Clustering of galaxies around AGNs in the HSC Wide survey^†

Abstract

1 Introduction

Most galaxies have a supermassive black hole (SMBH) with mass greater than ∼ 10⁶ M_⊙ at their center (Richstone et al. 1998). Observations of the local Universe have revealed that the mass of the SMBH correlates with the several properties of the bulge component of the host galaxy (Magorrian et al. 1998; Ferrarese & Merritt 2000; Gebhardt et al. 2000; Ho 2007). This observational evidence suggests that a SMBH and its host galaxy co-evolve in a coordinated way in spite of the nine orders of difference in their physical size scale (Kormendy & Ho 2013).

SMBHs grow through the accretion of gas from their host galaxies or large-scale environment. Accretion in a secular mode, which arises through internal dynamical processes such as bar or disk instability or external processes driven by galaxy interaction, is one of the mechanisms to deliver the gas into the SMBH (Kormendy & Kennicutt 2004). As the mass accretion rate of the secular mode cannot be as high as to maintain the activity seen in bright quasi-stellar objects (QSOs) (Menci et al. 2014), this mode could operate in lower-luminosity active galactic nuclei (AGNs).

A merger of galaxies can induce gravitational torques which drive inflows of cold gas toward the center of galaxies (e.g., Hopkins et al. 2008). Observational evidence has been obtained that shows the relation between AGN activity and a galaxy merger (e.g., Sanders et al. 1988; Treister et al. 2012). The activity of the bright QSOs could be explained by this model. Although the accretion can be at its most efficient mode, it is also expected that AGN feedback promptly operates and stops the gas inflows when the mass of the SMBH becomes as large as 10⁹ M_⊙ (Fanidakis et al. 2013).

As an alternative process to make a SMBH evolve above 10⁹ M_⊙, quiescent gas accretion from the hot halo (Kereš et al. 2009; Fanidakis et al. 2013) and/or recycled gas from evolving stars (Ciotti & Ostriker 2001, 2007) has been proposed. According to the predictions of semi-analytical modeling by Fanidakis et al. (2013), AGNs fueled in the hot-halo mode are located in more massive dark matter halos than the AGNs fueled in the merger-driven starburst mode.

The mass of the host dark matter halo that AGNs reside in can be inferred from the auto-correlation function of AGNs at distance scale >1 Mpc. According to the analysis of auto-correlation of SDSS QSOs by Ross et al. (2009), the halo mass is almost constant at ∼ 2 × 10¹² h ^{− 1} M_⊙ in the redshift range from 0.3 to 2.2. It is also possible to estimate the halo mass from the cross-correlation between AGNs and galaxies if the auto-correlation functions of galaxies are precisely obtained. According to the cross-correlation

studies, the dark matter halo mass is estimated to be 10¹²–10^13.5 h ^{− 1} M_⊙ depending on the detection wavelength of the AGNs (e.g., Hickox et al. 2009; Krumpe et al. 2012). Studies on clustering and/or environments of AGNs have also been reported elsewhere (e.g., Croom et al. 2005; Coil et al. 2009; Silverman et al. 2009; Donoso et al. 2010; Allevato et al. 2011; Bradshaw et al. 2011; Shen et al. 2013; Mountrichas et al. 2013; Zhang et al. 2013; Georgakakis et al. 2014; Krumpe et al. 2015; Ikeda et al. 2015).

Although the number of AGN clustering studies published so far is large, the studies focused on the relation between the mass of the central BH, which is the most fundamental property on which the history of mass accretion is imprinted, and also the properties of galaxies such as color and luminosity function around it are very limited. Since the interaction in the scale of groups or clusters of galaxies can induce concurrent activities of star formation, mass accretion to the central BH, and transition to the red sequence in the constituent galaxies, the contribution of such large-scale phenomena to the evolution of SMBHs can be inferred from the surrounding galaxies.

Shen et al. (2009) measured the clustering of QSOs for samples divided by their BH mass at redshifts 0.4–2.5 and did not find significant dependence, except for the most massive sample, for which marginally larger clustering was found on the ∼2σ level. Komiya et al. (2013) examined the dependence of the AGN–galaxy clustering on the BH mass at a redshift range from 0.3 to 1.0 using the UKIRT Infrared Deep Sky Survey (UKIDSS) data for the galaxy samples, and found that the cross-correlation length increases above 10^8.2 M_⊙. Krolewski and Eisenstein (2015) also examined the BH mass dependence of the AGN–galaxy clustering at redshift ∼0.8 using Sloan Digital Sky Survey (SDSS) and Wide-field Infrared Survey Explorer (WISE) data for the galaxy samples, and found no significant relationship between clustering amplitude and BH mass. Krumpe et al. (2015) measured clustering of soft X-ray and optically selected AGNs at redshifts from 0.16 to 0.36 and detected a weak dependence on the mass at a significance level of 2.7σ, while they didn’t detect significant dependence on the Eddington ratio. They conclude that the mass dependence is the origin of the observed weak X-ray luminosity clustering dependence.

Extending the data set of Komiya et al. (2013), Shirasaki et al. (2016) derived, for the first time using a statistically significant number of samples, color and absolute magnitude distributions of galaxies around AGNs, and found that the increase of the cross-correlation length found by Komiya et al. (2013) is due to the increase in the number density of red galaxies. Those results indicate that the most massive SMBHs are evolved in dark matter halos more massive than the lower-mass SMBHs, and the surrounding galaxies also evolve in a coordinated way with the SMBHs which are mostly located in the center of host halo. To extend further the study given in Shirasaki et al. (2016) up to redshifts ∼3, which covers the era of the peak of star formation and mass accretion rate for SMBHs, we require a deeper wide multi-band survey.

The Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) is a multi-band imaging survey conducted with the HSC on the 8.2 m Subaru Telescope. The survey consists of three layers: Wide (1400 deg², r ∼ 26), Deep (27 deg², r ∼ 27), and UltraDeep (3.5 deg², r ∼ 28). The HSC-SSP Wide survey provides the first opportunity to investigate the environment of AGNs up to redshift three with unprecedented statistics. Using the unique data set of the HSC-SSP Wide survey, this paper’s purpose is to measure not only the clustering of galaxies around AGNs but also their color and luminosity distribution as a function of SMBH mass at five redshift groups from 0.6 to 3.0. The results obtained in this work will give us a unified picture of evolution of galaxies and SMBHs under the large-scale structure of the Universe at their most important stage.

Throughout this paper, we assume a cosmology with Ω_m = 0.3, Ω_λ = 0.7, h = 0.7, and σ₈ = 0.8. All magnitudes are given in the AB system. All the distances are measured in comoving coordinates. The correlation length is presented in unit of h⁻¹ Mpc. The group and parameter names that are frequently refereed to in the text are summarized in table 11 of the Appendix.

2 Data sets

2.1 AGNs

The AGN samples used in this paper were drawn from the QSO properties catalog of Shen et al. (2011, hereafter S11) and the SDSS DR12 Quasar catalog (DR12Q) of Pâris et al. (2017). We used the S11 catalog as a reference for the BH mass estimate so as to be consistent with the previous studies (Komiya et al. 2013; Shirasaki et al. 2016), and the BH masses derived from the DR12Q catalog and spectral measurements were calibrated with those derived in S11.

To check the consistency between the BH masses derived by different relations, we compared them for the same objects. The left-hand panel in figure 1 shows the comparison of BH masses given in S11, |$M_{\rm BH,Mg\, {\small{II}}}$|(S11), and those calculated for the same object in DR12Q, |$M_{\rm BH,Mg\,{\small{II}}}$|(DR12Q), using equation (1). We found there is a systematic offset of 0.24 dex and scatter of 0.22, so we have corrected for the offset to the mass calculated using equation (1).

Fig. 1.

Comparisons of BH masses derived by different methods for the same object. Left-hand panel shows the comparison between the BH masses as given in S11 (Shen et al. 2011) and those calculated for the same object in DR12Q (Pâris et al. 2017) using equation (1). Right-hand panel shows the comparison between the BH masses calculated for an object in DR12Q using equation (1) and (2). The solid lines represent linear expressions fitted to the data points. (Color online)

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The right-hand panel in figure 1 shows the comparison of BH masses calculated for objects in DR12Q using equation (1), |$M_{\rm BH,Mg\, {\small{II}}}$|(DR12Q), and equation (2), |$M_{\rm BH,C\, {\small{IV}}}$|(DR12Q). A systematic offset of 0.07 dex and scatter of 0.48 dex were found between them. Thus the offset of |$M_{\rm BH,C\, {\small{IV}}}$|(DR12Q) to |$M_{\rm BH,Mg\, {\small{II}}}$|(S11) was estimated to be 0.17, and the corresponding correction was made to |$M_{\rm BH,C\, {\small{IV}}}$|(DR12Q). As mentioned in Mejia-Restrepo et al. (2016) and is apparent from figure 1, |$M_{\rm BH,C\, {\small{IV}}}$| has a larger uncertainty than the mass measured based on other emission lines, so we used M_{BH, Mg ii}, whenever it was available, as a mass estimator prior to |$M_{\rm BH,C\,\small{IV}}$|⁠. The AGN samples for which BH mass is estimated from the |$C\,\small{IV}$| line are mostly at z ≥ 2.3. The effect of the large uncertainty of the C iv BH mass is limited only to the results for z ≥ 2.0.

Coatman et al. (2017) recently showed that an empirical correction to C iv BH masses based on the blueshift of the C iv emission line reduces the uncertainty. To apply the correction requires an accurate measure of the AGN systemic redshift. Thus, we decided to use the relation of equation (2) which does not require precise spectroscopic measurements.

The systematic offset and scatter between M_{BH, H β} and |$M_{\rm BH, Mg\, {\small{II}}}$| given in the S11 catalog are 0.009 dex and 0.38 dex, respectively, as shown in figure 10 of Shen et al. (2011). Thus, no correction to M_{BH, H β} is required.

For AGNs appearing in both catalogs, we used the redshift and BH mass of the S11 catalog. The redshift range of the AGNs was chosen to be 0.6–3.0, so that it overlaps with the highest redshift bin (z = 0.6–1.0) of the previous studies (Komiya et al. 2013; Shirasaki et al. 2016), in order to cross-check between both the results and extend up to the limit of sensitivity of this analysis. The BH mass range was set to 10⁷–10¹¹ M_⊙. We selected 6166 AGNs which are in the redshift and BH mass ranges and are located within the footprint of HSC-SSP Wide survey.

2.2 Galaxies

The galaxy sample was collected from the HSC-SSP S15b Wide survey data set. HSC-SSP is a three-layered, multi-band (grizy plus four narrow-band filters) imaging survey made with the HSC (Miyazaki et al. 2012, 2018) on the 8.2 m Subaru Telescope. The total area and the depth of observation will be 1400 deg² with r ∼ 26 (Wide layer), 27 deg² with r ∼ 27 (Deep layer), and 3.5 deg² with r ∼ 28 (UltraDeep layer).

We used the data set derived from the Wide layer. The observed locations and effective area are summarized in table 1. The typical depths of the observation are 26.8, 26.4, 26.4, 25.5, 24.7 for the g, r, i, z, and y bands, respectively. The detail of survey itself is described in Aihara et al. (2018b), and the content of the S15b data set is in Aihara et al. (2018a). The S15b data set was analyzed through the HSC pipeline (version 4.0.1) developed by the HSC software team using codes from the Large Synoptic Survey Telescope (LSST) software pipeline (Ivezic et al. 2008; Axelrod et al. 2010). The photometric and astrometric calibrations are made based on data obtained from the Panoramic Survey Telescope and Rapid Response System first imaging survey (Pan-STARRS1: Magnier et al. 2013; Schlafly et al. 2012; Tonry et al. 2012).

The photometric magnitude used in this work is a CModel magnitude. The galactic reddening was corrected according to the dust maps derived by Schlegel, Finkbeiner, and Davis (1998).

The analysis performed in this paper is based on two galaxy samples; one is the i-band detected sample which is drawn from all sources selected by the criteria for the i band as described below and measured to be brighter than 27 mag in the i band regardless of the detection in the other four bands; the other is the four-band detected sample which is selected by enforcing the same criteria for griz bands except for the magnitude cut, which is adapted only to i-band data, regardless of the detection in the y band. Since the observations in the y band are shallower than the others, the detection in the y band was not required to avoid the bias to redder galaxies. For the cross-correlation analysis, we used the i-band detected sample. When we measure the distribution of galaxy color and luminosity around AGNs, we used the four-band detected sample. The term “detected” used here means that the source satisfies the criteria defined below and has a non-NULL magnitude.

The criteria used to select i-band detected samples are the following:

 iflags_pixel_edge is not True

 AND iflags_pixel_interpolated_any is not True

 AND iflags_pixel_saturated_any is not True

 AND iflags_pixel_cr_any is not True

 AND iflags_pixel_bad is not True

 AND icmodel_flux_flags is not True

 AND icentroid_sdss_flags is not True

 AND detect_is_tract_inner is True

 AND detect_is_patch_inner is True

 AND deblend_nchild = 0

where iflags_pixel_edge is true if the source is near the edge of the frame; iflags_pixel_interpolated_any is true if any pixels in the source footprint have been interpolated due to saturation or cosmic rays; iflags_pixel_saturated_any is true if any pixels are saturated; iflags_pixel_cr_any is true if any pixels are masked as cosmic rays; iflags_pixel_bad is true if any pixels are masked for non-functioning or in severely vignetted areas; icmodel_flux_flags is false if the cmodel measurement fails; icentroid_sdss_flags is false if the SDSS centroiding algorithm fails; detect_is_tract_inner and detect_is_patch_inner are true if the source is in the inner region of a tract and patch, which is used to select a source of primary detection; and deblend_nchild is the number of children this source was deblended into. Similar flag checks were performed for the other bands.

In addition to the above criteria, we adapted a criterion:

 flags_pixel_bright_object_center is not True

to remove the galaxy samples in bright source masks only for those located at ≥2 Mpc from the AGN. The bright source masks implemented in this data release are over-conservative in the choice of radius, providing a drawback that decreases the significance of the clustering. Thus we did not adapt the bright source mask to the galaxy samples located at <2 Mpc from the AGN.

We found that there is a non-negligible number of false detections in the deblended sources, especially at larger magnitudes. To remove the false detections, we selected only the deblended sources which are brighter than 27 mag in the i band and also brighter than m_{i, top} + 6 mag, where m_{i, top} is an i-band magnitude brightest in the deblended sources which belong to the same parent. To avoid saturation in HSC photometry, no magnitude data brighter than 20 mag were used for any of the five bands.

2.3 AGN data set selection

In the analysis of this paper, we treated each AGN and its surrounding galaxies as a set. Hereafter, we refer to the unit of the data set as an AGN data set. In this section we describe the criteria to include the AGN data sets for analysis.

For each AGN data set, we measured the surface density of galaxies in annuli spaced by 0.2 Mpc out to 10 Mpc from the position of the AGN. We kept only those AGN in which >60% of the area of all annuli at ≥2 Mpc around it and >80% of the area at <2 Mpc were included in the survey footprint and not masked by bright sources. By this selection, among the original 6166 AGN data sets, 346 data sets were removed from the i-band detected sample and 585 were removed from the four-band detected sample. Thus 5820 and 5581 AGN data sets passed this selection for i-band and four-band detected samples, respectively.

The spatial uniformity of the galaxy samples in the AGN field was also examined to identify the AGN data sets that are significantly contaminated by nearby galaxies and stellar groups or showing non-uniformity for any other reason. For this purpose, we calculated two parameters for the radial number density distribution of galaxies, χ² and σ_max, where χ² is a square sum of the deviation from the number density distribution fitted to the observed data using equation (6), which will be derived in subsection 3.1, and σ_max is a maximum deviation from the density distribution. Adapted criteria for those parameters are χ²/n ≤ 3.0 and σ_max ≤ 5. By this selection, 268(236) AGN data sets were removed from the 5820(5581) AGN data sets for the i-band (four-band) detected sample. Thus 5552(5345) AGN data sets passed all the above selections.

Figure 2 shows the mass vs redshift distribution of the AGNs that were selected according to the conditions described above and used in the cross-correlation analysis in this paper. Figures 3 and 4 show histograms of redshift and BH mass, respectively. We divided the redshift range into five groups as shown in figure 2, which we call z0, z1, z2, z3, and z4 for z = 0.6–1.0, 1.0–1.5, 1.5–2.0, 2.0–2.5, and 2.5–3.0, respectively. For each redshift group, except for z4, the BH mass range was divided into two groups, M8 and M9, such that each group has a similar number of AGNs rather than being divided at the same mass. This is because the effect of sample variance becomes dominant when the number of AGN samples is small and it is difficult to homogenize the samples among different mass groups by the division at constant mass for all the redshifts. The mass group was divided at log (M_BH/M_⊙) = 8.4, 8.8, 9.0, and 8.9 for z0, z1, z2, and z4 redshift groups, respectively, which allows us to make the statistical uncertainties even for both mass groups. The mass dependence of the z4 redshift group was not examined, since the number of samples in the z4 group is too small to do so.

Fig. 2.

Distribution of redshift and BH mass of 5552 AGNs which are used in cross-correlation analysis using i-band detected galaxy samples. (Color online)

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Fig. 3.

Distribution of BH mass for the samples shown in figure 2. (Color online)

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Fig. 4.

Distribution of redshift for the samples shown in figure 2. (Color online)

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Table 2 shows the number of AGN data sets which passed all the selection criteria described above for each data set. The i-band detected galaxy samples were used for cross-correlation analysis, and the four-band detected samples were used for deriving the color distribution and luminosity function of clustering galaxies, and they were also used to measure the dependence of cross-correlation length on galaxy luminosity. The redshift-matched samples were used for examining the BH mass dependence at each redshift.

3 Analysis method

3.1 Cross-correlation length

The cross-correlation function between AGNs and galaxies was calculated using the method described in our previous papers (Shirasaki et al. 2011, 2016; Komiya et al. 2013). The analysis method is briefly described here.

In calculating n(r_p), we masked the central 10″ around each AGN to avoid blending problems with the AGN. Around a bright source there is a region where the number density of the galaxy selected by the criteria described in subsection 2.2 is significantly reduced due to blending with the bright source and/or increase in the background noise level. That region needs to be counted as a dead region in calculating an effective area around AGNs.

Fig. 5.

ϕ₋₁₈ parameters of equation (11) derived from literature (Gabasch et al. 2004, 2006; Dahlen et al. 2005, 2007; Parsa et al. 2016). Our parametrization is shown with a thick line. (Color online)

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Fig. 6.

M  _* parameter of equation (12) derived from literature (Gabasch et al. 2004, 2006; Dahlen et al. 2005, 2007; Parsa et al. 2016). Our parametrization is shown with solid lines. (Color online)

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Fig. 7.

α parameter of equation (13) derived from literature (Gabasch et al. 2004, 2006; Dahlen et al. 2005, 2007; Parsa et al. 2016). Our parametrization is shown with a dotted line.

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The root mean square (rms) of the difference between parameters from the literature and those calculated by the parametrization of equations (10)–(13) is 0.15 mag for log (ϕ₋₁₈), 0.28 mag for M_*, and 0.14 mag for α. The error of log (ϕ₋₁₈) by 0.15 corresponds to a systematic error of r₀ by ∼20% for γ = 1.8.

The error of M_* significantly affects the luminosity densities at the bright end of M < M_*, as the slope of the luminosity function becomes steeper there. Thus, comparison was made between the number densities at M < M_* calculated using the parameters from the literature, ρ_lit, and those calculated with the above parametrization, ρ_par. According to the comparison, the rms of the relative error (ρ_lit − ρ_par)/ρ_par is 0.36 for 40 sets of luminosity functions from the literature, which corresponds to an upper deviation of cross-correlation length of δr₀ = 0.28 × r₀, that is, 28% of the cross-correlation length, and a lower deviation of δr₀ = 0.16 × r₀, i.e., 16%, for γ = 1.8. When the comparison is made by extending to a lower luminosity side as M > −17, the rms of the relative error is 0.16 for 20 sets of luminosity functions of z < 1.5, which corresponds to upper and lower deviation of 10% and 8% for r₀, respectively.

3.2 Color and absolute magnitude distributions for galaxies

To calculate the color and absolute magnitude for the same rest-frame bandpass at different redshifts, we performed spectral energy distribution (SED) fitting using the EAZY software developed by Brammer, van Dokkum, and Coppi (2008) and calculated color and magnitude at fixed bandpasses. For the redshift z0, z1, and z2 groups (z = 0.6–2.0), the color is defined as D₁ = M_λ270 − M_λ380 and the absolute magnitude is M_λ310, where M_λ270, M_λ380, and M_λ310 represent absolute magnitudes at wavelengths 270, 380, and 310 nm, respectively. For the redshift z2, z3, and z4 groups (z = 1.5–3.0), the color is defined as D₂ = M_λ165 − M_λ270 and the absolute magnitude is M_λ220, where M_λ165, M_λ270, and M_λ220 represent absolute magnitudes at wavelengths 165, 270, and 210 nm, respectively. For the redshift z2 group, we calculated the distributions for both definitions in order to compare between them.

Although EAZY can be used to estimate photometric redshift (photo-z), it was used here to interpolate the observed SEDs of all the sources assuming its redshift to be the same as the AGN redshift. This is because the photo-z is not well constrained at the redshifts explored in this work, as the structure around 400 nm, which is primarily used to determine the photo-z, is out of the observed passband. For this reason, photo-z was not used in our analysis and the clustering of galaxies was measured by stacking the galaxy distribution around AGNs and subtracting the constant density, which is a contribution from foreground/background galaxies, from the distribution.

4 Results

4.1 Cross-correlation function

First we present the cross-correlation functions derived by using the i-band detected galaxy samples for each redshift group. To also test for the dependence on galaxy luminosity, two galaxy samples were constructed with different threshold magnitudes. The threshold magnitudes were chosen to be |$M_{90\%}$| and |$M_{50\%}$|⁠, where |$M_{90\%}$|(⁠|$M_{50\%}$|⁠) represents the absolute magnitude where the averaged detection efficiency estimated as described in subsection 3.1 is 90%(50%). The absolute magnitude is measured in the i-band observer frame as calculated with m_i − DM, where m_i is i-band apparent magnitude and DM is distance modulus for the AGN redshift. The values of |$M_{50\%}$| and |$M_{90\%}$| are summarized in the second and third columns of table 4.

Figure 8 shows the distributions of average number density of galaxies with absolute magnitude brighter than |$M_{50\%}$| for five redshift groups. The model functions of equa-tion (6) fitted to the observations are also plotted in the same figure. The corresponding projected cross-correlation functions calculated using equation (5) are shown in figure 9. The estimated fitting parameters are summarized in the upper parts of table 5 for each threshold magnitude.

Fig. 8.

Radial distribution of galaxy surface density around AGNs for each redshift group. i-band detected galaxy samples with absolute magnitude brighter than |$M_{50\%}$| are used, where |$M_{50\%}$| represents the magnitude where detection efficiency is 50%. (Color online)

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Fig. 9.

Projected cross-correlation functions derived from data shown in figure 8. Solid lines represent the power-law model fitted to the data. (Color online)

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The cross-correlation lengths are plotted as a function of redshift in figure 10 for each threshold sample. The result shows that the cross-correlation length increases as the redshift increases, and is also larger for more luminous galaxy samples. Therefore, for examining the BH mass dependence, it is important to match the distribution of redshift and galaxy luminosity for different BH mass gruops.

Fig. 10.

Cross-correlation length as a function of redshift. Squares and triangles represent the cross-correlation length derived using galaxies brighter than |$M_{50\%}$| and |$M_{90\%}$|⁠, respectively, where |$M_{50\%}$| (⁠|$M_{90\%}$|⁠) represents the magnitude where detection efficiency is 50% (90%). (Color online)

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To reduce the effect of redshift dependence in the comparisons between the different BH mass groups, we constructed redshift-matched samples for each redshift group. The redshift-matched samples were constructed by selecting the same number of AGN data sets for each Δz = 0.02 bin. The projected cross-correlation functions calculated for the redshift-matched samples are shown in figure 11 for four redshift groups z0, z1, z2, and z3. The mass dependence for the z4 group was not examined due to poor statistics. In this figure, the circles represent lower BH mass groups (M8) and the squares represent higher BH mass groups (M9). Galaxy samples brighter than |$M_{90\%}$| were used. The estimated fitting parameters are summarized in the bottom part of table 5.

Fig. 11.

Comparisons of projected cross-correlation functions derived for mass groups of M8 (circles) and M9 (squares). Each panel represents the result for redshifts z0, z1, z2, and z3. Redshift-matched AGN samples and galaxy samples brighter than |$M_{90\%}$| are used. Solid lines represent the power-law model fitted to the data points. (Color online)

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The cross-correlation lengths are plotted as a function of BH mass in figure 12. From these results, no significant difference is seen between the two mass groups.

Fig. 12.

Cross-correlation lengths plotted as a function of average BH mass obtained for data shown in figure 11 (blue solid markers). Note that the galaxy sample for these data sets are dominated by blue galaxies. The result obtained by Shirasaki et al. (2016), for which galaxy samples are dominated by red galaxies contrary to the current data set, is shown with crosses. The result obtained using the data selected by color to construct a data set comparable with the result of Shirasaki et al. (2016) is shown with open circles. (Color online)

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For comparison with the previous results (Shirasaki et al. 2016) derived using UKIDSS and SDSS data for galaxy samples, the results obtained for red galaxy samples (D₁ ≥ 1.4) as described in the next subsection are also plotted. In their work, Shirasaki et al. (2016) calculated cross-correlation functions between AGNs and galaxies, which were mostly red galaxies, at redshifts <1.0, and obtained the result that the cross-correlation length depends on BH mass but does not depend on redshift. Our current result at higher redshifts indicates its strong dependence on redshift and not on BH mass. The different behavior partly comes from the difference in the properties of galaxy samples; that is, the galaxy samples in the previous work are dominated by red-type galaxies and mostly dimmer than characteristic luminosity L_* of the Schechter function, while those in the current work are dominated by blue-type galaxies and mostly consist of galaxies brighter than L_* at higher redshifts. As shown in the following subsection, the clustering of galaxies significantly increases above L_*, which introduces redshift dependence to the cross-correlation length.

4.2 Galaxy luminosity-dependence of cross-correlation length

As larger clustering was indicated for more luminous galaxies as shown in figure 10, we calculated cross-correlation lengths for flux-limited samples derived from the four-band detected samples to examine the dependence on the luminosity of galaxies more closely. To calculate the absolute magnitude for the same rest-frame bandpass at different redshifts, we performed SED fitting using the EAZY software developed by Brammer, van Dokkum, and Coppi (2008) and calculated the magnitude at a fixed bandpass. The observed magnitudes at g, r, i, z, and y bands are used in the SED fitting. The flux-limited galaxy samples were constructed based on absolute magnitude M_λ310 for z0, z1, and z2, and M_λ220 for z2, z3 and z4, where M_λ310 and M_λ220 represents the absolute magnitude at wavelength 310 nm and 220 nm, respectively.

Fig. 13.

Cross-correlation length as a function of average absolute magnitude of galaxies measured in M_λ310 or M_λ220. The cross-correlation lengths were calculated using the galaxy samples which are brighter than given threshold magnitudes. Dotted lines represent functions of equation (20) fitted to the data points. (Color online)

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Fig. 14.

Cross-correlation length as a function of M_* − 〈M_λ310〉 or M_* − 〈M_λ220〉. 〈M_λ310〉 and 〈M_λ220〉 are the average absolute magnitudes of galaxies measured at rest-frame wavelengths of 310 nm and 220 nm, respectively, and the cross-correlation lengths were calculated by using the galaxy samples which are brighter than the threshold magnitude. Dotted lines represent functions of equation (20) fitted to the data points. (Color online)

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From these figures, it is apparent that the cross-correlation length rapidly increases at magnitudes brighter than M_*, and it also increases with increasing redshift when compared for the same M_* − M. r_{0, min} corresponds to the cross-correlation length calculated for the whole galaxy samples of each redshift group. Due to the difference in the detection threshold of galaxy luminosity, the average luminosity for all the galaxy samples is larger for the higher redshift groups than for the lower ones. Thus the difference of r_{0, min} is due to the difference in galaxy luminosity as well as the difference in redshift.

4.3 Color distributions of galaxies around AGNs

Color distributions of galaxies around AGNs were derived by the subtraction method described in subsection 3.2, and the results are shown in figure 15 for color parameter D₁ at z0 to z2 and in figure 16 for D₂ at z2 to z4. Redshift-matched AGN samples were used for this analysis. The galaxy samples used are the four-band detected samples, and the threshold magnitude for the galaxy was chosen to be |$M_{50\%}$|⁠, which is an absolute magnitude where the average detection efficiency is 50%. The measured values of |$M_{50\%}$| are summarized in the fourth and sixth columns of table 4.

Fig. 15.

Color (D₁) distributions derived for redshift-matched AGNs and |$< M_{50\%}$| galaxy samples calculated as shown in equation (17). The panels in the left-hand column are the distributions for combined mass groups (M8 + M9), and on the right of each row are the distributions for individual mass groups of M8 and M9. The top three panels are those for redshift z0, and the middle and bottom panels are for z1 and z2, respectively. The solid lines represent the results of double Gaussian fitting. The dashed vertical lines represent the boundary-defining blue and red galaxies in this paper. (Color online)

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Fig. 16.

Color (D₂) distributions derived for redshift-matched AGNs and |$<\! M_{50\%}$| galaxy samples calculated as shown in equation (17). The panels in the left-hand column are the distributions for combined mass groups (M8 + M9), and the two panels on the right of each row are the distributions for individual mass groups of M8 and M9. The top three panels are those for redshift z2, and the middle and bottom panels are for z3 and z4, respectively. The solid lines represent the results of double Gaussian fitting. The dashed vertical lines represent the boundary-defining blue and red galaxies in this paper. (Color online)

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The panels in the left-hand column in the figures show the excess color density of D₁ or D₂ distributions for combined M8 + M9 groups, and they are placed in increasing order of their redshifts from top to bottom. The two panels on the right-hand side of each row are those for M8 and M9 groups at the corresponding redshift, respectively. In the case of the z4 group, only the distribution of the whole mass group is shown, as the number of samples is too small to split the sample into two mass groups for the analysis of mass dependence. D₁ is defined as a difference between magnitudes at rest-frame wavelengths of 270 nm and 380 nm for redshift groups z0, z1, and z2, and D₂ is a color between magnitudes at 165 nm and 270 nm for redshift groups z2, z3, and z4. The magnitudes were calculated by performing SED fitting using the EAZY software (Brammer et al. 2008) as described in subsection 3.2.

The color distributions were fitted with a double Gaussian model in which the two Gaussian functions correspond to red (smaller D₁) and blue (larger D₁) galaxy types. The fitted model functions are plotted in the same figures. As can be seen from the color distributions in figures 15 and 16, blue galaxies dominate the clustered component in our galaxy samples.

In the fit to the D₁ distribution for the z2 (M8 + M9) group shown in figure 15, the Gaussian parameters for each component were not well constrained. This is partly because there is a tendency for the distribution of the blue component to shift to the redder side as the redshift increases, and the components overlap in higher fractions for that group. Thus we fixed the Gaussian parameters of the red component to those obtained for the z1 (M8 + M9) group. In the cases of z3 and z4 shown in figure 16, the red component is barely visible, thus the Gaussian parameters for the red component were fixed to those obtained for D₂ distribution of z2 (M8 + M9).

The fitting for the M8 and M9 samples was performed by fixing the Gaussian parameters to those obtained for the combined M8 + M9 samples except for the z0 group. In the case of z0, the peak positions of the blue component are slightly different between the M8 and M9 groups. Thus, the Gaussian parameters for the blue component were derived independently. Those fitting parameters are summarized in table 6.

The fractions of the blue galaxy for the combined groups made up of the M8 and M9 mass groups are around 0.7–1.0, and there is a marginal indication that the blue fraction increases at higher redshifts. Care needs to be taken in the comparison of the different redshifts by noting the difference in the galaxy samples. The galaxy samples at higher redshift are biased to more luminous galaxies, and it is also expected that the fraction of red galaxies increases along with the increase in luminosity as observed in the color–magnitude diagrams of the local galaxies. Thus the observed redshift dependence of the blue fraction is biased to the red component at higher redshift, and it is expected that the increase in the blue fraction is more or less enhanced if the bias is corrected.

As already mentioned above, the peak position of the blue galaxy is found to shift to the redder side as redshift increases. We also found that the peak position shifts to the redder side for brighter galaxies of the same redshift, so the shift of the peak position to the redder side at higher redshift is partly due to the dependence of the color on the absolute magnitude of the galaxy.

The obtained blue galaxy fractions are plotted in figure 17 as a function of BH mass for each redshift group. A decreasing trend of blue fraction with BH mass is found for all redshifts except for z1. The result of z1 might have suffered from the sample variance. This can be tested by adding more samples from the upcoming HSC-SSP survey.

Fig. 17.

Blue galaxy fraction at the central region (<2 Mpc from AGNs) as a function of BH mass. These were derived from the fittings shown in figure 15 and 16. Galaxy samples brighter than |$M_{50\%}$| were used. (Color online)

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In the previous work of Shirasaki et al. (2016) that used SDSS and UKIDSS for galaxy samples, the blue galaxy fraction was less than ∼0.2 at redshift group z0 of this work, as the galaxy sample was strongly biased to red-type galaxies. In that work they also obtained the result that red galaxies more luminous than M_IR = −20 were strongly clustered around AGNs of M_BH > 10^8.2 M_⊙. To test the consistency with the previous result on the cross-correlation with red galaxies, we calculated the cross-correlation lengths for red galaxies in the z0-M8 and z0-M9 groups separately.

We extracted red galaxies defined as D₁ ≥ 1.4, and restricted their brightness to |$M_{\lambda 310} < M_{90\%} (=\! -18.8)$|⁠. To calculate the cross-correlation function, we need to know the average number density of these galaxy types at the corresponding redshift, |$\bar{\rho }_{0, \rm red}$|⁠. It was estimated as |$\bar{\rho }_{0} (1-f_{\rm blue})$| using the blue fraction determined for z0-M8 group. Then we obtained the cross-correlation lengths for red galaxy samples as r_{0, red} = 6.35 ± 1.22 for z0-M8, and r_{0, red} = 8.73 ± 1.02 for z0-M9. The values of r_{0, red} are plotted in figure 12 and compared with the previous work. They are consistent with each other.

4.4 Luminosity functions of galaxies around AGNs

Next we examined the absolute magnitude distributions of the galaxy clustered around AGNs. The left(right)-hand panel of figure 18 shows the distributions of M_λ310 (M_λ220) for z0, z1, and z2 (z2, z3, and z4) redshift groups. The excess densities were calculated as in equation (18) and corrected for their detection efficiencies calculated as described in subsection 3.1. They are plotted for M_λ310, |$M_{\lambda 220} < M_{50\%}$|⁠.

Fig. 18.

Absolute magnitude distributions of galaxies around AGNs calculated as in equation (18). Detection efficiencies were corrected and plotted for |$M<M_{50\%}$|⁠. The left-hand panel shows the distributions measured in M_λ310 for z0, z1, and z2 groups. The right-hand panel shows the distributions measured in M_λ220 for z2, z3, and z4 groups. The solid lines represent the luminosity function calculated by the parametrization used in this work and scaled by a factor calculated from the cross-correlation length obtained for |$M_{50\%}$| galaxy samples. The scaling factor was calculated as in equa-tion (21). The dashed lines represent Schechter functions fitted to the data points. The arrows at the top of the panels indicate the 90% detection limit. (Color online)

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To test if the overdensity can be explained by the uncertainty of the M_* parameter used in the parametrization of luminosity function model, we measured the M_* parameters for the observed magnitude distributions by fitting the Schechter function to them and compared them with the values given by the parametrization. In the fitting α was fixed to −1.2. The results are summarized in table 7 and compared in figure 19 with the parametrization (thick solid lines) and literature values (open markers). The obtained M_* are typically smaller (i.e., brighter) than M_* given by the parameterization by >1 mag, well exceeding the uncertainty of M_*, 0.28 mag, expected for the parametrization. Thus it is unlikely that the overdensity is attributable only to the uncertainty of the assumed luminosity function.

To investigate the galaxy type that contributes to the overdensity at the bright end, we derived the magnitude distributions for blue and red galaxies separately. They were classified at D₁ = 1.4 or D₂ = 0.8. Figure 20 shows the comparisons between the magnitude distributions for blue and red galaxies. Both galaxy types contribute to the overdensity.

Fig. 19.

Comparison of M_* parameters measured for clustering galaxies around AGNs (filled circles and filled triangles) and those calculated from the parametrization (thick solid lines). M_* values derived in literature (Gabasch et al. 2004, 2006; Dahlen et al. 2005, 2007; Parsa et al. 2016) are also plotted. (Color online)

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Fig. 20.

Absolute magnitude distributions for blue and red galaxies calculated as in equation (18). The dashed lines represent the luminosity function calculated by the parametrization used in this work and scaled by a factor calculated from the cross-correlation length. The scaling factor was calculated as in equation (21). The solid lines represent Schechter functions fitted to the data points. The arrows at the top of the panels indicate the 90% detection limit. (Color online)

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M  _* parameters measured for the distributions are summarized in table 8 and plotted in figure 21. The obtained M_* parameters for red galaxies are systematically brighter than those for blue galaxies by more than two sigma at redshift z0, z1, and z2 for measurements at 310 nm. No statistically significant difference is found for the values for z2, z3, and z4 measured at 220 nm, which is mostly due to poor statistics and lower resolution of D₂ parameters on the deconvolution of the two components.

Fig. 21.

Comparison of M_* parameters measured for blue and red galaxies. These are obtained by fitting Schechter functions to the data points in figure 20.

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We also investigated whether there is a difference in the luminosity functions of clustering galaxies for lower and higher BH mass groups. Figure 22 shows the comparisons between the magnitude distributions for the M8 and M9 mass groups, and M_* parameters measured for them are summarized in table 9 and plotted in figure 23.

Fig. 22.

Absolute magnitude distributions for M8 and M9 mass groups. The dashed lines represent luminosity function calculated by the parametrization used in this work and scaled by a factor calculated from the cross-correlation length. The scaling factor was calculated as in equation (21). The solid lines represent Schechter functions fitted to the data points. The arrows at the top of the panels indicates the 90% detection limit. (Color online)

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Fig. 23.

Comparison of M_* parameters measured for M8 and M9 mass groups. These are obtained by fitting Schechter functions to the data points in figure 22.

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The obtained M_* parameters for the M9 group are systematically brighter than those for the M8 group by more than two sigma at redshifts z0 and z1. No statistically significant difference is found for the values at redshift z2 (for both 310 nm and 220 nm) and z3. The results may indicate the enhancement of bright galaxies around AGNs with higher BH mass ( > 10^8.5 M_⊙) at redshift <1.5, while at redshift ≥1.5 the luminosity function of a galaxy is similar around AGNs with BH mass of ≥ 10⁸ M_⊙.

4.5 AGN linear bias and dark matter halo mass hosting AGNs

The AGN–galaxy cross-correlation functions can be used to measure the linear bias of AGN distribution then to estimate the average mass of dark matter halos hosting the AGNs. Using the relation between the halo mass and its bias obtained by numerical simulation, we can estimate the halo mass by assuming that the AGNs are located in halos with a similar bias.

To derive the linear bias of AGNs from the AGN–galaxy cross-correlation function, we should know also about the auto-correlation function of galaxies. It is not, however, determined only from the data set used in this work. Thus, we assume that auto-correlation functions measured by Zehavi et al. (2011), which were derived by using the SDSS galaxies at redshifts <0.25, does not change up to redshift =3. Since the galaxy auto-correlation functions measured at higher redshifts (e.g., Ishikawa et al. 2015) are almost the same as those measured by Zehavi et al. (2011), it can be a good approximation.

The primary cause of the larger clustering of our galaxy samples is due to the evolution of, i.e., decrease in, the M_* parameter in the luminosity function at neighbors of AGNs, as shown in the subsection 4.4. To reduce the effect of the M_* evolution and derive ξ_AG for <M_* galaxies, we calculated the cross-correlation lengths from the magnitude distributions of the clustering galaxies, n_fit(M), which were obtained by fitting the Schecher function to the observation in estimating M_* for the measured magnitude distributions. The parameter α of the Schecher function was fixed to −1.2. The magnitude distributions, n_fit(M), are shown in figure 18 as dashed lines.