The Host-galaxy Properties of Type 1 versus Type 2 Active Galactic Nuclei

Our sample is drawn from X-ray-detected sources in the COSMOS-Legacy Survey (Civano et al. 2016). This survey reaches a flux limit three times deeper than the XMM-COSMOS Survey (Cappelluti et al. 2009; Brusa et al. 2010), and it also covers a larger area (∼2 deg²) than the C-COSMOS Survey (Elvis et al. 2009; Civano et al. 2012). Therefore, the COSMOS-Legacy Survey allows us to obtain a larger and more complete AGN sample compared to previous works (e.g., Merloni et al. 2014). The COSMOS-Legacy Survey samples most of the cosmic accretion power (e.g., Aird et al. 2015; Yang et al. 2018a). In this sense, the sources studied in this work are typical AGNs in the distant universe. The survey reaches ≈10 times below the knee luminosity of the X-ray luminosity function at z ≈ 1.5–3, the cosmic epoch when mergers are most important to galaxy evolution (e.g., Conselice et al. 2014). In this epoch, the aforementioned merger-driven coevolution scenario might be crucial in shaping SMBH and galaxy growth. Therefore, the COSMOS-Legacy Survey is ideal for probing the possible differences between type 1 and type 2 sources.

In addition, dilution by host-galaxy starlight is low in the X-ray band, thus allowing us to construct pure AGN samples even down to modest luminosities (e.g., Brandt & Alexander 2015; Xue 2017 and references therein). The X-ray catalog with optical and infrared (IR) identifications in COSMOS is available in Marchesi et al. (2016). The high angular resolution of Chandra (∼05) in the COSMOS-Legacy Survey enables reliable cross-matching between the X-ray catalog and IR-to-ultraviolet (UV) catalogs (Marchesi et al. 2016).

We select 3744 sources that are not stars with nonzero redshift from Marchesi et al. (2016). Then we remove sources outside of the UltraVISTA area or masked in optical broad bands (Capak et al. 2007) to ensure accurate spectral energy distribution (SED) fitting results, following previous works (e.g., Kashino et al. 2019; Yang et al. 2018a, 2018b). The UltraVISTA area has deep near-infrared (NIR) imaging data that are essential in estimating photometric redshifts and M_⋆, and the masked regions do not have accurate photometry because they are located beside bright sources or have bad pixels. Indeed, we find that the photometric-redshift quality⁶ in the masked regions is three times worse than that in the unmasked region, indicating that removing the sources is necessary. We have also tested including the masked sources with spectroscopic redshifts when analyzing far-infrared (FIR)-based SFRs, and we find that the results in Section 4.2 do not change qualitatively, indicating that removing these sources does not cause significant biases. In total, 2463 sources are left after removing the masked sources. We adopt the redshifts in Marchesi et al. (2016), and 1434 sources have reliable spectroscopic redshift measurements. We derive physical parameters for our sources below and release them in a source catalog. A part of our source catalog is displayed in Table 1, and the full version is available in the online supplementary materials.

Photometric data from the near-ultraviolet (NUV) to NIR are from the COSMOS2015 catalog (Laigle et al. 2016), the latest catalog containing multiwavelength photometry in COSMOS. To ensure that fluxes are consistent over the full wavelength range, we correct the fluxes using the following formulae:

$$\begin{eqnarray}&&{f}_{i,j}^{\mathrm{TOT},0}={f}_{i,j}^{\mathrm{APER}3}{10}^{-0.4{o}_{i}},\mathrm{and}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{f}_{i,j}^{\mathrm{TOT}}={f}_{i,j}^{\mathrm{TOT},0}{10}^{0.4({{EBV}}_{i}{F}_{j}+{s}_{j})},\end{eqnarray} \tag{ 2 }$$

where ${f}_{i,j}^{\mathrm{APER}3}$ is the 3'' diameter aperture flux; ${f}_{i,j}^{\mathrm{TOT},0}$ is the uncorrected total flux of the source; ${f}_{i,j}^{\mathrm{TOT}}$ is the corrected total flux and is adopted when performing SED fitting; i is the object identifier, and j is the filter identifier; o_i is a single offset allowing for the conversion from aperture magnitude to total magnitude; ${{EBV}}_{i}{F}_{j}$ represents the foreground Galactic extinction, where EBV_i is the reddening value of the object and F_j is the extinction factor; s_j is a systematic offset. All these correction factors are available in the COSMOS2015 catalog. Formulae to correct flux errors are similar, except that the errors should be multiplied by another factor representing the effect of correlated noise, which is also available in the COSMOS2015 catalog.

FIR photometry is vital to constrain SFR, especially for type 1 host galaxies with low SFRs because optical to UV emission from the AGN component may be mistakenly attributed to starlight without FIR photometry (Section 3.3), and thus even upper limits on FIR fluxes are worth utilizing. The 100 and 160 μm fluxes are from the 24 μm prior catalog in the public data release of the Herschel-Photodetector Array Camera and Spectrometer (PACS) Evolution Probe (PEP; Lutz et al. 2011). The 250, 350, and 500 μm fluxes, which were observed using the Herschel-Spectral and Photometric Imaging Receiver (SPIRE), are from the XID+ catalog of the Herschel Multi-Tiered Extragalactic Survey (HerMES; Oliver et al. 2012; Hurley et al. 2017). The XID+ catalog also uses 24 μm detected sources as a prior list for extracting fluxes. We adopt 2'' as our matching radius and use 24 μm positions in these two catalogs when matching with other catalogs because 24 μm positions are more accurate than positions at longer wavelengths.

For the XID+ catalog, we take the maximum of (84th–50th percentile) and (50th–16th percentile) of marginalized flux probability distributions as estimated errors S_err assuming Gaussian uncertainties for each band. We remove sources with signal-to-noise ratio S/S_err < 3. Fluxes of all the selected sources are above 5 mJy at 250 μm, 5 mJy at 350 μm, and 7 mJy at 500 μm, and thus the Gaussian approximation to uncertainties is valid according to the documentation for the COSMOS-XID+ catalog of HerMES.

For sources undetected at 100 μm or 160 μm, we use a method similar to that in Stanley et al. (2015) to estimate their flux upper limits in each band. We perform aperture photometry at about 300 positions around a nondetection point in residual maps, taking the 68.4th percentile of the distribution of the measured flux densities as the 1σ upper limit on the nondetection, and multiply the value by 3 to get the 3σ flux upper limit. We do not derive flux upper limits at 250, 350, and 500 μm because there are no public residual maps for those bands and the SPIRE maps are confusion-limited, making estimating background fluxes using only the simple aperture photometry method infeasible.

Marchesi et al. (2016) compiled and fitted the available optical/NIR spectra for the X-ray AGNs in the COSMOS-Legacy Survey. They classified a source as type 1 if it had at least one broad emission line with FWHM > 2000 km s⁻¹; otherwise, they classified it as type 2. We adopt their classifications⁷ and obtain 1162 sources in total, including 326 spectroscopic type 1 sources and 836 spectroscopic type 2 sources. This case is labeled as "Case 1."

Although spectroscopic classifications are reliable, they inevitably suffer from incompleteness issues, because 1301 sources among our X-ray AGNs do not have spectroscopic classifications. To address such problems, we classify AGNs without spectroscopic classifications in Marchesi et al. (2016) based on their host-galaxy morphologies and optical variability. For point-like sources, the host galaxies do not contribute much to the observed emission, and thus the nuclei are unlikely obscured; for highly variable sources, their emissions are also dominated by AGNs because host galaxies generally do not have detectable variability (Salvato et al. 2009). These morphology and variability classification schemes are widely adopted in the literature (e.g., Salvato et al. 2011; Merloni et al. 2014), and we also adopt these classifications for sources without spectra. We will also test the reliability of the classifications in this section.

We use the morphology parameter in Leauthaud et al. (2007) to identify point sources. They selected point sources in deep COSMOS Hubble Space Telescope/Advanced Camera for Surveys F814W images (Koekemoer et al. 2007). The optical variability measurements are from Salvato et al. (2011), who measured the variability in the C-COSMOS field and the XMM-COSMOS field. Following Salvato et al. (2011), we define sources with VAR > 0.25 mag as varying sources, where VAR is defined in Salvato et al. (2009). We will call the method that selects type 1 AGNs with point-like host morphology or VAR > 0.25 mag as the QSOV (short for point-like or varying) method hereafter. Based on the QSOV method, an additional QSOV type 1 sample of 355 sources is selected among 1301 AGNs that do not have information about spectral type, with a fraction of 27.3%. Consequently, 946 sources are left, and we will call this sample the QSOV type 2 sample.

As a reliability check of the QSOV method, we apply it to the spectroscopic type 1 sample containing 326 sources, and we find that 235 sources satisfy the criterion, with a fraction of 72.5%. The high fraction indicates that the method is reliable for selecting type 1 AGNs. Indeed, we find that the QSOV type 1 sample tends to have bluer rest-frame U − V colors than the type 2 samples, indicating the presence of type 1 AGNs. We also plot the distributions of the magnitudes in the i⁺ band for the spectroscopic type 1 sample, the QSOV type 1 sample, and all of the type 2 samples, including the spectroscopic type 2 sample and the QSOV type 2 sample, in Figure 1. The figure shows that the QSOV type 1 sources are generally fainter than other sources. Therefore, it is possible that their optical faintness prevents robust spectroscopic identification of their type 1 nature.

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We add the QSOV type 1 and type 2 sources into the type 1 and type 2 samples in a new case, which is labeled as "Case 2" hereafter. Case 2 is the same as the classification scheme of Merloni et al. (2014). Compared to Case 1, the samples in Case 2 are more complete. We summarize the properties of each case in Table 2, and the cases can be used together to assess any sensitivity of our conclusions to AGN type classification issues.

Below we will analyze all of the parameters in both cases independently. We find that the results are similar, and thus our results should be robust. Besides, we also try applying a magnitude cut (F814W magnitude < 24) and find that our conclusions are not affected when the magnitude cut is applied, which further improves the reliability. However, since the magnitude cut reduces our sample size significantly and may cause bias toward higher M_⋆ and SFR, we do not show the results with the magnitude cut below.

We calculate 2–10 keV luminosity corrected for absorption, L_X, using the following formula assuming a power-law spectrum with photon index Γ = 1.8:

$$\begin{eqnarray}&&{L}_{{\rm{X}}}=4\pi {D}_{L}^{2}{\left(1+z\right)}^{{\rm{\Gamma }}-2}\displaystyle \frac{{10}^{2-{\rm{\Gamma }}}-{2}^{2-{\rm{\Gamma }}}}{{E}_{2}^{2-{\rm{\Gamma }}}-{E}_{1}^{2-{\rm{\Gamma }}}}{f}_{{E}_{1}\sim {E}_{2}}{\eta }^{-1}(i,{E}_{1},{E}_{2}),\end{eqnarray} \tag{ 3 }$$

where ${f}_{{E}_{1}\sim {E}_{2}}$ is the flux between E₁ and E₂ in the observed frame, E₁ and E₂ are in keV, D_L is the luminosity distance at redshift z, and η(i, E₁, E₂) is a factor to correct absorption between E₁ and E₂ for source i. Note that η(i, E₁, E₂) is available in Marchesi et al. (2016). We use hard-band (E₁ = 2 keV, E₂ = 7 keV) fluxes for sources detected in the hard band (74.3%), full-band (E₁ = 0.5 keV, E₂ = 7 keV) fluxes for sources detected in the full band and undetected in the hard band (25.0%), and soft-band (E₁ = 0.5 keV, E₂ = 2 keV) fluxes for sources only detected in the soft band (0.7%) as ${f}_{{E}_{1}\sim {E}_{2}}$ to calculate L_X. Such a prioritization is chosen to minimize the effect of absorption, which is less significant for harder X-ray photons.

Figure 2 displays our samples in the L_X−z plane. Spectroscopic type 1 AGNs and QSOV type 1 AGNs tend to have higher L_X compared to type 2 AGNs because the fraction of unobscured AGN increases with L_X (e.g., Merloni et al. 2014). Besides, QSOV type 1 AGNs have lower L_X than spectroscopic type 1 AGNs because the QSOV type 1 sample is generally fainter.

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We use the Bayesian-based code CIGALE⁸ (Noll et al. 2009; Serra et al. 2011; Boquien et al. 2019) to perform SED fitting. The median number of photometric bands in our SEDs is 32, and 84% of our sources have over 30 photometric bands available. The relatively large number of bands increases our fitting reliability. We adopt an exponentially decreasing SFR model for the star formation history (SFH). Stellar templates are from models in Bruzual & Charlot (2003) with metallicity of 0.0001, 0.0004, 0.004, 0.008, 0.02, or 0.05, and a Chabrier initial mass function (Chabrier 2003) is assumed when measuring M_⋆. Dust attenuation is assumed to follow a Calzetti extinction law (Calzetti et al. 2000), allowing E(B − V) of the young stellar population to vary between 0 and 1 with a step of 0.1, and E(B − V) of the old stellar population is assumed to be scaled down by 0.44 compared to that of the young one. Nebular and dust emission are also implemented in CIGALE (Draine & Li 2007; Noll et al. 2009). As for the AGN component, we use AGN templates in Fritz et al. (2006), allowing f_AGN to vary between 0 and 1 with a step of 0.05, where f_AGN is the fractional contribution of the AGN to the total IR luminosity. The angle between the line of sight and accretion disk, ψ, is set to be 0° for type 1 sources and 90° for type 2 sources. The optical depth τ at 9.7 μm is fixed to 6.0. Our settings are similar to those of many other works (e.g., Laigle et al. 2016; Yang et al. 2018b).

We obtain SFR and M_⋆ from the output results. Figure 3 displays example SEDs for type 1 and type 2 AGNs. The total SEDs are decomposed into the AGN components and galaxy components, with the latter being further decomposed into the stellar, nebular, and dust components.

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CIGALE adopts energy conservation for galaxies; that is, all of the energy absorbed in the UV-to-optical band is assumed to be reemitted by dust. The figure shows that dust emission dominates in the FIR band. Therefore, we can have a tight constraint on the amount of dust as well as its attenuation based on the FIR data. Consequently, a better constraint on unattenuated stellar emission in the UV-to-optical band is obtained, from which CIGALE can derive SFR. Thus FIR photometry is very important for SFR calculation, especially for type 1 hosts because AGNs significantly contribute to their UV-to-optical emission, and the decomposition of the AGN component and galaxy component is difficult without FIR photometry. Indeed, SFR can be roughly estimated from single-band FIR photometry assuming typical SEDs (e.g., Chen et al. 2013; Yang et al. 2017).

In the rest-frame NIR band, the galaxy component often contributes more than the AGN component because the emission from the AGN is weak while stellar emission peaks in that band. Such contrast improves the reliability of measured M_⋆ because NIR flux is critical in deriving M_⋆ (e.g., Ciesla et al. 2015; Yang et al. 2018b).

We also investigate possible differences between the cosmic environments of type 1 hosts and type 2 hosts. We probe both host-galaxy local (sub-Mpc) and global (∼1–10 Mpc) environment based on the latest work on the cosmic environment in COSMOS by Yang et al. (2018a), who utilized a new technique to construct a measurement of the density field and the cosmic web up to z = 3 for COSMOS. To assess the local environment, they define a dimensionless overdensity parameter for each source:

$$\begin{eqnarray}&&1+\delta =\displaystyle \frac{{\rm{\Sigma }}}{{{\rm{\Sigma }}}_{\mathrm{median}}},\end{eqnarray} \tag{ 4 }$$

where Σ is surface number density, and Σ_median is the median value of Σ within z ± 0.2 at redshift z. They also mapped the sources to the field, filaments, or clusters of the cosmic web to assess the global environments. However, cluster signals are often dominated by noise at high redshift (z ≳ 1.2) when clusters are still forming and are usually in the form of protoclusters, and hence they only assign the global environment of sources into field and filament categories above z = 1.2. Generally, the overdensity (1 + δ) rises from the field to cluster environments, but there are substantial overlapping ranges of the overdensity for sources in different cosmic-web categories.

Since the z and L_X distributions are different for different types of AGNs (Figure 2), we need to control for them to avoid a possible difference in M_⋆ caused by different z or L_X. For example, AGNs tend to be found in massive galaxies with log M_⋆ ≳ 10.5 at z ≳ 1 (e.g., Yang et al. 2018b), while AGN host galaxies are less massive at z ∼ 0 (e.g., Heckman & Best 2014). Therefore, this redshift-related bias may affect our results if redshifts are not carefully controlled in our analysis. We divide the log L_X−z plane into a grid with Δz = 0.2 and Δlog L_X = 0.3 dex. Denoting the numbers of type 1 hosts and type 2 hosts in a grid element G as N_G,1 and N_G,2, respectively, we randomly select min{N_B,1, N_B,2} type 1 sources as well as the same number of type 2 sources in the considered grid element. After repeating the procedure in each bin, we can construct new type 1 and type 2 samples with similar distributions of z and L_X.

The new samples change every time we repeat the above procedures because we select sources randomly. We only show a typical example of the new samples in Case 1 here. We select 241 type 1 sources and 241 type 2 sources. Figure 4 displays the distributions of z and L_X for the 482 selected sources, which visually shows the similarity of their distributions for the two different types of AGNs after controlling for z and L_X. We also use a two-sample Kolmogorov–Smirnov test (K-S test) to examine their consistency: the p-values of z and L_X are 1.00 and 0.98, respectively, indicating that the two parameters have been controlled acceptably. Distributions of M_⋆ are displayed in Figure 5. The figure shows that the M_⋆ of type 1 hosts tends to be smaller than those of type 2 hosts. The K-S test shows that the difference is statistically significant with p-value = 3 × 10⁻⁷ (≈5σ), which is much smaller than our nominal p-value of 0.05 (2σ; see Section 1).

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We utilize a bootstrapping method to calculate errors of mean log M_⋆ ($\overline{\mathrm{log}\,{M}_{\star }}$) for type 1 and type 2 sources and their difference (${\rm{\Delta }}\overline{\mathrm{log}\,{M}_{\star }}={\overline{\mathrm{log}{M}_{\star }}}_{\mathrm{type}1}-{\overline{\mathrm{log}{M}_{\star }}}_{\mathrm{type}2}$). First, we perform bootstrap resampling on our samples 1000 times, and we repeat the above procedures, controlling for z and L_X, deriving host $\overline{\mathrm{log}\,{M}_{\star }}$ for each type of AGN, and calculating ${\rm{\Delta }}\overline{\mathrm{log}\,{M}_{\star }}$. Then we can obtain hundreds of $\overline{\mathrm{log}\,{M}_{\star }}$ and ${\rm{\Delta }}\overline{\mathrm{log}\,{M}_{\star }}$. Finally, we can derive their mean values and (84th–16th percentile)/2 of their distributions, and the latter values are adopted as 1σ uncertainties. It is necessary to calculate the error of ${\rm{\Delta }}\overline{\mathrm{log}\,{M}_{\star }}$ straightforwardly using the bootstrapping method instead of estimating it based on the log M_⋆ errors of type 1 and type 2 sources. The latter method to estimate the error of ${\rm{\Delta }}\overline{\mathrm{log}\,{M}_{\star }}$ is incorrect because it ignores the covariance between ${\overline{\mathrm{log}{M}_{\star }}}_{\mathrm{type}1}$ and ${\overline{\mathrm{log}{M}_{\star }}}_{\mathrm{type}2}$. Indeed, ${\overline{\mathrm{log}{M}_{\star }}}_{\mathrm{type}1}$ and ${\overline{\mathrm{log}{M}_{\star }}}_{\mathrm{type}2}$ are correlated with each other after controlling for z and L_X, and thus their covariance is not zero. Table 3 shows $\overline{\mathrm{log}\,{M}_{\star }}$ and ${\rm{\Delta }}\overline{\mathrm{log}\,{M}_{\star }}$ for both types of AGN hosts in Case 1 and Case 2, which indicates that type 1 sources have slightly smaller M_⋆ with a difference around 0.2 dex. The significance that the difference deviates from zero is around 4σ.

Table 3.  $\overline{\mathrm{log}\,{M}_{\star }}$ of Type 1 and Type 2 Samples

Case	${\overline{\mathrm{log}{M}_{\star }}}_{\mathrm{type}1}$	${\overline{\mathrm{log}{M}_{\star }}}_{\mathrm{type}2}$	Difference
Case 1	10.48 ± 0.04	10.71 ± 0.03	−0.22 ± 0.05
Case 2	10.51 ± 0.02	10.63 ± 0.02	−0.12 ± 0.03
Case 3	10.52 ± 0.03	10.71 ± 0.03	−0.19 ± 0.04

Note. Case 1 and Case 2 are defined in Section 3.1. We follow parameter settings of the AGN component in Buat et al. (2015) in Case 3, and the samples are the same as those in Case 1. The M_⋆ of type 2 populations seems to be slightly higher than those of type 1 sources.

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As a reliability check, we explore whether the difference in M_⋆ is sensitive to our parameter settings in SED fitting by adopting other settings in the AGN template fritz2006 in CIGALE. Buat et al. (2015) argued that setting a large angle between the line of sight and the accretion disk ψ (e.g., 80° or 90°) to represent type 1 AGNs may lead to an unrealistic contribution from the AGN component in the UV band. Therefore, they adopt different settings for type 1 AGNs (ψ = 0° and optical depth at 9.7 μm of τ = 1.0) from our settings in Section 3.3 (ψ = 90° and τ = 6.0). We follow their settings and label this case as Case 3. The results of M_⋆ analyses in Case 3 are displayed in Table 3. From the table, we can see that type 1 sources do have slightly smaller M_⋆ no matter which samples and parameter settings are adopted.

To probe a possible redshift evolution of such an M_⋆ difference, we show M_⋆ as a function of z in Figure 6. The figure indicates that M_⋆ of type 1 host galaxies is always smaller than that of type 2 hosts in each redshift bin. Besides, there is not an apparent dependence on z of M_⋆.

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4.2.1. SFRs in Our Sample

Generally, there are two methods to calculate SFR for AGN host galaxies: one is SED fitting, as we described in Section 3.3; the other method that is widely used is based on single-band FIR photometry. Previous studies based on different SFR measurement techniques reached qualitatively different conclusions about SFRs for type 1 versus type 2 hosts (e.g., Merloni et al. 2014; Bornancini & García Lambas 2018). To investigate this controversy, we estimate SFRs based on both SED fitting and FIR flux techniques, respectively.

In the latter method, FIR SEDs are assumed to be mainly contributed by cold dust, for which the temperatures do not vary significantly among different sources. We follow the method in Chen et al. (2013) and Yang et al. (2017) to calculate FIR-based SFR with FIR (100, 160, 250, 350, and 500 μm) fluxes. For FIR photometry at wavelength λ, we calculate the ratio between the observed flux S_λ and the monochromatic flux of a given template at the corresponding observed-frame wavelength λ (${S}_{\lambda }^{{\rm{T}}}$), and we derive the total infrared photometry L_IR using the following equation:

$$\begin{eqnarray}&&{L}_{\mathrm{IR}}=\displaystyle \frac{{S}_{\lambda }}{{S}_{\lambda }^{{\rm{T}}}}{L}_{\mathrm{IR}}^{{\rm{T}}},\end{eqnarray} \tag{ 5 }$$

where ${L}_{\mathrm{IR}}^{{\rm{T}}}$ is the 8–1000 μm luminosity of the adopted template.

Here, we use the templates in Kirkpatrick et al. (2012), among which a "z ∼ 1 SF galaxies" template with ${L}_{\mathrm{IR}}^{{\rm{T}}}=4.26\times {10}^{11}{L}_{\odot }$ is adopted for sources at z ≤ 1.5 and a "z ∼ 2 SF galaxies" template with ${L}_{\mathrm{IR}}^{{\rm{T}}}=2.06\times {10}^{12}{L}_{\odot }$ is adopted for sources at z > 1.5. The priority of the adopted wavelength is 500 μm > 350 μm > 250 μm > 160 μm > 100 μm. Such a priority level is used to avoid AGN contamination as much as possible (e.g., Stanley et al. 2017).

Table 4 shows the fractions of sources in our sample detected in each FIR band, and only 32.1% of our sources are detected in at least one FIR band. We can derive SFRs from FIR photometry for these detected sources. These sources also have reliable SED-based SFRs because CIGALE adopts energy conservation to constrain the stellar component based on the FIR photometry (Section 3.3). Figure 7 compares FIR-based SFRs with SED-based SFRs in Case 2. As the figure shows, these two kinds of SFRs are generally consistent within 0.5 dex for sources with logSFR ≳ 0.5, but FIR-based SFRs tend to be larger than SED-based SFRs. Such a bias is unlikely mainly caused by blending issues; that is, the flux of a faint source beside a bright source may be systematically overestimated (e.g., Magnelli et al. 2014). Indeed, the Herschel observations in the COSMOS field are relatively shallow (Oliver et al. 2012), and thus blending is not strong. Furthermore, the XID+ tool that was used to extract Herschel fluxes in COSMOS has been proved to mitigate this issue well and thus should give reliable estimates of the fluxes of crowded sources (Hurley et al. 2017). The bias might be primarily driven by a selection effect, as reported in Bongiorno et al. (2012) and Yang et al. (2017): at a given SED-based SFR, Herschel-detected sources tend to have higher FIR fluxes and thus higher FIR-based SFRs. The bias is more significant for sources with low SED-based SFRs because it is more difficult for sources with low SFRs to reach the detection threshold; thus, the detected ones are more likely to reside in the upper envelope of the SFR_FIR/SFR_SED distribution. The bottom panel of Figure 7 also indicates that the difference between the two SFR measurements is similar for both types of sources. Therefore, systematic errors on derived SFRs depend weakly on AGN type for sources within this SFR range, indicating that AGN light pollution for FIR-detected type 1 AGNs is unlikely to affect our SED fitting results systematically.

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Table 4.  Fractions of Sources Detected in Each FIR Band in Our Sample

Wavelength (μm)	100	160	250	350	500
Detection rate	15.8%	14.0%	26.6%	17.1%	5.9%

Note. For the same observing instrument (PACS at 100 and 160 μm; SPIRE at 250, 350, and 500 μm), the detection rate decreases as wavelength increases.

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As the first step to probe possible differences in SFRs between the two types of AGNs, we compare their host SFRs for FIR-detected sources. We control for z and L_X simultaneously using the same method as that in Section 4.1. As a typical example, we select 74 sources of each type in Case 1 after controlling for the parameters. We plot their FIR-based and SED-based SFRs in Figure 8. Type 1 and type 2 sources that are detected in the FIR band appear to have similar FIR-based SFRs with p-value = 0.88 using the K-S test, as well as SED-based SFRs with p-value = 0.76. We also repeat the procedure in several redshift bins and do not find statistically significant differences in SFRs for FIR-detected type 1 and type 2 populations. Therefore, we conclude that FIR-detected type 1 and type 2 sources have similar SFRs, as shown by both FIR-based and SED-based SFR measurements.

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For sources undetected by Herschel, SFRs derived from SED fitting may be affected by contamination from AGN emission at UV to optical wavelengths. Therefore, we stack Herschel fluxes to calculate typical FIR-based SFRs. Since sources are highly crowded in the SPIRE maps, we do not stack undetected sources in the SPIRE maps. For the PACS maps, we only stack sources in the 160 μm map, which is less affected by AGN contamination than the 100 μm map. We also find that all of the coverages of our sources are larger than half of the central coverage of the map. Therefore, our stacking procedure is not significantly affected by considerable noise in low-coverage regions, which may reduce the reliability of stacking (Santini et al. 2014).

To stack fluxes, we calculate net flux in the 160 μm residual map for each FIR-undetected source and adopt fluxes in the PEP catalog for FIR-detected sources. We derive mean values of the fluxes as stacked fluxes for type 1 and type 2 populations in three redshift bins: z < 1.4, 1.4 ≤ z < 2.0, and z ≥ 2.0. Then we convert the stacked fluxes to stacked average SFRs using Equation (5) with the average redshifts of the sources in each redshift bin. Finally, we average the SFRs in the three redshift bins weighted by the number of selected sources in each bin, and the resulting value is adopted as the mean FIR-based SFR in the whole redshift range.

We show mean FIR-based SFRs and mean SED-based SFRs of both populations, as well as their differences after controlling for z and L_X in Case 1 and Case 2, in Table 5. The differences are defined as the values of the type 1 sample subtracting those of the type 2 sample. Again, we use the bootstrapping method described in Section 4.1 to estimate the errors. The results of both cases indicate that type 1 and type 2 sources generally have similar average SFRs, while the FIR-based SFRs in Case 2 seem to be different. The significance of the difference is 2.04σ, which is slightly more significant than our threshold (2σ; see Section 1). Since we have four trials considered in Table 5, it is not surprising to find a 2.04σ deviation for a single trial (see the Bonferroni correction). This 2.04σ deviation corresponds to an overall significance of only 1.4σ for the whole sample based on the Bonferroni correction, and thus the deviation may simply be due to statistical fluctuations. Therefore, the host SFRs of type 1 and type 2 AGNs appear similar. We note that this similarity in average SFR holds not only for the FIR-based SFR but also for the SED-based SFR, indicating that the SED-based SFR measurements are not significantly biased. We attribute this reliability of the SED-based SFRs to the inclusion of FIR photometry (and upper limits) in the SED fitting, which effectively constrains the stellar population based on energy conservation (Section 3.3).

Table 5.  Average SFRs of Type 1 and Type 2 Samples

Parameter	Case 1			Case 2
	Type 1	Type 2	Difference	Type 1	Type 2	Difference
$\mathrm{log}\overline{\mathrm{SFR}}$, FIR (M⊙ yr−1)	1.62 ± 0.11	1.87 ± 0.08	−0.25 ± 0.13	1.72 ± 0.07	1.89 ± 0.05	−0.17 ± 0.08
$\mathrm{log}\overline{\mathrm{SFR}}$, SED (M⊙ yr−1)	1.98 ± 0.07	1.88 ± 0.05	0.11 ± 0.07	2.06 ± 0.10	1.90 ± 0.04	0.16 ± 0.11

Note. The "$\mathrm{log}\overline{\mathrm{SFR}}$, FIR" is converted from stacked 160 μm fluxes. Redshift and L_X are controlled to be similar for type 1 and type 2 sources. Both cases are defined in Section 3.1. The differences are defined as the values of the type 1 sample subtracting those of the type 2 sample.

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We also calculate FIR-based average SFRs in Case 1 in three redshift ranges: z < 1.4, 1.4 ≤ z < 2.0, and z ≥ 2.0, and the results are displayed in Figure 9. Note that the significance of the difference at 1.4 ≤ z < 2.0 is only 1.9σ, below our nominal significance threshold (2σ). Therefore, the figure indicates that type 1 and type 2 AGNs have similar average SFRs over the whole redshift range, and there is no apparent redshift trend of the difference in the SFRs.

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4.2.2. A Further Test for the SFR Measurements

We note that both methods of deriving SFR mentioned above rely on FIR photometry more or less, and thus they are not exactly independent. Therefore, we use the H_α luminosity as an independent SFR indicator and perform a simple cross-test for the methods among inactive galaxies.

The observed H_α fluxes are from the Fiber Multi-Object Spectrograph (FMOS)-COSMOS Survey (Silverman et al. 2015; Kashino et al. 2019). We select 1472 sources based on the following criteria: they have available H_α fluxes in the FMOS-COSMOS Survey so that we can derive their H_α-based SFRs, they are included in the COSMOS2015 catalog so that we can conduct SED fitting for them to obtain their SED-based SFRs, and they are undetected in the COSMOS-Legacy Survey so that they are normal galaxies instead of active galaxies generally. The last requirement aims to prevent AGNs from contaminating the observed H_α fluxes, and thus the H_α fluxes should be reliable. To obtain the intrinsic fluxes for these sources, we correct the observed fluxes based on the Calzetti extinction law (Calzetti et al. 2000):

$$\begin{eqnarray}&&{F}_{i}({{\rm{H}}}_{\alpha })={F}_{o}({{\rm{H}}}_{\alpha }){10}^{0.4{E}_{n}(B-V)k({{\rm{H}}}_{\alpha })},\,\mathrm{and}\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&k({{\rm{H}}}_{\alpha })=3.325,\end{eqnarray} \tag{ 7 }$$

where F_i(H_α) and F_o(H_α) are the intrinsic and observed H_α fluxes, respectively; E_n(B − V) is the color excess for nebular gas emission lines, which is derived from SED fitting. We then use the calibration in Section 2.3 of Kennicutt (1998) to convert the H_α luminosities L(H_α) to SFRs:

$$\begin{eqnarray}&&\mathrm{SFR}({M}_{\odot }\,{\mathrm{yr}}^{-1})=7.9\times {10}^{-42}L({{\rm{H}}}_{\alpha })(\mathrm{erg}\,{{\rm{s}}}^{-1}).\end{eqnarray} \tag{ 8 }$$

We compare H_α-based SFRs, FIR-based SFRs, and SED-based SFRs in Figure 10. All of the sources have H_α-based and SED-based SFRs, but some lack FIR-based SFRs. Therefore, we stack the FIR photometry to obtain the average FIR-based SFRs, and the stacking method has been described in Section 4.2.1. The figure shows that the three SFR measurements are generally consistent with each other.

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This additional independent cross-check further justifies the reliability of our SFR measurements. However, it is infeasible to further quantitatively assess the sensitivity of our methods in detecting the SFR differences of our AGN samples. This is because, to do this, we need H_α samples that have sample sizes, redshift distributions, and M_⋆ distributions matched with the AGN samples. However, the H_α sample size of FMOS-COSMOS is not sufficiently large to perform such a task. Also, nonnegligible measurement uncertainties of H_α-based SFRs likely exist, and the H_α method might not be sufficiently precise to gauge the accuracy of the FIR and SED methods.

We match our sources with the catalog containing environment measurements in Yang et al. (2018a) with a matching radius of 05 and obtain 1996 matched sources. The unmatched sources are mainly near the edge of the field or large masked regions in the COSMOS2015 survey, and they are filtered out in Yang et al. (2018a) to improve the reliability of density measurements.

We use log(1+δ) as the indicator for overdensity (see Section 3.4 for its definition). We control for z and M_⋆ using the method in Section 4.1, and we show the results in Case 1 and Case 2 in Table 6. The results in both cases indicate that the overdensities are similar for the two AGN populations. Therefore, AGN type is unrelated to the local environment, at least in the case of surface number density.

On larger scales, we investigate whether a particular type of AGN tends to reside in a certain kind of cosmic-web environment. As mentioned in Section 3.4, the global environment is classified as "field," "filament," or "cluster," and only "field" and "filament" are defined above z = 1.2. We examine whether the fractions of sources in field (f_field), filament (f_filament), and cluster (f_cluster) environments are different for different AGN types. Again, we control for z and M_⋆ and show the results in Table 7. The results show that the differences in f_field, f_filament, and f_cluster between type 1 sources and type 2 sources are insignificant.

We are unable to divide our sources into more redshift bins because our sample size is not sufficiently large. When controlling for SFR or L_X as well, we also find that the local and global environments are similar.