THE SPACE DENSITY OF COMPTON-THICK ACTIVE GALACTIC NUCLEUS AND THE X-RAY BACKGROUND

It is now clear that most accretion of mass onto supermassive black holes is obscured from our view (e.g., Fabian 1999; Treister et al. 2004). Observations of nearby active galactic nuclei (AGNs) suggested that the local ratio of obscured to unobscured sources is ∼4:1 (e.g., Risaliti et al. 1999). A similarly high fraction of obscured AGNs has been used to explain the spectrum and normalization of the extragalactic X-ray background (XRB), as shown by the latest AGN population synthesis models (Treister & Urry 2005; Gilli et al. 2007). The XRB gives an integral constraint to the AGN population and its evolution; the most recent deep surveys show that ∼90% of the observed 2–8 keV XRB radiation can be attributed to resolved AGNs (Hickox & Markevitch 2006 and references therein).

The most obscured AGNs known are those in which the neutral hydrogen column density (N_H) in the line of sight is higher than the inverse Thomson cross section, N_H ≃ 1.5 × 10²⁴ cm⁻². These are the so-called Compton-thick (CT) AGNs. If the obscuring column density is smaller than ∼10²⁵ cm⁻², direct emission from the nucleus is still visible at energies greater than ∼10 keV, while the radiation at lower energies is completely obscured by photoelectric absorption; in this case we have a transmission-dominated CT AGN. For sources with N_H>10²⁵ cm⁻², the X-ray emission is significantly affected by Compton scattering at all energies, fully obscuring the direct AGN emission and leaving only the much fainter reflection component to be detected; these are reflection-dominated AGNs.

Contrary to the situation for less-obscured sources, not much is known about the number density of CT AGNs. Thanks to the deep Chandra and XMM-Newton surveys it is now clear that the fraction of moderately obscured, Compton-thin AGN is on average ∼3/4 of all AGNs, and is higher at lower luminosities (Ueda et al. 2003; Treister & Urry 2005; Barger et al. 2005) and higher redshifts (La Franca et al. 2005; Ballantyne et al. 2006; Treister & Urry 2006), but there are no comparable constraints on the number of CT AGNs. About a dozen CT AGNs have been identified in the local universe (Della Ceca et al. 2008a and references therein). In fact, two of the three nearest AGNs are CT (NGC 4945 and the Circinus galaxy; Matt et al. 2000). Based on a sample of 49 local Seyfert 2 galaxies, Guainazzi et al. (2005) estimated that ∼50% of all obscured AGNs (N_H>10²² cm⁻²) are CT, and similar estimates were made by Risaliti et al. (1999) based on much smaller numbers.

However, so far there has been no systematic study of the statistical properties of CT AGNs with a well defined selection function. Hence, while it has been hypothesized that CT AGNs can contribute up to ∼30% of the XRB (Gilli et al. 2007) and represent a significant fraction of the cosmic accretion onto supermassive black holes (Marconi et al. 2004), this has not been demonstrated. Now, thanks to the wide-area surveys at high energies performed with the International Gamma-Ray Astrophysics Laboratory (INTEGRAL)/IBIS (Beckmann et al. 2006; Krivonos et al. 2007) and the Swift/Burst Alert Telescope (BAT; Tueller et al. 2008), it is possible to study a well defined sample of CT AGNs in the local universe. Furthermore, since most of the absorbed energy is reemitted at mid-infrared (mid-IR) wavelengths, deep observations with the Spitzer observatory can be used to select CT AGN candidates at high redshift, z ∼ 2 (Daddi et al. 2007; Fiore et al. 2008; Alexander et al. 2008), yielding an upper limit to the number density of these sources.

In this paper, we constrain the number density of CT AGNs in the local universe from high-energy observations, and at high redshift using a combination of X-ray and mid-IR data. We compare the observed numbers of CT AGNs with expectations from AGN population synthesis models that explain the XRB emission and we study the degeneracies affecting these models. Finally, we compute the implied density of supermassive black holes as a function of redshift, including transmission-dominated CT accretion. When required, we assume a ΛCDM cosmology with h₀ = 0.7, Ω_m = 0.3, and Ω_Λ = 0.7, in agreement with the most recent cosmological observations (Spergel et al. 2007).

One of the best ways to find CT AGN is by observing at high energies, namely E>10 keV. The hard X-ray spectrum of a CT AGN is characterized by at least three components: an absorbed power law with an upper cutoff at ∼300 keV (e.g., Nandra & Pounds 1994), a Compton reflection hump which peaks at ∼30 keV (Magdziarz & Zdziarski 1995), and an iron Kα line at ∼6.4 keV. Not all components are clearly observed in all AGNs (e.g., Soldi et al. 2005; Beckmann et al. 2004), perhaps because of the low signal to noise of some of the observations. One clear advantage of high-energy observations is that photoelectric absorption has minimal effects, so transmission-dominated CT AGNs can easily be detected. It is only when the source becomes reflection dominated that the emission at E>10 keV is affected.

Current observations at E>10 keV are available only at relatively high fluxes, and hence low redshifts, z < 0.05. While BeppoSAX (Boella et al. 1997) was successfully used for targeted observations of known Seyfert galaxies, it is only now, thanks to the INTEGRAL (Winkler et al. 2003) and Swift (Gehrels et al. 2004) satellites, that large-area surveys at these energies have been done.

Using the IBIS coded-mask telescope (Ubertini et al. 2003), INTEGRAL surveyed ∼80% of the sky down to a flux of 5 mcrab in the 17–60 keV. The catalog of Krivonos et al. (2007) reports the properties of 130 sources detected in these all-sky observations and classified as AGNs. A large number of unidentified sources remain in this catalog, 48, but only seven are found at high galactic latitude (|b|>5°), and thus of likely extragalactic origin. Five of the 130 AGNs are CT AGNs.

We carried out a very deep survey with INTEGRAL/IBIS, with a total exposure time of ∼3 Ms, in the XMM-Large Scale Survey (XMM-LSS) region, reaching a flux limit of ∼3 × 10⁻¹² erg cm⁻² s⁻¹ in the 20–40 keV band (S. Virani 2009, in preparation). A total of 15 sources, all AGNs, are found in this survey, including the prototypical CT AGN, NGC 1068. We also found another CT AGN candidate, not detected in X-rays before. However, an accurate N_H determination has not been obtained for this source yet, and hence it is not included in our sample. NGC 1068 was also included in the catalog of Krivonos et al. (2007) and hence is already in our sample.

Recently, Tueller et al. (2008) presented a catalog of 103 AGNs detected in an all-sky survey with the Swift/BAT. The 14 sources classified as blazars and BL Lac were excluded from our sample. Eighty-nine of the remaining AGNs are at high galactic latitudes, |b|>15°, where only one source remains unidentified. The fraction of unidentified sources is much smaller for Swift compared to INTEGRAL because of follow-up observations with Swift's dedicated X-ray telescope. In the Tueller et al. (2008) catalog, there are five AGNs with estimated N_H greater than 10²⁴ cm⁻². However, we caution that these N_H measurements were obtained by fitting a single absorbed power law to the X-ray spectrum, while it is known that heavily absorbed AGNs have more complex spectra (e.g., Vignati et al. 1999; Levenson et al. 2006).

We added to our sample the source NGC 7582, which has N_H ∼ 10²³ cm⁻² in Tueller et al. (2008) but has been shown with XMM/Newton data to have a very complex spectrum with strong evidence for mildly CT absorption, N_H ∼ 10²⁴ cm⁻² (Piconcelli et al. 2007). With the improved sensitivity of the Suzaku telescope (Mitsuda et al. 2007), it is possible to perform detailed X-ray spectroscopy for some of the sources detected by Swift/BAT included in the catalog of Tueller et al. (2008), revealing in some cases CT absorption. We added to our sample the source NGC 5728, which as reported by Comastri et al. (2007) from Suzaku observations is obscured by a CT gas with N_H ≃ 2.1 × 10²⁴ cm⁻². We also added the source ESO 005–G004 which based on the Suzaku observations reported by Ueda et al. (2007) is a heavily obscured, CT AGN.

In summary, INTEGRAL and Swift found 130 and 103 AGNs, respectively, in their wide-area surveys; 76 sources (∼58%) were detected by both surveys. (This fraction is not larger due to the differences in sky coverage and the nonuniform depth of the observations.) We then found 15 AGNs in deep 3 Ms INTEGRAL observations, one of them the CT AGN NGC1068. INTEGRAL detected five CT AGNs, while Swift found eight. However, there is incomplete overlap between the two samples and we note that the disparate energy ranges make direct comparison of fluxes difficult. The INTEGRAL-detected CT sources are: NGC 4945, Circinus, Markarian 3, NGC 3281, and NGC 1068; the Swift/BAT CT AGNs are: NGC 4945, Markarian 3, NGC 3281, NGC 7582, NGC 5728, NGC 5252, NGC 6240, and ESO 005–G004.

The number of CT AGNs found by these surveys is surprisingly low, compared to the sample of known CT AGNs in the local universe. In a study of optically selected Seyfert 2 galaxies with hard X-ray information, Risaliti et al. (1999) found 16 CT AGNs in a total of 45 Seyfert galaxies, although four were later demonstrated to most likely not be CT (NGC 1386, IC 3639, NGC 5005, and NGC 4939; Maiolino et al. 1998; Ghosh et al. 2007; Gallo et al. 2006). Of the remaining 12 CT sources, three were detected by Chandra and/or XMM, while the rest are mostly reflection-dominated sources, too faint to be detected by either INTEGRAL or Swift even though they are nearby, moderate luminosity AGNs. In fact, Awaki et al. (2009) recently confirmed the CT nature of NGC 2273, one of the sources in the Risaliti et al. (1999) sample, which is however too faint to be detected by INTEGRAL or Swift.

Recently, Della Ceca et al. (2008a) published a list of 18 CT AGNs with detections at E>10 keV. Of these, seven were detected by Swift and/or INTEGRAL, while the remaining 11 were studied with pointed BeppoSAX observations, and are typically fainter than the INTEGRAL/Swift detection threshold. We use all these samples, suitably amended as necessary, to place constraints on the number density of CT AGNs.

An alternative way to find CT sources is by studying the water maser emission in AGN. Because large amounts of molecular gas are required to produce the maser amplification, AGNs with detected water maser emission are in general heavily obscured along the line of sight. In fact, Greenhill et al. (2008) recently reported that from a sample of 42 AGNs known to show water maser emission, 95% have N_H>10²³ cm⁻² and 60% are CT. Since these AGNs were not detected at high energies by either INTEGRAL or Swift, we do not include them here; however, we note that water maser emission appears to be a highly efficient way to identify a large number of heavily obscured sources.

2.1. The log N–log S Distribution

Figure 1 shows the cumulative number counts of AGNs, with CT sources shown separately, as a function of hard X-ray flux. In order to avoid the necessity of specifying a standard spectrum to convert fluxes to different energy bands, we show the INTEGRAL and Swift sources separately, but note that a good agreement (within ∼40%) in the normalization between the two distributions exists if a standard band conversion is assumed. At these high fluxes, the slope of the log  N–log  S is Euclidean, implying a uniform spatial distribution, as expected given the low redshifts of these sources. We also compare with the distribution predicted by the AGN population synthesis model with which Treister & Urry (2005) fit the XRB, and find in general good agreement in slope and normalization.

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The log  N–log  S relations for the five CT AGNs detected by INTEGRAL and the eight sources observed by Swift/BAT are also consistent with Euclidean slopes, with normalizations of 10⁻⁴ deg⁻² at fluxes of ∼5 × 10⁻¹¹ and ∼9 × 10⁻¹¹ erg cm⁻² s⁻¹ in the INTEGRAL and Swift bands, respectively. (For a power-law spectrum with Γ = 1.8, for example, F_{14−195,Swift} ∼ 2.3F_17−60, INTEGRAL for most column densities N_H ≲ 24 cm⁻².) About twice as many CT AGNs at low redshifts were reported in the sample of Risaliti et al. (1999). Since all these CT AGNs have detections at high energies, we plot them in Figure 1. Clearly, they fall significantly below the extrapolation of the observed log  N–log  S, suggesting high levels of incompleteness in the Risaliti et al. (1999) sample. This is not surprising given that these sources do not come from a flux-limited survey but from pointed observations.

A possible source of incompleteness in our sample of CT AGNs comes from the difficulty in measuring the amount of absorption in these sources, given that they have in general very complex X-ray spectra. As noted by Tueller et al. (2008), sources that are not well characterized in X-rays by an absorbed power law are good candidates to be heavily obscured AGNs. In their Swift/BAT sample, a total of 46 sources with complex spectra were reported. Of those, 18 have an optical classification of Seyfert 1.5 or lower, and hence it is very unlikely that they are CT AGNs. Considering the very extreme assumption that the remaining 28 sources are all CT AGNs increases the normalization of the CT AGN log  N–log  S by only a factor of ∼2. This is because a large fraction of the complex-spectrum sources have fluxes fainter than that of NGC 6240, one of the faintest confirmed CT AGNs in the Swift sample. In any case, it is important to remark that according to a detailed study by Winter et al. (2009), while all these complex-spectrum sources are highly obscured, only half a dozen have some evidence of CT column densities. Hence, we conclude that the observed log  N–log  S is not affected significantly by this possible source of incompleteness.

For the transmission-dominated AGNs in our sample (i.e., excluding NGC 1068), we find volume densities for L_X>10⁴² erg s⁻¹ of 5.5^+8.6_−3.1 × 10⁻⁵ Mpc⁻³ and for L_X>10⁴³ erg s⁻¹ of 2.2^+2.9_−1.1 × 10⁻⁶ Mpc⁻³. Because this is a flux-limited sample, luminosity and redshift are strongly correlated. For example, a source with X-ray luminosity of 10⁴², 10⁴³, or 10⁴⁴ erg s⁻¹ can only be detected up to z ≃ 0.005, 0.015, or 0.045, respectively. Thus, the source densities inferred here are valid only up to these limiting redshifts, corresponding to distances of ∼21, 63, and 190 Mpc. Also, because there is a significant correlation between luminosity and fraction of obscured sources (e.g., Ueda et al. 2003; Barger et al. 2005), CT AGNs are found only up to z = 0.024 in this sample, even though unobscured sources have been found by Swift/BAT up to z ∼ 0.1. That is, CT AGNs preferentially have low luminosities, so they are found mostly at low redshift. In effect, the flux limit prevents us from detecting the many CT AGNs at higher redshift. The derived volume densities for CT AGNs at z ≃ 0 are fully consistent with the values derived by Della Ceca et al. (2008b) from three INTEGRAL sources only.

Taking into account the densities reported here, the number of CT AGNs relative to the X-ray-selected AGN population is 5.3 × 10⁻⁵/2.2 × 10⁻⁴ = 24% for sources in the L_X = 10⁴²⁻⁴³ erg s⁻¹ range, while for sources with L_X = 10⁴³⁻⁴⁴ erg s⁻¹ this fraction is 2.2 × 10⁻⁶/2.9 × 10⁻⁵ = 7.5%. This calculation uses the luminosity function of Ueda et al. (2003). However, similar numbers are obtained if the La Franca et al. (2005) luminosity function is used instead. Hence, the relative fraction of CT AGNs decreases by about a factor of 3 for an order of magnitude increase in luminosity. For Compton-thin sources, according to Treister et al. (2009), the fraction of obscured sources (N_H ⩾ 10²² cm⁻²) decreases from 100% at L_X = 10⁴² erg s⁻¹ to ∼60% at L_X = 10⁴³ erg s⁻¹, implying a decrease of about a factor of 2. Therefore, the decrease in the fraction of CT AGNs is comparable to the decrease in the fraction of obscured Compton-thin AGNs, a reasonable agreement given the statistical errors in our sample. This is in agreement with the conclusions of Fiore et al. (2009), who found a similar decrease in CT AGNs with increasing luminosity in their high-redshift IR-selected sample.

2.2. N_H Distribution

A key ingredient in our understanding of the AGN population and of the properties of the obscuring material is the distribution of line-of-sight column densities, parameterized in terms of the neutral hydrogen column density, N_H. In Figure 2, we show the observed N_H distribution for the sources in the Swift/BAT sample of Tueller et al. (2008) obtained from very simple spectral fitting assuming an intrinsic absorbed power-law spectrum; the distribution from the AGN population synthesis models of Treister & Urry (2005), adapted to the flux limit of the Swift/BAT sample; the distribution assumed by Gilli et al. (2007); and the distribution predicted by the galaxy evolution models of Hopkins et al. (2006).

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The N_H distribution observed in the Swift sample is relatively flat, before a strong decline at N_H>10²⁴ cm⁻². This decline corresponds to a relatively low number of CT AGNs in this sample, as mentioned before. In contrast, the N_H distribution used in the XRB population synthesis model of Treister & Urry (2005) had roughly the same number of sources with N_H in the 10²³–10²⁴ and 10²⁴–10²⁵ cm⁻² ranges, because of an incorrect assumption about the normalization of the HEAO 1 A-2 XRB. This translates into a discrepancy of a factor of ∼3 more CT AGN assumed by that model than is observed in the BAT sample. A similar unrealistically high number of CT AGNs was assumed in the work of Gilli et al. (2007). The relationship between the number of CT AGNs and the XRB is explored in detail in Section 3 below.

For relatively unobscured sources, N_H < 10²² cm⁻², the Tueller et al. (2008) N_H distribution is significantly different from that observed in the deepest X-ray fields. For example, for the sources in the Chandra Deep Field North and South, Treister et al. (2004) reported a sharp peak at N_H = 10²⁰ cm⁻² and almost no AGNs in the 10²⁰–10²¹ cm⁻² range. The discrepancy at low values of N_H between the Swift/BAT and the deep fields samples could be due to the difficulty in measuring low N_H values at higher redshifts, as discussed by, e.g., Akylas et al. (2006). The N_H distribution in the population synthesis model of Treister & Urry (2005) matches well the observed distribution in the Chandra Deep Fields, but has some significant differences with the distribution of Tueller et al. (2008). This discrepancy, however, is not relevant for our present work, which focuses on the most obscured AGN.

2.3. Comparison with Models

3.1. Parameter Degeneracies

The spectrum of CT AGNs at high energies, even for transmission-dominated sources, is often dominated by the Compton reflection component (e.g., Matt et al. 2000), which has a strong peak at E ∼ 30 keV (Magdziarz & Zdziarski 1995). The observed spectrum of the XRB, which we now know is just the integrated emission from previously unresolved AGN, also has a peak at about the same energy (Gruber et al. 1999). Hence, it was suspected for a long time that CT AGNs provide a significant contribution to the XRB emission. In fact, in the early work of Comastri et al. (1995) the contribution of CT AGNs to the XRB is ∼20%, similar to the value assumed in the population synthesis models of Ueda et al. (2003), Treister & Urry (2005), and Gilli et al. (2007); Shankar et al. (2009) report a slightly higher contribution of ∼30% at ∼20 keV.

Because it is very hard to measure the number density of CT AGNs, even locally, AGN population synthesis models have assumed it to be a fixed fraction of the obscured, Compton-thin sources, typically ∼0.5–1 times as many. In Figure 3, we show the fraction of all AGNs that are CT, compared to the observed fraction in the INTEGRAL and Swift samples as a function of hard X-ray flux. At fluxes of ∼10⁻¹¹ erg cm^{−2 −1}, the fraction of CT AGNs in the model of Gilli et al. (2007) is ∼15%, while the observed value is ∼6 ± 5% for INTEGRAL and ∼8 ± 3% for the Swift sample. For comparison, in Figure 3 (solid line) we show the predicted CT AGN fraction as a function of flux for the model of Treister & Urry (2005) with the number of CT AGNs modified to match the INTEGRAL and Swift observations presented here. The Treister & Urry (2005) model assumes a nearly constant fraction of CT AGNs, while the Gilli et al. (2007) model assumes a steep increase in the number of CT AGNs at fluxes fainter than ∼10⁻¹⁴ erg cm⁻² s⁻¹. This is due to the assumed luminosity dependence of the fraction of obscured sources in the Gilli et al. (2007) model, which decreases steeply above luminosities of ∼10⁴³ erg s⁻¹ and is flat at lower luminosities. While such faint fluxes are still out of reach for current hard X-ray observatories, it will be possible to test this flux regime with Nuclear Spectroscopic Telescope Array (NuSTAR) and the International X-ray Observatory (IXO). However, the luminosity dependence of the fraction of obscured AGNs assumed by the model of Gilli et al. (2007) can already be ruled out, in particular at high luminosities, by observations of Compton-thin AGNs at lower energies (Hasinger 2008; Treister et al. 2009).

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The fact that the XRB does not constrain the number density of CT AGNs can be explained by strong degeneracies in other parameters, like the assumed spread in spectral index (Gilli et al. 2007; Shankar et al. 2009), high-energy cutoff, etc. When trying to constrain the number density of CT AGNs, the most important parameter is the normalization of the Compton reflection component, which is directly related to the AGN luminosity at ∼30 keV, where the CT AGN contribution is maximal. Given that even the nearest AGNs have only low signal-to-noise observations at E>10 keV, the normalization of the Compton reflection component is not well constrained by observations of individual sources. From a sample of 22 Seyfert galaxies, excluding CT sources, Malizia et al. (2003) concluded that both obscured and unobscured sources have similar reflection components with normalization values in the range R ∼ 0.6–1 (in units of 2π). A similar value of R ≃ 1 was reported by Perola et al. (2002) based on BeppoSAX observations of a sample of nine Seyfert 1 galaxies. Although with large scatter, normalizations for the average reflection component of 0.9 for Seyfert 1 and 1.5 for Seyfert 2 were measured from BeppoSAX observations of a sample of 36 sources (Deluit & Courvoisier 2003). Early population synthesis models for the XRB assumed values of R = 1.29 for unobscured sources and 0.88 for obscured AGNs (Comastri et al. 1995; Gilli et al. 1999). In contrast, the models of Ueda et al. (2003), Treister & Urry (2005), and Ballantyne et al. (2006) assumed a constant value of R = 1 (equivalent to a solid angle of 2π) for both obscured and unobscured sources. Gilli et al. (2007) assumed the same normalizations as Comastri et al. (1995), R ∼ 1.3 and 0.88; however, for high-luminosity sources, L_X>10⁴⁴ erg s⁻¹, the reflection component was not included (R = 0 ).

For a given number of CT AGNs, the resulting intensity of the XRB at ∼30 keV is directly linked to the assumed normalization of the reflection component. In Figure 4, we show the values of the normalization of the Compton reflection component and CT AGN number density that produce XRB intensities in the 20–40 keV region consistent with the latest observed values from INTEGRAL (Churazov et al. 2007) and Swift (Ajello et al. 2008). This is the energy range in which the contribution of CT AGN to the XRB is maximal and hence can be best constrained. For comparison, the parameters assumed by the model of Gilli et al. (2007) lie in the upper left region of Figure 4, at a density of CT AGN roughly three times higher than the observed value of ∼2 × 10⁻⁶ Mpc⁻³ and average Compton reflection component normalization of ∼0.6. (The latter is a rough estimate, since they assumed R = 0.88 for obscured sources at low luminosities, and R = 0 at high luminosities.) The model of Treister & Urry (2005) assumed a similarly high number of CT AGNs and a higher normalization of the Compton reflection component, and hence resulted in a higher intensity of the XRB, consistent with the HEAO 1 (Gruber et al. 1999) measurements increased by 40%, similar to what was assumed by Ueda et al. (2003) and Ballantyne et al. (2006) in order to match the observations of the XRB at lower energies by Chandra and XMM. Such a high value of the XRB intensity at E ∼  10–50 keV is now ruled out by new INTEGRAL (Churazov et al. 2007), Swift (Ajello et al. 2008), and BeppoSAX (Frontera et al. 2007) data. Given the degeneracies with other model parameters, it is unlikely that the XRB could be used to constrain the average value of R. High signal-to-noise observations of individual sources at E>10 keV are required for this purpose.

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3.2. A New X-Ray Background Fit

Since both the number density of CT AGNs and the normalization of the Compton reflection component can now be constrained independently, we can attempt to match the observed spectrum and intensity of the XRB. In Figure 5, we show our new fit, which matches the INTEGRAL and Swift observations at E>10 keV, which are ∼10% higher than the HEAO 1 normalization. The original fit of Treister & Urry (2005), which has a factor of ∼4 more CT AGN, is also shown. Not surprisingly, the effects of changing the number of CT AGNs are most important in the E = 10–100 keV region.

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The new XRB fit matches both the INTEGRAL and Swift/BAT observations at E>10 keV and the Chandra measurements at lower energies (which are ∼30% higher than the HEAO 1 A-2 observations). Recently, a new measurement of the XRB intensity at E = 1.5–7 keV using the Swift XRT (X-ray telescope) was presented by Moretti et al. (2009). These new data confirmed that the original HEAO 1 normalization should be increased by ∼30% and ∼10% at low and high energies, respectively. In contrast, the AGN population synthesis model of Gilli et al. (2007) assumed the original HEAO 1 intensity at all energies, which translates into a relatively lower contribution from unobscured sources. In order to produce the necessary hard spectrum, Gilli et al. (2007) had to assume a relatively high number of obscured sources at high luminosities, i.e., an unusual, inverted dependence of the obscured fraction of AGNs as a function of luminosity (Hasinger 2008; Treister et al. 2009).

Assuming a fixed value of the Compton reflection component, how much can the number of CT AGNs change and still match the XRB, given the existing uncertainties in the intensity measurements? The INTEGRAL measurements of the XRB, reported by Churazov et al. (2007), have uncertainties of ∼5% including both statistic and systematic effects. Similarly, the Swift measurements have estimated errors of ∼3% (Ajello et al. 2008). Both measurements are consistent with each other but are ∼10% higher than the original HEAO 1 intensity. Translating this ∼5% uncertainty into an uncertainty in the number of CT AGNs, we conclude that the total number of CT AGNs can be changed by a factor of 55% and still be consistent with the current measurements of the XRB. However, this calculation does not include the uncertainty in the normalization of the Compton reflection component, which is by far the dominant factor. For comparison, the statistical errors for the measurement of the 10 CT AGNs detected combining the Swift and INTEGRAL surveys correspond to an uncertainty of ∼30% (Gehrels 1986), i.e., the direct detection of CT AGNs is much better than the XRB for determining the number of CT AGNs.

Given that the number of CT AGNs in the local universe is effectively constrained by the Swift and INTEGRAL surveys, it is now possible to estimate the total contribution of CT AGN to the XRB, as well as its redshift dependence. In order to do that, we integrate the total X-ray emission from the CT AGN in our population synthesis model and divide it by the observed XRB intensity. To facilitate the comparison with the local sources observed by Swift and to make sure that the effects of absorption are negligible, we perform this integration over the 14–195 keV band. In Figure 6, we show the resulting redshift dependence of the fractional contribution to the hard XRB radiation. As can be seen, the total contribution of CT AGNs to the XRB is ∼9%, and about 50% of it comes from sources at z < 0.7. Similarly, we conclude that ∼2% of the XRB is provided by CT AGNs at z>1.4, while CT AGNs at z>2 only contribute ≲1% to the XRB. Conversely, the 5% uncertainty in the absolute measurement of the XRB intensity translates into an uncertainty of a factor of ∼5 in the number of CT AGNs at z>2. Hence, the number of CT AGNs at high redshift is largely unconstrained by the XRB.

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In Figure 6, we further compare this expected redshift dependence to the integrated fluxes from individually detected CT AGNs. At z ≃ 0, we integrate the emission from the eight sources detected by Swift/BAT. At higher redshifts, we use the sample of CT AGN candidates detected in X-rays in the Chandra Deep Field South reported by Tozzi et al. (2006), which includes 14 reflection-dominated AGNs and six transmission-dominated AGNs with N_H>10²⁴ cm⁻². In the same field, Georgantopoulos et al. (2007) found a total of 18 CT AGN candidates, but only eight of them with a measured N_H greater than 10²⁴ cm⁻²; the remaining sources were selected based on their flat X-ray spectra. All six transmission-dominated CT AGNs in the sample of Tozzi et al. (2006) are included in the work of Georgantopoulos et al. (2007). However, no overlap is found between the reflection-dominated CT AGN candidates reported by Tozzi et al. (2006) and the flat-spectrum sources of Georgantopoulos et al. (2007). Hence, it is possible that either selection of heavily obscured sources is highly incomplete. In order to compare properly with the local sample, in Figure 6 we show separately the contribution from the transmission-dominated AGNs and from all sources in the sample of Tozzi et al. (2006). We separated the sample at z = 1.5, to have the same number of sources in each redshift bin. As expected, most of the contribution to the XRB comes from the transmission-dominated sources, which are in general brighter in the X-ray band. The agreement at low redshift is not surprising, since by construction our model was adjusted to match the Swift/BAT observations. However, it is very interesting that also for the high-redshift sources the calculated contribution of CT AGN to the XRB agrees well with the limits from deep surveys.

As shown in the previous section, the number of CT AGNs at high redshift is largely unconstrained by the XRB or by current hard X-ray surveys. Since a large fraction of the absorbed energy in heavily obscured AGNs is reemitted at mid-IR wavelengths, deep Spitzer data have been used to find CT AGN candidates at z ⩾ 2. Daddi et al. (2007) used the excess in mid-IR luminosity (compared to UV estimates of star formation rates) to find obscured AGNs not individually detected in X-rays. Similarly, Fiore et al. (2008) used a combination of red optical-to-near-IR colors and high 24 μm luminosity to select CT AGN candidates at z ∼ 2. In both cases, very high source densities have been estimated for mid-IR-selected CT AGNs, e.g., Daddi et al. (2007) reported a sky density of ∼3200 deg⁻², similar to that of all previously known AGNs at those redshifts in the Chandra Deep Fields. Somewhat surprisingly, very little overlap is found between the two selection methods, implying the possible presence of interlopers. If these candidates are confirmed, a very large number of CT AGNs exist at high redshift, considerably larger than the local population. This is qualitatively consistent with the evolution in obscuration detected by Treister & Urry (2006) for Compton-thin sources. Recently, Alexander et al. (2008) reported the confirmation of seven CT AGNs using optical and mid-IR spectroscopy in the Chandra Deep Field North region, implying a similarly high density for CT AGN at high redshift.

In order to quantify the density of CT AGN at high redshift and to compare with local observations and AGN luminosity functions, in Figure 7 we present the available measurements of the comoving volume density of CT AGN candidates as a function of redshift. Our measurement of the density of CT AGN at z = 0 is ∼2.2× 10⁻⁶ Mpc⁻³, for sources with L_X>10⁴³ erg s⁻¹, as shown in Section 2.1. At higher redshifts and luminosities, we infer the space density from several samples. Five X-ray-selected CT AGN candidates were found in the Spitzer Wide-area InfraRed Extragalactic survey (SWIRE; Polletta et al. 2006); these are transmission-dominated CT AGNs and all of them have intrinsic X-ray luminosities greater than 10⁴⁵ erg s⁻¹ (magenta open circle, Figure 7). Twenty X-ray-selected CT AGNs were found by Tozzi et al. (2006) in the Chandra Deep Field South; in this case, we separated the sample into two redshift bins and computed the comoving number density separately for sources with L_X>10⁴³ and L_X>10⁴⁴ erg s⁻¹ (squares, Figure 7). Finally, we also show the comoving number density estimated from the mid-IR CT AGN candidates in the samples of Daddi et al. (2007), Fiore et al. (2009), and Alexander et al. (2008).

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The expected comoving number density for CT AGN as a function of redshift was computed using the models of Treister & Urry (2005). Briefly, we used the hard (2–10 keV) X-ray luminosity function and AGN evolution of Ueda et al. (2003), with the N_H distribution and luminosity dependence of the fraction of obscured AGNs of Treister & Urry (2005). In addition, we include the evolution of the relative number of obscured sources reported by Treister & Urry (2006). The normalization of the relative number of CT AGNs was chosen to match the observed numbers at z ∼ 0. This model fits the observed XRB spectral shape and normalization, as shown in Figure 5. The resulting comoving density of CT AGN as a function of redshift is shown in Figure 7 for sources with L_X>10⁴², 10⁴³, and 10⁴⁴ erg s⁻¹.

While the observed density of X-ray-selected CT AGNs with L_X>10⁴³ erg s⁻¹ is in pretty good agreement with the expectations at all redshifts, at higher luminosities the observed values are mostly higher than the expectations. In fact, the comoving density for L_X>10⁴⁵ erg s⁻¹ sources from SWIRE is almost 2 orders of magnitude higher than the expected value. However, it is important to note that this comoving density is derived from CT AGN candidates based on the spectral properties derived from low signal-to-noise observations, and also the number of sources detected is small, so the uncertainties are large. The values for X-ray-selected CT AGNs with L_X>10⁴⁴ erg s⁻¹ are also higher than expectations, but in this case only by factors of ∼2–3. Similarly, the densities inferred from mid-IR-selected CT AGNs are systematically higher than the expected values at all luminosities, typically by 1 order of magnitude.

This discrepancy between expectations and observations at high redshift can be interpreted in several ways. One obvious possibility is that the observations at low redshift are missing a significant number of CT AGNs, which are included in the high-redshift samples. In fact, we have shown before that the high-energy surveys performed by INTEGRAL and Swift are mostly complete for transmission-dominated sources, but miss a significant fraction of the reflection-dominated AGNs. While the sample of Risaliti et al. (1999) includes these sources, it is based on pointed observations and hence it is highly incomplete as well (Figure 1). Also, it is very likely that the high-redshift IR-selected samples include both transmission- and reflection-dominated sources. Another possibility is that the high-redshift samples, both X-ray- and mid-IR-selected, include a significant number of interlopers. These could be either less-obscured AGNs in the case of X-ray selection or non-active galaxies undergoing significant but dusty star formation, and thus showing high mid-IR luminosities not due to AGN activity. Finally, it is possible that CT AGNs follow a different evolution than Compton-thin sources. It is important to note that the (1 + z)^0.4 evolution in the ratio of obscured to unobscured AGN found by Treister & Urry (2006) for Compton-thin sources is already included in the predicted volume densities. Hence, if both the low- and high-redshift observed samples are not systematically missing a significant number of sources, the excess of CT AGNs at high redshift implies a different (stronger) evolution for these heavily obscured sources than for obscured but Compton-thin AGNs.

Because AGNs are powered by accretion of gas onto a supermassive black hole, the AGN luminosity function represents the history of cosmic accretion (Soltan 1982). Hence, the AGN bolometric luminosity can be converted into a mass accretion rate, assuming an efficiency for the conversion = L/$\dot{m}$c² (typically, ≃ 0.1). Then, the comoving black hole mass density can be written (following Equation (17) of Yu & Tremaine 2002) as

$$\begin{eqnarray} \rho (z)\!\!\!\! &=&\!\!\!\! \int _z^{\infty }\frac{dt}{dz}dz\int _{L_{\rm min}}^{L_{\rm max}}\frac{(1-\epsilon)\textnormal {BC}(L_X)L_X}{\epsilon c^2}\Psi (L,z) \nonumber \\ &&\!\!\!\! \times \int _{N_{{\rm H},{\rm min}}}^{N_{{\rm H},{\rm max}}}f(N_{\rm H},L)dN_{\rm H}dL, \end{eqnarray} \tag{ 1 }$$

where Ψ(L, z) is the evolving AGN luminosity function, BC(L_X) is the bolometric correction starting from the 2–10 keV luminosity, and f(N_H, L) is the "N_H function," or the fraction of sources at a given luminosity with a given N_H. For this calculation, we used the 2–10 keV luminosity function of Ueda et al. (2003) and the N_H function with a luminosity dependence described in Section 3.2 of Treister & Urry (2005). The bolometric correction was calculated using the spectral energy distribution of a completely unobscured AGN as specified by Treister et al. (2006), as appropriate for the unified model of AGN. Additionally, we updated the spectral library with the new relation between X-ray (at 2 keV) and UV (2500 Å) luminosities using the value of the slope of the power-law extrapolation reported by Steffen et al. (2006),

$$\begin{eqnarray} &&\alpha _{ox}=(-0.077\pm 0.015)\log (L_{ {2\, {\rm keV}}})+(0.492\pm 0.387). \end{eqnarray} \tag{ 2 }$$

With these assumptions, the bolometric correction ranges from ∼25 for L_X = 10⁴² erg s⁻¹ to ∼100 for L_X = 10⁴⁵ erg s⁻¹, in approximate (factor of ∼2) agreement with the values assumed by other authors (e.g., Kuraszkiewicz et al. 2003; Marconi et al. 2004; Barger et al. 2005; Hopkins et al. 2007).

In previous works (e.g., Yu & Tremaine 2002), the AGN luminosity function was integrated from L_min = 0 to L_max = ∞, which leads to very large extrapolations in particular at the faint end. In the present case, we use the same integration limits used by Treister & Urry (2005) in their AGN population synthesis model, namely, L_min = 10^41.5 erg s⁻¹, L_max = 10⁴⁸ erg s⁻¹, N_H,min = 10²⁰ cm⁻², and N_H,max = 10²⁵ cm⁻². The number of CT AGNs in this model is matched to the INTEGRAL and Swift results, as reported above. With these assumptions, and using the typical value of = 0.1, we obtain a value for the local black hole mass density of ρ (z = 0) = 4.5× 10⁵ M_☉ Mpc⁻³. This calculation agrees well with the values estimated from observations: ρ = 4.6^+1.9_−1.4 × 10⁵ M_☉ Mpc⁻³ (Marconi et al. 2004) and ρ = (3.2–5.4) × 10⁵ M_☉ Mpc⁻³ (Shankar et al. 2009).

In Figure 8, we present the black hole mass density as a function of redshift estimated from our calculation, together with the curves presented by Marconi et al. (2004) and Yu & Tremaine (2002). The main differences with the work of Marconi et al. (2004) are in the number of CT AGNs (they assumed four times more), the assumed bolometric correction (our is three times times higher at low luminosities) and the redshift limit of the integration. Of these, the bolometric correction dominates, such that our derived local black holes mass density is slightly larger, even with the reduced number of CT AGNs. Note that the bolometric correction of Marconi et al. (2004) was obtained from observations of high-luminosity sources only, while our bolometric correction was tested by observations of fainter sources as well (Treister et al. 2006). A remarkably good agreement is found between our results and the recent work of Shankar et al. (2009). Compared to Yu & Tremaine (2002), we find twice the local integrated black hole mass density, because they used an optical quasar luminosity function and evolution, which peaks at a higher redshift, z ∼  2, and evolves strongly. In contrast, the Ueda et al. (2003) luminosity function, which includes lower luminosity and obscured sources, peaks at z≃ 1.1. In our calculation, the vast majority of the black hole growth occurs at low redshift (∼50% from z = 1.3 to 0), which matches observations of AGNs detected in X-rays (e.g., Barger et al. 2001).

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The space density of CT AGN is consistent with, but cannot be constrained by, the observed local black hole mass density. In addition, analogous to the weakness of the XRB integral constraint on the number of CT AGNs, numerous degeneracies with other parameters, like the assumed bolometric correction and efficiency, are important. Even taking into account only the uncertainties in the local black hole mass density, we could still increase the number of CT AGNs in the local universe by factors of ∼3. Hence, we can conclude that direct observations of CT AGNs at high energies, like the INTEGRAL and Swift observations discussed here, are currently the only way to constrain the population of heavily obscured supermassive black holes.

In this paper, we constrain the space density of CT AGN in the local universe using the recently available wide-area surveys at high energies performed by INTEGRAL/IBIS and Swift/BAT. A total of 10 CT AGNs at z < 0.03 were found by either INTEGRAL and/or Swift. These observations are complete for transmission-dominated CT AGNs, but are probably still missing heavily obscured sources with N_H>10²⁵ cm⁻². We find that the space density of local CT AGN follows a Euclidean distribution with a normalization of ∼10⁻⁴ deg⁻² at fluxes of ∼5 × 10⁻¹¹ and ∼9 × 10⁻¹¹ erg cm⁻² s⁻¹ in the 17–60 keV and 14–195 keV bands, respectively. This is about three to four times smaller than the values expected from recent AGN population synthesis models that fit the extragalactic XRB (Treister & Urry 2005; Gilli et al. 2007), and thus modifications to those models are required.

We present here a new population synthesis model for the XRB, with the number of CT AGNs constrained by the INTEGRAL and Swift number counts. We find that the fraction of AGNs that are CT at F_{20−100 keV} ∼ 10⁻¹¹ erg cm⁻² s⁻¹ is ∼5%. We show that the XRB by itself cannot be used to constrain the number of CT AGNs, mainly due to degeneracies with other parameters, the most important of which is the normalization of the Compton reflection component. We find that the total contribution of CT AGN to the XRB is ∼9%, with only ≲1% from CT AGN at z>2. Hence, taking into account the 5% uncertainty in the XRB intensity measurements, the number of CT AGNs at high redshift is essentially unconstrained by the XRB, even if all the other parameters could be fixed.

We calculate the local black hole mass density inferred from AGN activity using Soltan's argument (Soltan 1982), taking into account the contribution from CT AGN estimated in this work. For an accretion efficiency $\eta \equiv L/\dot{m} c^2=0.1$, we find an integrated local black hole mass density of 4.5 × 10⁵ M_☉ Mpc⁻³, in excellent agreement with recent estimates based on measured masses of local dormant black holes. Considering the current uncertainties in these estimates, we conclude that only the direct observations of CT AGN such as those discussed in this paper can effectively constrain the number of heavily obscured AGNs. Based on the number density of CT AGNs presented here, our best estimate of the fractional contribution of CT AGNs to the total accreted black hole mass is <10%.

Using a combination of X-ray and mid-IR selection, the space density of CT AGN at high redshift is starting to be constrained. We find that observed densities are systematically higher than expected from the evolving AGN luminosity function measured from less-obscured sources, assuming N_H-independent evolution of the local CT AGN population. This can be explained in three ways, any or all of which could be the case. First, the local sample might be incomplete, particularly because even hard X-ray selection is biased against reflection-dominated CT AGN. Second, the high-redshift samples may be contaminated by strongly star-forming galaxies or other interlopers. Third, CT AGNs may evolve more strongly than less-absorbed sources, implying a relatively larger number of CT AGNs in the early universe. To decide this question requires the help of observations with the new generation space-based hard X-ray observatories. While mid-IR selection of heavily obscured AGNs is very promising, these samples are inevitably affected by the presence of interlopers, in particular from star-forming galaxies, and by the lack of accurate measurements of the amount of obscuration.

Hard X-ray selection provides a cleaner sample of CT AGN, since N_H values can be measured directly and there is almost no contamination from star-forming galaxies at these energies. Several different approaches are currently being planned for the next generation of high-energy (E>10 keV) missions, to provide a large and complete sample of CT AGN up to z ∼ 3. The Energetic X-ray Imaging Survey Telescope⁷ (EXIST; Grindlay 2005) will perform an all-sky survey in the 20–80 keV energy band to flux limits of ∼6 × 10⁻¹³ erg cm⁻² s⁻¹, finding thousands of heavily obscured AGNs up to z ∼ 1 and high-luminosity CT quasars at all redshifts. With a complementary approach, the NuSTAR⁸ (Harrison 2008), with a scheduled launch date of 2011 August, will perform targeted observations of fields of ∼1 deg² to flux limits of ∼2 × 10⁻¹⁴ erg cm⁻² s⁻¹, hence ∼20 times deeper than EXIST, in the 6–79 keV band, for exposure times of ∼1 Ms; these observations will be able to find low-luminosity CT AGNs up to z ∼ 2–3. Similarly, the planned New X-ray Telescope⁹ (NeXT; Takahashi et al. 2008), scheduled for launch in 2013 will provide imaging and spectroscopy in the 5–80 keV energy band with an angular resolution <17 and a spectral resolution of ∼1.5 keV. Another focusing hard X-ray observatory, Simbol-X,¹⁰ is targeted for launch in 2014 (Ferrando et al. 2004). Simbol-X will perform pointed observations with a field of view of ∼12' and an angular resolution of ∼30."

Finally, it is important to note that for z ∼ 2 the Chandra and XMM observed energy band of 2–10 keV corresponds to a rest-frame energy of ∼6–30 keV, so the effects of obscuration are less important. Unfortunately even the deepest Chandra data available now only detect a few photons for the CT AGN candidates at z ∼ 2 (e.g., Tozzi et al. 2006), thus preventing detailed spectral fitting that could provide a deeper physical understanding of the nature of these sources. The proposed IXO¹¹ will provide an outstanding opportunity to study these highly obscured high-redshift sources. As reported by Alexander et al. (2008), the IXO will be able to detect thousands of photons for the CT AGN detected in the Chandra Deep Fields observations for similar, ∼1 Ms, exposure times, yielding high signal-to-noise spectra for these sources. Deep observations at high energies with NuSTAR, EXIST, and Simbol-X will provide large samples of heavily obscured AGN at z ∼ 1–3, while the improved sensitivity and spectral resolution of the IXO will allow us to study in detail the spectra of CT AGNs at z ∼ 2–3.

We thank the anonymous referee for very useful comments. We acknowledge support from NASA/INTEGRAL grants NNG05GM79G and NNX08AE15G. Support for the work of ET was provided by the National Aeronautics and Space Administration through Chandra Postdoctoral Fellowship Award Number PF8-90055 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8-03060. S.V. acknowledges support from a graduate research scholarship awarded by the Natural Science and Engineering Research Council of Canada (NSERC).

Facilities: INTEGRAL (IBIS), Swift (BAT), CXO (ACIS), XMM (EPIC), Spitzer (IRAC, MIPS).