tokens: stronger than the CF– L bol correlation. What causes this discrepancy? There are some possibilities, such as the difference in (i) redshift, (ii) sample selection (i.e., our sample is limited to type 1 quasars, while the sample in Ricci et al. 2017 is not), and (iii) definition of CF (i.e., is employed in this work, while a fraction of X-ray-obscured sources is employed in Ricci et al. 2017 ). It is hard to quantify, however, the influence of the difference in the sample selection and definition of the CF on the correlation strength, and it is beyond the scope of this work. We thus argue for the possibility that the difference in redshift could cause the discrepancy. Ricci et al. ( 2017 ) targeted nearby AGNs with a median redshift of z ∼ 0.037, whereas we focus on AGNs with much higher redshift up to z = 0.7. Figure 12 shows the redshift dependence of the CF– λ Edd relation. We find that the CF of AGNs with z 0.12 (which is similar to that of the sample in Ricci et al. 2017 ) tends to strongly depend on λ Edd , with a correlation coefficient of r = − 0.49 ± 0.32, while CF– λ Edd for AGNs at z > 0.2 shows weaker correlations than that at z 0.12. This indicates that the aforementioned discrepancy can be explained by the difference in redshift between the samples in Ricci et al. ( 2017 ) and this work. We also remind that our correlation analysis would be affected by the Malmquist bias, which could make the correlation strength weaker, as discussed in Section 4.2.2 . Figure 12. CF as a function of λ Edd . The blue, green, orange, and gray shaded regions represent quasars with z 0.12, 0.12 z 0.2, and z > 0.2 and the entire sample, respectively. This result also might suggest that the CF decreases with increasing redshift for at least z 0.7, a trend that is consistent with what is reported in Toba et al. ( 2014 ), although there is large uncertainty. On the other hand, the fraction of obscured X-ray AGNs increases with redshift for the same luminosity (e.g., Ueda et al. 2014 ). This discrepancy might be caused by the difference in sample selection and definition of CF. 4.6.2. BH Mass Dependence Recently, Kawakatu et al. ( 2020 ) constructed a model of a nuclear starburst disk supported by the turbulent pressure from Type II supernovae and investigated how the CF depends on AGN properties by taking account of anisotropic radiation pressure from AGNs. They found that the CF strongly depends on λ Edd for AGNs with M BH 10 8 M ⊙ , while the dependence of the CF on λ Edd is much weaker for AGNs with M BH > 10 9 −10 10 M ⊙ . Although they did not incorporate the AGN polar dust outflow, it is worth checking the dependence of the CF– λ Edd correlation on M BH . Figure 13 shows how the difference in M BH would affect the correlation strength of CF– λ Edd . The resultant r of CF– λ Edd for quasars with , , and are −0.56 ± 0.07, −0.50 ± 0.05, and −0.52 ± 0.22, respectively. This result indicates that the CF of quasars with 10 8 M ⊙ strongly depends on λ Edd .
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