AEGIS: DEMOGRAPHICS OF X-RAY AND OPTICALLY SELECTED ACTIVE GALACTIC NUCLEI

The AEGIS-X survey (Laird et al. 2009, L09 hereafter) has obtained 200 ks exposures over the entire Extended Groth Strip (EGS; Davis et al. 2007; see Section 2.2.1) using Chandra ACIS-I. It covers an area of 0.67 deg² and reaches a limiting flux of 5.3 × 10⁻¹⁷ erg cm^-2 s⁻¹ in the 0.5–2 keV band and 3.8 × 10⁻¹⁶ erg cm^-2 s⁻¹ in the 2–10 keV band at the deepest point. It provides a unique combination of depth and area, bridging the gap between the ultra-deep pencil-beam surveys, such as the Chandra Deep Fields (CDFs) and the shallower, very large area surveys. Its areal coverage is nearly three times larger than the CDF-North and South combined. Compared to the Chandra imaging in the Cosmic Evolution Survey field (Chandra-COSMOS; Elvis et al. 2009), our survey is slightly deeper but covers a slightly smaller area. A detailed comparison of area and flux limits among these state-of-the-art X-ray surveys is given by Elvis et al. (2009).

The data reduction and point source catalogs of AEGIS-X are presented by L09. The reduction basically followed the techniques described by Nandra et al. (2005) with new calculations of the point-spread function (PSF; see L09). L09 used a wavelet detection algorithm run with a low threshold of 10⁻⁴ to identify candidate X-ray detections. Counts and background estimates were then extracted within an aperture corresponding to the 70% encircled energy fraction (EEF) for each candidate source and used to calculate the probability that the source is a spurious detection. All sources with a false-positive probability (p) less than 4 × 10⁻⁶ in any of the bands (soft, hard, ultra-hard, or full band) are included in the final catalog. The X-ray count rate was estimated using the 90% EEF aperture. Unlike L09, we converted the count rate to flux using a photon index of Γ = 1.9, which is more appropriate for unabsorbed sources (e.g., Nandra & Pounds 1994; Nandra et al. 1997). We also assumed this power-law spectrum to measure K-corrections from the observed X-ray flux to the rest-frame bands. Both fluxes and luminosities in this paper are reported for the rest-frame bands: 0.5–2 keV for the soft band and 2–10 keV for the hard band. The hardness ratio is defined as HR = (H − S)/(H + S), where S and H are the observed counts in the 0.5–2 keV and 2–7 keV bands, respectively. The HRs were computed using a Bayesian method following Park et al. (2006) and using the BEHR package (version 07-11-2008). They are not K-corrected.

For sources detected (p < 4 × 10⁻⁶) in some bands but not others, if the false-positive probability (p) in an undetected band is less than 0.01, we still make a flux measurement for that band. Throughout this paper, unless otherwise noted, detection refers to having p < 4 × 10⁻⁶. In certain cases, we treat sources detected in other bands but having 4 × 10⁻⁶ < p < 0.01 in the 2–7 keV band as "detections" to increase the size of the sample with 2–10 keV flux measurement.

The AEGIS X-ray source catalog presented by L09 contains 1325 sources. All but eight are inside the boundaries of the DEEP2 CFH12K photometry catalog (Coil et al. 2004). Based on a maximum-likelihood matching method (Sutherland & Saunders 1992), 895 sources are uniquely matched²⁰ to the DEEP2 photometric catalog with a likelihood ratio (LR) greater than 0.5 (L09), corresponding to a 68.0% optical identification rate. The estimated contamination rate is ∼6%. If limited to R_AB < 24.1, which is the DEEP2 survey limit, the optical identification rate is 53.5%.

2.2.1. DEEP2

2.2.2. MMT/Hectospec Follow-up

We measured the emission-line fluxes in each spectrum after fitting and subtracting the stellar continuum. As in Yan et al. (2006), each spectrum was fitted by a linear combination of two templates after blocking the wavelengths corresponding to emission lines. The templates were constructed using the Bruzual & Charlot (2003) stellar population synthesis code. One template features a young stellar population observed 0.3 Gyr after a 0.1 Gyr starburst with a constant SFR. The other template is an old 7 Gyr simple stellar population. Both templates are modeled assuming solar metallicity and a Salpeter initial mass function. After subtracting the stellar continua, we simply summed the flux around the emission lines and divided by the median continuum level of the original spectrum (before subtraction) in two bracketing sidebands to get equivalent widths (EWs). The definitions for the central bands and sidebands are the same as in Yan et al. (2006).

Emission-line luminosity estimates require accurate flux calibration and correction for slit losses. Both are difficult to measure to better than 10% accuracy. On the other hand, broadband photometry usually has much smaller errors. Using broadband photometry, we can apply K-corrections to get the rest-frame total flux in an artificial filter corresponding to our sidebands in EW measurements. Combining this with the EW measurements yields total line flux and luminosity, avoiding the need for spectrophotometric flux calibration (Weiner et al. 2007). The accuracy of this method relies on the assumption that the emission-line EW does not vary spatially within a galaxy. This assumption may not be accurate for AGNs, since the narrow-line regions subtend smaller scales than the stars in the host galaxies, leading to slightly larger [O iii] EWs in the central regions of AGN hosts. However, for galaxies whose angular sizes are small compared to the seeing, the smearing of light by the atmosphere will make the emission-line EW more uniform across the galaxy. X-ray sources are frequently massive galaxies. The median angular FWHM of our main sample of X-ray sources (0.3 < z < 0.8) in the R-band is 127, which is slightly larger than the slit width and the seeing. Therefore, this procedure will only mitigate the error caused by the slit loss but not eliminate it, and the emission-line luminosity may be overestimated for AGNs. However, we expect the resulting bias and uncertainty in the emission-line luminosity to be far smaller than those in the X-ray luminosity or other uncertainties involved in the analysis, such as X-ray variability and unknown extinction corrections.

We used the DEEP2 CFH12K photometry catalog (Coil et al. 2004) and Blanton & Roweis's (2007) k-correct code v4_1_4 to derive the rest-frame absolute magnitudes for the sidebands around Hβ and [O iii]. We then converted the magnitudes to fluxes and multiplied them by the EWs to compute the total line fluxes and luminosities. The uncertainties for the emission-line EWs were scaled up according to the differences from repeated observations, following Balogh et al. (1999) and Yan et al. (2009). The EW uncertainties are propagated into the luminosity uncertainties, along with uncertainties from photometry and K-corrections. Throughout the paper, we call an emission line detected if the EW is at least twice as large as its uncertainty. For non-detections, the luminosity upper limits are taken to be twice the uncertainties, i.e., 2σ.

Besides studying the X-ray selected sample, we have also investigated the X-ray properties of the optically selected sample. Therefore, we estimated the X-ray flux upper limits for sources not detected in X-ray. When extracting the X-ray counts at positions of the optical sources, we found that many of them have significant counts above the background. In many cases, the probability that the counts arise from background fluctuation is less than 0.1%. The number of such cases is much higher than the expected number of false-positive cases, suggesting that many of them could be truly associated with the optical sources. It is very tempting to include them as X-ray detections to increase the sample size. However, because the X-ray PSF is usually larger than the PSF in the optical images, the X-ray flux could come from other untargetted galaxies nearby or even galaxies beyond the optical photometry detection threshold. Therefore, we only quote X-ray flux upper limits for these sources although the X-ray flux could be significant.

We estimate the X-ray flux upper limits using the Bayesian method (Helene 1984; Kraft et al. 1991, L09). However, unlike L09, who used a power law prior for the source flux distribution, we used a constant, non-negative prior (Kraft et al. 1991) with minimal assumptions made about the source flux distribution. This gives more conservative upper limits than the power-law prior. As we do not require an X-ray detection, we do not suffer from Eddington bias. Our upper limits correspond to the 95% confidence limit (2σ). In detail, the method applies the Bayes' theorem,

$$\begin{equation} P(s|N,b) \propto L(N|s,b) \pi (s), \end{equation} \tag{ 1 }$$

where L(N|s, b) is the conditional probability of observing N counts given the expected source counts s and expected background counts b; it follows the Poisson distribution,

$$\begin{equation} L(N|s,b) = {(s+b)^N \over N!} e^{-(s+b)}. \end{equation} \tag{ 2 }$$

π(s) is the prior probability distribution of the expected source counts; following Kraft et al. (1991), we adopt a step function for π(s), which is a constant when s > 0 and is zero otherwise. Bayes' theorem yields the posterior distribution function, P(s|N, b), for the expected source counts given the observed counts and the expected background.

Here we assume that the error in the estimated background is small, thus b is known. For each source, the total counts were estimated in an elliptical aperture that contains 70% of the energy in the simulated PSF. The aperture was obtained using the PSF look-up table provided by L09. The mean background counts for each source were derived the same way as by L09 but were estimated for the aperture with EEF (enclosed energy fraction) of 70% instead of the 90% EEF aperture. Given the observed counts and the expected background counts, we estimated the upper limit of the source counts using the formulae given in Kraft et al. (1991). The count limit was then converted to a flux limit and K-corrected by assuming a power-law photon index of Γ = 1.9.

The classification of AGN and star-forming galaxies is usually achieved by the use of optical emission-line ratio diagnostics (Baldwin et al. 1981, hereafter BPT; Veilleux & Osterbrock 1987). One most commonly used diagram involves two sets of line ratios: [N ii] λ6583/Hα and [O iii] λ5007/Hβ (Figure 1). In such a diagram, a.k.a. the BPT diagram, the star-forming galaxies populate a sequence from the upper left to the lower center which is the consequence of a correlation between metallicity and ionization parameter. With increasing metallicity, the ionization parameter and hence [O iii]/Hβ decrease. Galaxies to the right and upper right of the star-forming sequence are AGN hosts, which include Seyferts ([O iii]/Hβ>3) and low-ionization nuclear emission-line regions (LINERs, [O iii]/Hβ < 3). AGNs produce higher [O iii]/Hβ and [N ii]/Hα ratios than star-forming galaxies because of two reasons. First, AGNs have much higher ionization parameters so that they are capable of doubly ionizing more oxygen atoms. Second, their photons are more energetic than those from massive stars and can generate a more extended partially ionized region, where [N ii] is produced. The exact line ratios depend on the elemental abundances and the strength and shape of the ionizing spectra. For a more detailed discussion, see Stasińska et al. (2006). Nonetheless, the line ratio diagnostics provide a powerful way to distinguish AGN-dominated galaxies from star-formation-dominated galaxies.

Two empirical demarcations are commonly used for defining AGNs and illustrated in Figure 1. Kewley et al. (2001) provided a demarcation based on extreme starburst models. It is a fairly conservative limit for defining AGNs. Kauffmann et al. (2003) proposed a more inclusive demarcation. Galaxies that lie between the two demarcations are often referred to as composite galaxies that have both AGNs and star formation. Since SDSS fiber apertures include both the nucleus and the host galaxy, a lot of galaxies in this region are probably composites. However, this name is misleading in two ways. First, galaxies outside this intermediate region could also be composite galaxies. Second, some galaxies inside this region do not have to be composites, and there are evidences against the composite assumption. Using HST/STIS observations, Shields et al. (2007) showed that in many such objects identified in the Palomar survey (Ho et al. 1995), the line ratios do not become more AGN-like on smaller apertures (10–20 pc), contrary to the expectation for composites that smaller apertures will include less star formation contribution. Therefore, we choose to refer to the region in between the two demarcations as the "Transition Region". For the regions above and below, we refer to them as "AGN" and "star-forming", respectively. Note, our definition of "Transition Region" is different from that of the "Transition Objects" as defined by Ho et al. (1997) based on a set of line ratios including [O i]/Hα and using nuclear spectra.

As mentioned in Section 1, it is observationally very expensive to apply the traditional AGN diagnostics at z > 0.4 due to the inaccessibility of [N ii] and Hα in the visible window. Weiner et al. (2007) proposed a "pseudo-BPT" diagram using rest-frame H-band magnitude, M_H, to replace the [N ii]/Hα ratio. For star-forming galaxies, M_H, a proxy for stellar mass, correlates with the metallicity-indicating [N ii]/Hα ratio. Thus, this method can distinguish Seyferts in relatively massive hosts from low-mass, low-metallicity star-forming galaxies. However, because the correlation between stellar mass and [N ii]/Hα breaks down for AGN host galaxies, the separation between star-forming galaxies and AGNs is not very clean. Inspired by Weiner et al. (2007), we propose a more effective classification method employing the optical U − B color of galaxies in place of the [N ii]/Hα ratio. Below we first demonstrate this method using a galaxy sample from SDSS; then we explain why it works and why color works better than stellar mass.

The galaxy sample used in Figure 1 is selected from the Sloan Digital Sky Survey (SDSS, York et al. 2000)—Data Release Six (Adelman-McCarthy et al. 2008) by requiring 0.05 < z < 0.1, r < 19.77, and all four emission lines detected at more than 2σ significance. The emission lines are measured in the same way as by Yan et al. (2006). As discussed above, we separate this sample into three classes: star-forming galaxies, transition region galaxies, and AGNs. Figure 2 replaces the horizontal axis with the rest-frame U − B color.²¹ The AGN hosts (panel c) are still in the upper right portion of the diagram, separated from the star-forming galaxies. The transition region galaxies overlap primarily with the star-forming galaxies in U − B color. If we limit attention to pure AGNs, the U − B color provides an effective alternative to the [N ii]/Hα ratio for selecting a sample.

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In choosing an empirical demarcation in the new diagnostic diagram, our preference is to limit contamination to the AGN sample. This new method certainly cannot select all galaxies containing AGNs down to the demarcation of Kauffmann et al. (2003) without being heavily contaminated by star-forming galaxies. We thus place the line just above the area populated by pure star-forming galaxies, which still allows us to retain most AGNs classified by the Kewley et al. (2001) limit. The demarcation we use is given by

$$\begin{equation} \log ({[{\rm O}\,{\mathsc {iii}}]}/\rm{H\beta }) > {\rm max}\lbrace 1.4-1.2(U-B), -0.1\rbrace, \end{equation} \tag{ 3 }$$

where max{a, b} denotes the greater value of a and b, and U − B is the rest-frame color in the AB magnitude system. This is illustrated by the lines in Figure 2. The horizontal cut is a bit arbitrary: red galaxies with low [O iii]/Hβ ratio could be either transition region objects or very dusty star-forming galaxies. There are relatively few of them. We leave the fine tuning for future work.

With this demarcation (Equation (3)), we find 95.7% (7138 out of 7459) of the AGNs selected using the Kewley et al. (2001) demarcation are still classified as AGNs using the new method. If we include all objects in the transition region as AGN hosts, the completeness of the new method drops to 54.3% (9757 out of 17969). About 1.9% (190 out of 9947) of the new "AGNs" were classified as star-forming galaxies under the old method; these we consider contamination.

The new classification method is based on the fact that nearly all BPT-identified AGNs are found in red galaxies or those with intermediate colors between red and blue (hereafter, green galaxies), but hardly any are found in very blue galaxies. There are several reasons. First, blue galaxies are less massive and have smaller bulge-to-disk ratios than red galaxies. Smaller bulges host smaller BHs (Magorrian et al. 1998; McLure et al. 2006). The bluer a galaxy is, the less massive its BH is, and at a fixed Eddington ratio, the less luminous the AGN will be. Thus, a lower fraction of the AGNs in blue galaxies will be found above the observational flux threshold than those in green or red galaxies. Second, star formation in blue galaxies could overwhelm weak or moderate AGNs so that the combined line ratios still put them in the star-forming sequence on the BPT diagram. Both of these effects tend to hide AGNs in blue galaxies. There may also be other physical effects that we do not yet understand. Nonetheless, this observational fact allows us to use host galaxy color to reproduce the BPT selection of AGNs.

On the other hand, nearly all red/green galaxies that have high [O iii]/Hβ ratios are found to be AGNs. This is because high [O iii]/Hβ ratios require high ionization parameters which are produced in two types of sources: AGN and low-metallicity hot stars. Low-metallicity stars are only forming in very blue star-forming galaxies. Therefore, when limited to red or green galaxies, the high [O iii]/Hβ ratios have to be due to an AGN.

Therefore, the rest-frame U − B color can be used to track AGN activity in a similar fashion as the BPT diagram, because it correlates positively with the bulge mass and metallicity, and correlates negatively with the SFR. Other colors or spectral index (e.g., D_n(4000)) could also be employed provided they satisfy these criteria.

What kind of AGNs will our method miss? First of all, this method is not intended to select broad-line AGNs (Type 1) in which the broadband color is not dominated by the host galaxy. Among narrow-line AGNs, one might worry that this method will miss those Seyferts with high L_[O iii]/M_BH which are shown to live in blue star-forming galaxies (Kauffmann et al. 2007). However, since our demarcation is tilted, we will not miss the majority of these Seyferts: their "blue" colors are redder than our limit. We tested this using our SDSS sample described in Section 3.2. We derived L_[O iii]/M_BH following Kauffmann et al. (2007) and selected the 5% of AGNs (defined using the Kewley demarcation) with the highest values of L_[O iii]/M_BH, 77% of these are still classified as AGNs in our new diagram. This fraction is lower than that for all AGNs since these galaxies do fall on the blue edge of the AGN sample. Nonetheless, our new method can recover the great majority of them.

LINERs will be missed by this method if they live in blue galaxies, which will make them LINER-star-forming composites. On the BPT diagram, they will belong to the transition region. We will not be complete for this category. The fraction missed depends on where we put the demarcation and which method we regard as giving the "correct" classification for each galaxy, if it can be well defined. By lowering the demarcation to include more transition region galaxies, we would have more "contaminations" from the BPT star-forming sequence. However, some of these "contaminations" could also be AGN–SF composites. Regarding to SF–AGN composites, our method has a similar selection bias as the BPT diagrams, but with different detailed dependences.

Locally, we do not find low-metallicity AGNs (Stasińska et al. 2006). If there exist at higher-z, they could be missed by both our methods and the traditional BPT diagram.

There is also much evidence now suggesting that many luminous AGNs have previously had a star formation episode (Kauffmann et al. 2003; Jahnke et al. 2004; Sánchez et al. 2004; Silverman et al. 2008), so they have bluer host galaxies than their inactive counterparts. Would we miss the AGNs in these galaxies? The answer is "No." Most post-starbursts in SDSS and DEEP2 have redder U − B colors than the median star-forming galaxy (Yan et al. 2009), because the U band covers the blue side of the Balmer break. We therefore do not expect to miss AGNs in most post-starbursts, at least up to z ∼ 0.8.

The principal advantage of this method is that it requires fewer emission lines than the traditional one. Hence, it can be applied to higher redshift galaxies and suffers less from incompleteness due to missing line detections, especially in low signal-to-noise (S/N) spectra.

One might expect that stellar masses would perform equally well as a replacement for [N ii]/Hα. However, this is not the case. Figure 3 shows how mass compares with rest-frame U − B color in their correlations with [N ii]/Hα. The sample used is selected from SDSS DR6 with 0.02 < z < 0.1, M_* > 10⁹ M_☉, and by requiring both [N ii] and Hα are detected at more than 2σ significance. The stellar masses are derived as a by-product in K-correction (Blanton & Roweis 2007). We imposed a redshift-dependent stellar mass cut so that at all redshifts the sample is complete to a certain stellar mass limit for all colors. With this cut, for each galaxy, we computed the maximum volume over which a galaxy with that stellar mass would be included in the sample, V_max. Figure 3 plots the 1/V_max-weighted distribution in [N ii]/Hα versus M_* and [N ii]/Hα versus U − B spaces. These reflect the distributions of all galaxies in a volume-limited sample down to M_* > 10⁹ M_☉ that have a reliable [N ii]/Hα measurement.

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In Figure 3, the rest-frame U − B color shows a much better correlation with [N ii]/Hα ratio than stellar mass does. The difference is especially dramatic at log([N ii]/Hα)> − 0.2, where the trend for stellar mass becomes horizontal. These high [N ii]/Hα galaxies are mostly AGN-host galaxies that are old and have very low or zero SFRs (as indicated by their red colors). Both [N ii]/Hα and color increase with metallicity in passively evolving galaxies (see Groves et al. 2004 for the dependence of [N ii]/Hα on metallicity for AGNs), and hence they remain correlated as metallicity changes. However, although stellar mass correlates with metallicity for star-forming galaxies, stellar mass stops growing once the star formation stops. Thus, it no longer correlates with the [N ii] abundance or [N ii]/Hα ratio. Therefore, color provides a better alternative to [N ii]/Hα than stellar mass does.

Lamareille et al. (2004) and Lamareille (2010) investigated the use of [O ii] λ3727/Hβ EW ratio as an alternative to [N ii]/Hα. This enables the application to redshifts as high as our method, though it also requires that [O ii] lines are covered in the spectra. This method also has trouble differentiating the transition region from the star-forming galaxies. Under their method, 84.5% of all Seyferts and LINERs (above the Kewley et al. 2001 demarcation) are classified as AGNs, smaller than our completeness of 95.7%. The contamination from the star-forming sequence (below the Kauffmann et al. 2003 demarcation) to the AGN category is 2.6%, larger than our number of 1.9%.

The SDSS galaxy sample we used is at z < 0.1. We have shown above that the new method works at this redshift. Does it still work at higher redshifts?

We can test our new AGN/star-forming classification method between redshifts 0.2 and 0.4, where the traditional line ratio diagnostics are still available within the optical window. We used the spectroscopic data obtained in the EGS by the DEEP2 survey and with Hectospec to test the method. The results are shown in Figure 4. The traditional method identified 40 emission line AGNs that are above the Kewley et al. (2001) demarcation.²² The new method identified 36 of them and missed 4, corresponding to a 90% completeness. It also picked up eight objects from the transition region with no contamination from star-forming galaxies. It is also encouraging to note that as about many X-ray sources (11 out of 12) are identified as AGNs in the new diagram as in the traditional diagram (10 out of 12).

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Because galaxies are bluer at higher redshift (Blanton 2006), in principle, our demarcation should shift blueward slightly. By comparing the color–magnitude diagram of the DEEP2 sample at z ∼ 0.9 with that of an SDSS galaxy sample at z ∼ 0.1, we found the division between red and blue galaxies shifts by 0.14 mag in U − B between these redshifts (Cooper et al. 2008; Yan et al. 2009), which is consistent with the passive evolution prediction (van Dokkum & Franx 2001). The corresponding shift between z = 0.3 and z = 0.1 is about 0.04. For the sample we will discuss later, which has 0.3 < z < 0.8 and a median redshift of z ∼ 0.55, the shift is about 0.08 from z ∼ 0.1. These shifts are quite small and insignificant for our results. Considering our sample covers a wide redshift range, for simplicity, we do not apply these shifts.

Most (83%) optically classified AGNs that are also detected in X-rays have L_X(2–10 keV)>10⁴² erg s⁻¹, which confirms their identity as AGNs. The correlations between the emission line and X-ray luminosities of this population establish prototype relations for AGNs. Both [O iii] and hard X-ray are good indicators for AGN bolometric luminosity (Heckman et al. 2004 for [O iii]; Elvis et al. 1994 for X-ray). Because [O iii] originates from the narrow-line region, which is outside the obscuring dusty torus, it is usually regarded as an isotropic luminosity indicator. While X-rays can penetrate dust easily, they can be absorbed by a high column density of neutral gas in the torus. Among Type 1 AGNs, for which we have an unobstructed view of the accretion disk, X-ray luminosity is found to correlate with [O iii] luminosity (Mulchaey et al. 1994; Heckman et al. 2005). Therefore, comparing X-ray with [O iii] can reveal the level of X-ray absorption (Maiolino et al. 1998; Bassani et al. 1999).

Figure 7 compares [O iii] emission with X-ray in both flux and luminosity. Type 1 AGNs have a slightly larger median log(L_X(2–10 keV)/L_[O iii]) ratio (1.83 dex) and a narrower distribution than our Type 2 AGNs (median = 1.42 dex, see Table 2). However, the L_X(2–10 keV)/L_[O iii] difference between Type 1 and Type 2 AGNs depends on how the sample is selected. Heckman et al. (2005) showed that in a hard-X-ray-selected sample of local AGNs, Type 1 and Type 2 AGNs exhibit L_X(2–10 keV)/L_[O iii] ratios indistinguishable from each other. However, in a sample selected by [O iii] luminosity, many Type 2's can be present with low X-ray luminosity, presumably due to absorption. The Type 1 AGNs then have a median ratio much larger than that of Type 2 and have significantly less variation in the ratio than Type 2 AGNs. The unambiguous AGNs are effectively a hard-X-ray-selected sample; there is a small difference between Type 1 and Type 2 but not nearly as large as the difference in an [O iii]-selected sample. Table 2 compares the median and distribution widths for the various samples.

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Thirty X-ray sources have [O iii]/Hβ ratios and U − B colors that place them in the star-forming area of the emission-line diagnostic diagram. X-rays can be produced in star-forming galaxies by high-mass X-ray binaries, low-mass X-ray binaries, supernova remnants, and hot interstellar medium heated by supernova (Fabbiano 1989) in addition to possible AGNs. Many authors have shown that in starburst galaxies without an AGN, the total X-ray luminosity correlates with the SFR (Nandra et al. 2002; Bauer et al. 2002; Ranalli et al. 2003; Grimm et al. 2003; Colbert et al. 2004; Persic et al. 2004; Hornschemeier et al. 2005; Georgakakis et al. 2006; Persic & Rephaeli 2007; Rovilos et al. 2009). Thus, the expected X-ray flux from the sources related to SF can be predicted if the SFR is known. We used the Ranalli et al. (2003) calibration to estimate the expected X-ray luminosity from sources related to star formation.

Figure 8 compares observed X-ray luminosities with SFRs computed from Hβ. Moustakas et al. (2006) provide an empirical calibration to derive SFR from the observed Hβ strength. The calibration coefficients depend on the rest-frame B-band absolute magnitudes (M_B) of the galaxies. We linearly interpolated between the points given in Table 1 of Moustakas et al. (2006). This is equivalent to applying an average extinction correction in bins of M_B. As shown by Moustakas et al. (2006), when lacking a reliable extinction measurement from Hα/Hβ ratio, this empirical Hβ calibration can achieve a SFR estimate good to ±40% (1σ).

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Most of the X-ray-loud composite galaxies have X-ray luminosities much higher than star formation can account for in both the soft and hard bands. The excess is more than two orders of magnitude in the extreme cases. A large fraction of the X-ray luminosity in these objects must come from a central AGN. These galaxies therefore appear to be undergoing both star formation and nuclear activity. Since AGN will also contribute to the total Hβ luminosity, the SFR could be overestimated, which leads to an underestimate of the AGN component.

Further evidence for the coexistence of SF and a central AGN comes from the distribution of the L_Hβ/L_X(2–10 keV) ratio as a function of the observed X-ray HR, plotted in Figure 9. X-ray-loud composite galaxies have L_Hβ/L_X(2–10 keV) ratios higher than typical AGNs but lower than pure star-forming galaxies. Based on the Ranalli et al. (2003) relation between L_X(2–10 keV) and SFR, and Kennicutt's (1998) relation between L_Hα and SFR, assuming case B Balmer decrement Hα/Hβ = 2.85, typical star-forming galaxies should have L_Hβ/L_X(2–10 keV) greater than 1 (assuming A_V ⩽ 2). Unambiguous and Type 1 AGNs have an L_Hβ/L_X(2–10 keV) lower by two orders of magnitude, around 10⁻². However, most X-ray-loud composite galaxies have intermediate ratios in L_Hβ/L_X(2–10 keV). The simplest explanation is that they are composite objects having both star formation and active nuclei. Most of their Hβ emission originates from star-forming H ii regions, while most X-ray emission originates from matter around the SMBH. For example, assuming the intrinsic L_Hβ/L_X(2–10 keV) ratio for AGNs is 10⁻² and for pure star-forming galaxies is 10, a galaxy with log L_Hβ/L_X(2–10 keV) = −1, in the absence of extinction, 90% of the Hβ emission comes from star-forming H ii regions, and 10% comes from the narrow-line region around an AGN. In contrast, 1% of the hard X-ray emission comes from X-ray binaries and supernova remnants, and 99% comes from the AGN. If extinction on Hβ is present at the same level for both the star-forming and nuclear regions, the resulting proportions do not change. Figure 9 shows a relatively clean separation between unambiguous AGNs and X-ray-loud composite galaxies in the L(Hβ)/L_X versus HR diagram. This supports the hypothesis that our classification scheme is separating objects with different natures.

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NGC 6221 provides a local example of a composite object (Levenson et al. 2001) with the X-ray flux dominated by the nucleus and the visible spectrum dominated by the surrounding starburst. As Levenson et al. (2001) showed, besides X-ray, one can detect the AGN component in NGC 6221 by the additional broad component of the [O iii] line in a high S/N nuclear spectrum or with high-resolution optical or NIR imaging. Our objects are much more luminous than such local examples but otherwise have similar characteristics.

Because the Hβ emission in X-ray-loud composite galaxies is dominated by star-forming H ii regions, the SFR derived from it are not too far off: they could be overestimated by ∼10%. As shown in Figure 8, the inferred SFRs in these galaxies range from a couple to tens of  M_☉ yr⁻¹ with a median of 10  M_☉ yr⁻¹, typical of z ∼ 1 star-forming galaxies (Noeske et al. 2007) and similar to the range of SFR found among X-ray selected AGNs at z ∼ 0.8 (Silverman et al. 2009). The extinction correction applied is only correct on average but not accurate for each individual galaxy. We therefore advise against overinterpreting individual SFR values before better extinction estimates are made.

An alternative explanation for the X-ray-loud composite galaxies might be that these objects are pure AGNs without star formation, but the X-ray luminosity is heavily absorbed by a large column density of gas. This cannot be the case for two reasons. First, it conflicts with the optical classification. Second, this possibility is not supported by the X-ray HR as shown in Figure 9. The HR is a very rough indicator of the X-ray spectral shape, which relates to the level of absorption. An unabsorbed X-ray spectrum has a low HR (∼−0.5). Because the opacity is larger for less energetic photons, more absorption generally leads to a harder spectrum and a larger HR. Though this correlation is loose and is dependent on redshift (Trouille et al. 2009), nonetheless, as shown in Figure 9, nearly all of our composite galaxies have low HRs, consistent with being unabsorbed.

The lower panel of Figure 9 shows L(Hβ)/L_X(0.5–2keV) versus the HR. The X-ray-loud composite galaxies still mainly populate a region different from unambiguous AGNs, but the separation between the two classes is not as clean as for the hard band. This is because extinction in the soft band decreases L_X(0.5–2keV) as HR increases, and the overall distribution of points shows an overall counterclockwise rotation.

Figure 9 shows a few X-ray-loud composite galaxies outside their normal region on the plot. At least some of them are likely to be composites of two separate objects rather than a single composite galaxy. This is established for one case, DEEP2 object 12016714,²⁴ which has Hβ/L_X(2–10 keV) even lower than the typical value for unambiguous AGNs. HST/ACS imaging reveals that the single object in the DEEP2 CFH12K catalog is in fact two galaxies separated by 15. The bluer one is brighter in R and thus was targeted by DEEP2. However, the X-ray point source is centered on the other, redder, galaxy. In total, 14 of our 30 X-ray-loud composite galaxies were imaged by HST/ACS (Lotz et al. 2008). From visual inspection, two others (DEEP2 12004519, 13049115) out of the 14 are actually close pairs whose components were not separable in the ground-based images, and we cannot tell which component contributed either the spectrum or the X-ray flux. Based on these very rough statistics, we expect 20% of all X-ray-loud composite galaxies in our sample could be unrelated objects that cannot be separated by the limited resolution (06–1'' FWHM) of the ground-based images used for photometry.

XBONGs are X-ray sources found in quiescent galaxies for which both [O iii] and Hβ are undetected (<2σ). First, we need to confirm the origin of the X-ray emission. Besides AGNs, X-ray binaries and hot gas in normal galaxies can also produce X-ray emission. Most of the galaxies in this category are red galaxies with early-type morphology. As shown by Fabbiano et al. (1992) and Hornschemeier et al. (2005), the X-ray luminosity in early types has contributions from both X-ray binaries and hot gas, whose total luminosity correlates with the stellar mass (log L_X ∝ 1.8log M_*). We converted the relation given by Hornschemeier et al. (2005) to our bands assuming a thermal Bremsstrahlung spectrum with T = 1 keV and estimated the expected luminosities for our sources. Only 3 out of the 32 X-ray sources among quiescent galaxies are both consistent with this origin in HR and have luminosities (in both soft and hard bands) within a factor of three of the Hornschemeier et al. (2005) relation. These objects could possibly be normal galaxies without active nuclei. Therefore, we conclude that 29 out of the 32 sources in this category appear to have their X-ray emission dominated by an AGN.

Yuan & Narayan (2004) argued that XBONGs are powered by a radiatively inefficient accretion flow resulting in the lack of emission-line regions and UV/optical bump. Others (Moran et al. 2002; Trump et al. 2009b) have suggested that the narrow-line emission in these objects is diluted by the host galaxy, while Rigby et al. (2006) argued that heavy extinction in the host galaxy is responsible for the lack of optical emission lines. However, none of these analyses has tried to evaluate how much narrow-line emission is expected given the observed X-ray flux and whether the non-detections are beyond expectations. For our sample of XBONGs, we compare their emission-line upper limits with their X-ray luminosity to address this problem.

Here, we only use the term XBONG to refer to galaxies without any detectable line emission in the DEEP2 or Hectospec spectra. Previous literature on XBONGs (e.g., Rigby et al. 2006) has included X-ray AGNs that are optically classified as star-forming galaxies. As discussed above, these galaxies do appear to host weak AGNs which are drowned out by the line emission from star-forming H ii regions. Because the majority of star-forming galaxies are spiral disk galaxies, they will show a wide range of axis ratios. The inclusion of these X-ray-loud composites in the "optically dull" AGN sample of Rigby et al. (2006) can explain the wide range of axis ratios they found, which were incorrectly used to argue for host extinction effect.

In our analysis, we only focus on those sources without any emission lines, which are sometimes referred to as absorption-dominated, quiescent, or passive galaxies. Six of our 29 AGN-dominated XBONGs actually have [O ii] λ3727 significantly (>2σ) detected. For consistency, we still count them as XBONGs as if [O ii] were not covered in the spectra. These objects would likely be classified as LINERs in a standard BPT diagram as they have very high [O ii]/Hβ ratios (Yan et al. 2006).

Figure 10 shows the [O iii] flux upper limits versus hard-X-ray flux distribution for XBONGs in our sample along with more typical AGNs. The [O iii]-to-X-ray ratios of the XBONGs are consistent with other AGNs. Their [O iii] upper limits are not low enough to indicate that they are significantly weaker in their narrow-line emission relative to their X-ray emission, and they could simply be the tail of the distribution in [O iii]-to-X-ray ratio. In fact, many of our XBONGs show weak [O iii] emission that is just slightly short of the 2σ detection threshold. The median significance of the [O iii] EW measurement (EW divided by its uncertainty) among XBONGs is 1.2; 60% are more than 1σ significant.

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The XBONGs in our sample have much lower X-ray fluxes than the typical XBONGs discussed in the literature. All our sources have hard X-ray flux lower than 6.7 × 10⁻¹⁵ erg s^-1 cm⁻², a factor of four lower than the prototype XBONG discussed by Comastri et al. (2002), which has an X-ray flux of F_2–10 keV = 2.5 × 10⁻¹⁴ erg s^-1 cm⁻². A simple explanation for this is that DEEP2 spectra, with their higher than typical spectral resolution and S/N, are able to probe significantly deeper on [O iii] flux amid the stellar light and thus reveal optical AGN signatures for much fainter objects than before. The sample shown here includes both spectra from the DEEP2 survey and spectra taken in the MMT/Hectospec follow-up program. The latter data have lower spectral resolution. If limited to DEEP2-only sources (solid squares in Figure 10), the XBONGs are even fainter: i.e., objects which would be classified as XBONGs in the Hectospec data yield significant detections if observed by DEIMOS.

Therefore, before we consider any complicated possibilities to explain XBONGs, we should evaluate the simplest explanation for the non-detection of [O iii] in these AGNs: given the observed X-ray flux, the expected [O iii] line strength assuming typical AGN flux ratios is simply beyond our detection capability. Our measurements of [O iii] upper limits are consistent with this explanation. The [O iii]-to-X-ray flux ratios for our XBONGs are consistent with those of other narrow-line AGNs and Type 1 AGNs. They are simply near the tail of the [O iii] flux distribution at the corresponding X-ray flux. We do not need to invoke higher than usual host galaxy extinction to explain them, nor any other physical mechanism to suppress the narrow-line strength. If these galaxies have the same [O iii]-to-X-ray ratio as Type 1 AGNs, the emission lines would not have been easily detectable in our spectra. Therefore, we see no reason to postulate that they are a different type of object, given the current observations.

If dilution were the main cause for emission lines in these galaxies to be undetected, we would expect that XBONGs should have a brighter rest-frame magnitude in bands bracketing [O iii] than those X-ray sources with similar hard-X-ray luminosities. We investigate this by comparing a sample of our XBONGs with a sample of unambiguous AGNs matched in hard-X-ray luminosity. We limit both samples to objects with hard-X-ray (2–10 keV) luminosity between 10^41.8 erg s^-1 and 10^42.8 erg s^-1. We can then compare their absolute magnitudes in the continuum bands bracketing [O iii], which we used to derive the [O iii] luminosity in Section 2.3. It turns out that the two samples have indistinguishable distributions in this magnitude. The median [O iii] sideband magnitudes (AB) for the two samples are also very similar: −20.8 for the XBONGs and −20.9 for the unambiguous AGNs. There is no systematic difference between the two samples. In only one object—the XBONG with the highest [O iii] flux upper limit—is the host galaxy so bright (M = −23.25) that it is conceivable that dilution could be responsible for the non-detection. In most cases, dilution by the host galaxy is not stronger in XBONGs than in other AGN hosts.

If extinction in the host galaxies was the main cause for the emission lines to be undetected, these galaxies would be significantly redder than other AGN hosts and have smaller axis ratios (b/a). We checked this using the above luminosity-matched comparison sample. The median U − B color is 1.14 for the XBONGs and 1.07 for the luminosity-matched unambiguous AGN sample. A Kolmogorov–Smirnov test on the two distributions indicates that the probability of obtaining the observed difference, given the null hypothesis that the two samples are drawn from the same parent distribution, is 37%, meaning the difference is not statistically significant. To produce such a difference by extinction only requires an A_V of 0.33 mag (assuming R_V = 3.1), which will only dim the [O iii] emission lines by 30% or 0.15 dex. Therefore, extinction cannot be the primary reason for the nondetection of emission lines. Additionally, 11 out of the 29 AGN-dominated XBONGs were imaged with HST/ACS. The smallest axis ratio found among them is 0.37 in the F814Wband. Their axis ratio distribution is indistinguishable from that of the unambiguous Type 2 AGNs, as shown in Figure 11.

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The fraction of XBONGs in our sample at 0.3 < z < 0.8 is smaller than previously reported in the literature in the same redshift range (∼30% in Trump et al. 2009a if limited to 0.3 < z < 0.8) and depends strongly on X-ray flux. Among all 146 spectroscopically identified X-ray sources that have both [O iii] and Hβ well covered in the spectra, we have 32 XBONGs, 29 of which are definitely AGNs. This is 19.9% ± 3.3%. If we limit to DEEP2 spectra only, which have better quality, the fraction is slightly lower, 14.7% ± 3.5% (15 out of 102 sources). Figure 12 shows the fraction of XBONGs as a function of hard X-ray flux, among sources that have a measurable hard X-ray flux. The fraction decreases strongly toward higher X-ray flux. This is consistent with the simple explanation above that XBONGs are purely the result of observational limitations rather than comprising a physically distinct class of AGNs.

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We thus find no evidence suggesting that those X-ray sources with no detected emission lines must be a separate population from other emission-line AGNs; neither greater dilution nor higher than usual host galaxy extinction appears consistent with our observations. To rule out the null hypothesis that they are the same as other emission-line AGNs, we need to obtain much higher quality spectra. Until the time we detect their emission lines and find their emission-line-to-X-ray ratio is distinctively lower than other AGNs, or until we push the emission-line upper limits to a correspondingly low level, there is no reason to classify them separately. Collecting high-quality spectroscopic data is the best way forward.

The combination of the three classes of objects discussed above comprises the whole sample of objects that are detected in ∼200 ks Chandra exposures, spectroscopically identified, brighter than I_AB of 22, and have redshifts between 0.3 < z < 0.8. Most of these objects, regardless of their X-ray luminosity, host an AGN. When classified with optical emission-line diagnostics, they fall into three classes: emission-line AGNs, star-forming galaxies, and quiescent galaxies. This reveals the weakness of optical classification when compared with X-ray selection. Optical AGN selection not only selects on the bolometric luminosity of the AGN, it also selects on other properties of the host galaxy, primarily SFR. In the absence of extinction affecting emission lines and absorption of X-rays, a narrow-line AGN with a 2–10 keV luminosity of 1.7 × 10⁴² erg s^-1 can be easily drowned out in emission-line luminosity by an SFR of 10 M_☉ yr^-1, a case in which 97% of the Hβ emission comes from star-forming H ii regions, but 97% of the hard X-ray flux comes from the AGN.

Most XBONGs should not be counted toward the incompleteness of the optical AGN selection, because the intrinsic bolometric luminosity of these AGNs is simply beyond the detection limit of the optical selection. However, the emission-line detection limit in the optical spectra is not simple to estimate. The detectability depends on many factors: the line flux, the stellar continuum flux, the sky background flux, and the complexity of the stellar continuum modeling. It also depends on many parameters of the observations, such as the exposure time and the seeing at the time of observation, which could vary even in the same survey.

Optical selection is also sensitive to extinction, which we have not discussed in detail. For AGN narrow-line regions, it is usually not a severe concern except in edge-on disk galaxies. The median extinction on [O iii] among typical Type-2 Seyferts is around 1.0 mag (LaMassa et al. 2009; Diamond-Stanic et al. 2009). Extinction can be corrected for when attenuation measurements are available, or one can exclude edge-on disk galaxies from the analysis.

Perhaps the most fundamental weakness of optical diagnostics is its dependence on high quality spectra, which becomes increasingly expensive to obtain for fainter galaxies. Many X-ray sources have very faint optical counterparts or no counterparts. In our investigation, we only considered objects with I_AB < 22 for completeness and S/N reasons. In fact, based on photometric redshifts obtained from the CFHT Legacy Survey (Ilbert et al. 2006), about 40% of X-ray sources with an optical counterpart in CFHTLS and with 0.3 < z_phot < 0.8 have I_AB > 22. Compared to our sample, most of them are probably less massive galaxies, which have less massive BHs. The AGN demographics of these sources could also be different. We leave this for future investigations.

Of the objects which are identified as AGNs from their emission-line ratios but lacking X-ray detections, all but one are Type 2 AGNs. Figure 13 plots the upper limits for the 2–10 keV flux and luminosity for these sources along with the unambiguous AGNs. Most of the optical-only AGNs lie to the upper left of the Heckman et al. (2005) relation, i.e., they have much lower L_X(2–10 keV)/L_[O iii] ratios. This is consistent with the conclusions of Heckman et al. (2005) based on local AGN samples: optically selected samples have much lower median L_X(2–10 keV)/L_[O iii] ratio than X-ray selected samples and have broader distributions in flux ratio. This indicates that optically selected samples include more heavily absorbed sources and possibly Compton-thick sources, which are missed by X-ray-selection techniques. Therefore, an AGN sample selected based on a hard-X-ray luminosity threshold in 2–10 keV will not be a complete bolometric-luminosity-limited sample due to cases of heavy absorption and Compton-scattering of X-ray photons.

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Another potential explanation for the high [O iii]-to-X-ray ratio of these objects is that they have star formation contributing significantly to the [O iii] flux but not the X-ray. This cannot be the case for two reasons. First, these galaxies are classified as AGNs according to their emission-line ratios indicating that their [O iii] flux must be dominated by an AGN. Second, star formation would make these galaxies appear bluer than other AGNs. The U − B color distribution for optical-only AGNs is statistically indistinguishable from that of the unambiguous Type 2 AGNs. Therefore, the high [O iii]-to-X-ray ratios of optical-only AGNs cannot be due to contamination by star formation.

One might worry that these optical-only AGNs are dusty star-forming galaxies. For most of them, this cannot be the case. The stellar mass distribution of these optical-only AGNs is statistically indistinguishable from those AGNs detected in the X-ray (the unambiguous AGNs). On the other hand, they are much more massive than those star-forming galaxies with the same [O iii]/Hβ ratios. The latter has a median stellar mass of 10^9.9 M_☉, which is only one-tenth of the median mass of optical-only AGNs, 10^11.0 M_☉. The difference is much larger than their respective standard deviations, a factor of 2.8 for the star-forming galaxies and a factor of 2.3 for the optical-only AGNs. The two drastically different stellar mass distributions demonstrate that the majority of optical-only AGNs cannot be dusty star-forming galaxies.

Some may also argue that our emission-line selection includes both Seyferts and LINERs (low-ionization nuclear emission-line regions), and some fraction of LINERs could be powered by processes unrelated to accretion onto SMBHs (Binette et al. 1994; Sarzi et al. 2010). The recent study by Sarzi et al. (2010) using data from the SAURON survey showed that ionization processes other than AGN photoionization can contribute up to 2 Å of [O iii] EW with LINER-like [O iii]/Hβ ratios in integrated spectra taken with an SDSS fiber aperture. Many (35%, 101 out of 291) of our emission-line-selected AGNs have [O iii]/Hβ (or lower limits) greater than 3, satisfying the traditional definition for Seyferts (Ho et al. 1997). 35% (67 out of 190) of the remaining objects in our emission-line AGN sample, which we call LINERs, have [O iii] EWs greater than 3 Å, thus definitely having substantial AGN contribution. In fact, 13% of those LINERs with [O iii] EW less than 3 Å in our sample are also detected at X-ray wavelengths, suggesting many of them are indeed AGNs, rather than powered by shocks or old stellar populations.

To evaluate what fraction of genuine AGNs are not detected in the hard X-ray due to the absorption of the X-ray emission, we need to take into account the variable sensitivity limit across each Chandra pointing. Thus, we first estimate how many of the optically selected AGNs would be detectable in the observed 2–7 keV band if they were not absorbed, and then compare this with the actual number of 2–7 keV detections. We limit this calculation to the DEEP2 optical-AGN sample because the Hectospec observation gave priorities to X-ray sources in target selection. We also exclude weak LINER sources with [O iii]/Hβ < 3 and EW([O iii]) < 3 Å to limit contamination from sources not photoionized by an AGN. This is a very conservative AGN sample. Including both Type 1 and Type 2 optical AGNs, we have a sample of 140 objects. Our results do not change at all if we strictly limit to only Seyferts, i.e., excluding all the LINERs regardless of [O iii] EW.

Assuming the observed [O iii] fluxes reflect the intrinsic luminosities of the AGNs, we estimated the unabsorbed hard-X-ray fluxes for all optical AGNs using the median hard-X-ray-to-[O iii] ratio of Type 1 AGNs in our sample, which is 1.83 dex. Given the X-ray exposure map, the background map, and the redshift of each source, assuming an unabsorbed power-law spectrum with a photon index of Γ = 1.9, we converted the flux of each source to the expected source counts in the 2–7 keV band. We then calculated, for each source, the probability of observing enough counts to qualify it as an X-ray detection in the hard band, given the background counts at the position. The sum of these probabilities is the total number of detectable AGNs if their X-rays were not absorbed at all. Dividing the number of actual hard-X-ray detections by the sum of the probabilities yields the X-ray detection fraction, i.e., the fraction of actual detections out of all potentially X-ray detectable AGNs if the X-rays were not absorbed. For the 140 objects in the sample defined above, the sum of their hard band detection probabilities is 128.31. In reality, only 37 sources (29%) are detected in the hard band. If we limit to Seyferts only ([O iii]/Hβ>3), the fraction is the same: out of 91 Seyferts in our sample, the sum of their potential 2–7 keV detection probability is 88.42; while only 26 sources (29%) are actually detected.

The X-ray detection fraction in bins of [O iii] luminosity is plotted in Figure 14. The fraction of hard X-ray detection among all potentially detectable AGNs decreases toward lower [O iii] luminosity. At the bright end, ∼50% of all AGNs are detected in the 2–7 keV band, which includes unabsorbed and moderately absorbed AGNs. At the faint end, the detection rate rolls off because more and more moderately absorbed AGNs fall below the detection threshold.

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This demonstrates the weakness of X-ray selection relative to optical selection. Depending on the survey depth, X-ray selection can miss a substantial population of AGNs due to absorption and, in some cases, Compton scattering of X-rays by clouds exterior to the accretion disk but interior to the narrow-line region. At L_[O iii] > 10^40.5 erg s^-1, the overall hard X-ray detection fraction is 29.5% ± 4.1%. Assuming an [O iii] bolometric correction of 3500 (Heckman et al. 2004), this corresponds to L_bol > 1.1 × 10⁴⁴ erg s^-1 or intrinsic, unabsorbed L_X(2–10 keV)>2.1 × 10⁴² erg s^-1 if the median flux ratio of Type 1 AGNs is applied. Above this threshold in intrinsic luminosity, 70% of all potentially detectable AGNs would not be detected (at p < 4 × 10⁻⁶) in the 2–7 keV band in 200 ks Chandra images due to X-ray absorption and/or scattering.

Using our emission-line selected AGN sample, we can evaluate whether the absorbing column density distribution among high-z AGNs is different from that in the local universe. Following most local studies, we focus on Seyfert 2 galaxies only. As shown by Bassani et al. (1999), the column density corresponds closely to the HX/[O iii] ratio. By applying the observed hard-X-ray-to-[O iii]-ratio distribution of a local sample of Seyfert 2s to our high-z sample, we can simulate the expected detection fraction of high-z Seyferts if the column density distribution among Seyfert 2s does not evolve with redshift.

For the local Seyfert 2 sample, we employed the [O iii]-selected sample collected by Heckman et al. (2005). They provide the observed HX/[O iii] ratios without any correction for extinction of [O iii] or absorption of X-ray, which is ideal for our purpose. There are 32 Seyfert 2s in this sample, 29 of which have 2–10 keV X-ray data available. We combined ratios randomly drawn from this local sample with the observed [O iii] fluxes of our high-z Seyfert 2s to predict their rest-frame 2–10 keV luminosities. With inverse K-correction and conversion from flux to counts (both assuming Γ = 1.9), we predicted the observed 2–7 keV counts distribution and the total detection fraction. The effect of Γ in inverse K-correction and the flux-to-counts conversion largely cancel out. Assuming the unabsorbed spectral index will lead to a slight underestimate²⁵ of the observed counts and a lower limit on the detection fraction. With 5000 simulations, we find the expected 2–7 keV detection (p < 4 × 10⁻⁶) fraction has a mean of 39% and a dispersion of 5%. In reality, only 25% ± 5% of our Seyfert 2s are detected in the 2–7 keV band, which is 2σ smaller than expected if the column density distribution does not evolve with redshift. This suggests that an average Seyfert 2 galaxy between redshift 0.3 and 0.8 has at least the same, or marginally higher, column density than the average local Seyfert 2 galaxy.

We also ran simulations with different detection thresholds to see whether the increased detection fraction of Seyferts will lead to different conclusions. The results are listed in Table 3. For the two more relaxed detection thresholds, the differences between the actual detection fraction and the expected detection fraction are smaller and less significant (∼1.3σ). Therefore, we conservatively conclude that, at the current statistical significance, the column density distribution among Seyferts at higher-z is similar to that in the local universe, which suggests the fraction of Compton-thick AGNs are also similar to that in the local universe (∼50%; Bassani et al. 1999; Risaliti et al. 1999).