Covering factor in AGNs: Evolution versus selection

Abstract

In every proposed unification scheme for active galactic nuclei (AGNs), an integral element is the presence of circumnuclear dust arranged in torus-like structures, partially obscuring the nuclear (accretion-associated) radiation. A crucial model parameter in this context is the covering factor (CF), which can be defined as the ratio of the infrared luminosity of the dusty torus, $L_ IR $, to the accretion disk bolometric luminosity, $L_ agn $. Recent research has discussed the potential redshift evolution of the CF. Our study aims to determine whether this observed evolution is genuine or if selection effects significantly influence it. Based on cross-matched multiwavelength photometrical data from the five major surveys (SDSS, GALEX, UKIDSS, WISE, SPITZER), a sample of over 17,000 quasars was derived. The main parameters of quasars, such as black hole masses and the Eddington ratios, were calculated based on the spectroscopic data. The data were divided into two redshift bins: Low-$z$ quasars (redshift from 0.7 to 1.1) and High-$z$ quasars (from 2.0 to 2.4). The associated smaller datasets with higher quality data were constructed from the WISE W3 and W4 detections with S/N\,$>5$ and the Spitzer MIPS 24\,mu m photometry. The CF was determined by computing the ratio of integrated luminosities IR $ and $L_ agn $, using two methods: power-law fitting and the area between all photometric points. We explored different selection effects and their influence on CF estimates. Finally, statistical tests were employed to assess the hypothesis of CF evolution within the higher-quality datasets. 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. Luminosities obtained through direct integration of all photometric data points exhibit higher accuracy compared to values derived from a power-law approximation. The Efron Petrosian test confirmed the presence of luminosity evolution with redshift for both $L_ IR $ and $L_ agn $. The Low-$z$ and High-$z$ samples both exhibit a similar correlation between $L_ agn $ and $L_ IR low -z 0.11$ and log high -z 0.13$. Additionally, the Spitzer low -z 0.11$ and log high -z No discernible evolution of the CF was observed in the subsample of quasars with high supermassive black hole (SMBH) mass bin or high luminosities, as the CF values for Low-$z$ and High-$z$ quasars have the same distributions. The relationship between $L_ IR $ and $L_ agn $ deviates slightly from the expected 1:1 scaling, suggesting a more intricate connection between CF and $L_ agn $. However, no statistically significant dependence of CF on luminosities could be claimed across the entire dataset (merged redshifts). It is worth noting that the Low-$z$/low-luminosity portion of the CF distribution is influenced by contamination, possibly due to polar dust, as suggested in the literature, while the High-$z$/high-luminosity segment is affected by observational biases.