The empirical relation between the mass of SMBHs and the properties of their host galaxies is considered to be one of the most important outcomes caused by their coevolution over the cosmic timescale (e.g., Magorrian et al. 1998; Ferrarese & Merritt 2000; Kormendy & Ho 2013). Theoretical models for explaining the tight correlations have been proposed, but the origin is still unclear. To understand the nature of these correlations, it is critically important to study them beyond the local universe, characterizing how and when the relations have been established and evolved until now. So far, a large number of observational studies have extensively investigated the redshift dependence of the BH-to-bulge mass ratio of M
•/M
⋆ and overall suggested its positive redshift dependence, i.e., the ratio increases with redshift (Bennert et al. 2011; Schramm & Silverman 2013; Ding et al. 2020). Beyond z ∼ 6, the Atacama Large Millimeter/submillimeter Array (ALMA) is a powerful tool to measure the dynamical mass of gas in quasar host galaxies and allows us to explore the early stage of the BH/galaxy correlation (e.g., Wang et al. 2010, 2013; Venemans et al. 2017). In addition, observations with the Subaru HSC provide low-luminosity and less-massive BH samples, which are unique populations to determine the M
•/M
⋆ ratio at z > 6 (Izumi et al. 2019, 2021). Figure 11 shows the distribution of z > 6 quasars compiled in Izumi et al. (2021), together with those in the local universe (Kormendy & Ho 2013). First, the brightest z > 6 quasars with M
1450  −25 mag tend to have M
•/M
⋆ ratios higher than those seen in the local universe. Namely, the mass ratio for those brightest objects is boosted by a factor of ∼10 (blue dashed line; Pensabene et al. 2020). On the other hand, the fainter quasars with M
1450 >−25 mag appear to follow the local relation, although those BHs are considered to grow at rates of ≳ 0.05 SFR and will be overmassive at lower redshifts.
15


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In this paper, overmassive BHs are referred to as a BH population with a BH-to-galaxy mass ratio higher than that observed in the local universe; 



M•/M⋆≳4.9−0.5+0.6×10−3

 (Kormendy & Ho 2013). We employ this terminology to clearly contrast the difference between the overmassive and undermassive BH population with respect to the local value (see Figure 11). Note that a previous study by Agarwal et al. (2013) used a term of “obese BH,” which refers to a BH population dominating over the stellar mass of its host galaxy at least in the initial growing stage (i.e., M
•/M
⋆ > 1). We note that for all of the z > 6 samples, the values of the x-axis are not the bulge mass of their host galaxies but the dynamical mass measured by [C ii] 158 μm lines. In general, the dynamical mass is considered to be higher than the true bulge mass. With a high-resolution ALMA observation, Izumi et al. (2021) found that the gas dynamics of the core component of a low-luminosity quasar at z = 7.07 (HSC J1243+0100) is governed by rotation associated with a compact bulge and estimated its mass as ∼50% of the [C ii]-based dynamical mass. Therefore, the correlation at z > 6 might be shifted to the left if the conversion factor from the dynamical mass to the bulge mass is taken into account.
Citation: Izumi et al. 2019
Citation function: Uses
Citation: Ding et al. 2020
Citation function: Background