALEX, UKIDSS, WISE, SPITZER), a sample of almost 2,000 quasars was derived. The main parameters of quasars, such as black hole masses and the Eddington ratios, were calculated based on the spectroscopic data. The data were divided into two redshift bins: Low-$z$ (redshift ~1) and High-$z$ (redshift ~2) quasars. We identified an issue with the accuracy of the WISE W4 filter. Whenever feasible, it is recommended to utilize SPITZER MIPS 24 $\mu$m data. The calculated median CF values for the highest quality SPITZER data are comparable within errors $\log$ CF$_{\textrm{low}-z} = -0.19\pm 0.11$ and $\log$ CF$_{\textrm{high}-z}= -0.18\pm 0.11$. The Efron & Petrosian test confirmed the presence of luminosity evolution with redshift for both $L_{\rm IR}$ and $L_{\rm agn}$. Both the Low-$z$ and High-$z$ samples exhibit a similar correlation between $L_{\rm agn}$ and $L_{\rm IR}$. No discernible evolution of the CF was observed in the subsample of quasars with high SMBH mass bin or high luminosities. The relationship between $L_{\rm IR}$ and $L_{\rm agn}$ deviates slightly from the expected 1:1 scaling. However, no statistically significant dependence of CF on luminosities could be claimed across the entire dataset.