The disk-torus system in active galactic nuclei: possible evidence of highly spinning black holes

We study the ratio $R$ between the luminosity of the torus and that of the accretion disk, inferred from the relativistic model KERRBB for a sample of approximately 2000 luminosity-selected radio-quiet Type I active galactic nuclei from the Sloan Digital Sky Survey catalog. We find a mean ratio $R \approx 0.8$ and a considerable number of sources with $R \gtrsim 1$. Our statistical analysis regarding the distribution of the observed ratios suggests that the largest values might be linked to strong relativistic effects due to a large black hole spin ($a > 0.8$), despite the radio-quiet nature of the sources. The mean value of $R$ sets a constraint on the average torus aperture angle (in the range $30^{\circ} < \theta_{\rm T} < 70^{\circ}$) and, for about one-third of the sources, the spin must be $a > 0.7$. Moreover, our results suggest that the strength of the disk radiation (i.e., the Eddington ratio) could shape the torus geometry and the relative luminosity ratio $R$. Given the importance of the involved uncertainties on this statistical investigation, an extensive analysis and discussion have been made to assess the robustness of our results.