SUPERMASSIVE BLACK HOLE GROWTH IN STARBURST GALAXIES OVER COSMIC TIME: CONSTRAINTS FROM THE DEEPEST CHANDRA FIELDS

Samples were drawn from two fields with deep X-ray through infrared coverage: the Extended-Chandra Deep Field-South (E-CDF-S), which includes the ∼2 Ms Chandra Deep Field-South (CDF-S), and the Extended Groth Strip (EGS). The primary sample of star-forming galaxies and AGNs was constructed using all sources with Spitzer MIPS detections at 70 μm in the Far-Infrared Deep Extragalactic Legacy (FIDEL) survey. The FIDEL data comprise very deep coverage of ≳ 90% of the E-CDF-S and EGS fields at 24 μm and 70 μm. Source catalogs were created from the DR2 mosaic images¹⁰ using the DAOPHOT tool.¹¹ Aperture fluxes measured by DAOPHOT were corrected using the point source function derived by Frayer et al. (2006) to derive the total fluxes. No color corrections were performed, as they are expected to be ≲ 10% for the bulk of our sources. We use the FIDEL 70 μm catalog as the basis of our sample because emission at this wavelength should suffer less from spectral complexity and have a smaller AGN contribution for sources at redshifts up to ∼3 than emission at 24 μm. For example, at z ≳ 1, 24 μm observations would sample rest-frame emission at λ ≲ 12 μm where complex spectral features from PAH emission and silicate absorption are present in the spectra of many ULIRGs and AGNs (e.g., Weedman et al. 2005; Armus et al. 2007; Desai et al. 2007).

Before attempting to identify the counterparts at other wavelengths, we made a cut at a 70 μm signal-to-noise ratio (S/N) of 3, above which the median positional uncertainty in the 70 μm sources is ≲ 3″ (although it reaches ∼8″ near our adopted S/N cutoff) and completeness is high (≈85%). The S/N and completeness of the 70 μm detections were estimated using simulations in which fake sources were inserted in the images and their fluxes recovered. To exclude regions of very low exposure near the survey edges, where spurious sources are more common even at S/N > 3, we also made a cut at an exposure time of 1000 s (exposure times were taken from the exposure maps provided with the FIDEL catalogs). With this cut on exposure time, the total areal coverage of regions with both deep X-ray and mid-to-far-infrared data is ≈1100 arcmin² in the E-CDF-S and ≈1400 arcmin² in the EGS. The S/N and exposure-time cuts result in total source numbers of 567 and 725 in the E-CDF-S and EGS, respectively. The 70 μm flux limit for our sample varies with the exposure time (by a factor of up to ∼5) and reaches a minimum flux density of ≈1.8 mJy in the GOODS-S region of the E-CDF-S.

Due to the large point spread function of the Spitzer MIPS instrument and to source blending, 70 μm source positions can be uncertain by large amounts (the simulations described above give errors of up to ∼8″ for a source with S/N = 3). To minimize the number of spurious counterparts, we performed a crossmatch between the 70 μm and 24 μm catalogs using a probabilistic matching method (described in detail in Luo et al. 2010) that takes into account both the estimated source positional errors and their fluxes (e.g., Sutherland & Saunders 1992; Ciliegi et al. 2003). This method tends to recover a larger fraction of true counterparts than the standard method that uses a single fixed matching radius and ignores flux information when selecting among possible counterparts. Using this method, we find that the expected fraction of spurious 24 μm-to-70 μm crossmatches is ≲ 10%, a value ≈40% lower than that obtained with the standard method using a fixed matching radius that recovers approximately the same number of total counterparts.¹² With this method, 527 E-CDF-S and 678 EGS 70 μm sources with S/N > 3 matched to a 24 μm source. Since the 24 μm data are much deeper than the 70 μm data for these fields (by a factor of ≳ 30), we can reasonably expect that all 70 μm sources should have 24 μm counterparts. Indeed, a visual inspection of the ≈6% of 70 μm sources that lack 24 μm matches suggests that most suffer from significant blending that has distorted their shapes (and hence centroids). By requiring a 24 μm match for each 70 μm source, we eliminate these problematic sources that likely have positions and fluxes in error by large amounts.

Additionally, ≈25% of the 70 μm sources with identified 24 μm counterparts have more than one 24 μm source within ≈4″. Such multiple matches could imply significant blending is present in the 70 μm images, possibly leading to spurious crossmatches and to misestimates of the 70 μm flux. To minimize spurious crossmatches, we can use the observed distribution of 24/70 μm color for sources with unambiguous counterparts to select reliably the correct counterpart from multiple matches. To this end, we compared the 24/70 μm colors of each possible counterpart to the observed distribution of colors for 70 μm sources with single matches. If two counterparts had colors that differed significantly (by >2σ) from the mean and the reliabilities determined from the probabilistic matching process were similar for the two, the counterpart with the color closer to the mean was chosen. In this way, we chose a different counterpart from that preferred by the probabilistic matching in ≈5%–10% of cases (depending on the field) with multiple matches. Additionally, in some cases with multiple nearby 24 μm sources, blending in the 70 μm images can be significant. However, we find that on average only ≈5% of the 24 μm sources have 70 μm counterparts. Given that we find multiple 24 μm sources for ≈25% of the 70 μm sources, each with an average of 2.2 24 μm sources within ≈4″, we expect blending to have a significant effect on the measured 70 μm flux in only 1.2 × 0.25 × 0.05 ≈ 1.5% of the 70 μm sources. At this level, the presence of blended sources should not affect our results significantly, and we therefore do not attempt to correct for them further.

Using this 70 μm sample as the basis, we crossmatched the sources with the following X-ray, optical, and infrared catalogs. For the E-CDF-S, we used the Chandra X-ray catalogs of Luo et al. (2008; CDF-S) and Lehmer et al. (2005; E-CDF-S); the COMBO-17 (Classifying Objects by Medium-Band Observations in 17 filters; Wolf et al. 2004), MUSYC (Multiwavelength Survey by Yale-Chile; Gawiser et al. 2006), and MUSIC (Grazian et al. 2006) optical and near-infrared catalogs; and the SIMPLE (Spitzer IRAC/MUSYC Public Legacy survey in the Extended-CDF-S) mid-infrared catalog (Damen et al. 2009). For the EGS, we used the Chandra X-ray catalogs of Laird et al. (2009), the optical CFHTLS¹³ and CFH12K (Coil et al. 2004) catalogs, the near-infrared Palomar catalog (Bundy et al. 2006), and the IRAC catalog of Barmby et al. (2008).

Since all of our 70 μm sources are required to have counterparts in the 24 μm data, we can use the more precise 24 μm positions (with typical uncertainties of ∼1″) when matching to the optical catalogs, thereby reducing the number of likely spurious optical-to-70 μm matches. Additionally, since many of our sources should have radio counterparts (since radio emission is often associated with starbursts and AGNs), we can further refine the positions using the highly accurate astrometry of the radio-source catalogs available from Very Large Array surveys of the fields (with typical source positional uncertainties of ≲ 02). To this end, we performed crossmatching (again using the probabilistic matching method) between the 24 μm sources and the 20 cm catalogs of Miller et al. (2008) in the E-CDF-S and version 1.0 of the AEGIS20 catalog¹⁴ in the EGS. We found radio matches to 219 (≈41%) E-CDF-S sources and 166 (≈25%) EGS sources (note that the 20 cm EGS survey does not cover the entire field). Due to the low spatial density of radio sources in these surveys, we expect ≲ 1% of these matches to be spurious.

We next searched for optical counterparts to the 70 μm sources by 24 μm or radio source position. For 70 μm sources with an identified radio counterpart, we used a matching radius of 05 (due to the much smaller positional uncertainties, probabilistic matching was not used). For sources without a radio counterpart, we used a radius of 1″. When multiple optical matches occur, we selected the source with the smallest separation. With these matching radii, we expect ≲ 7% of the optical-to-70 μm matches to be spurious. We then crossmatched the X-ray source positions to the 24 μm or radio source position, using a variable matching radius that depends on the positional uncertainty of the X-ray source. We followed the method used in Luo et al. (2008) and define the matching radius as r = 1.5Δ_X, where Δ_X is the X-ray positional uncertainty given in the catalogs. Lastly, we used a matching radius of 075 to identify matches to mid-infrared Spitzer IRAC sources and a radius of 1″ to match to UV Galaxy Evolution Explorer (GALEX) sources. Table 1 summarizes the results of the crossmatching. In total, the final sample comprises 1022 unique 70 μm sources with identified optical counterparts, of which 158 have an identified X-ray counterpart.

To obtain redshift estimates for our 70 μm sources, we followed the process described above to crossmatch (using a 05 radius) the optical source positions to all publicly available spectroscopic redshift catalogs of the E-CDF-S and EGS (e.g., Cristiani et al. 2000; Bunker et al. 2003; Dickinson et al. 2004; Le Fèvre et al. 2004; Stanway et al. 2004; Strolger et al. 2004; van der Wel et al. 2004; Davis et al. 2007). When more than one spectroscopic redshift was available for a given source, the redshift of the higher quality (judged by the quality flags provided with the catalog) was used. If two spectroscopic redshifts were deemed of equal quality or the quality was unknown, the average was taken. In such cases, the difference between the two redshifts was typically ≲ 10%. In total for all three fields, 408 (≈40%) of 1022 sources have high-quality spectroscopic redshifts determined from two or more spectral features.

Although the majority (≈60%) of our sources lack high-quality spectroscopic redshifts, almost all have high-quality photometric data in multiple bands from near-UV to mid-infrared wavelengths. Although Wolf et al. (2004) produced a high-quality photometric redshift catalog for the entire E-CDF-S, new near- and mid-infrared data (from the MUSYC JHK and SIMPLE IRAC surveys; see Table 1 for the fraction of 70 μm sources in each field with near- and mid-infrared detections) have recently become available that should be particularly helpful in deriving accurate photometric redshifts for sources at higher redshifts (z > 1.4), which are generally not available in the Wolf et al. catalog.¹⁵ Additionally, no photometric redshift catalog is currently publicly available for the EGS. Therefore, we can use all existing photometric data to obtain additional and improved photometric redshifts for our sample. To this end, we used the publicly available Zurich Extragalactic Bayesian Redshift Analyzer (ZEBRA; Feldmann et al. 2006) to derive redshifts for the sources that lack a spectroscopic redshift, except for CDF-S X-ray sources, for which we use the photometric redshifts of Luo et al. (2010), derived using a very similar method but with a more sophisticated treatment of the photometry (e.g., including upper limits for non-detections). Details of the parameters used as input to ZEBRA to derive the photometric redshifts and estimates of the quality of the resulting redshifts are given in the Appendix.

In general, the most secure photometric redshifts are those for bright sources (m_R < 24 AB mags), which comprise the great majority (≈93%) of our final sample of 1022 sources. In Figure 1, we compare the photometric redshifts derived by ZEBRA to spectroscopic ones for the subsample of 408 sources in our final sample with spectroscopic redshifts. Assuming that the spectroscopic redshifts are accurate and the spectroscopic sources are representative of the entire sample, ≈97% of our sources will have redshifts with |z_true − z|/(1 + z_true) < 0.2. For AGNs only (identified following Section 2.6), of which 55 of 108 have spectroscopic redshifts, the fraction of such sources is ≈94%. However, the spectroscopic sample is unlikely to be fully representative, and we therefore expect that the true fraction of sources with incorrect redshifts will be higher by roughly a factor of three (see the Appendix for details), but still within acceptable limits (≲ 10%).

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Lastly, it should be noted that an important consequence of obtaining redshift estimates for all of the 70 μm sources in our sample with identified optical counterparts is that our study will not suffer from strong biases related to incomplete redshift coverage. For example, an incomplete sample based on redshift surveys that target AGNs or X-ray sources preferentially (e.g., Zheng et al. 2004) would result in an artificially high AGN fraction.

The rest-frame mid-infrared luminosity of a typical starburst galaxy or AGN is dominated by reprocessed emission from dust. Such emission gives a direct measure of the strength of the star formation or AGN emission that the dust reprocesses. Therefore, it is of interest to investigate how the AGN fraction relates to this luminosity. To derive the rest-frame luminosities, we first constructed observed-frame mid-infrared SEDs from the available Spitzer data, which span observed-frame wavelengths from 3.6 μm to 70 μm (due to the large positional uncertainties inherent to the 160 μm data, these data were not used). The observed SED was then shifted to the rest frame of the source using its redshift. We then used linear interpolation in log space to derive the monochromatic luminosity at a rest-frame wavelength of 30 μm (L₃₀; model SED were not used, as a variety of AGN, starburst, and hybrid sources that are difficult to model are expected to be present). This wavelength was chosen to lie within the wavelength coverage of the observed SEDs of most objects, negating the need for large extrapolations. We show the rest-frame mid-infrared luminosities as a function of redshift in Figure 2(a). It is clear from this figure that the sensitivity limits of the FIDEL survey are such that our sample is roughly complete only for sources with L₃₀ > 10¹² L_☉. Below this luminosity, the completeness varies with redshift, being ≈100% at L₃₀ > 10¹¹ L_☉ to z = 1 and at L₃₀ > 10¹⁰ L_☉ to z = 0.5.

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Additionally, the mid-infrared color (typically calculated using the observed-frame fluxes in the IRAS bands as F_25 μm/F_60 μm) of a source gives an indication of the temperature of the emitting dust: higher ratios indicate relatively more emission at shorter wavelengths, indicative of emission from warmer dust. Cooler dust temperatures are likely to be associated with dust heated by young stars, whereas warmer temperatures are more likely to be indicative of dust heated by AGN emission (e.g., de Grijp et al. 1985; Sanders et al. 1988). Therefore, it is of interest to examine the mid-infrared colors for our sample. In Figure 2(b), we plot the ratio of 24/70 μm flux (which, for our purposes, we consider to be equivalent to the ratio of 25/60 μm flux) against the redshift, and in Figure 3, we plot it against the 70 μm flux. For local sources, ratios below log (F_24 μm/F_70 μm) ≈ −0.7 are generally indicative of emission from cool dust, whereas higher ratios are indicative of warm dust (e.g., de Grijp et al. 1985; Sanders et al. 1988).

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It should be noted that the observed mid-infrared color for a given galaxy is a strong function of the redshift: at higher redshifts (z ≳ 1.5), the portion of the spectrum measured by observed-frame 24 μm emission suffers from increasing spectral complexity due to the possible presence of strong absorption and emission features below rest-frame wavelengths of ≈10 μm. Additionally, there is evidence that high-redshift (z ≳ 1.5) galaxies exhibit stronger PAH emission features than local galaxies of the same luminosity (e.g., Murphy et al. 2009) that will add further redshift-dependent changes to the color. Therefore, it is difficult to infer directly a dust temperature from the mid-infrared color in sources at z ≳ 1.5 (e.g., Papovich et al. 2007; Mullaney et al. 2010). In Section 5.3, we investigate how the inclusion or exclusion of AGN hosts with warm mid-infrared colors affects our results.

The purpose of this study is to quantify the AGN fraction in mid-infrared sources; therefore, a reliable means of identifying the bulk of the AGN population is critical. Since AGNs are one of only two types of luminous X-ray point sources in the distant universe (the other being starburst galaxies), and X-rays are not readily absorbed by surrounding material, the X-ray observations are extremely efficient at identifying AGNs (e.g., Brandt & Hasinger 2005). In particular, the rest-frame 0.5–8.0 keV luminosity and the hard-to-soft X-ray band ratio are useful properties in distinguishing between AGNs and starbursts. We therefore use the Chandra X-ray source catalogs of the CDF-S, E-CDF-S, and EGS to calculate the X-ray properties of our sources.

For the E-CDF-S field, we use the 2 Ms CDF-S X-ray source catalog of Luo et al. (2008) and the 250 ks E-CDF-S X-ray source catalog of Lehmer et al. (2005). For the ≈200 ks EGS, we use the X-ray source catalog of Laird et al. (2009). Since a number of differences exist between the EGS catalog and the other two catalogs in the band definitions used to measure counts and fluxes (e.g., the full band is defined as 0.5–7.0 keV in the EGS catalog and 0.5–8.0 keV in the CDF-S and E-CDF-S catalogs), we used a simple power-law model to convert counts and fluxes to a uniform system. For these conversions, we first derive the effective power-law index from the band ratio given in the EGS catalog following the method used in Section 3.3 of Luo et al. (2008). Briefly, we find the power-law model (including an assumed Galactic column density) that reproduces the observed band ratio. For sources with a low number of counts (≲ 30 counts total; for details, see Luo et al. 2008), we adopt Γ = 1.4, a value representative of faint sources. We then use the effective power-law index to convert counts measured in the EGS bandpass to the corresponding E-CDF-S bandpass. X-ray luminosities and band ratios (the ratio of flux in the 2.0–8.0 keV band to that in the 0.5–2.0 keV band) were then calculated directly from the catalog fluxes.

To identify AGNs among the X-ray sources, we follow the identification criteria used by Bauer et al. (2004), which we outline briefly here. AGNs were first identified based on their intrinsic, rest-frame 0.5–8.0 keV luminosities. An estimate of the intrinsic absorption is needed to derive this luminosity. By assuming that the AGN X-ray spectra are well represented by an intrinsic power law with a photon index of 1.8, we can use the band ratio (the ratio of counts in the 2–8 keV band to the 0.5–2 keV band) to derive a basic estimate of the intrinsic N_H (see Section 3.1 for details of the fitting procedure). Sources with rest-frame L_{0.5 − 8.0 keV} ≳ 3 × 10⁴² erg s⁻¹ are likely to be AGNs, since starbursts generally have luminosities below L_{0.5 − 8.0 keV} ≲ 10⁴² erg s⁻¹. However, to ensure that luminous starbursts are not misclassified as AGNs, we calculated the predicted 2–10 keV luminosities from star formation from the relations of Persic & Rephaeli (2007). Persic et al. find that the scaling relation for ULIRGs is different from that of lower-SFR objects. Therefore, we use the following relation from Persic & Rephaeli (2007) to estimate the 2–10 keV luminosity due to star formation for systems with SFR ≲ 100 M_☉ yr⁻¹:

For systems with SFR ≳ 100 M_☉ yr⁻¹, Persic & Rephaeli (2007) found that a somewhat different scaling was preferred:

For the purposes of this calculation, we determined the SFR following Section 3.4 by assuming, conservatively, that the entire observed 70 μm flux is due to star formation. The predicted rest-frame 2–10 keV luminosity was converted to an observed-frame 0.5–8 keV flux assuming a Γ = 2 power-law spectrum and the source redshift. We then classified as AGNs all sources with both L_{0.5 − 8.0 keV} ≳ 3 × 10⁴² erg s⁻¹ and with an observed luminosity >3 times that predicted from the SFR.

Next, sources were classified by the hard-to-soft X-ray band ratio: sources with band ratios above 0.8 (corresponding to effective photon indices Γ ≲ 1) were classified as AGNs, as starbursts almost always have softer X-ray spectra (with Γ ≳ 1). Lastly, in addition to these purely X-ray-based criteria, we also use the X-ray-to-optical flux ratio as a further discriminator of AGN activity. We classify sources with f_{0.5 − 8.0 keV}/f_R > 0.1 as AGNs, where f_R is the R-band flux. Using these criteria, we identified AGNs in 108 (≈10%) of the 1022 70 μm sources for the combined E-CDF-S and EGS fields. The majority of identified AGNs meet more than one selection criterion. In particular, of 108 AGNs, 12 were identified uniquely using L_{0.5 − 8.0 keV} ≳ 3 × 10⁴² erg s⁻¹ (which identified 94 AGNs in total), 9 using Γ ≲ 1 (which identified 47 AGNs in total), and 7 using f_{0.5 − 8.0 keV}/f_R > 0.1 (which identified 83 AGNs in total). Therefore, we expect that few, if any, non-AGNs are misidentified as AGNs in our sample.

The remaining 50 non-AGN X-ray sources have properties consistent with starbursts and are considered to be such in the following analysis. The fraction of X-ray sources identified as starbursts in our sample (≈30%) is higher than typical starburst fractions determined for flux-limited X-ray samples (e.g., Bauer et al. 2004, find ≈10%–20% of the CDF-S X-ray sources are starbursts). However, these samples were selected differently from our mid-infrared-selected sample, which naturally includes a high fraction of luminous starbursts and should therefore be expected to have a higher fraction of X-ray-detected starbursts than would a comparable X-ray selected sample.

2.6.1. Highly Obscured AGNs

The bolometric luminosity is commonly inferred from the mean, intrinsic energy distribution of a sample of representative AGNs (e.g., Elvis et al. 1994). The bolometric correction, which essentially gives the fraction of the bolometric luminosity emerging in a given band, can then be determined. Due to the relative ease with which AGN X-ray emission may be cleanly measured, the X-ray bolometric correction is commonly used (e.g., Hopkins et al. 2007). However, a number of complications exist with this method. First, knowledge of the intrinsic absorption is needed. For bright X-ray sources, the absorbing column density can be obtained directly through spectral fitting. For sources with few counts, the band ratio can provide a basic estimate of the absorption (e.g., Alexander et al. 2005a), but some uncertainty will remain. Second, the bolometric correction is known to vary with AGN luminosity, due to the luminosity dependence of the power-law slope between 2500 Å and 2 keV (denoted α_OX), although this dependence is well quantified (e.g., Steffen et al. 2006). Third, the intrinsic spread in AGN SEDs, possibly due in part to variability, is known to result in an uncertainty of a factor of several in the bolometric correction (Hopkins et al. 2007; Vasudevan & Fabian 2007).

For the purposes of this study, we use the luminosity-dependent X-ray bolometric corrections of Hopkins et al. (2007), determined for unobscured (type-1) quasars, which transform the intrinsic 2–10 keV luminosity to the bolometric luminosity and account for the luminosity dependence of the SED on α_OX, the power-law slope between 2500 Å and 2 keV. To use this correction, we need estimates of the intrinsic luminosity and hence of the obscuring column densities for the AGNs in our sample. Recently, Tozzi et al. (2006) performed X-ray spectral fitting of the AGNs in the CDF-S to derive reliable estimates of the column densities. We use the values of the column density derived by Tozzi et al. (2006) when possible. For sources not included in the Tozzi et al. sample (80 of 108 AGNs), we estimate the column density using the observed X-ray band ratio for each source as follows.

First, we model the X-ray emission using an absorbed power-law model in xspec with both intrinsic and Galactic absorption. In xspec, the model is defined as wabs×zwabs×zpow. The photon index of the power-law component was fixed to 1.8 (e.g., Turner et al. 1997) and the redshift of the zwabs and zpow components was fixed to that of the source. We additionally fixed the Galactic column density to N_H = 8.8 × 10¹⁹ cm⁻² for the E-CDF-S (Stark et al. 1992) and to N_H = 1.3 × 10²⁰ cm⁻² for the EGS (Dickey & Lockman 1990). Next, for each source, we used this model to find the intrinsic column density that reproduces the observed band ratio. To account for the Chandra response, we extracted aim-point responses from the event files used to construct the catalogs and used the appropriate responses during the fitting. Band ratios were taken from the catalogs, except in the EGS, where they were calculated from the provided counts and adjusted to the aim-point values using the source and aim-point effective exposure values. Approximately 10% of the X-ray AGNs were not detected in the soft band, implying a very hard spectrum and resulting in a lower limit to the band ratio. For these sources, we use the column density that corresponds to the lower limit.

Inferred column densities for the AGNs in our infrared-selected sample vary from N_H < 10¹⁹ cm⁻² to N_H ≈ 10²⁴ cm⁻². In general, our values agree reasonably well with those derived by Tozzi et al. (2006) for a sample of 194 X-ray-identified AGNs in the CDF-S with detections in both the hard and soft bands (σ ≈ 1 dex; see Figure 4). Some of the scatter is due to differences between the redshifts used by Tozzi et al. and those used by us (which have been supplemented with new spectroscopic redshifts and the high-quality photometric redshifts discussed in Section 2.3). For 53 (≈25%) of the 194 sources, our redshifts differ by more than 20% from those used by Tozzi et al. Although the agreement between our values of the column density and those of Tozzi et al. is good overall, at values of N_H ≳ 3 × 10²³ cm⁻², our estimates of the column density appear to be systematically low. A number of these sources were identified by Tozzi et al. as Compton-thick. Unfortunately, due to the typically faint X-ray fluxes for such sources, their reliable identification is difficult (e.g., Tozzi et al. 2006) and beyond the scope of this paper.

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Since our sources were chosen to be luminous 70 μm emitters, it is possible that the X-ray flux includes a contribution from star formation. Such a contribution could result in derived values of the column density that are systematically low. To determine if this effect is likely to be significant in the objects in our sample, we follow the procedure used in Section 2.6 to estimate the expected contribution from star formation using the relations of Persic & Rephaeli (2007). As before, we estimated upper limits on the SFRs by assuming that the entire observed 70 μm flux is due to star formation. We find that the predicted contribution from star formation to the observed 2–8 keV luminosity is ≲ 10% in all cases, with a mean value of ≈0.8%. Therefore, in our AGN-selected sample, the AGN emission likely dominates in the X-ray band, and emission related to star formation is not expected to have a significant effect on the derived column densities. This conclusion is supported by Figure 4, in which the column densities of AGNs in 70 μm sources (shown in blue) do not differ systematically from those of the whole population, with the exception of the lowest column densities (N_H ≲ 10²¹ cm⁻²), where our values of the column density do appear to be systematically low. However, the corrections required to correct the observed fluxes for these low column densities are modest and have little effect on our derived bolometric luminosities.

The resulting column densities and the absorbed power-law model described above were used to calculate corrections to transform the observed-frame 0.5–8 keV fluxes to unabsorbed, rest-frame fluxes. To illustrate the range of corrections that we find, we plot the corrections required to transform from observed 0.5–8 keV fluxes to rest-frame 2–10 keV fluxes as a function of redshift in Figure 5 (cf. Alexander et al. 2008a). The corrections generally range from ≈0.5 to 2, but one source with a high column density requires a correction of ≈5–6. We then estimate the bolometric correction required to scale the rest-frame 2–10 keV luminosity to a bolometric luminosity from the models of Hopkins et al. (2007).

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Lastly, we can obtain basic fiducial estimates of the black-hole accretion rate from the bolometric luminosity by assuming an efficiency for the conversion of the rest mass of the accreting material to luminosity. We adopt an efficiency of = 0.1, typical of AGNs accreting at rates ∼10% or more of the Eddington rate (e.g., Marconi et al. 2004). The accretion rate is then where c is the speed of light.

Driven by studies of the infrared background, a great deal of work has gone into constructing model infrared AGN SEDs from the observed SEDs of large samples of AGNs. We consider three recent model SEDs to estimate the AGN contribution to the mid-infrared emission: the type-1 and type-2 AGN models of Silva et al. (2004), the type-1 AGN models of Hopkins et al. (2007), and a mean SED of AGNs from a flux-limited Swift BAT survey (Tueller et al. 2008; Winter et al. 2009).

Silva et al. (2004) constructed type-1 and type-2 AGN infrared SEDs using a sample of 33 Seyfert galaxies and 11 quasars with available nuclear mid-infrared and X-ray fluxes. They constructed intrinsic SEDs by interpolating the observed SEDs (up to rest-frame λ ≈ 20 μm). Beyond λ ≈ 20 μm, they extrapolated from the observed SEDs using the radiative-transfer models of Granato & Danese (1994) for a number of different absorbing column densities. In a more recent study, Hopkins et al. (2007) construct a model SED for type-1 quasars using a number of components at different wavelengths, including a mean optical spectrum and a power-law X-ray spectrum. In the infrared, they adopt the mean spectrum from Richards et al. (2006). Lastly, Mullaney et al. (2010) use a sample of 36 AGNs detected with Spitzer and the Swift BAT from the sample of Winter et al. (2009), selected to have no strong indication from PAH features of a significant contribution from star formation to the mid-infrared emission. These X-ray selected AGNs should be fairly representative of the AGNs in our sample. Mullaney et al. (2011) have constructed an average mid-infrared SED from these sources using a combination of Spitzer IRS spectra and IRAS photometry (which provide coverage at wavelengths beyond those covered by the IRS spectra). These three studies provide some of the best determinations of the mid-infrared SEDs of AGNs currently available.

To normalize the AGN SEDs to the observed X-ray luminosity, we assume that the mid-infrared SED scales linearly with the bolometric AGN luminosity over the luminosity range of our sample (i.e., that the AGN luminosity is the principle determinant of the infrared luminosity; see, e.g., Haas et al. 2003). This approximation holds well for the luminosity-dependent AGN SEDs of Hopkins et al. (2007), which include effects such as the dependence of α_OX on the AGN luminosity (e.g., Steffen et al. 2006). The bolometric luminosity was derived following Section 3.1 and scales with the intrinsic X-ray luminosity approximately as L^AGN_bol∝L_2-10 keV^1.39 over the luminosity range of our sample. The models of Silva et al. (2004) and the average BAT AGN SED that we use are luminosity independent (i.e., their shapes do not change as a function of AGN luminosity). For consistency with the Hopkins et al. models, we scaled the type-1 AGN Silva et al. models to have the same 2500 Å luminosity as the (type-1 AGN) Hopkins et al. models at a given bolometric luminosity. This same scaling was also used when scaling the type-2 AGN Silva et al. models. For the BAT AGN SED, the scaling was set such that the average L_IR of the BAT sample (calculated from the observed fluxes using the relation of Sanders & Mirabel 1996) is recovered correctly from the bolometric luminosity corresponding to the average L_X of the BAT sample.

Figure 6 compares the three AGN models (scaled as described above) for AGN bolometric luminosities of log (L_bol/L_☉) = 11.5 and log (L_bol/L_☉) = 12.5. The left two panels show type-1 AGN SEDs and a starburst SED (from Chary & Elbaz 2001) chosen to have roughly the same rest-frame 24 μm luminosity as the AGN SEDs. The two AGN SEDs agree to within a factor of 2–3 over the infrared region (the Silva et al. models predict higher infrared flux out to ≈70 μm). As the difference between the two type-1 AGN models is smaller than the expected systematic errors, we adopt the more recent model of Hopkins et al. for subsequent analysis of the type-1 AGNs. The starburst SED, while having approximately the same rest-frame 24 μm luminosity as the AGN SEDs, clearly dominates at longer wavelengths, due to the lower temperature of dust the reprocesses emission from young stars.

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The right panels of Figure 6 show the average BAT AGN SED and the type-2 AGN SEDs of Silva et al. (2004) for a variety of N_H values, again with starburst SEDs chosen to have approximately the same 24 μm luminosity as those of the AGNs overlaid. At higher values of N_H, the Silva et al. type-2 AGN SEDs show heavy extinction at wavelengths below ∼10 μm compared to the type-1 AGN SEDs shown in the left panels. In general, however, between ∼20 and 70 μm (the approximate range probed by our observed-frame 70 μm data) the Silva et al. SEDs are very similar, both among the type-2 AGN models of different N_H and when compared to the type-1 AGN model. The average BAT AGN SED, however, has higher luminosity at wavelengths beyond ∼40 μm (by up to a factor of ∼3 over the probed wavelength range) compared to the Silva et al. models. This difference will result in larger predicted observed-frame 70 μm fluxes for type-2 AGNs with z ≲ 0.75 when the BAT AGN SED is used. For sources at higher redshift (which include most of the high-luminosity sources), the predicted 70 μm fluxes from the two models will agree closely. As this difference will primarily affect only the lower-luminosity sources (as low-redshift sources tend to have lower luminosities), which generally have low predicted AGN contributions, our results are not significantly changed from those obtained using the Silva et al. models. Therefore, we adopt the Silva et al. models for the type-2 AGNs models used in the next section.

We can use the model AGN SEDs to predict the AGN contribution to the observed 70 μm flux. Before doing so, we divided the AGN sample into subsamples based on the presence of type-1 AGN optical characteristics in either the Bauer et al. (2004) catalog, the COMBO-17 catalog, or the DEEP2 catalog. In these catalogs, non-type-1 AGNs are simply AGNs that are not clearly type-1 AGNs, so the non-type-1 AGNs are likely to include some type-1 AGNs with more subtle characteristics. In total, 18 (≈17%) of the 108 AGNs in our sample were identified as type-1 AGNs. We used type-1 AGN models to predict the mid-infrared fluxes of the type-1 AGNs and type-2 AGN models with the appropriate intrinsic column density to predict the mid-infrared fluxes of the non-type-1 AGNs. We then used the intrinsic, unabsorbed 2–10 keV flux derived earlier (see Section 3.1) to normalize the models (effectively a bolometric correction) and used linear interpolation (in log space) of the model SEDs to derive the observed-frame 70 μm flux or luminosity. In Figure 7, we compare the observed 70 μm luminosity to the one predicted by the models. In general, the predicted 70 μm luminosity is much lower than that observed for the majority of AGNs in our sample.

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Critical to this comparison is the normalization of the SED, which depends on an accurate estimate of the intrinsic X-ray flux. As discussed in Section 3.1, our sample of X-ray-detected AGNs does not show evidence from X-ray band ratios of being highly extincted (the majority of inferred column densities are ≲ 2 × 10²³ cm⁻²). Therefore, the corrections required to convert observed X-ray fluxes to unabsorbed, intrinsic fluxes are typically modest and should not be subject to large uncertainties. Indeed, it is clear from Figure 7 that the predicted (observed-frame) AGN 70 μm luminosity (derived from the redshifted AGN model) is consistent with the observed one in all but one system. For this one system (in which the predicted luminosity exceeds the observed one by a factor of ∼3), X-ray variability may account for the discrepancy, if this AGN was observed in a state of higher-than-average X-ray luminosity (conversely, variability may also lead to underestimates of the AGN luminosity in some sources observed in lower-than-average states). We emphasize that, because our results depend only on properties averaged over many systems, they should not be strongly affected by such variability. To illustrate this point, in Figure 8 we plot our predicted average fractional 70 μm contributions from the AGNs to the observed flux, binned on 1 dex bins, against the observed mid-infrared color for the AGNs in our sample with z < 1.5. The mid-infrared color has been found to be a rough indicator of the AGN contribution, with warmer colors indicating higher AGN contributions, at least out to z ∼ 1.5; beyond this redshift, the color is less reliable (e.g., Mullaney et al. 2010). There is a clear trend between the two indicators: systems with high predicted AGN contributions to the observed 70 μm flux tend to have warmer colors than systems with low predicted AGN contributions. Therefore, on average, it appears that our method produces estimates of the AGN contribution to the mid-infrared flux that are generally consistent with dust temperatures indicated by the mid-infrared color. Further comparisons to other estimates of the relative AGN contribution, such as those from spectra decomposition of mid-infrared spectra, will provide useful tests of systematic errors in our method. However, such analyses are beyond the scope of this work.

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Additionally, as the AGNs can contribute significantly to the observed mid-infrared emission, sources of a given SFR and redshift that host AGNs will be detected more readily than those that lack AGNs. To avoid biasing our SFR-selected sample toward systems with AGNs, we constructed an unbiased sample (henceforth known as the “SFR sample”) by eliminating sources in which the net 70 μm flux (after subtracting the AGN's contribution) results in a signal-to-noise ratio that falls below our adopted limit (S/N = 3; see Section 2). We found that 23 (20%) of 108 AGNs fell below this limit in the combined E-CDF-S and EGS samples (shown as open symbols in Figure 7). The SFR sample is used only to study the AGN activity as a function of SFR. When we examine the AGN activity as a function of other properties (e.g., mid-infrared color), the full sample of 108 AGNs is used. We note that most of the AGNs that were eliminated have log (F_24 μm/F_70 μm) > −0.7 and are predicted to contribute a large fraction (≳ 50%) of the 70 μm flux. In the SFR sample of 85 AGNs (of 1022 70 μm sources in total), only two AGNs have an estimated contribution to the observed 70 μm flux of more than 50%. Therefore, this cut eliminates most of the sources for which the determination of the SFR is likely to be subject to large systematic uncertainties (i.e., those in which AGN-powered emission likely dominates at 70 μm).

Lastly, due to intrinsic differences of the SEDs of systems with the same SFR, some systems at a given SFR will have 70 μm fluxes that fall below our adopted flux limit, resulting in our sample being incomplete at the given SFR. We correct for this incompleteness by estimating the scatter about the relation used by Chary & Elbaz (2001) for local starbursts. We estimated a scatter of ∼0.5 dex in the observed flux at 30–70 μm at all SFRs, and we have used this value to estimate the likely number of missed starbursts for each detected one. We did this by generating, for each detected source, a normal distribution of fluxes around the observed 70 μm flux. We then calculate the fraction of sources that fall below the flux limit for the detected source under consideration and correct the total number of starbursts by the sum over all sources. We assume that these missed sources, since they are presumably cooler than the average starburst for a given L_IR, do not host AGNs. Again, as in the rest of our analysis, we do not include any evolution in the starburst SEDs, as such evolution is currently poorly understood. This correction is generally small, and is significant only for those sources detected near the flux limit. Additionally, where the AGN fraction is high (such as at high SFRs), the effect of this correction is reduced (since the fraction of non-AGN hosts, which is being adjusted, is by definition lower).

As discussed in Section 1, mid-to-far-infrared observations sample a significant fraction of the energy emitted by massive stars in dusty environments, with much of the remainder emerging at UV wavelengths. Therefore the total SFR may be estimated as the sum of the rate inferred from direct UV emission and the rate inferred from the reprocessed, infrared emission (e.g., Daddi et al. 2007a).

To trace the infrared emission associated with star formation, we use the observed-frame 70 μm luminosity. A number of recent studies (e.g., Shi et al. 2007; Tadhunter et al. 2007; Vega et al. 2008) have found that, at a given SFR, the observed-frame 70 μm emission suffers from significantly less AGN contamination and spectral complexity than 24 μm or shorter-wavelength emission, particularly at higher redshifts (z ≳ 1.5). However, the contribution from AGNs to the 70 μm emission can still be significant. Therefore, for sources hosting an AGN, we estimated the AGN contribution to the 70 μm luminosity using empirical AGN SEDs (see Section 3 for details). The net observed-frame 70 μm luminosity was then converted to a rest-frame, 8–1000 μm luminosity (denoted L_IR) using the dusty starburst models of Chary & Elbaz (2001), which are luminosity dependent, and the prescription of Sanders & Mirabel (1996). The resulting L_IR was then converted to an SFR using the relation of Kennicutt (1998), which assumes a Salpeter (1955) initial mass function, as follows:

We also investigated the use of other publicly available dusty starburst models and found that, for our sample and using the observed-frame 70 μm flux (which samples rest-frame wavelengths ≳ 20 μm), there is little practical difference (≲ 50% in L_IR) between the Chary & Elbaz models that we adopt and those of Dale & Helou (2002) or Rieke et al. (2009).¹⁶ We note that all of these models are derived from local samples of starburst galaxies and hence could differ systematically from the sources in our study (which are generally at redshifts of 0.5–1.5). However, Elbaz et al. (2002), in a study of infrared-luminous galaxies, found good agreement out to z ∼ 1 between the radio-derived SFRs and those derived from the infrared emission. At z ∼ 2, Daddi et al. (2007b) also find reasonable agreement between various indicators of SFR, including the infrared (we note, however, that submillimeter galaxies, at z ≳ 2, likely have lower dust temperatures for a given SFR than local ULIRGs, e.g., Pope et al. 2007; Coppin et al. 2008). Since the choice of model makes little difference for the values of L_IR that we derive and a clear consensus as to the most appropriate model for high-redshift, high-luminosity sources has yet to emerge, we adopt the models of Chary & Elbaz for all further analysis.

As stated above, an additional important component of the bolometric emission from star formation emerges in the UV. This “direct” emission must be included when deriving the total SFR. To this end, the rest-frame UV luminosity was estimated using the rest-frame B-, V-, and R-band fluxes derived from the observed SED by fitting galaxy templates using ZEBRA or by simple linear interpolation (when possible). The UV conversions from two recent studies, Daddi et al. (2004) and Bell et al. (2005), were used to transform the UV luminosity to an SFR. The Daddi et al. relation uses the 1500 Å rest-frame luminosity to calculate the UV SFR as SFR₁₅₀₀/(M_☉ yr⁻¹) = 1.13 × 10⁻²⁸(L₁₅₀₀/L_☉). Bell et al. use the 2800 Å luminosity to estimate the UV SFR as SFR₂₈₀₀/(M_☉ yr⁻¹) = 8.99 × 10⁻²⁹(L₂₈₀₀/L_☉). At z ≲ 1.5, the 1500 Å rest-frame emission is sampled only by GALEX observations. Therefore, to avoid large extrapolations for sources at z ≲ 1.5, we use the Daddi et al. relation only for those sources that have GALEX detections (≈40%). The Daddi et al. and Bell et al. estimates, which typically agree to within a factor of a few, were then averaged to obtain the UV SFR, SFR_UV. The total SFR is then calculated as SFR_tot = SFR_IR + SFR_UV. It should be noted that no correction is applied to account for extinction in the UV, as emission that is absorbed by dust will be reprocessed and is therefore included in the infrared-derived SFR. Since emission from the AGN may dominate at UV wavelengths, we assumed that the fraction of emission emerging in the UV from star formation for the AGN sources is the same as that for the non-AGN sample on average (i.e., the extinction in the UV is similar). For the sample as a whole, the UV SFRs generally represent <50% of the total SFR. Figure 2(c) shows the distribution of SFRs. It is clear from this figure that the sample is approximately complete to z = 1.0 (z = 2.0) for sources with SFR ≳ 100 M_☉ yr⁻¹ (SFR ≳ 600 M_☉ yr⁻¹).

We begin by showing in Figure 10 the AGN fraction as a function of the mid-infrared color of our 70 μm sources. It is clear from this figure that the fraction is a strong function of the mid-infrared color, rising from 5%–10% at the smallest values of the ratio (F₂₄/F₇₀) (indicative of cooler dust temperatures) to ∼60%–70% at the largest values. The traditional dividing point of this ratio for z ∼ 0 sources between dust powered by AGN-dominated emission and that powered by star formation-dominated emission is at log (F₂₅/F₆₀) ≈ −0.7 (e.g., de Grijp et al. 1985; Sanders et al. 1988). This division also occurs at roughly the same ratio when Spitzer bands are used (i.e., log [F₂₄/F₇₀] ≈ −0.7) and appears to hold out to at least z ∼ 1.5 (e.g., Mullaney et al. 2010). Indeed, at approximately this ratio, the AGN fraction appears to reach its maximum, implying that ∼60%–70% of such sources host an AGN. Below log (F₂₄/F₇₀) ≈ −0.7, the fraction of sources of a given color that hosts an AGN falls rapidly as the color indicates cooler temperatures. Although care must be taken in interpreting the color at z ≳ 1.5 due to the increasing complexity of typical AGN and starburst spectra at the rest-frame wavelengths sampled by the 24 μm band in particular, this result extends the analyses of Mullaney et al. (2010) by showing that the mid-infrared color is a useful indicator of luminous AGN activity in the distant universe.

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In Figure 11, we plot the AGN fraction against the rest-frame 30 μm luminosity of the source (note that this quantity includes any AGN contribution). It is clear from this figure that the fraction of sources hosting an AGN depends on the rest-frame mid-infrared luminosity, with higher fractions in sources with higher luminosities. The dependence becomes stronger when lower-luminosity AGNs are excluded, such that the fraction of sources hosting an AGN with L_{0.5 − 8.0 keV} ⩾ 10⁴³ erg s⁻¹ rises with the mid-infrared luminosity from a few percent at L₃₀ ≈ 10¹⁰ L_☉ to ∼60% at L₃₀ ≈ 5 × 10¹² L_☉. Therefore, more luminous mid-infrared sources, such as ULIRGs, are ∼10 times more likely to host a luminous AGN than lower-luminosity sources, such as local starbursts. Such a result is to be expected if the AGN contributes to the mid-infrared emission, and the average contribution increases with increasing AGN luminosity (as is suggested by Figure 7).

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The peak in the AGN fraction (f_AGN ∼ 50%–60%) in Figure 11 at the highest mid-infrared luminosities (corresponding broadly to ULIRG luminosities) is consistent with the fraction (≈60%) of local ULIRGs at these SFRs identified by Alexander et al. (2008a) as hosting X-ray AGNs or classified as Seyfert galaxies by Veilleux (2006). It is also consistent with the total AGN fraction of ∼ 50%–65% implied by the detection rate of highly obscured AGNs (identified using Spitzer spectroscopy) in a sample of local ULIRGs studied by Imanishi et al. (2007). We note, however, that the luminosity cutoffs indicated in Figure 11 do not strictly correspond to LIRG and ULIRG cutoffs since, for example, cooler ULIRGs may have rest-frame 30 μm luminosities below the indicated cutoff. Furthermore, the differing selection criteria of these studies makes it likely that they probe AGNs of different luminosities on average (as noted earlier and indicated in Figure 11, the minimum AGN luminosity to which we are sensitive varies with the redshift and hence rest-frame 30 μm luminosity). However, if we restrict the sample of Alexander et al. (2008a) to those systems hosting an X-ray AGN with L_{2 − 10 keV} ⩾ 10⁴³ erg s⁻¹, which matches our selection criteria more closely, we find that 4 of 10 local ULIRGs host such an AGN, with an implied AGN fraction of ∼40%, in good agreement with our result. Therefore, our results suggest that the AGN fraction in the distant ULIRGs in our sample is similar to that of local ULIRGs and, furthermore, that the relation between AGN activity and star formation in these two populations is similar.

Figure 12 shows the cumulative AGN fraction for AGNs with L_{0.5 − 8.0 keV} ⩾ 10⁴¹ erg s⁻¹ and L_{0.5 − 8.0 keV} ⩾ 10⁴³ erg s⁻¹ as a function of SFR. Before calculating an SFR, we subtracted the expected AGN contribution from the observed 70 μm flux as described in Section 3.3. We then used the procedure described in Section 3.4 to infer an SFR from a given net 70 μm flux. It is clear from this figure that the AGN fraction in sources with lower SFRs (SFR ∼ 10 M_☉ yr⁻¹) depends strongly on the AGN luminosity (L_{0.5 − 8.0 keV}). When lower-luminosity AGNs are included, the fraction of sources hosting an AGN at low SFRs is quite high at ∼10%–20%. When only higher-luminosity AGNs are considered (L_{0.5 − 8.0 keV} ⩾ 10⁴³ erg s⁻¹), the AGN fraction at low SFRs is much lower, rising from ≈4%–5% at SFRs of roughly 10 M_☉ yr⁻¹ to ∼40% at the highest SFRs as f_AGN∝SFR^0.75.

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Additionally, SMGs, which generally lie at high redshift (z ∼ 2) where the reprocessed emission from cool dust peaks at observed-frame submillimeter wavelengths, have larger average SFRs than most of the sources present in our sample. Their typical SFRs are on the order of 1000–3000 M_☉ yr⁻¹, and the reprocessed emission in these systems appears to be largely powered by star formation (e.g., Alexander et al. 2005a; Menéndez-Delmestre et al. 2007; Valiante et al. 2007; Pope et al. 2008). SMGs also appear to have a high AGN fraction (∼20%–50%; Alexander et al. 2005b; Laird et al. 2010), and are thought to be the short-lived phase of rapid accretion during a massive merger. Their relation to local ULIRGs is unclear (e.g., Sajina et al. 2007; Symeonidis et al. 2009), but the two classes appear to share many of the same properties, with SMGs being roughly scaled up by an order of magnitude in far-infrared luminosity and SFR (Sajina et al. 2007; Valiante et al. 2007). We note that although our sample does not contain a sufficient number of SFR ≳ 1000 M_☉ yr⁻¹ objects to determine a reliable AGN fraction in this regime, extrapolation of our determination of the AGN fraction (Figure 12) to SFRs of ∼2000 M_☉ yr⁻¹ results in an AGN fraction roughly consistent with the fractions found by Alexander et al. (2005b) and Laird et al. (2010) for SMGs using independent methods and a different field (the CDF-N).

To investigate whether the AGN fraction has a dependence on redshift, we plot in Figure 13 the AGN fraction against the SFR for two subsamples divided by the median redshift of the AGN sample, z = 0.9. Due to the sensitivity limits of the FIDEL survey, at high redshifts only the most luminous 70 μm sources (with correspondingly high SFRs) are detected. Conversely, at low redshifts, no very luminous 70 μm sources are present in the survey fields. Due to this effect, the two subsamples do not have sufficient overlap to judge whether there is any dependence of the AGN fraction with redshift at a given SFR. Additionally, as discussed earlier, the minimum AGN luminosity for which the cumulative fraction is calculated changes with the SFR, as indicated in Figure 13. This changing minimum is largely responsible for the trend of decreasing AGN fraction with increasing SFR seen at z < 0.9 in the left panel of Figure 13. Two opposing effects sum to create this trend: (1) the number of lower-luminosity AGNs per bin decreases with increasing SFR due to a steady rise in the minimum cutoff AGN luminosity with increasing redshift (and hence SFR) and (2) the contribution to the cumulative fraction from higher-luminosity AGNs increases with the SFR (a trend visible in the right panel). Overall, the net effect is a gradual decrease in the AGN fraction with increasing SFR at z < 0.9. At z > 0.9, the change in the cutoff AGN luminosity across the sampled range of SFR is small, and should not have a large effect on the overall trend.

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To examine the effects that AGNs with warm mid-infrared colors (i.e., those sources that may have large AGN contributions to their 70 μm fluxes) have on our results, we have further filtered our sample to exclude all sources with log (F₂₄/F₇₀) ≳ −0.7. The only significant effect of this filtering is reducing the AGN fraction overall (and to reduce the sample such that a smaller range of SFRs is probed). The same trends are present both with and without this filtering.

It is now well established that black holes and their host bulges are intimately connected (e.g., Ferrarese & Ford 2005). To illustrate how the growth rates of the AGNs in our sample compare to those of their bulges, we binned our AGN sample by SFR and calculated the mean bolometric AGN luminosity (calculated following Section 3.1) in each bin. In this comparison, we implicitly assume that the bulge growth rate is approximated by the total SFR, although this may not be strictly true (e.g., in late-type galaxies). In the left panel of Figure 14, we compare these luminosities to the 8–1000 μm luminosities from star formation derived following Equation (3).

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It appears that, in systems identified as having AGNs, the SMBHs and bulges in our sample are growing concurrently on average, across a wide range of SFRs (roughly two orders of magnitude), and at relative rates that would produce or maintain the scaling observed locally (calculated using the conversions described above and assuming ; e.g., Häring & Rix 2004). We note that we are likely missing many systems with low SFRs that would fall mostly in the lowest bin. Depending on the average AGN luminosity of such systems, our value for the average AGN luminosity in this bin could be biased either high (if the missed systems have weak AGN activity on average) or low (if they have strong AGN activity on average). The effect of systems in the latter category (with high L_{AGN, bol} and low L_{SF, IR}) will be reduced somewhat due to the global increase in specific SFR with redshift, which will tend to reduce the fraction of luminous AGNs that lack significant star formation. Nevertheless, the uncertainty in the lowest bin is large and its value should be treated with caution.

However, because many galaxies at a given SFR lack luminous AGN activity, the average AGN luminosity (and hence SMBH growth rate) across all galaxies in a given bin will be somewhat lower. We can estimate this average AGN luminosity by multiplying through by the appropriate AGN duty cycle (traced by the AGN fraction shown in Figure 12). This estimate is shown by the solid line in the left panel of Figure 14 and is well below that expected from the local scaling relation (with the exception of the lowest-SFR bin, which, as noted above, is likely strongly affected by incompleteness), implying that the bulges in our sample could be growing at a faster rate on average relative to their SMBHs than expected from the local relation. However, we note that the bulge growth rate will often be significantly less than the total SFR of the galaxy and, for this reason (among others discussed in the next section), this average AGN luminosity should be interpreted as an approximate lower limit to the true one.

Additionally, in the right panel of Figure 14, we show the distribution of the ratio of the SFRs of the host galaxies to the SMBH accretion rates calculated in Section 3.1. Again, it is clear that the ratio of SFR to accretion rate for our sample of AGNs is broadly consistent with that expected from the median observed ratio of bulge mass to black-hole mass found locally, although our sources tend to lie at slightly higher ratios (median ). However, given the uncertainties in the calculation of these quantities, our results agree well with expectations from the M_BH–M_bulge relation and studies of the volume-weighted bulge and SMBH growth in local galaxies (e.g., Heckman et al. 2004).

In both panels of Figure 14, there is large scatter about the local scaling. Much of this scatter may be due to the systematics discussed above, but could also indicate that some of the systems are undergoing large deviations (by factors of up to ∼100) from concurrent SMBH-bulge growth.

A number of photometric redshift catalogs are available for the E-CDF-S (e.g., Wolf et al. 2004; Grazian et al. 2006) that have proved very useful to studies such as ours of the average properties of large samples of galaxies. Recently, however, new optical, UV, and near-to-mid-infrared data have become available for the E-CDF-S, as well as for the CDF-N. These data should allow derivation of photometric redshifts that are generally of improved quality and that additionally include sources with fainter fluxes. To supplement the spectroscopic redshifts used in the work described in this paper and others (e.g., Xue et al. 2010), we have produced photometric redshift catalogs for nearly all detected optical sources in the 2 Ms CDF-S and CDF-N and the 250 ks E-CDF-S. Although we do not use photometric redshifts for the CDF-N in this paper, we include them here for completeness and ease of reference. In this appendix, we briefly describe our method of deriving photometric redshifts and present estimates of their quality by comparing to spectroscopic redshifts in these fields (further details are given with the catalog).¹⁷

For the E-CDF-S, we constructed photometric catalogs using the following catalogs: the MUSYC BVR-detected optical catalog (Gawiser et al. 2006), the COMBO-17 optical catalog (Wolf et al. 2004, 2008), the GOODS-S MUSIC catalog (Grazian et al. 2006), the MUSYC near-infrared catalog (Taylor et al. 2009), the SIMPLE Spitzer IRAC catalog (Damen et al. 2009), the GALEX UV catalog (NUV and FUV) from the GALEX Data Release 4, and the GOODS-S deep U-band catalog (Nonino et al. 2009). In the CDF-N, the following catalogs were used: the GOODS-N HST ACS and Spitzer IRAC photometric catalogs (Dickinson et al. 2003), the CDF-N Spitzer IRAC catalog derived from unpublished IRAC archival data, the GALEX Hubble Deep Field–North deep imaging survey catalog from the GALEX Data Release 4, and the ACS GOODS-N region K_s (<24.5) catalog (Barger et al. 2008). The sources were crossmatched by position using a matching radius of 05–1″ (depending on the positional uncertainty of the catalogs). The final E-CDF-S photometric catalog comprises a total of 105,825 unique sources, and the CDF-N catalog comprises 48,858 sources.

ZEBRA (Feldmann et al. 2006) was used for the photometric redshift derivation. Default values were used for most parameters. The reader is referred to documentation included with the catalog for further details. In the E-CDF-S, photometric redshifts were obtained for a total of 100,318 sources (5507 of the original 105,825 sources had detections in fewer than 3 optical bands and were not fit). Of these, 1957 are identified as stars, either photometrically or spectroscopically (including 26 white dwarfs). The remaining 97,712 sources and 649 X-ray AGNs were fit best by galaxy and AGN/galaxy hybrid templates, respectively. In the CDF-N, 47,224 sources and 308 X-ray AGNs were fit best by the galaxy and AGN/galaxy hybrid templates, and 1323 were identified as stars (including 6 white dwarfs). Tables 2 and 3 give the derived photometric redshifts, the available spectroscopic redshifts, and the photometry used by ZEBRA for these sources.

Table 2. Photometric Redshift Catalog for the E-CDF-S

R.A.	Decl.	zphot					zspec	Ref.	Template	X-Ray ID	GOODS flag
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
53.0203740	−27.7246863	0.105	0.105	0.123	0.105	0.172	−1.0	−1	Galaxy	−1	0
53.0203700	−27.7045750	0.728	0.715	0.732	0.694	0.740	0.735	17	Galaxy	−1	0
53.0203695	−27.5503508	1.271	0.768	1.558	0.187	2.525	−1.0	−1	Galaxy	−1	0
53.0203590	−27.7484474	0.956	0.899	0.996	0.858	1.064	−1.0	−1	Galaxy	−1	0

Notes. The full table contains 96 columns as follows. Columns 1–2: source position in degrees, Column 3: photometric redshift, Columns 4–7: estimate of the 68% and 95% confidence intervals of the photometric redshift, Column 8: spectroscopic redshift (if available), Column 9: source of the spectroscopic redshift (numbers correspond to those given in the references for this table), Column 10: type of the best-fit template, Column 11: ID of the associated X-ray source (if any) from the 2 Ms CDF-S catalog of Luo et al. (2008) or the 250 ks E-CDF-S catalog of Lehmer et al. (2005), Column 12: flag indicating whether the source is inside the GOODS-S region, Columns 13–96: the photometry used in the fit. References. (1) Vanzella et al. 2008; (2) Le Fèvre et al. 2004; (3) Szokoly et al. 2004; (4) Croom et al. 2001; (5) Dickinson et al. 2004; (6) van der Wel et al. 2004; (7) Bunker et al. 2003; (8) Stanway et al. 2004; (9) Mignoli et al. 2005; (10) Silverman et al. 2010; (11) Cristiani et al. 2000; (12) Strolger et al. 2004; (13) Ravikumar et al. 2007; (14) Stanway et al. 2004; (15) Treister et al. 2009; (16) Popesso et al. 2009 (VIMOS VLT low-resolution survey); (17) Popesso et al. 2009 (VIMOS VLT medium-resolution survey); (18) Grazian et al. 2006; (19) Zheng et al. 2004.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Table 3. Photometric Redshift Catalog for the CDF-N

R.A.	Decl.	zphot					zspec	Ref.	Template	X-Ray ID	GOODS flag
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
189.3129730	62.3347588	2.521	2.406	2.631	2.296	2.718	−1.0	−1	Galaxy	−1	1
189.3709259	62.3344383	0.277	0.227	0.326	0.182	0.436	0.277	1	Galaxy	−1	1
189.4083252	62.3435631	0.072	0.020	0.111	0.020	0.138	−1.0	−1	Galaxy	−1	1
189.3067932	62.3343468	0.258	0.225	0.304	0.198	0.539	0.278	2	Galaxy	−1	1

Notes. The full table contains 47 columns as follows. Columns 1–2: source position in degrees, Column 3: photometric redshift, Columns 4–7: estimate of the 68% and 95% confidence intervals of the photometric redshift, Column 8: spectroscopic redshift (if available), Column 9: source of the spectroscopic redshift (numbers correspond to those given in the references for this table), Column 10: type of the best-fit template, Column 11: ID of the associated X-ray source (if any) from the 2 Ms CDF-N catalog of Alexander et al. (2003), Column 12: flag indicating whether the source is inside the GOODS-N region, Columns 13–47: the photometry used in the fit. References. (1) Barger et al. 2008; (2) Cowie et al. 2004; (3) Wirth et al. 2004; (4) Reddy et al. 2006; (5) Barger et al. 2003; (6) Trouille et al. 2008; (7) Chapman et al. 2005.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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To assess the quality of the photometric redshifts derived by ZEBRA, comparisons are made to secure spectroscopic redshifts (given Tables 2 and 3). We used a number of quantities to assess the quality of the photometric redshifts derived by ZEBRA: the normalized median absolute deviation (Maronna et al. 2006), σ_NMAD = 1.48 × median(|Δz − median(Δz)|/[1 + z_spec]), which gives an indication of the quality of the photometric redshifts after the exclusion of outliers (Brammer et al. 2008); the average absolute scatter, AAS = mean(|Δz|/[1 + z_spec]), which includes the effects of outliers; and the percentage of outliers with and , where Δz = z_phot − z_spec. Table 4 gives the quantities defined above for the photometric redshifts derived by ZEBRA for a number of subsamples.

Table 4. Photometric Redshift Quality Estimators

Case	Sample	No.	σNMAD	AAS
E-CDF-S field
(a)	All sources	2304	0.0116	0.0262	2.00%	3.04%
(b)	mR ⩽ 24 galaxies (trained)	1699	0.0118	0.0215	1.12%	1.88%
(c)	mR ⩽ 24 galaxies (blind)	1738	0.0345	0.0501	3.86%	8.46%
(d)	mR ⩽ 24 galaxies (blind-C17)a	1530	0.0291 [0.0244]	0.0404 [0.0574]	2.87% [7.12%]	6.00% [9.61%]
(e)	mR > 24 galaxies (trained)	605	0.0113	0.0396	4.46%	6.28%
(f)	mR > 24 galaxies (blind)	619	0.0612	0.1142	14.05%	25.20%
(g)	mR > 24 galaxies (blind-C17)a	230	0.0500 [0.1057]	0.0607 [0.1811]	3.81% [25.22%]	14.62% [40.43%]
(h)	X-ray AGNs (trained)	283	0.0094	0.0140	1.06%	2.12%
(i)	X-ray AGNs (blind)	315	0.0436	0.0931	14.92%	24.44%
(j)	X-ray AGNs (blind-C17)a	217	0.0495 [0.0251]	0.0835 [0.0738]	13.52% [11.98%]	22.53% [20.28%]
CDF-N field (GOODS-N region)b
(k)	All sources	2672	0.0229 [0.0440]	0.0480 [0.0819]	4.27% [8.42%]	8.68% [16.84%]
(l)	mR ⩽ 24 galaxies	1837	0.0227 [0.0362]	0.0409 [0.0497]	2.78% [3.54%]	6.26% [9.80%]
(m)	mR > 24 galaxies	835	0.0234 [0.0753]	0.0637 [0.1526]	7.54% [19.16%]	14.01% [32.34%]
(n)	X-ray AGNs	164	0.0142 [0.0760]	0.0380 [0.1505]	3.66% [20.73%]	7.32% [26.22%]
CDF-N field (non-GOODS-N region)b
(o)	All sources	2687	0.0245 [0.0440]	0.0538 [0.0819]	5.02% [8.41%]	10.98% [16.86%]
(p)	mR ⩽ 24 galaxies	1848	0.0256 [0.0364]	0.0478 [0.0497]	3.63% [3.52%]	9.58% [9.85%]
(q)	mR > 24 galaxies	839	0.0226 [0.0744]	0.0671 [0.1528]	8.10% [19.19%]	14.06% [32.30%]
(r)	X-ray AGNs	212	0.0118 [0.0804]	0.0457 [0.1617]	4.72% [21.70%]	7.08% [29.72%]

Notes. ^aTo obtain these numbers, we used sources with spectroscopic redshifts that have photometric redshifts in both the ZEBRA and COMBO-17 catalogs. Values in brackets are derived from the COMBO-17 catalog. ^bValues given for the CDF-N are obtained from the fully trained subsamples. Values in brackets are derived from the photometric redshift catalog of P. Capak et al. (2008, private communication) based on the photometric catalog of Capak et al. (2004).

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We note that, although the above indicators are commonly used to assess the quality of photometric redshifts, the implicit assumption in their interpretation is that the spectroscopic subsample is representative of the full sample. This assumption is unlikely to be entirely true, particularly when the spectroscopic sample is small relative to the number of sources in the total sample or, as is often the case, is brighter on average than the total sample. Additionally, the template-improvement step used in our derivation introduces a bias, as we have optimized the templates for the spectroscopic subsample. The spectroscopic subsample will therefore likely have significantly better quality than the full sample (unless, again, the spectroscopic subsample is fully representative). To assess the importance of these effects, we carried out “blind” tests for each of the three E-CDF-S subsamples (the bright galaxy sample, the faint galaxy sample, and the X-ray AGN sample) as follows. For each subsample, we randomly used ≈3/4 of the spectroscopic sources for the training procedure described above and used the remaining ≈1/4 of the spectroscopic sources to test the quality of the resulting photometric redshifts. This process was repeated eight times for each subsample to ensure statistically meaningful source numbers for the test sample. The results of these blind tests (see Table 4) give the fairest assessment of the overall quality of the photometric redshifts. In general, it appears that the use of fully trained subsamples gives values for AAS, σ_NMAD, and outlier fractions that are biased low by a factor of ∼2–3.

Lastly, a number of other photometric redshift catalogs exist for the E-CDF-S and CDF-N. In Table 4, we compare the quality of our redshifts to those from two widely used photometric redshift catalogs: the COMBO-17 catalog of the E-CDF-S (Wolf et al. 2004, 2008) and the Capak et al. (2004) catalog of the CDF-N. It is clear that the photometric redshifts derived by ZEBRA are comparable or superior to those of the COMBO-17 and Capak et al. catalogs in most respects. We also note that the catalog of Capak et al. has an unusual deficit of sources with 2 ≲ z ≲ 3; such a deficit is not present in our catalog. Lastly, we note that the photometric redshift catalog of E-CDF-S X-ray sources produced by Luo et al. (2010), which uses upper limits and deblended photometry when deriving photometric redshifts, supersedes the catalog presented here for E-CDF-S X-ray sources.