A CONNECTION BETWEEN OBSCURATION AND STAR FORMATION IN LUMINOUS QUASARS

The sample studied in this work comes from the 9 deg² Boötes survey region covered by the NOAO Deep Wide-Field Survey (NDWFS, Jannuzi & Dey 1999). Boötes is unique among extragalactic surveys because of its large area and the excellent multiwavelength coverage from space- and ground-based telescopes, which make possible statistical study of the rare luminous AGNs.

In this work, we use the multiwavelength photometry catalog from Brown et al. (private communication), which is the same as the one used in Chung et al. (2014). This catalog covers the optical to mid-IR bands, including the NDWFS optical observations in the Bw, R, and Ibands, near-IR photometry from the NOAO NEWFIRM survey (J, H, and Ks, Gonzalez et al. 2010), and the Spitzer Deep Wide Field Survey (SDWFS, Ashby et al. 2009) of the four bands of mid-IR observations from the Spitzer Infrared Array Camera (IRAC) at 3.6, 4.5, 5.8, and 8 μm. In addition, the mid-IR photometry from the Spitzer Multi-band Imaging Photometer (MIPS) at 24 μm is also included (IRS GTO team, J. Houck (PI), and M. Rieke). In this catalog, the optical to near-IR photometry was extracted from a matched aperture for each band. For the Bw, R, I, H, and Ks bands, the photometry was measured from images smoothed to a common point-spread function (PSF) with a 135 FWHM; while for the J band, the photometry was measured from images smoothed to a common PSF with a 160 FWHM. To ensure consistency in the photometry, we use 6'' aperture photometry from optical bands through the IRAC bands in the mid-IR to account for the large IRAC beam size. For the MIPS data, we use PSF photometry instead of aperture photometry due to the still larger beam size of MIPS. The 5σ flux limits of the optical to near-IR broadband photometry are 25.2, 23.9, 22.9, 21.1, 20.1, and 18.9 (Vega magnitudes) for the Bw, R, I J, H, and Ks bands, respectively. For the mid-IR wavelengths, the 5σ flux limits are 6.4, 8.8, 51, 50, and 170 μJy for the 3.6, 4.5, 5.8, 8.0, and 24 μm bands, respectively. An extensive description of the multiband photometry extraction can be found in Brown et al. (2007).

We also make use of the far-IR observations from the publicly available Herschel Multi-tiered Extragalactic Survey (HerMES, Oliver et al. 2012). We rereduced and mosaiced the Boötes SPIRE observations (Alberts et al. 2013), which include a deep ∼2 deg² inner region near the center of the field and a shallower ∼8.5 deg² outer region. We specifically focused on removing striping, astrometry offsets, and glitches missed by the standard pipeline reduction. We also convolved the raw maps with a matched filter (see Chapin et al. 2011), which aided in source extraction by lowering the overall noise and deblending sources. From this we generated a matched filter catalog with a 5σ detection threshold. In this catalog, we consider SPIRE sources with fluxes larger than 20 mJy as unambiguously detected. Completeness simulations show that these catalogs are 95% complete in the inner region and 69% complete in the outer regions above a flux of 20 mJy. We also find minimal flux boosting for low-SNR sources above this flux cutoff (see Section 2.2 in Alberts et al. 2013 for the details of the completeness simulation). We match the positions of the SPIRE catalog to the I-band positions with a matching radius of 5''. We tested the rate of spurious matches by offsetting the SPIRE source positions by 1' in a random direction and matching the randomly shifted catalog to the Boötes catalog. We found that with a radius of 5'', our matching between the SPIRE and Boötes catalog only yielded <2% spurious matches.

In addition, we also match the positions of the Brown et al. (2007) catalog to the publicly available Wide-field Infrared Survey Explorer (WISE) All-sky catalog (Wright et al. 2010) and obtain the profile-fit photometry magnitudes in the W1, W2, W3, and W4 bands (3.4, 4.6, 12, and 22 μm ).

As a complementary measurement of the AGN accretion rate and absorption by gas, we utilize X-ray data from the XBoötes survey, which is a mosaic of 126 short (5 ks) Chandra ACIS-I images (Kenter et al. 2005; Murray et al. 2005) covering the entire NDWFS. XBoötes contains 3,293 X-ray point sources with at least four counts in the AGES survey region. The conversion factors from count rates (in counts s⁻¹) to flux (in ${\rm erg}\ {{{\rm s}}^{-1}}$) for the XBoötes are 6.0 × 10⁻¹² ${\rm erg}\ {{{\rm s}}^{-1}}$ count⁻¹ in the 0.5–2 keV band and 1.9 × 10⁻¹¹ ${\rm erg}\ {{{\rm s}}^{-1}}$ count⁻¹ in the 2–7 keV band, which are derived for a 5 ks on-axis observation and assuming a canonical unabsorbed AGN X-ray spectrum (see Section 3.3 of Kenter et al. 2005).

For this study, we use spectroscopic redshifts (spec-zs) from AGES when possible. For the sources without a spec-z, we adopt the photometric redshifts (photo-zs) calculated using techniques combining artificial neural network and template-fitting algorithms (Brodwin et al. 2006). The uncertainty of this set of photo−zs is σ = 0.06(1 + z) for galaxies and σ = 0.12(1 + z) for AGNs. We note that the uncertainties for AGNs are dominated by the difference between photo−zs and spec-zs for the type I AGNs. The uncertainties in the photo−zs for QSO2s are difficult to estimate accurately, as only 9% of the QSO2s have spec-z measurements. For these 32 QSO2s, the uncertainty of the photo−zs is σ = 0.06(1 + z), which is consistent with the uncertainty for the galaxy population. Recently, spectroscopic follow-up of 35 WISE-selected, optically obscured quasars by Hainline et al. (2014) also found a photo−z derived from a template-based algorithm (Assef et al. 2010a) with a similar accuracy. This is not surprising, since the optical SED for the heavily obscured AGNs is dominated by the host galaxy, which has more spectral features and should allow for a more accurate photo−z measurement.

An upper limit for the QSO2 photo−z uncertainties can be estimated based on different approaches. H07 obtained an uncertainty of σ_z = 0.25(1 + z) by comparing the Brodwin et al. 2006 photo−zs to the photo−zs estimated by fitting three different galaxy templates to the Bw, R, I photometry. Since the accuracy of the photo−zs based on fitting three galaxy templates to three optical photometric observations is limited, the σ_z = 0.25(1 + z) uncertainty is a very conservative upper limit. For this study, we adopt the photo−z uncertainty upper limit of σ_z = 0.25(1 + z) from H07. However, this is a very conservative estimate, since the photo−z uncertainties for the QSO2s with host-galaxy-dominated optical SEDs are likely to be much smaller. A full discussion of the photo−z uncertainties is given in Section 8.

The AGNs in this work are drawn from the quasar sample of H11, which is a subset of quasars from the H07 mid-IR AGN sample. The H07 AGNs were identified based on the IRAC color–color selection criterion of Stern et al. (2005). For the redshift range of the H07 sample ($0.7\lt z\lesssim 3.0$), the IRAC filters probe wavelengths at which the characteristic power-law continuum from the reprocessed AGN radiation starts to dominate. At these wavelengths, the light from old stellar populations is characterized by a Rayleigh–Jeans tail of a blackbody radiation with temperature higher than 2,500 K, which peaks at wavelengths different from both the AGN accretion disk and the reprocessed AGN emission. In addition, dust emission at near-sublimation temperature heated by the AGN is significantly stronger than that heated by massive stars; thus AGNs can be easily identified by their mid-IR color (e.g., Lacy et al. 2004; Stern et al. 2005; Donley et al. 2012). These reprocessed photons at mid-IR wavelengths are less affected by obscuration than the optical and the X-ray photons due to their much smaller absorption cross section. Therefore, even heavily obscured AGNs can be identified using mid-IR selection criteria.

An important feature of the H07 catalog is that the AGNs were selected from the IRAC Shallow Survey (ISS, Eisenhardt et al. 2004), which has shallower flux limits than the later SDWFS survey. While the Stern et al. (2005) AGN selection can be contaminated by SF galaxies in deep mid-IR surveys (e.g., Donley et al. 2012), the contamination is negligible at the shallow flux limits of ISS (see Hickox et al. 2007; Assef et al. 2010a; Assef et al. 2011).

H07 also showed that the distribution of the optical (R) band to mid-IR (4.5 μm) colors is bimodal for the luminous mid-IR quasars. This bimodality can be easily explained by the difference between the SEDs of unobscured and obscured quasars. For mid-IR-selected quasars, the AGN dominates the mid-IR wavelengths, while for obscured quasars, the nuclear emission at optical wavelengths is heavily absorbed. Thus the SED in the R band for obscured quasars is similar to those of normal galaxies (e.g., Polletta et al. 2006; Hickox et al. 2007, and R. Hickox et al. 2015 in preparation). H07 has shown that the mid-IR-selected quasars can be separated into two distinct populations of quasars with an empirical color cut at R − [4.5] = 6.1. Most ($\sim 80\%$) of the quasars in H07 with R − [4.5] < 6.1 are spectroscopically confirmed as type 1 quasars; therefore in this work we refer to these unobscured quasars with R − [4.5] < 6.1 as QSO1s. As for quasars with R − [4.5] > 6.1, due to the limited depth of AGES, only $\sim 5\%$ have spectroscopic measurements and can be classified as type 2 quasars spectroscopically. However, H07 have extensively studied the quasars with R − [4.5] > 6.1 and have shown that these quasars are consistent with bright, obscured X-ray AGNs with N_H > 10²² cm⁻² and with AGN bolometric luminosities L_AGN > 10⁴⁵ ${\rm erg}\ {{{\rm s}}^{-1}}$. Therefore, we refer to the obscured quasars with $R-[4.5]\gt 6.1$ as QSO2s.

This empirical classification based on the quasar mid-IR to optical color has been shown to be broadly consistent with both the spectroscopically classified sources (Donoso et al. 2014) and the X-ray hardness ratio (defined as HR = (H − S)/(H + S), where H and S are the photon counts in the 2–7keV band and 0.5–2 keV band, respectively) classification criteria (Hickox et al. 2007; Usman et al. 2014). Since we lack spectroscopic confirmation for the majority of the QSO2s, it is possible that the QSO2s are different from the optical type 2 quasars. Recently, Lacy et al. (2013) have also studied the optical and near-IR spectroscopy of mid-IR AGNs selected using the Donley et al. (2012) IRAC color criteria and found that a significant fraction ($\sim 33\%$) of the AGNs with evident mid-IR power-law continuum have no significant emission lines consistent with the optical emission line diagnostics (e.g., Baldwin et al. 1981), suggesting that these mid-IR obscured AGNs are more deeply obscured than the optically selected type 2 AGNs. This has also been suggested by the recent study of Hainline et al. (2014).

To minimize the uncertainty in the measurements of quasar and host galaxy properties due to the scattering in the photo-zs, we focus on the H11 quasar sample, which is a subsample from H07. The H11 quasar sample focuses on the redshift range 0.7 < z < 1.8 and limits the QSO1s to those with broad optical emission lines and robust spec-z measurements from AGES. For the QSOs in this redshift range, all of the sources have I < 18, and the spectroscopic QSO1 sample is highly complete. For the QSO2s in this redshift range, only 32 ($\sim 9\%$) of the QSO2s have spec-z measurements. For the rest of the QSO2s, we adopt the photo-zs from Brodwin et al. (2006). This subset of QSOs have been used in the study of clustering properties of QSO1s and QSO2s in H11, which showed that in the redshift range 0.7 < z < 1.8, the sample is highly complete at the shallow flux limits of ISS. The mid-IR selection of this particular sample is shown to suffer less than <20% contamination from star-forming galaxies (Hickox et al. 2011). Since the purpose of this work is to compare the star formation properties of QSO1s and QSO2s, it is important to make sure that any difference in SF properties is not driven by the presence of starburst galaxy interlopers. Additionally, even for bright mid-IR quasars the starburst contribution in the MIR may be nonnegligible. Therefore, we rely on SED decompositions to disentangle the AGN and starburst components. The details of the SED decomposition are laid out in Section 3. Our SED-fitting results show that all of the H11 QSOs have a nonnegligible (>20%) AGN component. Based on the SED-fitting results, $\sim 3\%$ of the H11 QSOs would have ${{L}_{{\rm AGN}}}\$ less than the QSO criterion (${{L}_{{\rm AGN}}}\ \gt {{10}^{45}}$ erg s⁻¹). We therefore limit our focus to the sample of 546 QSO1s and 345 QSO2s that satisfies the QSO luminosity criterion and comprises $\sim 97\%$ of the H11 sample.

As a demonstration of the sample used in this work, we show the distribution of the IRAC [3.6] − [4.5] to [5.8] − [8.0] colors and the R − [4.5] to L_AGN distributions of the quasar sample in Figure 1. We note that in Figure 1(a), a small number of the H07 sources have [3.6] − 4.5 and [5.8] − [8.0] colors that lie outside the Stern et al. (2005) AGN selection wedge. The Stern et al. (2005) AGN selection wedge and the H07 sample were defined using the original ISS catalog in which the mid-IR photometry was derived using the standard aperture correction, which is different from the PSF profile-fitting corrections for individual sources in the Brown et al. (2007) catalog. Moreover, the updated IRAC photometry comes from SDWFS, which is two times deeper than the ISS. Thus, it is not surprising that a small fraction ($\sim 4\%$) of the original H07 sample does not meet the original Stern et al. (2005) criterion. However, the QSO sample in Figure 1(a) shows a tight [5.8] − [8.0] to [3.6] − [4.5] distribution, which is not seen in the similar Figure 1(a) of H11, which uses the original ISS photometry. This suggests that the majority of our sample does have power-law-like mid-IR SED with the high-precision photometry of SDWFS (e.g., see Figure 22 in H07). For the purpose of completeness we do not exclude the sources outside of the updated AGN selection wedge, since these sources might still have a nonnegligible AGN component that can be identified by the SED fits. However, we note the exclusion of this small fraction of sources has little effect on the average properties of the QSOs. We also show the redshift and flux distributions of the sample in Figure 2, which shows that the redshift distributions of the QSO1s and QSO2s are similar.

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Our SED-fitting procedures utilize the four empirical SED templates spanning 0.03–30 μm described in Assef et al. (2010a, A10 hereafter). A10 have shown that the nonnegative combinations of three different galaxy templates and a single AGN template, with the addition of extinction to the AGN component only, can robustly describe the optical to mid-IR SEDs of a wide variety of AGNs selected using Spitzer IRAC color (Assef et al. 2010a) or WISE color (Assef et al. 2010b; Chung et al. 2014). However, these templates do not include the far-IR wavelengths that are crucial for this work.

To extend the A10 AGN template to the far-IR, we create ad hoc AGN templates by replacing the hot-dust component of the A10 AGN template with the average infrared quasar template from Netzer et al. (2007) and the three infrared AGN templates (for low-, mean-, and high-luminosity AGNs) from Mullaney et al. (2011), which cover a wide range of AGNs with different mid-IR to far-IR properties. This is based on the assumption that the SED of the hot accretion disk around the SMBH is the same for all the radiatively efficient AGNs and that the differences are due to variable extinction and different spectral shapes in the mid- and far-IR wavelengths due to different distributions of dust. To account for the extinction at the AGN templates, we use the Draine (2003) extinction law with R_V = 3.1, which mainly attenuates the SED at $\lambda \leqslant 30\;\mu {\rm m}$ and also produces the silicate absorption features at mid-IR wavelengths that are common among AGN. The extinction strength is treated as a free parameter with a range of 0 < A_v < 48.

For the host galaxy templates, we consider two different components: the contribution from the stellar population of the galaxy, which accounts for the optical to near-IR emission, and a starburst component, which represents the mid- to far-IR dust emission from reprocessed stellar light. For the stellar population component, we follow the approach described in A10 by assuming that the stellar population in any galaxy is comprised of the nonnegative combination of the three empirical galaxy templates with populations of starburst (Im), continuous star-forming (Sbc), and old stars (elliptical), respectively (Assef et al. 2008; 2010a). Unlike the elliptical template, the Sbc and Im templates both contain hot-dust components in addition to the stellar population SEDs. Since the dust component does not extend to the far-IR wavelengths that we require and will be taken into account in the starburst templates, which we will choose later on, we replace the dust emission (λ > 4.9 μm ) in the Sbc and Im templates with the SED identical to the elliptical galaxy to create empirical stellar population templates with no dust emission. At these wavelengths the stellar SEDs are dominated by low-mass stars similar to the elliptical template. For our mid-IR-selected quasar sample, the starlight contribution is negligible at the wavelengths where hot-dust emission dominates.

For the starburst component, we use the 105 starburst templates from Chary & Elbaz (2001) and the 64 starburst templates from Dale & Helou (2002). The Chary & Elbaz (2001) and Dale & Helou (2002) starburst templates cover a wide range of SEDs for various prototypical local star-forming galaxies, with L_IR in the range between ${{10}^{8}}-{{10}^{13.5}}{{L}_{\odot }}$. For SF galaxies at z > 1, these templates have been shown to be reliable when used to estimate SF-related L_IR with monochromatic SPIRE observations (e.g., Elbaz et al. 2011). However, as pointed out by Kirkpatrick et al. (2012), the starburst galaxies at higher redshift have different dust temperatures and SED shapes. Although the effect of the different dust temperature on the estimation of $L_{{\rm IR}}^{{\rm SF}}$ is small when the wavelengths of the SPIRE bands probe the peak of the cold-dust emission, it is still important to include high-redshift starburst templates to accommodate the possibly different SED shapes of high-redshift starbursts. Therefore, we also include the z ∼ 1 and z ∼ 2 average starburst SED templates from Kirkpatrick et al. (2012) in our SED-fitting analysis. We thus adopt a total of 171 starburst templates in our SED-fitting analysis.

Given these SED templates described above, we fit the observed photometry with an iterative χ² minimization algorithm (Levenberg–Marquardt) to minimize the function.

$$\begin{eqnarray}&&\begin{array}{ccccccccccccccc} {{\chi }^{2}}=\mathop{\sum }\limits_{i=0}^{{{n}_{{\rm filters}}}} \\ \;\frac{{{F}_{{\rm obs},i}}-a{{F}_{{\rm star},i}}-b\ {\rm ext}(E(B-V)){{F}_{{\rm AGN},i}}-c{{F}_{{\rm starburst},i}}}{\sigma _{i}^{2}}. \\ \end{array}\quad \end{eqnarray} \tag{ 1 }$$

Here F_obs,i is the observed flux in the ith band and σ_i is its uncertainty. F_galaxy,i, F_AGN,i, and F_starburst,i are the fluxes of the stellar (optical), AGN (optical to far-IR), and starburst (far-IR) templates for filter i. The function ext gives the extinction of the AGN flux in band i, given the color excess E(B − V). We optimize a, b, c, and E(B − V) to minimize the χ².

While uniform NUV to mid-IR photometric coverage is available for all of the sources in our sample, only $\sim 18\%$ of them have a SPIRE 250 μm detection with a flux larger than the 20 mJy. Since our sample is selected to have AGN-dominated mid-IR SED, the far-IR photometry is essential to constrain the average SF properties. For the sources with direct far-IR detections, we fit their multiwavelength photometry with the SED templates described in the previous section. For the 731 sources without direct far-IR detections, we use a stacking analysis to constrain their average far-IR flux.

We stack the QSOs without direct far-IR detections in bins of R − [4.5] (see Section 4.2) and bins of L_AGN (derived in H11 from interpolations between the IRAC photometry and the MIPS 24 μm photometry). The uncertainty of the stacked flux is determined by bootstrap resampling. We created 10,000 random samples by drawing objects from the original samples with replacement until the number of objects in each random sample is the same as the number in the original sample. The uncertainty of the stacked flux is the variation in the stacked fluxes of the random samples. The details of the far-IR stacking analysis can be found in Section 3.1.1 of Alberts et al. (2013). The results of the stacking analysis are given in Table 1.

Table 1.  Results of Far-IR Stacking Analysis

Average f250 in Bins of R-4.5
R − [4.5] (Vega)	4.7	5.4	6.6	7.5
S250(mJy) (ND)	6.5 ± 0.73	7.9 ± 0.59	7.3 ± 0.75	8.5 ± 1.00
S250(mJy) (All)	8.0 ± 0.84	11. ± 0.77	16. ± 1.50	18. ± 0.21
$\langle z\rangle$ (All)	1.31	1.20	1.19	1.31
Average f250 in Bins of LAGN
${\rm log} \langle {{L}_{{\rm AGN}}}\rangle$ [erg s−1]	45.2	45.6	46.1	46.5
S250(QSO1)(mJy)	3.7 ± 0.82	5.4 ± 0.70	5.2 ± 0.75	7.7 ± 0.95
S250(QSO2)(mJy)	3.5 ± 0.94	8.8 ± 1.40	5.1 ± 0.66	8.4 ± 2.70
z (Average)	0.98	1.17	1.36	1.49

Notes. Results from the far-IR stacking analysis described in Section 4.2. The top half of the table shows the results for sources binned in R − [4.5]. The first row shows the results for the far-IR nondetected (ND) sources only, and the second row shows the result for the entire QSO sample. The average redshift for all QSOs in each bin is also given. The bottom half of the table shows the results for the entire QSO1 and QSO2 samples binned in their AGN bolometric luminosity. The average redshift for each R − [4.5] and L_AGN bin is also listed; we note that there is only a <0.02 average redshift difference between the QSO1s and QSO2s.

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To estimate the average SF luminosity of the far-IR nondetected QSOs, we assume that their 250 μm fluxes and 250 μm flux uncertainties are equal to the averages found from the stacking analysis for the sources with similar values of both R − [4.5] and L_AGN. We find that for the majority of the SPIRE nondetected sample, the best-fit SED reproduces the observed average far-IR flux well.

From SED-fitting results with far-IR fluxes stacked in bins if R − [4.5] and L_AGN, we find that $\sim 85\%$ of the quasars have a prominent AGN hot-dust component (AGN component >50%) at mid-IR wavelengths covered by the IRAC bands. All of the quasars have a nonnegligible (>20%) AGN component, confirming that the H11 sample consists of powerful quasars. However, the AGN dominates the quasar SED even at 24 μm for more than half of our sample. Therefore, the SF properties of these powerful quasars are primarily constrained by their far-IR photometry. For individual sources with only the stacked SPIRE flux to anchor the starburst component, this approach of using stacked far-IR flux can lead to inaccurate $L_{{\rm IR}}^{{\rm SF}}$. However, the main purpose of this work is not to determine the $L_{{\rm IR}}^{{\rm SF}}$ for individual QSOs. Instead, we take this approach to constrain the AGN contamination in the average far-IR SF luminosity with the well-fitted mid-IR AGN SED, which can robustly determine the average $L_{{\rm IR}}^{{\rm SF}}$ for different QSO populations. We note that when we compare the stacked fluxes from either the R − [4.5] bin or the L_AGN bin with the best-fit AGN component, we find that the average AGN contribution at 250 μm is only 5%, and none of the QSOs in our sample have an AGN component that contributes more than 40% at 250 μm. Since the average intrinsic SEDs for AGNs are expected to fall more rapidly in more luminous systems (Mullaney et al. 2011), a starburst component is essential to reproduce to average flux at 250 μm. Examples of the best-fit SEDs are shown in Figure 3.

With the best-fit SEDs, we calculate the total infrared luminosity for each QSO ($L_{{\rm IR}}^{{\rm tot}}$) by integrating the best-fit SEDs from $8-1000\;\mu {\rm m}$. For each source in our sample, we also calculate the L_IR of the starburst component by integrating the host galaxy component of the best-fit SED over the same wavelength range ($L_{{\rm IR}}^{{\rm SF}}$ hereafter).¹³ We find that for our sample, the average ratio between $L_{{\rm IR}}^{{\rm SF}}$ and $L_{{\rm IR}}^{{\rm tot}}$ is $\sim 55\%$, indicative of a nonnegligible AGN contribution to $L_{{\rm IR}}^{{\rm tot}}$ in these mid-IR luminous quasars. This is also consistent with the Kirkpatrick et al. (2012) results of the study combining Spitzer IRS spectra and multiband Herschel photometry for z ∼ 1 and z ∼ 2 ULIRGs. However, the far-IR flux probed by the SPIRE 250 μm band is dominated (>70%) by the starburst component for $\sim 90\%$ of our sample. This result confirms that quasar SEDs are still dominated by a starburst component at rest-frame wavelengths longer than 100 μm (e.g., Netzer et al. 2007; Mullaney et al. 2011; Rosario et al. 2012; Del Moro et al. 2013). Therefore, the average $L_{{\rm IR}}^{{\rm SF}}$ of powerful mid-IR quasars can still be robustly measured with the inclusion of far-IR photometry.

We next derive the bolometric AGN luminosity (L_AGN) by directly integrating the deabsorbed AGN component. We compare the L_AGN from our SED fitting with the L_AGN derived in H11 and find that our L_AGN is higher than the H11 L_AGN by an average of ∼0.1 dex. Since the derivation of L_AGN in H11 did not correct for the weak but nonnegligible dust obscuration and SF galaxy contamination in the mid-IR, it is not surprising that our L_AGN is different. However, the difference is small due to the fact that most of the quasars in this sample are dominated by the AGN, and the dust obscuration only weakly attenuates the SED at mid-IR wavelengths. We show the redshift distributions of $L_{{\rm IR}}^{{\rm tot}}$ and L_AGN in Figure 4.

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We begin with a very simple test by measuring the far-IR detection fraction above a flux limit of 20 mJy in the Herschel SPIRE 250 μm filter (f₂₅₀ hereafter) for QSO1s and QSO2s separately. In our survey region, the shallowness of the SPIRE observation implies that any quasars in our sample with a far-IR detection are at least as bright as luminous infrared galaxies (LIRGs, which are defined as galaxies with ${{L}_{{\rm IR}}}(8-1000\;\mu {\rm m})\gt {{10}^{11}}\;{{L}_{\odot }}$) at the same redshifts. At first glance, we find that among the 546 QSO1s, only 68 (12%) of them are detected in the SPIRE 250 μm filter, while 102 of the 345 (29%) QSO2s have far-IR detections.

We next use R − [4.5] as a rough proxy of the obscuration strength on the nuclear emission and study whether f₂₅₀ is related to the extinction at the R band. The primary goal of this analysis is to study whether the star formation properties of the quasar-hosting galaxies are related to the observed obscuration. Therefore, it is important to make sure the QSO1s and QSO2s are matched in key properties, i.e., redshift and AGN bolometric luminosity (L_AGN, estimated from the SED-fitting analysis discussed in Section 3). We divide our sample into four bins of R − [4.5] and calculate f₂₅₀ for each bin by applying statistical weights to each quasar so that the samples are matched in redshift and L_AGN in each bin. We find that the weighted f₂₅₀ increases rapidly with R − [4.5] for QSO1s. For QSO2s, f₂₅₀ is only weakly correlated with R − [4.5], but the f₂₅₀ of QSO2s is higher than that of QSO1s by a factor of 2. ± 0.2. We show the f₂₅₀ to R − [4.5] relation in Figure 5.

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Due to the flux limit of the SPIRE catalog, f₂₅₀ only reflects the fraction of QSOs hosted by galaxies with very luminous far-IR emission. To extend this analysis, we estimate the average 250 μm flux in bins of R − [4.5] to test if the far-IR flux of our quasar sample also evolves with R − [4.5]. To measure the average 250 μm flux (S₂₅₀) for all QSOs, we first estimate the average 250 μm flux for the sources without direct SPIRE observations, using the stacking analysis discussed in Section 3.2. Next, the stacked fluxes are combined with the sources individually detected in the far-IR to calculate the average S₂₅₀ for all QSOs. We show the average 250 μm flux (S₂₅₀) in the same R − [4.5] bins used for Figure 5, with results given in Table 1.

From the stacking analysis, we find that for QSOs without direct far-IR detections, there is no significant dependence of the average S₂₅₀ on R − [4.5]. However, the mean S₂₅₀ of the individually detected far-IR sources shows a R − [4.5] dependence similar to that of f₂₅₀. Therefore, driven by the increasing fraction of far-IR luminous sources, the average S₂₅₀ of the entire QSO sample is correlated with R − [4.5].

This result shows that for powerful mid-IR quasars with more dust attenuation at optical wavelengths, the average far-IR emission is stronger. This implies that at least part of the obscuration seen in the obscured QSOs might be due to the far-IR-emitting dust.

To further study the relation between AGN obscuration and $L_{{\rm IR}}^{{\rm SF}}$, we divide our QSO sample into bins of R − [4.5] as a proxy for AGN obscuration. To be consistent with Section 3.1 and avoid the uncertainties by the lack of spec-zs of QSO2s, we opt to use R − [4.5] instead of the E(B − V) derived from SED fitting as the proxy for nuclear obscuration, since the uncertainties of the photo−z limit the accuracy of our ability to measure E(B − V). We calculate the median AGN contribution at observed-frame R and [4.5] bands, using the best-fit SEDs in each bin. We find that toward redder R − [4.5] colors, the AGN contributes 89, 79, 29, and 12% at the R band and 74, 59, 43, and 60% at the [4.5] band. This suggests that the empirical R − [4.5] color is indeed a good proxy of AGN obscuration at optical wavelengths and that the QSO classification based on the R − [4.5] color is reliable. We then calculate the average $L_{{\rm IR}}^{{\rm SF}}$ ($\langle L_{{\rm IR}}^{{\rm SF}}\rangle$) in bins of R − [4.5]. We again estimate the uncertainty in $\langle L_{{\rm IR}}^{{\rm SF}}\rangle$ using bootstrap resampling.

We show the results in Figure 6(a). Even though the $L_{{\rm IR}}^{{\rm SF}}$ difference between QSO1s and QSO2s is large, $\langle L_{{\rm IR}}^{{\rm SF}}\rangle$ does not show the strong dependence on R − [4.5] seen for f₂₅₀ and the average S₂₅₀ (Figure 6(a)) within QSO1s and QSO2s. Additionally, the $L_{{\rm IR}}^{{\rm SF}}$ differences between the far-IR-detected QSO1s and QSO2s and the far-IR nondetected QSO1s and QSO2s are only 0.14 and 0.17 dex, which are not as significant as the 0.30 dex difference between all QSO1s and QSO2s. Thus the higher $\langle L_{{\rm IR}}^{{\rm SF}}\rangle$ of the QSO2 sample is mainly driven by its higher fraction of far-IR luminous SF galaxies.

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To explore the connections between AGN and host galaxy growth rates in different QSO populations, we separately divide the QSO1s and QSO2s into bins of L_AGN and measure the $\langle L_{{\rm IR}}^{{\rm SF}}\rangle$ for each bin. The uncertainties are again estimated by bootstrapping, as discussed in Section 5.1. We plot the L_AGN–$L_{{\rm IR}}^{{\rm SF}}$ relations for QSO1s and QSO2s in Figure 6(b). We find that both the QSO1 sample and the QSO2 sample have a positive $L_{{\rm IR}}^{{\rm SF}}$–L_AGN correlation with similarly shallow slopes, with ${\rm log} L_{{\rm IR}}^{{\rm SF}}\propto 0.25{\rm log} {{L}_{{\rm AGN}}}$ for QSO1s and ${\rm log} L_{{\rm IR}}^{{\rm SF}}\propto 0.27{\rm log} {{L}_{{\rm AGN}}}$ for QSO2s. However, the $\langle L_{{\rm IR}}^{{\rm SF}}\rangle$ for QSO2s is higher than that of QSO1s in each L_AGN bin by 0.28, 0.25, 0.32, and 0.28 dex.

For comparison, we also show the ${{L}_{{\rm AGN}}}-L_{{\rm IR}}^{{\rm SF}}$ model from Hickox et al. (2014), which assumes a direct, linear correlation between the average L_AGN and $L_{{\rm IR}}^{{\rm SF}},$ while the observed L_AGN is modulated by rapid variability. We calculate the Hickox et al. (2014) relation spanning the 0.7 < z < 1.8 redshift range in Figure 6 as the shaded region. We find that for all QSO2s besides those in the most luminous L_AGN bin, our result is consistent with the H14 model, and the QSO1s have $L_{{\rm IR}}^{{\rm SF}}$ slightly lower than the model predictions throughout the entire L_AGN range. However, for both types of QSOs, the slope of the $L_{{\rm IR}}^{{\rm SF}}$–L_AGN relation appears to be shallower than the prediction of the simple model, if we take the different average redshift in each L_AGN bin into account.

As was shown by the results in Table 1, the average redshifts for more luminous QSOs are higher. Although our far-IR stacking approach can reliably measure the average far-IR fluxes and hence the average $L_{{\rm IR}}^{{\rm SF}}$, it is important to note that the difference in the average redshift between the lowest and the highest L_AGN bins is 0.5, and it is possible that the observed correlation between $L_{{\rm IR}}^{{\rm SF}}$ and L_AGN is partially driven by the cosmic evolution of star formation and AGN accretion. Even though recent studies of the evolution of cosmic infrared luminosity density have shown that for the redshift range of the four L_AGN bins in Figure 6(b), the cosmic infrared luminosity is only weakly correlated with redshift (${{\rho }_{{\rm IR}}}\propto {{(1+z)}^{-0.3\pm 0.1}}$ for 1.1 < z < 2.85, Gruppioni et al. 2013), there is still a substantial evolution in the specific SFR (SFR per unit stellar mass) of "main-sequence (MS)" SF galaxies (e.g., Elbaz et al. 2011).

A simple estimate of the effect of MS galaxy SFR redshift evolution can be made by calculating the average $L_{{\rm IR}}^{{\rm SF}}$ for MS galaxies with ${{M}_{\star }}={{10}^{11}}\;{{M}_{\odot }}$ at the redshift range of our QSO sample. From the theoretical framework of dark-matter halo-abundance matching methods (e.g., Behroozi et al. 2013), ${{10}^{11}}\;{{M}_{\odot }}$ is the typical galaxy stellar mass hosted by dark-matter haloes of mass ${{M}_{{\rm halo}}}={{10}^{13.1}}[{{h}^{-1}}\;{{M}_{\odot }}]$, which is the halo mass reported in recent clustering studies of mid-IR QSOs (e.g., Hickox et al. 2011; DiPompeo et al. 2014; Donoso et al. 2014). At the redshift of each QSO in our sample, the $L_{{\rm IR}}^{{\rm SF}}$ for a ${{10}^{11}}\;{{M}_{\odot }}$ MS galaxy can therefore be evaluated using the redshift-dependent SFR-${{M}_{\star }}$ relation from Whitaker et al. (2012) and a Kennicutt relation, ${\rm SFR}=1.09\times L_{{\rm IR}}^{{\rm SF}}/{{L}_{\odot }}$ (Kennicutt 1998, modified for a Chabrier initial mass function). We find that the average $L_{{\rm IR}}^{{\rm SF}}$ for MS galaxies evaluated using this approach is consistent with the average $L_{{\rm IR}}^{{\rm SF}}$ in each L_AGN bin. This implies that for mid-IR quasars in this redshift range, the $L_{{\rm IR}}^{{\rm SF}}$ and instantaneous L_AGN might not be directly connected but still follow similar redshift evolution. This suggests that a common physical parameter (e.g., a common gas supply) might be driving the evolution of both SMBHs and galaxies. This is also consistent with the recent study of Rosario et al. (2013), which showed that the $L_{{\rm IR}}^{{\rm SF}}$–L_AGN correlation for broad-emission-line QSOs is consistent with a scenario in which quasars are hosted by normal star-forming galaxies.

For mid-IR-selected AGNs, contamination from star-forming galaxy interlopers is also an issue that might introduce biases to the measurements of AGN and star formation luminosities. While our SED-fitting results show that 95% of the sources in our sample are indeed powerful QSOs with AGN-dominated mid-IR SED, it is still very important to verify that the observed $L_{{\rm IR}}^{{\rm SF}}$–${{L}_{{\rm AGN}}}$ relation in Figure 6 is not caused by the incompleteness of our AGN selection criterion. In particular, a very powerful SF galaxy can harbor a heavily obscured AGN and still have starburst-like mid-IR SED. In such a case, the IRAC color of the SF galaxy would fall out of the Stern et al. (2005) selection wedge (e.g., Assef et al. 2010b; Kirkpatrick et al. 2012; Chung et al. 2014), and the sample selected with the Stern et al. (2005) wedge would show a biased $L_{{\rm IR}}^{{\rm SF}}$–${{L}_{{\rm AGN}}}$ relation.

By happenstance, the mid-IR color of typical star-forming galaxy templates occupies the lower-left corner of the Stern et al. (2005) wedge at the redshift range of this sample (e.g., Donley et al. 2012, Figure 17). Therefore, any AGN contribution in addition to the SF galaxy templates would easily promote a SF galaxy into the AGN identification wedge. This is particularly true for our sample of luminous quasars. We test this effect by first normalizing the 6 μm luminosity for AGN templates we used in the SED fitting described in Section 4 to L_AGN = 10⁴⁵ ${\rm erg}\ {{{\rm s}}^{-1}}$ to meet the minimum L_AGN criterion of our QSO sample. We next combine these normalized AGN templates with two archetypical starburst galaxy templates, M82 and Arp 220, from Polletta et al. (2007). We find that to have a star-forming galaxy falling out of the AGN identification wedge while having an L_AGN ∼ 10⁴⁵ erg s⁻¹, its $L_{{\rm IR}}^{{\rm SF}}$ must exceed 10⁴⁷ erg s⁻¹. This suggests that an SF galaxy must be a hyperluminous infrared galaxy (HyLIRG, ${{L}_{{\rm IR}}}\gt {{10}^{13}}\;{{L}_{\odot }}$) to be able to hide an underlying quasar-like AGN component. According to the far-IR luminosity function of Gruppioni et al. (2013), there would only be less than two HyLIRGs in the redshift range of our sample given the size of the Boötes survey region. Because of the large number of sources in the lowest L_AGN bin of our sample, the inclusion of the two additional QSOs hidden in HyLIRGs would only affect the average $L_{{\rm IR}}^{{\rm SF}}$ by 0.15 dex, which is still within the 2σ range of the original ${{L}_{{\rm SF}}}$.

We can also estimate biases in $L_{{\rm IR}}^{{\rm SF}}$ due to the sources not selected in the AGN identification wedge by examining the SEDs of the sources not classified as mid-IR QSOs. In the redshift range of our sample, there are 77 SPIRE-detected sources outside the Stern et al. (2005) wedge. When we fit the SEDs of these sources we find that most of these powerful SF galaxies have no significant AGN contribution in the mid-IR. For the sources without a mid-IR AGN component, we assume that AGN contributes <10% to the mid-IR monochromatic luminosity at 6 μm as an upper limit. Only four of the 77 have L_AGN satisfying the ${{L}_{{\rm AGN}}}\gt {{10}^{45}}$ erg s⁻¹ criterion. If we add these four sources into the lowest L_AGN bin, the average $L_{{\rm IR}}^{{\rm SF}}$ would only increase by 0.05 dex. Therefore, we conclude that the ${{L}_{{\rm SF}}}$–${{L}_{{\rm AGN}}}$ correlation observed in Figure 6 is not biased by the exclusion of heavily obscured quasars hidden in powerful SF galaxies.

We reiterate that the sources with a dominating starburst component have been removed from the final sample studied in this analysis based on the SED fits discussed in Section 3. Therefore, the higher far-IR detection fraction for QSO2s is not due to the inclusion of starburst interlopers in the mid-IR AGN sample. Another possible issue that can drive the higher far-IR detection fraction for the QSO2s are the photo−z uncertainties. We here examine this issue by testing the null hypothesis that QSO1s and QSO2s have exactly the same far-IR detection fraction and redshift distribution.

From the AGES catalog, we select all of the sources with broad emission lines (the BLAGNs). In the AGES catalog there are a total of 1,619 BLAGNs, of which 181 of them have a SPIRE 250 μm flux greater than 20 mJy. This far-IR detection fraction is similar to that for the QSO1 sample. To test if the uncertainties in photometric redshifts can boost the far-IR detection fraction, we randomly scatter the redshifts for all BLAGNs with the conservative uncertainty of σ_z = 0.25(1 + z) (discussed in Section 2.1). In each random realization, we select the sources with a randomly assigned redshift within 0.7 < z < 1.8 and calculate their far-IR detection fraction. We repeat this process 100 times and find that on average, the random sample would have a far-IR detection fraction of only $\sim 9\%$. This means that the uncertainty in the photometric redshift would actually decrease the observed far-IR detection fraction if the far-IR luminosity function and the redshift distribution are the same for QSO1s and QSO2s. This is likely due to the negative k-correction at 250 μm  for galaxies with typical cold-dust SEDs (e.g., Blain 1996; Negrello et al. 2007). The starburst cold-dust emission peaks at rest-frame $\sim 100\;\mu {\rm m},$ which corresponds to the SPIRE 250 μm for an object at z = 1.5. Therefore, the starburst galaxies at lower redshifts are not brighter than our far-IR-detected QSOs at observed-frame 250 μm due to the negative k-correction. High-redshift starbursts are also not likely to be included in our far-IR-detected sample, as the 250 μm filter probes the rapidly dropping Rayleigh–Jeans tail of the cold-dust emission for objects beyond the redshfit range of our sample.

Considering the significant difference of $\sim 17\%$ between the far-IR detection fractions of QSO1s and QSO2s, we confirm that the QSO2s are indeed more likely to be hosted by galaxies with strong far-IR emission than QSO1s.

Since the majority of QSO2s have only photo−zs, and luminosity measurements are redshift dependent, it is of extreme importance to confirm that the 0.3 dex average $L_{{\rm IR}}^{{\rm SF}}$ difference between QSO1s and QSO2s is not driven solely by the uncertainty of photo−zs. Similar to the previous subsection, we estimate the effect of the photo−z uncertainty by testing the null hypothesis that the QSO2s have the same $L_{{\rm IR}}^{{\rm SF}}\$ distribution as the QSO1s. We again randomly assign redshifts to the AGES BLAGNs based on their spec-zs and the uncertainty upper limit σ_z = 0.25(1 + z). For the sources with a randomly assigned redshift within the 0.7 < z < 1.8 range, we perform the SED analysis (described in Section 3), using the assigned redshift, to calculate their average $L_{{\rm IR}}^{{\rm SF}}\$. We repeat this process 100 times and find that the average $L_{{\rm IR}}^{{\rm SF}}\$ difference between the random samples and the original QSO1 sample is 0.08 ± 0.02 dex, which is much smaller in comparison to the observed 0.3 dex difference between QSO1s and QSO2s. We also note that σ_z = 0.25(1 + z) is a very conservative upper limit, so the effects of photometric redshift uncertainty are almost certainly smaller. The L_SF difference between QSO1s and QSO2s is not driven by the photo−z uncertainty.