Inferring Compton-thick AGN candidates at z>2 with Chandra using the >8 keV restframe spectral curvature

TL;DR

This paper develops and applies a spectral curvature method to identify Compton-thick AGN at high redshift using Chandra data, providing insights into their population and evolution.

Contribution

The study introduces a new spectral curvature technique for detecting high-redshift Compton-thick AGN and applies it to deep field data, offering a novel approach for future X-ray surveys.

Findings

Measured CT AGN fractions of 17% and 15-32% in different surveys.

Found no significant redshift evolution in CT AGN fraction at high redshift.

Provided spectral curvature equations applicable to future X-ray missions.

Abstract

To fully understand cosmic black hole growth we need to constrain the population of heavily obscured active galactic nuclei (AGN) at the peak of cosmic black hole growth ($z\sim$1-3). Sources with obscuring column densities higher than $\mathrm{10^{24}}$ atoms $\mathrm{cm^{-2}}$, called Compton-thick (CT) AGN, can be identified by excess X-ray emission at $\sim$20-30 keV, called the "Compton hump". We apply the recently developed Spectral Curvature (SC) method to high-redshift AGN (2<z<5) detected with Chandra. This method parametrizes the characteristic "Compton hump" feature cosmologically redshifted into the X-ray band at observed energies <10 keV. We find good agreement in CT AGN found using the SC method and bright sources fit using their full spectrum with X-ray spectroscopy. In the Chandra deep field south, we measure a CT fraction of $\mathrm{17^{+19}_{-11}\%}$ (3/17) for sources with observed luminosity $\mathrm{>5\times 10^{43}}$ erg $\mathrm{s^{-1}}$. In the Cosmological evolution survey (COSMOS), we find an observed CT fraction of $\mathrm{15^{+4}_{-3}\%}$ (40/272) or $\mathrm{32\pm11 \%}$ when corrected for the survey sensitivity. When comparing to low redshift AGN with similar X-ray luminosities, our results imply the CT AGN fraction is consistent with having no redshift evolution. Finally, we provide SC equations that can be used to find high-redshift CT AGN (z>1) for current (XMM-Newton) and future (eROSITA and ATHENA) X-ray missions.

Tables

Table 1. Table 1: SC values for the analyzed sample in the CDF-S.

XIDa	zb	Soft ctsc	Mid ctsd	Hard ctse	Total ctsf	SCg	CT candidate
710	2.03	45$\pm$10	17$\pm$10	16$\pm$10	77$\pm$17	0.06$\pm$0.29
369	2.21	101$\pm$17	54$\pm$13	25$\pm$13	180$\pm$25	-0.03$\pm$0.14
20	2.31	21$\pm$9	7$\pm$7	13$\pm$8	42$\pm$14	0.25$\pm$0.38
188	2.56	127$\pm$14	90$\pm$13	88$\pm$13	306$\pm$23	0.23$\pm$0.07
93	2.57	44$\pm$10	31$\pm$9	25$\pm$9	100$\pm$16	0.16$\pm$0.14
294	2.57	17$\pm$8	4$\pm$7	20$\pm$8	41$\pm$13	0.44$\pm$0.34	yes
687	2.58	268$\pm$22	167$\pm$18	98$\pm$16	533$\pm$33	0.06$\pm$0.05
137	2.61	147$\pm$14	109$\pm$12	95$\pm$12	351$\pm$22	0.20$\pm$0.05
86	2.73	89$\pm$15	55$\pm$12	74$\pm$13	218$\pm$23	0.26$\pm$0.09
149	2.81	197$\pm$17	172$\pm$15	168$\pm$16	537$\pm$28	0.25$\pm$0.04
546	3.06	201$\pm$16	185$\pm$15	247$\pm$17	633$\pm$28	0.32$\pm$0.04
674	3.08	26$\pm$8	11$\pm$7	7$\pm$8	45$\pm$13	-0.00$\pm$0.21
588	3.47	27$\pm$8	5$\pm$6	18$\pm$8	50$\pm$13	0.18$\pm$0.18
563	3.61	162$\pm$15	89$\pm$12	127$\pm$14	378$\pm$23	0.20$\pm$0.04
262	3.66	24$\pm$7	33$\pm$8	60$\pm$10	117$\pm$14	0.44$\pm$0.10	yes
412	3.7	65$\pm$10	74$\pm$10	108$\pm$12	247$\pm$18	0.35$\pm$0.06
403	4.76	9$\pm$5	4$\pm$4	12$\pm$5	24$\pm$8	0.42$\pm$0.31	yes

Table 2. Table 2: SC values for the analyzed sample in the COSMOS legacy survey. This table is available in its entirety in a machine-readable form in the online journal. A portion is shown here for guidance regarding its form and content.

IDa	zb	Soft ctsc	Mid ctsd	Hard ctse	Total ctsf	SCg	CT candidate	$N_H^{}{}_{}{}^h$ [${10}^{22}$ atoms/${\mathrm{cm}}^2$]	$N_H^{}{}_{}{}^i$ [${10}^{22}$ atoms/${\mathrm{cm}}^2$]
Lid$\_$471	2.0	7$\pm$4	8$\pm$4	6$\pm$3	23$\pm$6	0.41$\pm$0.38	yes	18.8	16.10
Lid$\_$1026	2.00	10$\pm$4	9$\pm$4	5$\pm$3	25$\pm$6	0.23$\pm$0.33		25.3	2.67
Lid$\_$249	2.00	24$\pm$6	6$\pm$3	2$\pm$3	33$\pm$6	-0.31$\pm$0.21		0	4.22
Cid$\_$545	2.01	14$\pm$5	6$\pm$3	2$\pm$3	23$\pm$6	-0.16$\pm$0.32		0	9.95
Lid$\_$635	2.01	6$\pm$3	2$\pm$3	7$\pm$4	16$\pm$5	0.71$\pm$0.6	yes	0	3.43
Cid$\_$1512	2.02	9$\pm$4	0$\pm$2	11$\pm$4	20$\pm$5	0.73$\pm$0.56	yes	56.4	56.40
Cid$\_$282	2.02	13$\pm$4	11$\pm$4	6$\pm$3	30$\pm$6	0.18$\pm$0.28		0	0.79
Cid$\_$351	2.02	54$\pm$8	20$\pm$5	11$\pm$4	86$\pm$10	-0.11$\pm$0.13		0	2.41
Cid$\_$424	2.02	8$\pm$4	6$\pm$3	7$\pm$3	22$\pm$5	0.46$\pm$0.41	yes	5.65	0.79

Equations

$${\text{SC}}_{\text{C}}(\mathrm{A},\mathrm{B},\mathrm{C})=-0.915\times \mathrm{A}+0.281\times \mathrm{B}+2.746\times \mathrm{C},$$

$$\mathrm{\Delta }{\text{SC}}_{\text{C}}=\sqrt{(-0.915\times \mathrm{\Delta A}{)}^2+(0.281\times \mathrm{\Delta B}{)}^2+(2.746\times \mathrm{\Delta C}{)}^2},$$

$${\text{SC}}_{\text{A}}(\mathrm{A},\mathrm{B},\mathrm{C})=-0.522\times \mathrm{A}+0.251\times \mathrm{B}+2.270\times \mathrm{C},$$

$${\text{SC}}_{\text{XMM}}(\mathrm{A},\mathrm{B},\mathrm{C})=-0.559\times \mathrm{A}+0.424\times \mathrm{B}+2.570\times \mathrm{C},$$

$${\text{SC}}_{\text{eROSITA}}(\mathrm{A},\mathrm{B},\mathrm{C})=-0.436\times \mathrm{A}+0.407\times \mathrm{B}+2.356\times \mathrm{C},$$

$${\text{CT}}_{\text{C}}(\mathrm{z})=-0.02\times {\mathrm{z}}^3+0.29\times {\mathrm{z}}^2+3.00\times \mathrm{z}-3.35,$$

$${\text{CT}}_{\text{A}}(\mathrm{z})=0.03\times {\mathrm{z}}^3-0.41\times {\mathrm{z}}^2+1.98\times \mathrm{z}-0.78,$$

$${\text{CT}}_{\text{XMM}}(\mathrm{z})=0.03\times {\mathrm{z}}^3-0.40\times {\mathrm{z}}^2+1.37\times \mathrm{z}-0.64$$

$${\text{CT}}_{\text{eROSITA}}(\mathrm{z})=0.04\times {\mathrm{z}}^3-0.54\times {\mathrm{z}}^2+2.07\times \mathrm{z}-1.40$$

$${\overline{\text{SC}}}_{\mathrm{I}}(A,B,C,z)=\frac{S{C}_I(A,B,C)}{C{T}_I(z)},$$

Full text

††pubyear: 2016††pagerange: Inferring Compton-thick AGN candidates at z>2 with Chandra using the >8 keV restframe spectral curvature–Inferring Compton-thick AGN candidates at z>2 with Chandra using the >8 keV restframe spectral curvature

1 Introduction

Active galactic nuclei (AGN) are believed to be powered during accretion episodes in which matter from galactic scales is accreted onto the central supermassive black hole (SMBH) (e.g., Soltan, 1982; Marconi et al., 2004; Merloni et al., 2006). During these accretion phases, periods of maximal growth occur in the SMBH (e.g., Ferrarese & Ford, 2005; Johnson et al., 2013). Due to the large amount of matter involved during the accretion of a SMBH, a significant fraction of AGN is obscured from sight (e.g., Balokovic et al., 2014; Brightman et al., 2014). Thus, to understand the evolution history of all the SMBHs through cosmic time, we need a complete census of the AGN population including the heavily obscured sources (e.g., Treister et al., 2009a; Ueda et al., 2014; Ricci et al., 2015; Buchner et al., 2015). The capability of the X-ray emission at energies >10 keV to penetrate obscuring matter makes them one of the best tools to study obscured AGN (Risaliti et al., 1999; Barger et al., 2003; Georgantopoulos & Akylas, 2009). The detection of AGN can, however, become very challenging when the absorption reaches Compton-thick (CT) levels (Georgantopoulos et al., 2010; Lanzuisi et al., 2015; Brandt & Alexander, 2015). We define an AGN as CT when it is surrounded by obscuring material with column density on the line of sight larger than the inverse Thomson cross-section ($\mathrm{N_{H}\geq\sigma_{T}^{-1}\approx 1.5\times 10^{24}\,atoms\,cm^{-2},}$ Comastri, 2016).

The study of highly obscured sources, such as CT AGN, is crucial to achieve a complete census of the accreting SMBH population and to obtain an unbiased X-ray luminosity function (e.g., Fabian & Iwasawa, 1999; Alexander, 2007; Georgakakis et al., 2015). Gilli et al. (2007) found that to explain the cosmic X-ray background (XRB) peak at $\sim 30$ keV the fraction of CT AGN must be equivalent to the fraction of moderately obscured sources (21 < $\mathrm{log(N_{H})}$ < 24). Their results agree with Fiore et al. (2008). Daddi et al. (2007) studied the population at $z\sim 2$ showing an excess in the mid-IR wavelength suggesting a space density of CT AGN of $\sim 2.6\times 10^{-4}$ Mpc*-3*. However, they found that even if the population of CT AGN has a large space density, the CT contribution to the still missing XRB is of the order of $10\%$–$25\%$. This result is consistent with what has been found by Treister et al. (2009b). The analysis of the hard X-ray luminosity function from Ueda et al. (2014) using X-ray data from Swift/BAT, MAXI, ASCA, XMM-Newton, Chandra and ROSAT reveals that the number of sources with column density between $\mathrm{log(N_{H})}=24$–$25$ must be equal to the number of sources with $\mathrm{log(N_{H})}=23$–$24$ to explain the cosmic XRB emission at 20 keV. This result is similar to what has been found by Gilli et al. (2007). X-ray spectral analysis of the 4 Ms Chandra Deep Field South (CDF-S) by Brightman & Ueda (2012) using spectral models from Brightman & Nandra (2011) showed a CT fraction in the nearby Universe of $\sim 20\%$ growing to $\sim 40\%$ at redshift $z=1$–$4$. However, Buchner et al. (2015) combined deep and wide-area Chandra and XMM-Newton X-ray surveys and they did not find any evidence of the redshift evolution of the CT fraction which they found to be $38^{+8}_{-7}\%$ on a redshift range from 0.5 to 2. This could be explained by the difference in the analyzed luminosity ranges as the sample in Buchner et al. (2015) includes sources with X-ray luminosities down to $10^{43.2}$ erg $\mathrm{s^{-1}}$. Ricci et al. (2015) found the CT fraction to be luminosity dependent with $32\pm 7\%$ at luminosities $\mathrm{log(L_{14-195keV})=}$40–43.7, while only $21\pm 5\%$ at higher luminosities $\mathrm{log(L_{14-195keV})=}$43.7–46. This result is similar to what found by Civano et al. (2015) who performed an analysis of the Cosmological Evolution Survey (COSMOS) field with NuSTAR, finding a CT fraction between 13$\%$ and 20$\%$ at redshift z=0.04–2.5. However, the result of Ricci et al. (2015) is corrected from bias, while the fraction in Civano et al. (2015) is not. We note that some studies have suggested that most of them "missing" XRB is expected to be produced by objects with intrinsic luminosity smaller than $\mathrm{10^{44}\,erg\,s^{-1}}$ and z < 1 (Gilli, 2013). In summary, despite extensive research there is still considerable disagreement about the fraction of CT AGN and their contribution to the XRB particularly at high-redshift.

In CT AGN, the majority ($>95\%$) of the hard X-ray (2 – 10 keV) emission is obscured/scattered (Risaliti et al., 1999; Matt et al., 2000). The X-ray spectra, however, feature a prominent Fe K$\alpha$ emission line with large equivalent width EW $>$ 1 keV (e.g. Nandra et al., 1997; Reynolds, 1999; Vignali & Comastri, 2002; Liu et al., 2016), and the Compton hump, peaking at $\sim$20 – 30 keV (Krolik, 1999; Nandra, 2006). The spectral curvature method was developed by Koss et al. (2016), to identify nearby ($z<0.03$) CT AGN candidates in Swift/BAT and NuSTAR using the ($>10$ keV) spectral curvature. The sensitivity of NuSTAR is $1\times 10^{-14}\;\mathrm{erg\;cm^{-2}\;s^{-1}}$ in the 10 – 30 keV range (Harrison et al., 2013), while Swift/BAT has a sensitivity of $10^{-11}\;\mathrm{erg\;cm^{-2}\;s^{-1}}$ in the deepest all sky maps (Krimm et al., 2013). Thus, both instruments select relatively bright sources compared to the faint high-redshift AGN detected by Chandra. The Chandra Deep Field South (CDF-S), which is the deepest survey of the Chandra X-ray observatory, has a flux limit of $5.5\times 10^{-17}\;\mathrm{erg\;cm^{-2}\;s^{-1}}$ in the 2 - 10 keV energy range (Xue et al., 2011). Hence, it can detect much fainter sources than NuSTAR such as high-redshift CT AGN.

In this article, we extend the Spectral Curvature (SC) method to high-redshift ($z>2$) AGN where the restframe Compton hump feature can be observed with Chandra. In section 2 we describe our simulations to define the method for Chandra, in section 3 we apply it to Chandra fields, and finally in section 4 we discuss implications. Throughout this work, we adopt $\Omega_{m}$= 0.27, $\Omega_{\Lambda}$= 0.73, and $H_{0}$ = 71 km s-1 Mpc*-1*. Errors are quoted at the 90% confidence level unless otherwise specified.

2 The Spectral Curvature method

To estimate the likelihood of a X-ray source to be CT, the SC method uses the distinctive spectral shape of CT AGN at energies higher than 10 keV. In this work, we follow the technique used for low-redshift sources (e.g., Koss et al., 2016) where we model an unobscured source with a power-law of $\Gamma$ = 1.9, and a heavily CT source as an AGN with line-of-sight column densities of $\mathrm{N_{H}}=5\times 10^{24}\;\mathrm{cm^{-2}}$ using the MYtorus spectral models from Yaqoob (2012). We choose the threshold at column density $\mathrm{N_{H}}=5\times 10^{24}\;\mathrm{cm^{-2}}$ to be consistent with Koss et al. (2016). The SC equation is modeled so that an unobscured source has a SC value of zero, while an heavily CT AGN has a SC value of one.

As a first step, we simulated the Spectral Curvature (SC) of obscured AGN at high-redshift with the XSPEC (version 12.9.0) fakeit tool. Figure 1, left panel, shows how the SC measure increases with higher column density. For simplicity, we assume $\mathrm{N_{H}}=10^{24}\;\mathrm{cm^{-2}}$ as the lower limit of column density for CT AGN. The coefficients of the SC equation are defined using weighted and averaged counts of simulated unobscured and CT sources in three different energy ranges divided by the total counts in the entire range (8-24 keV restframe) (Figure 1, right panel). Finally, since we worked with observations of objects at redshift $z>2$, the corresponding energy ranges in the observed frame are $[8-12]/(1+z)$, $[12-16]/(1+z)$ and $[16-24]/(1+z)$ keV.

2.1 The Spectral Curvature equation

We first consider the importance of energy-dependent vignetting and point spread function degradation with off-axis angle. We tested the behavior of the SC equations for off-axis sources by simulating spectra of unobscured, obscured and CT AGN at constant redshift z = 2, exposure time (4 Ms) and intrinsic luminosity of $5\times 10^{44}\;\mathrm{erg\;s^{-1}}$, using response files corresponding to different off-axis positions. The response files at different off-axis angles are obtained using the CIAO 4.9 tools mkacisrmf and mkarf111See cxc.harvard.edu/caldb/prop_plan/imaging/.. We averaged over 100 simulations to reduce the effect of Poisson noise. The coefficients of the spectral curvature equation show very little dependence on the off-axis position of the source in Chandra (Figure 4). Nevertheless, we note that above 8 arcmin off-axis distance the large PSF significantly reduces sensitivity in Chandra. On the other hand, the SC coefficients show a strong redshift dependency that can be corrected for using an additional redshift correction factor.

The SC equation for the Chandra at redshift $z=2$ is given by:

[TABLE]

where $\mathrm{A,\;B}$ and $\mathrm{C}$ are the normalized Chandra count rates in the three energy ranges $[8-12]/(1+z)$, $[12-16]/(1+z)$ and $[16-24]/(1+z)$ keV, with $z=2$. The subscript C indicates that we are referring to the Chandra telescope.

The error on the SC values depends on the error on the counts, $\mathrm{\Delta A\;,\Delta B}$ and $\mathrm{\Delta C}$, which is given by the Poisson statistics. Thus, the error on the SC equation is:

[TABLE]

We did not include the standard deviation on the calculated SC coefficient in the error propagation of the SC equation, since it is much smaller than the coefficient value itself and does not affect the total error much. Moreover, it is important to remember that A, B, and C are the counts in the three energy ranges normalized for the counts F in the full energy band $[8-24]/(1+z)$ keV.

Koss et al. 2016 showed that SC measurements are consistent for different telescopes. This means that we can apply the SC method to different satellites as, for example, the XMM-Newton and the future ATHENA telescope. The Wide Field Imager of the ATHENA telescope will span the energy range from 0.1 to 15 keV. Finally, eROSITA will scan the entire sky out to 10 keV. We calculated the SC equation for ATHENA and XMM-Newton at $\mathrm{z=1}$, since the two satellites can resolve the Compton hump starting from these redshifts because of their higher effective area at high energies. The SC equation for the different telescopes is given by:

[TABLE]

[TABLE]

[TABLE]

2.1.1 Redshift dependence

After applying the method developed in Koss et al. (2016) to the redshift interval from 2 to 5, the SC values and the thresholds between CT and non-CT sources depend significantly on the redshift. We therefore add a redshift parameter to the SC equation, so that the new input variables are the normalized counts in the three energy ranges (A, B, and C) and include the change with redshift.

We develop an equation so that SC$>0.4$ is a consistent boundary for CT sources with redshift. We choose to normalize the threshold to a value of 0.4 to be consistent with Koss et al. (2016). We achieved this by calculating the SC values of simulated CT sources at different redshift. These values can be fitted with good approximation by a third degrees polynomial. We normalize the SC equation by this third degree polynomial to achieve the simplest model that provides a CT selection value with redshift close to a constant value. The CT threshold is still slightly redshift dependent since the third degree polynomial only approximates the curve that describes the SC values of CT sources. The redshift correction factor is then:

[TABLE]

[TABLE]

[TABLE]

[TABLE]

The new SC equation has the form

[TABLE]

where I is $\{$C, A, XMM, eROSITA$\}$.

We tested the SC method on a sample of simulated X-ray spectra with different column densities and luminosities. The integration time for the simulation is set to 4 Ms, this determines a limit on the maximum number of counts obtained. From Figure 2 and Figure 3 we observe that the method successfully distinguishes between simulated sources with column densities below $\mathrm{N_{H}=10^{24}\;\,cm^{-2}}$ and CT sources. Moreover, from Figure 3 we can estimate where the SC method is less reliable for sources with very few counts due to the large error bars. We note that between 10 and 70 counts the SC method presents large uncertainties that could make uncertain the classification for single sources, however, the population can be studied in aggregate. Moreover, the method is less sensitive to sources with column densities exceeding $\mathrm{N_{H}=10^{25}\;\,cm^{-2}}$, since at these column densities the Compton hump intensity is reduced by Compton scattering. Thus, the SC method is better suitable for transmission-dominated ($\mathrm{N_{H}<10^{25}\;\,cm^{-2}}$) CT AGN.

3 Sample and data analysis

We applied the SC method to deep Chandra observations. Thanks to the high sensitivity of Chandra, we can find CT candidates even at redshift higher than 2. The deepest Chandra surveys are the CDF-S and the COSMOS legacy survey (Figure 5).

3.1 CDF-S

The Chandra Deep Field South (CDF-S) has an on axis flux limits reaches 3.2$\times$10*-17*, 9.1$\times$10*-18* and 5.5$\times$10*-17* erg cm*-2* s*-1* in the energy ranges 0.5 – 8 keV, 0.5 – 2 keV, and 2 – 8 keV respectively (Xue et al., 2011) (Figure 5). For this catalog, the reduced spectra have not been made public. Thus, we applied the SC method on the 4 Ms merged event file222The event file can be found on the CXC homepage (http://cxc.harvard.edu/cda/Contrib/CDFS.html). The coordinates and redshifts that we used, can be found in the catalog of Xue et al. (2011).

We excluded from the analysis the sources with angular distance greater than 8.7 arcmin from the image center (Figure 4) because of their significantly reduced sensitivity and exposure time. We extracted the net number of counts and the error on it using the CIAO tool dmextract. We extracted the net counts in the three energy ranges $[8-12]/(1+z)$, $[12-16]/(1+z)$ and $[16-24]/(1+z)$ keV. The error on the net counts are calculated directly with dmextract using the Gehrels statistic (Gehrels, 1986). The flux limit for the CDF-S is calculated for unobscured sources. Hence, the survey may miss sources with very high level of obscuration that fall below the detection limit, for example the reflection-dominated CT AGN ($\mathrm{N_{H}>1\times 10^{25}\,cm^{-2}}$).

3.2 COSMOS

The Chandra COSMOS Legacy Survey covers 2.2sq deg of the COSMOS field to a flux limit of 2.2$\times$ 10*-16*, 1.5$\times$ 10*-15* and 8.9$\times$ 10*-16* erg cm*-2* s*-1* in the 0.5 – 2, 2 – 10 and 0.5 – 10 keV bands, respectively (Civano et al., 2016) (Figure 5). The depth of the flux and the relatively large area of the COSMOS-Legacy survey are going to remain unrivaled until the advent of ATHENA (Civano et al., 2016).

We used the X-ray spectra of the sources in the COSMOS-legacy survey from Civano et al. (2016). For the purposes of our analysis, for each source in the Chandra COSMOS-Legacy sample we used XSPEC (version 12.9.0) to estimate the number of counts in the energy intervals $[8-12]/(1+z)$, $[12-16]/(1+z)$ and $[16-24]/(1+z)$ keV. The number of counts in the energy range is calculated by multiplying the count rate (obtained by calling the attribute rate of xspec.Spectrum) with the exposure time. To determine the errors on the number of counts, we applied Gehrels statistic (Gehrels, 1986). The exposure times of our sample range from 40 to 250 ks. We did not exclude sources at largest off axis angles. The flux limit for the COSMOS survey is calculated for unobscured source. Therefore, highly obscured sources are likely to be missed from the survey.

4 Results

4.1 CDF-S

By applying the SC method on 17 sources with luminosity higher than $5\times 10^{43}$ $\mathrm{erg\,s^{-1}}$ and with spectroscopic redshift in the 4 Ms CDF-S (see Table 1), we obtained three CT candidates (the three blue dots above the CT threshold line in Figure 6). Of these, only the one at redshift 3.66 has net number of counts higher than 100 (see Figure 6, middle source above the threshold). The source above the CT threshold at redshift 4.67 has coordinates RA = 3:32:29.27, Dec = -27:56:19.8 (XID403) and has been proposed as a CT candidate in Gilli et al. (2011). The SC value could be verified by applying the SC method to the coming 7 Ms CDF-S survey which will have tighter limits and smaller uncertainties.

Constraining our analysis to sources with spectroscopic redshift, the fraction of CT AGN selected in the CDF-S is 17${}^{+18.6}_{-11.0}\%$ (3/17 sources with spectroscopic redshift) assuming binomial statistics with 90$\%$ of confidence. The value we obtain is similar to what was found by Koss et al. (2016). However, the sample analyzed in the CDF-S is small. To have more reliable constraints on the CT AGN populations we will focus on the larger sample obtained from the COSMOS-legacy survey.

4.2 COSMOS

We calculated the SC values for the sources in the COSMOS-legacy survey between redshift 2 and 5 (Figure 7). The redshift and the column densities of the COSMOS sources can be found in the Marchesi et al. (2016a) catalog. The $\mathrm{N_{H}}$ therein are calculated from HR ratios and redshifts. In total we applied the method to 272 sources (see Table LABEL:table:COSMOS), 158 cataloged as Seyfert 1 (i.e. unobscured AGN showing both broad and narrow optical emission lines) and 68 cataloged as Seyfert 2 (i.e. obscured AGN showing only narrow optical emission lines).

We found that 14.5$\%$ (40/272) sources are selected as CT AGN. The SC method selects no CT candidate at redshift $z>3.5$, primarily due to the much smaller number of sources in the survey and their faintness. If we restrict the luminosity to $\mathrm{L_{X}>10^{44}\,erg\,s^{-1}}$ to avoid biases due to the flux limit of the COSMOS survey we find that the fraction of CT AGN is 8.9$\%$ (13/145). We chose to apply this luminosity cut, since we are comparing the obtained CT fraction in different redshift bins over a specific luminosity range so that it can be compared to other published studies (e.g. Ricci et al. (2015)) and because of the low statistical significance of the spectral curvature for sources just above the detection limit. The focus on higher luminosity AGN in this paper will likely exclude some number of absorbed AGN because of the well-known anti-correlation between fraction of absorbed AGN and luminosity (e.g. Hasinger (2008)). Considering the total sample of CT candidates (without luminosity cuts), 18/40 (45$\%$) are described as Seyfert 1 in the catalog. This means that 11.4$\%$ of sources that are considered unobscured in the optical is selected as CT AGN candidates. On the other hand, 22 sources are selected from the 68 cataloged as Seyfert 2. This means that the 32.4$\%$ of the Seyfert 2 is selected as CT. We also have to consider the possibility that the classification of Seyfert 1 and Seyfert 2 in the Marchesi et al. (2016a) catalog might have some uncertainties. Additionally, the definitions of Seyfert 1 and Seyfert 2 are based on optical spectra and X-ray (unobscured vs. obscured) schemes of classification do not always agree (e.g., Burtscher et al., 2016). To explore this possibility, we examined the SC values of the COSMOS sample for column densities $\mathrm{log(N_{H})}<23.5$ cm*-2* and $\mathrm{log(N_{H})}\geq 23.5$ cm*-2* (Figure 7, bottom panel). We found that only $8.6^{+4.3}_{-3.2}\%$ of the sources with $\mathrm{log(N_{H})}<23.5$ cm*-2* (in total 152) are selected as CT candidates, while we select as CT candidates $22.5^{+6.7}_{-5.7}\%$ of the sources with $\mathrm{log(N_{H})}\geq 23.5$ cm*-2* (in total 120). This means that the SC method typically agrees with CT AGN candidates sources with high values of $\mathrm{N_{H}}$.

We also compare our results with the $\mathrm{N_{H}}$ obtained from spectral fitting by Marchesi et al. (2016b). The only source with $\mathrm{N_{H}>10^{24}\,cm^{-2}}$ reported in Marchesi et al. (2016b) is Cid$\_$747. Its SC value is $\mathrm{0.24\pm 0.17}$ and thus the source is not selected as CT candidate by the SC method. Larger samples of CT AGN from X-ray spectral fitting would be useful for further comparison.

The mean value of spectral curvature for Seyfert 1 is 0.16$\pm$0.02, while for the Seyfert 2 we have a mean value of 0.26$\pm$0.03. This is a promising result, since Seyfert 2 defines sources obscured in the optical wavelengths and thus we expect to find all CT candidates in the Seyfert 2 population.

However, the number of selected Seyfert 1 is high and has to be investigated whether this is statistical noise. To test this we assumed that all the Seyfert 1 sources should be completely unobscured, i.e. a pure power-law, and their SC values should be zero. Then we randomly added noise consistent with the expected uncertainty. We repeated this 100 times in a bootstrap process to estimate the error. The average number of sources selected as CT AGN is 11.6$\%$ with standard deviation of 3.1$\%$, which is consistent with the fraction of selected Seyfert 1 suggesting this population is consistent with the false positive expected from statistical noise.

We also predict the false positive and negative rates of the SC method by inferring them from simulations. For simplicity, we assume a flat $N_{\rm H}$ distribution of sources with equal numbers at every column density between $10^{21}$ cm*-2* and $5\times 10^{24}$ cm*-2*. Sources between $10^{21}$ cm*-2* and $10^{24}$ cm*-2* can contribute to false positives and sources with $\mathrm{N_{H}}$ between $10^{24}$ cm*-2* and $5\times 10^{24}$cm*-2* can be missed false negatives because of statistical noise. At the exposure times in COSMOS, we found that the rate of false positives is between $9\%$ to $16\%$ for the shortest and longest exposures which is consistent with our previous false positive rate measurement. The rate of false negatives varies between $23\%$ and $44\%$ between the shortest and longest exposure suggesting that a significant fraction of transmission dominated CT AGN will be missed.

We also have to consider the possibility that the classification of Seyfert 1 and Seyfert 2 in the Marchesi et al. (2016a) catalog might have some uncertainties. Additionally, the definitions of Seyfert 1 and Seyfert 2 are based on optical spectra and X-ray (unobscured vs. obscured) schemes of classification do not always correspond (Burtscher et al., 2016). To explore this possibility, we examined the SC values of the COSMOS sample for column densities $\mathrm{log(N_{H})}<23.5$ cm*-2* and $\mathrm{log(N_{H})}\geq 23.5$ cm*-2* (Figure 7). We found that only $8.6^{+4.3}_{-3.2}\%$ of the sources with $\mathrm{log(N_{H})}<23.5$ cm*-2* (in total 152) are selected as CT candidates, while we select as CT candidates $22.5^{+6.7}_{-5.7}\%$ of the sources with $\mathrm{log(N_{H})}\geq 23.5$ cm*-2* (in total 120). This means that the SC method effectively selects as CT AGN candidates sources with high values of $\mathrm{N_{H}}$. Of the sources with $\mathrm{log(N_{H})}<23.5$ cm*-2*, 104 are cataloged as Seyfert 1 while 48 are tagged as Seyfert 2. In the $\mathrm{log(N_{H})}\geq 23.5$ cm*-2* regime, 66 source are considered as Seyfert 2 and 54 as Seyfert 1. However, since their line-of-sight column density is quite high, they can not be considered to be unobscured sources in the X-ray. In the high $\mathrm{N_{H}}$ case, $20.4\%^{+10.0\%}_{-7.8\%}$ Seyfert 1 and $24.2^{+9.4}_{-7.7}\%$ Seyfert 2 are selected as CT candidates.

Another possible explanation for the fraction of Seyfert 1 selected as CT candidates is that at these redshifts the reflection component of their X-ray spectra enters in the energy range we examine with the SC method. However, (e.g., Koss et al., 2016) tested a larger range of torus models and found that these sources would still be well below the CT limit.

Another issue is that the observed luminosity of faint CT sources will be below the flux limit of the survey. We therefore perform simulations to correct for highly obscured sources missed with Chandra. We calculate the ratio of intrinsic to observed luminosity as a function of redshift and column density in the rest frame energy band from 8 – 24 keV by simulating sources with different $\mathrm{N_{H}}$. Using this value, we can calculate which fraction of sources we are not able to detect with Chandra in different redshift bins and for different $\mathrm{N_{H}}$.

To estimate the fraction of faint undetected sources, we randomly draw the $\mathrm{N_{H}}$ of the simulated sources from two different $\mathrm{N_{H}}$ distributions at $z=2$: a linear distribution and the observed $\mathrm{N_{H}}$ distribution proposed by Ricci et al. (2015) and we calculate the fraction of sources too faint for Chandra to observe if the $\mathrm{N_{H}}$ is the one assumed. We obtained this fraction by simulating a population of unobscured sources using the fakeit tool of XSPEC and by comparing how many of these sources are below Chandra sensitivity if we apply the randomly draw $\mathrm{N_{H}}$. The luminosities and redshift of the unobscured simulated sources are comparable with those of the sources in the COSMOS sample. The integration time of the simulations is held constant to 4 Ms consistent with the survey. We repeat this calculation 1000 times, each time drawing a new random sample from the parent $\mathrm{N_{H}}$ distribution. Since we have a fraction of CT AGN equal to zero above z=3.5, we constrain this analysis to z = 2–3.5. The percentage of non detected sources in the redshift range z = 2–3.5 is 42.6$\%$ for the linear distribution and 44$\%$ for the $\mathrm{N_{H}}$ in Ricci et al. (2015). While the correction factor would be different in the cases of a $\mathrm{N_{H}}$ distribution centered on very low or very high column density values, observational and empirical estimations from Ricci et al. (2015) and Ueda et al. (2014) make this scenario unlikely.

We restrict our sample to the redshift range from 2 to 3.5 and the luminosity range of $\mathrm{L_{X}>10^{44}\,erg\,s^{-1}}$ to estimate the intrinsic fraction of CT AGN due to the difficulty correcting for flux sensitivity limits. This leads to an observed CT fraction of 8.9$\%$ (13/145). Assuming the observed column density distribution of Ricci et al. (2015) and the flux sensitivity limits of the COSMOS legacy survey, the fractions of CT sources falling below the flux limit are $85\%$ and $87\%$, respectively, in the redshift bins from 2 to 2.7 and 2.7 to 3.5 (see Figure 8). The fractions of non-CT sources that we do not detect in the same redshift bins are $28\%$ and 29$\%$. After applying the correction, we find that the fraction of CT AGN in COSMOS is $\sim 32\pm 11\%$.

5 Summary and Conclusions

We extended the Spectral Curvature method, developed by Koss et al. (2016), to Chandra observations at redshifts between 2 and 5. We summarize in the following our main findings:

• •

The SC method can be applied to high-redshift AGN observations. The redshift dependence can be corrected by adding a redshift parameter in the SC equation. The method successfully selects simulated CT sources from merely obscured ones.

• •

We applied the SC method to the CDF-S survey. The SC method selects three sources as CT candidates. One of these is the proposed CT AGN from Gilli et al. (2011) at redshift $z=4.67$. The fraction of CT AGN we selected from the sources with spectroscopic redshift is 17${}^{+19}_{-11}\%$.

• •

We applied the method also to the COSMOS-legacy survey, constraining our analysis to sources at redshifts between 2 and 5 with more than 10 counts. In total, the method selected 40 from 272 sources as CT candidates (14.5$\%$). After correcting for biases due to the redshift and accounting for the faint sources that Chandra is not able to detect, we obtain a CT fraction of $\sim 32\pm 10\%$ which is a value similar to the one found in Buchner et al. (2015).

• •

We find that the fraction of CT AGN does not show redshift evolution, which is comparable to the result found by Buchner et al. (2015) in the luminosity range $\mathrm{L_{2-10keV}=10^{43.2-46}\,erg\,s^{-1}}$. However, the fraction that we obtain is similar to the one found by Ricci et al. (2015) in the nearby Universe and by Civano et al. (2015) at redshift z=0.04–2.5 and much lower than the one obtained by Buchner et al. (2015). This could be explained by the larger luminosity range analyzed in Buchner et al. (2015).

Our measured CT fraction from COSMOS is somewhat higher though in agreement within error of the value of 22$\%$ found by Koss et al. (2016). The mean luminosity of our sample is $\sim 10^{44}$ $\mathrm{erg\,s^{-1}}$, while the mean luminosity of the BAT sources at redshift $z<0.03$ is $\sim 5\times 10^{42}$ $\mathrm{erg\,s^{-1}}$. The fraction that we obtain is similar to what has been found by Ricci et al. (2015) in the lowest luminosity bin $\mathrm{log(L_{14-195})}=$40.0–43.7 $\mathrm{erg\,s^{-1}}$.

Moreover, the SC method is insensitive to CT AGN of very higher column densities, e.g. $10^{25-26}$ cm*-2* which would not be detected in the X-rays. This means that we have to treat the obtained CT fraction as a lower limit. Indeed, the obtained fraction of CT sources is lower than predicted by the models from Gilli et al. (2007) and Treister et al. (2009a). Another issue is that the accretion rates of CT AGN may be much higher than their less obscured counterparts (e.g., Koss et al., 2016) and thus even a small fraction may be important for overall black hole growth.

As a further step, the SC method could be extended to other data samples. For example, the serendipitous Chandra Multiwavelength Project (ChaMP) contains a number of promising high-redshift quasars that could satisfy the requirement needed to apply the method. In the coming months, Chandra will perform an observation of the CDF-S totaling 3 Ms which will complete the present survey. The deeper exposures in the 7 Ms catalog will allow tighter constraints on the fraction of CT AGN at high-redshift.

Acknowledgements

M. K. acknowledges support from the SNSF through the Ambizione fellowship grant PZ00P2_154799/1. M.K. and K. S. acknowledge support from Swiss National Science Foundation Grants PP00P2_138979 and PP00P2_166159. The scientific results reported in this article are based on data obtained from the Chandra Data Archive.

This research made use of Astropy, a community-developed core Python package for Astronomy (Astropy Collaboration, 2013) and the NASA’s Astrophysics Data System.