Faint Quasars Live in the Same Number Density Environments as Lyman Break Galaxies at z ∼ 4

The HSC-SSP survey started in early 2014 and will include 300 nights until its completion by 2020. The HSC is equipped with 116 2K × 4K Hamamatsu fully depleted CCDs, among which 104 CCDs are used to obtain scientific data over a field of view of 15 in diameter. The detailed system design is summarized by Miyazaki et al. (2018). For the CCD dewar and camera system design, one should refer to Komiyama et al. (2018). This study is based on the Wide layer of the HSC-SSP, which has wide-area coverage and high sensitivity through five optical bands (g, r, i, z, and y) with transmission functions (Kawanomoto et al. 2018) that are roughly similar to the SDSS filter curves. The total exposure times are 10 minutes in the g and r bands and 20 minutes in the i, z, and y bands. The on-site quality assurance system for the HSC (OSQAH; Furusawa et al. 2018) is used in the HSC-SSP observations. The HSC data (DR S16A; Aihara et al. 2018b) in the Wide layer have already produced an extremely wide field image of >200 deg² with a median seeing value of 06–08. The survey design is presented in Aihara et al. (2018a). Data reduction is performed with the dedicated pipeline hscPipe (version 4.0.2, Bosch et al. 2018), which is a modified version of the Large Synoptic Survey Telescope software stack (Ivezic et al. 2008; Axelrod et al. 2010; Jurić et al. 2015). The astrometric and photometric calibrations are associated with the Pan-STARRS1 system (Schlafly et al. 2012; Tonry et al. 2012; Magnier et al. 2013). The fluxes and colors of the sources are measured with cModel, which is achieved by fitting two-component, point-spread function (PSF)-convolved galaxy models to the source profile (Abazajian et al. 2004).

We use the z ∼ 4 protocluster candidate catalog constructed from DR S16A (Toshikawa et al. 2018). We briefly summarize the key steps of the catalog construction here.

First, the g-dropout galaxies were selected from five independent fields: W-XMMLSS (R.A. = 1^h36^m00^s ∼ 3^h00^m00^s, decl. = −6°00'00'' ∼ −2°00'00''), W-Wide12H (R.A. = 11^h40^m00^s ∼ 12^h20^m00^s, decl. = −2°00'00'' ∼ 2°00'00''), W-GAMA15H (R.A. = 14^h00^m00^s ∼ 15^h00^m00^s, decl. = −2°00'00'' ∼ 2°00'00''), W-HECTOMAP (R.A. = 15^h00^m00^s ∼ 17^h00^m00^s, decl. = 42°00'00'' ∼ 45°00'00''), and W-VVDS (R.A. = 22^h00^m00^s ∼ 23^h20^m00^s, decl. = −2°00'00'' ∼ 3°00'00''). Here, the following criteria were used, as provided in van der Burg et al. (2010):

$$\begin{eqnarray}&&1.0\lt g-r,\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&r-i\lt 1.0,\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&1.5(r-i)\lt (g-r)-0.80,\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&r\leqslant {m}_{\mathrm{lim},3\sigma },\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&i\leqslant {m}_{\mathrm{lim},5\sigma },\end{eqnarray} \tag{ 5 }$$

where m_lim,3σ and m_lim,5σ are 3σ and 5σ limiting magnitudes, respectively. If the objects were not detected in the g-band filter at 3σ, their g-band magnitudes were replaced with the corresponding 3σ limiting magnitudes. The red galaxies at intermediate redshifts and dwarf stars could satisfy the color selection criteria. The contamination rate from these objects was evaluated as a maximum of 25% at i < 25.0 (Ono et al. 2018). The g-dropout selection completeness window was estimated to be z = ${3.8}_{-0.5}^{+0.5}$ by the Monte Carlo method (Ono et al. 2018), as illustrated in Figure 1.

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Owing to the sky conditions in the observation, the depth over the entire regions is inhomogeneous, which causes large scatter in the number of detected objects in the different fields, leading to difficulties in comparing the number densities among their fields. Thus, only homogeneous depth regions were used, where the g-, r-, and i-band 5σ limiting magnitudes were fainter than 26.0, 25.5, and 25.5 mag, respectively. The resultant effective area after removing the masked region around the bright objects was 121 deg². In this area, 259,755 g-dropouts down to i < 25.0 were detected.

Subsequently, the fixed aperture method was applied to determine the surface density contour maps of the g-dropout galaxies. Apertures with a radius of 18, corresponding to 0.75 physical Mpc (pMpc) at z ∼ 4, were distributed in the sky of the HSC Wide layer. This aperture size is comparable with the typical protocluster size at this epoch with a descendant halo mass of ≳10¹⁴ M_⊙ at z = 0 (Chiang et al. 2013). The resolution of the density map was 1 × 1 arcmin². The overdensity significance was defined by (N-$\bar{N}$)/σ, where N is the number of g-dropout galaxies in an aperture, and $\bar{N}$ and σ are the average and standard deviation of N over all of the fields, respectively. ($\bar{N}$, σ) was estimated to be (6.4, 3.2) (Toshikawa et al. 2018). It was assumed that the number density of the g-dropout galaxies in the masked regions was the same as the average. However, the apertures in which >50% of the area was masked were excluded. As the contaminants of foreground objects distribute randomly over the sky, the overdensity significance should not be greatly affected by the contamination (Toshikawa et al. 2012).

The protocluster candidates were defined as overdense regions with >4σ overdensity significance. Although large scatter exists owing to projection effects, the surface overdensity significance is closely correlated with the descendant halo mass at z = 0. Toshikawa et al. (2016) demonstrated that >76% of >4σ overdense regions of g-dropouts were expected to evolve into dark matter halos with masses of >10¹⁴ M_⊙ at z = 0, whereas overdense regions with less than 4σ significance could not be distinguished from fields owing to the projection effect. According to Toshikawa et al. (2018), as a result of the projection effect, the protocluster sample is biased to the richest structure, the average descendant halo mass of which is expected to be ∼5 × 10¹⁴M_⊙, with a high purity (>76%) but low completeness (∼6%). By clustering analysis, their mean halo mass at z ∼ 4 was estimated to be ${2.3}_{-0.5}^{+0.5}\times {10}^{13}{h}^{-1}{M}_{\odot }$, which is comparable to galaxy group halo mass (Toshikawa et al. 2018). It should be noted that the success rate of this technique has already been established by a previous study on the ∼4 deg² of the CFHTLS Deep Fields, as the precursor of this HSC protocluster research, followed by Keck/DEIMOS and Subaru/FOCAS spectroscopy (Toshikawa et al. 2016). The authors carefully checked each >4σ overdense region, and removed 22 fake detections of mainly the spiral arms of local galaxies (Aihara et al. 2018b). As a result, 179 protocluster candidates at z ∼ 4 in the HSC Wide layer with overdensity significance ranging from 4 to 10σ were obtained.

The z ∼ 4 quasar sample was constructed from the same DR S16A as used in Akiyama et al. (2018). We present the essence of the selection below.

The authors selected the quasar sample conservatively in the effective survey area of 172.0 deg², which is covered by grizy-bands and masked around bright objects (i < 22) to avoid possible failure of the HSC pipeline deblending process for faint objects in the outskirts of the bright objects (Akiyama et al. 2018). Stellar objects were extracted when their second-order adaptive moments (Hirata & Seljak 2003) were comparable to the PSF size.

The z ∼ 4 quasar candidates were selected by using the grz-band color–color selection,

$$\begin{eqnarray}&&r-z\,\lt \,0.65\,(g-r)-0.30,\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&r-z\,\lt \,3.50\,(g-r)-2.90,\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&g-r\,\lt \,1.50,\end{eqnarray} \tag{ 8 }$$

and izy-band color–color selection,

$$\begin{eqnarray}&&z-y\,\lt \,-2.25\,(i-z)+0.400,\end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray}&&-0.3\,\lt \,i-z.\end{eqnarray} \tag{ 10 }$$

The latter izy-band criterion was applied to remove contaminations such as red galactic stars and several outliers. Akiyama et al. (2018) limited the sample to i > 20 because bright objects (i < 20) are affected by saturation or nonlinearity effects. They carefully removed objects around bright stars and galaxies, as well as those close to faint halos and satellite tracks around bright stars to prevent unreliable photometry.

A total of 1668 quasar candidates, with photometric redshifts of $z={3.9}_{-0.3}^{+0.4}$ (Figure 1), were detected. The UV absolute magnitudes of the HSC quasars lie in the range of −26 to −22. The faintest UV magnitude is ∼4 mag fainter than that of the SDSS quasars selected at z ∼ 4 by Akiyama et al. (2018). The contamination rate of the HSC quasars is <40% at i < 23.5, and >50% at i > 23.5. We confirm that our results do not change, even if the sample is limited to bright quasars with i < 23.5 (Section 3). The completeness is higher than 80% at i < 23.0 and decreases to ∼40% at i = 24. Note that the survey area is wider than that of our g-dropout galaxies.

We cross-match the effective areas used in the protocluster and quasar searches to examine their possible correlation fairly. As a result, a cross-matched effective area of ∼98 deg² is established. In total, 146 protoclusters (210,627 g-dropout galaxies with i < 25.0) and 570 HSC quasars in the effective area are obtained. As the redshift distribution of the HSC quasars is slightly narrower than that of the g-dropout galaxies, as illustrated in Figure 1, we aim to determine not whether the g-dropout overdense regions host the HSC quasars, but whether the number density environments around the HSC quasars are overdense regions.

We derive the distribution of the local maxima of the overdensity significances within a typical protocluster radius centered on the HSC quasars. This simple approach is sufficient to understand whether or not the quasars reside in the protoclusters. Note that in this approach, we cannot assess the possible local clustering signal within <18 radius from the quasars, as the overdensity significances are calculated by using apertures with a radius of 18.

The distributions of the maximum overdensity significances within circles with radii of a = 1' centered on the quasars and random points are illustrated in the upper panel of Figure 2. Here, the random points are 570 points distributed uniformly on the cross-matched effective area, and their overdensity significance distribution is estimated by taking the average of 10,000 realizations. We find that the HSC quasars tend to reside in denser regions than the random points. In fact, the P-value in the Kolmogorov–Smirnov (KS) test for their distributions is estimated to be ∼0.

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To obtain a quantitative understanding of the number density-based environment of the HSC quasars, we also compare the overdensity distributions around the HSC quasars with those around the g-dropout galaxies. The probability distribution of the maximum overdensity significances within the a = 1' radius centered on the g-dropout galaxies is also depicted in the upper panel of Figure 2. The overdensity significance distribution of the quasars is found to be significantly the same as that of the g-dropout galaxies. Their KS test P-value is 0.09. This result implies that the clustering strength of quasars and g-dropout galaxies is similar at least at the scales probed herein (i.e., 18 and 3').

As shown in Figure 3, we also find that only 4 out of 570 ($={0.7}_{-0.4}^{+0.4} \%$, where the error is assumed as Poisson error) HSC quasars are associated with the >4σ overdense regions within the 18 separation.¹³ The positions of the protoclusters associated with the quasars are summarized in Table 1. Among the 570 randomly selected g-dropout galaxies, the fraction of those associated with the >4σ overdense regions within the separation radius of 18 is ${0.5}_{-0.3}^{+0.3} \%$. Here, the error is estimated by random sampling with replacement of the 570 g-dropout galaxies 10,000 times (bootstrap method). As a result, this ratio is the same as that of the HSC quasars within 1σ error. This suggests that the HSC quasars do not preferentially appear in the richest protoclusters.

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Table 1.  List of Protoclusters Associated with Quasars

Namea	R.A. (J2000)	Decl. (J2000)	Σb	Separationc
			(σ)	(pMpc)
QSO1	02h15m23.13s	−02°40'361	5.4	0.74
QSO2	02h18m5393	−05°33'076	5.9	0.54
QSO3	02h25m2723	−04°26'312	6.1	0.62
QSO4	14h47m1304	−01°21'586	4.6	0.42
QSO5	15h56m2298	+44°16'575	4.3	0.15
QSO6	22h14m5838	+01°07'361	4.5	0.55

Notes.

^aQSO4 and QSO6 are SDSS quasars, and the others are HSC quasars. ^bPeak significance of the protocluster. ^cSeparation from quasar to nearest protoclusters.

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Note that the radial size of the protocluster at z ∼ 4 could extend to a maximum of ∼30 (Chiang et al. 2013). Even if we use a radius of a = 3' (=1.2 pMpc) to evaluate the local maximum distribution of the overdensity significances, no significant difference of the overdensity significance distributions between the quasars and the g-dropout galaxies is found, as indicated in the lower panel of Figure 2. The KS test P-value for their distributions is 0.15. Moreover, only 22 out of 570 ($={3.9}_{-0.8}^{+0.8} \%$) quasars reside in the >4σ overdense regions.¹⁴ Again, the ratio is consistent with that of the g-dropout galaxies within 1σ error; among the 570 randomly selected g-dropout galaxies, the fraction of those associated with the protoclusters within the 30 separation is ${4.4}_{-0.9}^{+0.9} \%$. The results do not change even if the HSC quasar sample is limited to i < 23.5 bright ones as shown in Figure 2.

In our analysis, we can ignore quasar contaminants in the g-dropout galaxy sample as the quasar fraction of the g-dropout galaxies is only ∼0.01. Here, this value is estimated by using the g-dropout luminosity function, f, and the galaxy fraction, w, given by Ono et al. (2018), and taking a weighted-average of (1 − f) with weight w on a magnitude range of i < 25. In fact, even if we use a subsample of the faintest g-dropout galaxies with i > 24, where the quasar contamination is much lower (Ono et al. 2018), to measure the overdensity distribution, our results do not change (Figure 2).

We stack overdensity significance maps around the HSC quasars and the g-dropout galaxies with a radial scale of 10' (∼4 pMpc) to examine the possible difference in the galaxy density environments between the HSC quasars and g-dropout galaxies at any scale. Figure 4 presents the radial profiles of the stacked overdensity significance maps centered on the HSC quasars and the g-dropout galaxies. For a fair comparison of their density environments, we exclude the 570 HSC quasars from the g-dropout galaxy sample. We find that the galaxy density profile around the HSC quasars is statistically identical to that of the g-dropout galaxies at all scales within a 95% confidence interval.

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We found that 4 (22) out of the 570 HSC quasars; that is, ${0.7}_{-0.4}^{+0.4}$ $({3.9}_{-0.8}^{+0.8}) \%$ of the HSC quasars, are associated with the overdense regions with >4σ overdensity significances within 1.8 (3.0) arcmin separation at z ∼ 4 (but see the caveat explained in Section 4.2). Now, we need to confirm that this ratio is consistent with the perspective of the quasar halo mass.

We use the extended Press–Schechter (EPS) model (Press & Schechter 1974; Bond et al. 1991; Bower 1991; Lacey & Cole 1993) to examine whether or not the quasar halos at z ∼ 4 evolve into the cluster halos at z ∼ 0, or, in other words, their quasars can belong to protoclusters at z ∼ 4. According to the EPS model, the conditional probability ${P}_{2}({M}_{t2},{z}_{2}| {M}_{t1},{z}_{1})$ that a halo with a mass of M_t1 at a redshift of z₁ evolves into a halo with a mass of M_t2 at a later redshift of z₂ is estimated as follows (Hamana et al. 2006):

$$\begin{eqnarray}&&\begin{array}{l}{P}_{2}({M}_{t2},{z}_{2}| {M}_{t1},{z}_{1}){{dM}}_{t2}\\ \ \ =\ \displaystyle \frac{1}{\sqrt{2\pi }}\displaystyle \frac{{\delta }_{c2}({\delta }_{c1}-{\delta }_{c2})}{{\delta }_{c1}}{\left[\displaystyle \frac{{\sigma }_{1}^{2}}{{\sigma }_{2}^{2}\left({\sigma }_{1}^{2}-{\sigma }_{2}^{2}\right)}\right]}^{\tfrac{3}{2}}\\ \quad \ \times \ \exp \left[-\displaystyle \frac{{\left({\sigma }_{2}^{2}{\delta }_{c1}-{\sigma }_{1}^{2}{\delta }_{c2}\right)}^{2}}{2{\sigma }_{1}^{2}{\sigma }_{2}^{2}({\sigma }_{1}^{2}-{\sigma }_{2}^{2})}\right]\left|\displaystyle \frac{d{\sigma }_{2}^{2}}{{{dM}}_{t2}}\right|{{dM}}_{t2},\end{array}\end{eqnarray} \tag{ 11 }$$

where σ_i and δ_ci are the rms density fluctuation smoothed over spheres of a mass of M_ti at z_i and the critical overdensity threshold to collapse at z_i, respectively. Subsequently, the conditional mass function ${n}_{2}({M}_{t2},{z}_{2}| {M}_{t1},{z}_{1})$ is estimated from Equation (11) (Hamana et al. 2006):

$$\begin{eqnarray}&&\begin{array}{l}{n}_{2}({M}_{t2},{z}_{2}| {M}_{t1},{z}_{1}){{dM}}_{t2}\\ \quad \ \propto \ \displaystyle \frac{1}{{M}_{t2}}{P}_{2}({M}_{t2},{z}_{2}| {M}_{t1},{z}_{1}){{dM}}_{t2}.\end{array}\end{eqnarray} \tag{ 12 }$$

He et al. (2018) estimated the average halo masses of ${1.46}_{-1.01}^{+1.71}\times {10}^{12}{h}^{-1}{M}_{\odot }$ for the HSC quasars at $z={3.9}_{-0.3}^{+0.4}$ by means of clustering analysis. We set ${M}_{t1}={1.46}_{-1.01}^{+1.71}\,\times {10}^{12}{h}^{-1}{M}_{\odot }$, ${z}_{1}={3.9}_{-0.3}^{+0.4}$, and z₂ = 0.0. Thereafter, the halo mass distribution at z = 0 can be calculated from Equations (11) and (12). We find that ${8.4}_{-6.6}^{+14.6} \%$ of the halos with a mass of ${1.46}_{-1.01}^{+1.71}\times {10}^{12}{h}^{-1}{M}_{\odot }$ at z = 3.9 are expected to evolve into halos with a mass of $\gt {10}^{14}{M}_{\odot }$ at z = 0. The ratio is almost the same, with 1.2σ (0.7σ) significance, as that of the HSC quasars associated with the >4σ overdense regions out of the entire sample within 1.8 (3.0) arcmin separation. This means that our findings are consistent with the expected halo mass growth.

Our overdense region sample exhibits high incompleteness owing to the large redshift error of the g-dropout galaxies (Section 2.2). We quantitatively evaluate to what extent the possible clustering signals around the HSC quasars are diluted by this projection effect.

A quasar is assumed to exist in a typical protocluster-scale cylinder, with a diameter of 1.5 (1 + z) comoving Mpc (cMpc) along the celestial sphere direction and a height of 1.5 (1 + z) cMpc along the line-of-sight (LoS) direction at z = 3.9, which corresponds to the median redshift of the HSC quasars. The cylinder space is assumed to be an overdense region with n times the average galaxy density (cMpc⁻³) at the cylinder scale. By integrating the g-dropout selection function (Figure 1), the redshift window width of the g-dropout galaxy is estimated to be >10 times the cylinder scale (protocluster scale) along the LoS direction. Thus, a cylinder with n > 20 times the average density can be achieved for our >4σ overdense regions, using the definition of the overdensity significance (N-$\bar{N}$)/σ (Section 2.2). Conversely, if the vicinity of a quasar is an overdense region with < 20 times the average density, the density region is not detected as our protocluster sample. This implies that few >4σ overdense regions (the most prominent ones) are detected (the completeness is ∼6%; see Section 2.2), and therefore, a higher fraction of quasars may be associated with protoclusters.

In order to examine the possible dependency of the quasar environments on their luminosities, we compare our findings with the results of U18, in which the g-dropout galaxy number density environments of luminous quasars at z ∼ 4 were investigated by using HSC-detected protoclusters. The method for selecting the g-dropout galaxies and the protoclusters were the same as in the present study. The quasars were extracted from the SDSS quasar catalog based on SDSS DR12 (Pâris et al. 2017). The SDSS DR12 quasar catalog is the final SDSS-III quasar catalog, which contains 297,301 spectroscopically confirmed quasars over a wide redshift range of 0.041 <z < 6.440 in an area covering approximately 10,200 deg² of the sky. A total of 151 SDSS quasars are found in the effective areas of the HSC protocluster search within the g-dropout redshift range of z = 3.3–4.2. The UV absolute magnitudes of this sample are brighter than ∼−26. For details, please refer to U18.

We find that our results in the present study support our previous study of U18; 2 and 3 out of 151 SDSS quasars (${1.3}_{-0.9}^{+0.9} \%$ and ${2.0}_{-1.1}^{+1.1} \%$, where these errors are assumed to be Poisson errors) are found to be spatially associated with the >4σ overdense regions within 18 and 30 separations, respectively. Their ratios are consistent, within a 1σ error, with the case of the HSC quasars. This fact suggests that the number densities of the g-dropouts around the quasars are expected to be independent of their luminosity over a wide range of their UV absolute magnitudes, M_UV = −28 ∼ −22. This may arise from the fact that the halo mass is almost independent of the quasar luminosity (e.g., Eftekharzadeh et al. 2015). In fact, He et al. (2018) found that the halo masses of the HSC quasars were consistent with those of the SDSS quasars.¹⁵

As illustrated in Figure 3, two out of the four HSC quasars associated with the >4σ overdense regions, namely QSO1 and QSO2, could constitute possible quasar pairs with their projected separations of 96 (=4 pMpc). In Onoue et al. (2018), a quasar pair was defined as two quasars with their separation closer than the size of massive protoclusters that are expected to evolve into the descendant halos with halo masses of 10¹⁵M_⊙ at z = 0. Concretely, they extracted the quasar pairs with their projected proper distance of R_⊥ < 4 pMpc and velocity offset of ΔV < 3000 km s⁻¹. We define the two quasars with their projected proper distance R_⊥ < 4 pMpc as the "possible quasar pairs," as we have no information regarding the velocity offset in the HSC quasar sample. Our finding is likely to relate to the results found in the SDSS quasars by Onoue et al. (2018), whereby the SDSS quasar pairs tended to reside in the galaxy overdense regions at z ∼ 4. Spectroscopy is required for our possible quasar pairs to confirm the reality of the quasars and to measure their redshift differences.

Our findings show no preference of quasar activity in the z ∼ 4 richest protocluster environment, where gas-rich galaxy major mergers are expected to occur frequently (e.g., Gottlöber et al. 2001; Stewart et al. 2009; Jian et al. 2012; Hine et al. 2016). This fact is likely to be against the simple expectation that almost all gas-rich major mergers result in quasars. We show some implications for our results below.

First, the major merger rates in our protocluster regions may not be so high that we cannot confirm the enhancement in our statistical accuracy. The projection effect discussed in Section 4.2 prevents the detection of the possible enhancement. The major merger rates can be diluted to be <0.1 times owing to the effect. Using Hubble Space Telescope imaging combined with spectroscopic observation for the quasar-hosted protoclusters is necessary to estimate the exact merger rates (Hine et al. 2016).

Second, if the major mergers occur with nonnegligible probability in the protocluster regions, they may not activate SMBHs effectively. Almost all of the high-z quasars may not appear through the major mergers but secular processes (e.g., Fanidakis et al. 2012). Several recent observations have provided no evidence that quasar activity is enhanced by major mergers. Mechtley et al. (2016) examined whether or not quasar hosts exhibit distortions owing to major mergers by comparing 19 quasar host galaxies to 84 inactive galaxies at z ∼ 2. These authors found that there was no significant difference in the distortion fractions between the quasar hosts and inactive galaxies, meaning that the triggering mechanism of the quasars was not always a major merger. According to Yang et al. (2018), the accretion rates of SMBHs are strongly dependent on the stellar masses of the host galaxies, independently of their sub-Mpc or global 1–10 Mpc scale environment. Ricarte et al. (2019) also found that the relation between the black hole accretion rate and star formation rate does not depend on the host galaxy environments, and identified no evidence of a connection between black hole growth and galaxy mergers (but see Yoon et al. 2019). Trakhtenbrot et al. (2017) determined diverse host galaxy properties of luminous quasars at z ∼ 5 in terms of SMBH fueling mechanisms, suggesting that a galaxy merger may not be a necessary condition for either process, and other mechanisms that are not related to major mergers may drive the rapid growth of the most massive BHs. Ito et al. (2019) recently found that extreme UV-bright galaxies that are expected to have experienced a starburst phase caused by frequent mergers exist in our protocluster regions. Third, our optical observation might miss some quasars in the rich protoclusters owing to the quasars being in the dust-obscured phase, which appears immediately after experiencing a major merger (Hopkins et al. 2008). Recently, Kubo et al. (2019) stacked the Planck images of the same HSC protocluster regions as those used in the present study, and found a significant (>5σ) excess at mid-IR wavelengths, suggesting that the richest protoclusters at z ∼ 4 may also contain a significant population of obscured AGN. Combining these results with our findings appears to be challenging for the merger scenario (e.g., Hopkins et al. 2008), which predicts that quasars are the descendants of obscured AGNs. This study combined with that of Kubo et al. (2019) simply leads to the inconsistent argument that the progenitors and descendants are not in the same environment, although many uncertainties should be taken into account, such as the quasar duty cycle, and the duration between the major merger and quasar activation. Perhaps not all obscured AGNs will evolve into quasars. Moreover, some of them tend to evolve into high-z radio galaxies (HzRGs) in the most overdense regions (the most massive halos) because frequent mergers build up spins of the SMBHs and cause them to launch radio jets (Fanidakis et al. 2013; Hatch et al. 2014; Orsi et al. 2016). The quasar activity, which is maintained by the gas cooling and accretion onto a central SMBH, will be suppressed by radio-mode feedback in a massive halo (e.g., Fanidakis et al. 2013). As a result, HzRGs are expected to be associated with the richest protoclusters. Clustering measurements are absolutely essential for exact interpretations of the major merger scenario. We will conduct the clustering analysis of HzRGs and protoclusters based on the HSC-SSP data in forthcoming research.

One should refer to the possible enhancement of quasar activity due to cosmic cold gas. Cosmic cold gas inflow in the early universe could also provide a significant amount of gas supply to the SMBHs preferentially in large-scale overdense environments, so that quasar activity could be enhanced in the overdense regions in contrast to our observational results (e.g., Kereš et al. 2005; Dekel & Birnboim 2006; Di Matteo et al. 2008; Ocvirk et al. 2008; Sijacki et al. 2009; Costa et al. 2014). According to Dekel & Birnboim (2006), cold streams at z > 2 should still not be fully disrupted in rare massive halo objects with >10¹²M_⊙, even if they are diluted by a hot medium heated by quasar feedback. However, recent cosmological hydrodynamic simulations (e.g., Di Matteo et al. 2008) demonstrated that strong feedback on massive halos with >10¹²M_⊙ at z ∼ 6 stop the cold stream to penetrate into the central BH. These authors mentioned that even at z < 6 in massive halos the feedback energy clearly affects the inflowing cold gas.