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A Large Population of Obscured AGN in Disguise as Low Luminosity AGN in Chandra Deep Field South

Population synthesis models of actively accreting super-massive black holes (or active galactic nuclei -- AGN) predict a large fraction that must grow behind dense, obscuring screens of gas and dust. Deep X-ray surveys are thought to have provided the most complete and unbiased samples of AGN, but there is strong observational evidence that a portion of the population of obscured AGN is being missed. In this paper we use a sample of AGN derived from the deepest X-ray survey to date, the Chandra 7Ms GOODS-South Survey, to investigate the nature of low flux X-ray sources. We make full use of the extensive multi-wavelength coverage of the GOODS-South field, and cross-match our objects with wavelengths from the Radio to the IR. We find the low X-ray flux AGN in our sample have X-ray luminosities that indicate low-luminosity AGN classification, while their radio, infrared and optical counterparts indicate moderate to powerful AGN classification. We find the predicted column densities is on average an order of magnitude higher than the calculated column densities via X-ray detections for X-ray faint sources. We interpret our results as evidence of obscured AGN disguising as low-luminosity AGN via their X-ray luminosities. When we compare the estimation of the obscured AGN space density with and without these objects, we find a difference of 40% in the lowest X-ray luminosity regime probed by our sample.


INTRODUCTION
Theoretical models of galaxy formation predict that massive galaxies should have high star formation rates and larger gas reservoirs than that which is observed. It has been postulated that actively accreting supermassive black holes (SMBHs), known as active galactic nuclei (AGN), can inject energy into the gas and expel it and/or prevent it from cooling and collapsing into stars through a mechanism called feedback (e.g. Bower et al. 2006;Croton et al. 2006;Heckman & Best 2014). The ubiquity of SMBHs in the center of galaxies and the large energy release per gram of matter accreted onto the SMBH makes AGN feedback the most promising star formation regulation mechanism. Furthermore, star-formation and SMBH growth have similar evolutionary tracks (see Madau & Dickinson 2014, for a review). Theory suggests that feedback from growing SMBHs/AGN is able to successfully reproduce the properties of local massive galaxies (see Silk & Mamon 2012, for review), and explain the observed galaxy scaling relations and the quenching of star-formation in massive galaxies (e.g. Silk & Rees 1998;Fabian 1999;King 2003;Hopkins et al. 2006;Weinberger et al. 2018).
Some models of galaxy evolution and AGN feedback explain the observed scaling relations between SMBHs and galaxy host properties via a merging scenario. In these scenarios, AGN are triggered due to the gravitational torques produced as a result of the merger funnelling gas to the central parsecs of the galaxy. A key component of these models is the majority of SMBH growth is occurring behind large column densities, N H > 10 23 cm −2 (e.g. Cattaneo et al. 2005;Hopkins et al. 2008). These obscured sources are inherently difficult to observe, but their relative contribution to the total number of AGN can be estimated via AGN synthesis models for the cosmic X-ray background (e.g. Comastri et al. 1995;Gilli et al. 2001;Treister & Urry 2005;Gilli et al. 2007;Akylas et al. 2012;Ananna et al. 2019). Directly observing obscured AGN is possible, but emission at wavelengths less than 2 µm are significantly attenuated by the obscuring material. Over a wide range of energies (i.e 0.2-200 keV), X-ray observations are thought to provide one of the most reliable methods of selecting AGN and estimating the amount of obscuration (e.g. Brandt & Hasinger 2005;Xue et al. 2011;Liu et al. 2017); however this is not always true, as Comastri et al. (2011) and Donley et al. (2012) show that even some of the deepest X-ray surveys miss a substantial fraction of heavily obscured objects.
Obscured AGN can also be identified in the mid-infrared (MIR) due to the reprocessing of the obscured UV emission (e.g. Houck et al. 2005;Weedman et al. 2006;Yan et al. 2007;Polletta et al. 2008;Stern et al. 2012;Yan et al. 2013;Mateos et al. 2013). As noted in Hickox & Alexander (2018), color-color diagnostics may provide high completeness but only modest reliability due to sources not always having a prominent AGN component. Thus AGN hosted in strongly star-forming galaxies may not be identified. This limitation is compounded by the fact that at high-redshifts (z > 2), star formation and AGN activity peak. Aside from AGN identification, disentangling obscured vs un-obscured AGN from MIR colors alone is challenging due to the similarity between these two classes of AGN in their MIR SEDs (e.g. Buchanan et al. 2006;Mateos et al. 2012;Asmus et al. 2014;Hickox et al. 2017); thus, the combination of large and deep MIR and X-ray surveys are needed to build a large, statistically robust sample of obscured AGN.
The deepest X-ray survey to date is the Chandra Deep Field South (CDFS) survey which was centered on the GOODS-S region. Due to the severe amount of Compton scattering and absorption which attenuates the X-ray emission at the lower X-ray energies probed by Chandra, data at other other wavelengths must be used to quantify the level of potential AGN obscuration. The obscuring medium which absorbs the X-ray continuum photons re-radiates the energy at MIR wavelengths. The combination of X-ray and IR data has been critical in estimating the amount of obscuration in X-ray surveys with energies < 10 keV (e.g. Daddi et al. 2007;Donley et al. 2008;Fiore et al. 2009). Many studies using X-ray selected AGN select AGN as objects with measured luminosities of L X > 10 42 erg s −1 to avoid contamination from galaxies for which the X-ray luminosity is dominated by star formation. To fully understand the AGN population, it is essential to properly account for the possibility that sources with low observed X-ray luminosity may in fact be moderately to heavily obscured. In this paper we investigate the nature of these low luminosity sources.
In section 2 we describe the data acquisition and sample properties. In section 3 we present comparisons between the X-ray, radio, IR, and optical counterparts. In section 4 we discuss the implications of the existence of these sources in two different examples, and we summarize our findings in section 5. We use an h = 0.7, Ω m = 0.3, Ω Λ = 0.7 cosmology throughout this paper. fX < 3 × 10 −16 3 × 10 −16 ≤ fX < 10 −15 10 −15 ≤ fX < 5 × 10 −15 fX ≥ 5 × 10 −15 7MS flux limit Figure 2. Redshift versus Absorption Corrected or Intrinsic X-ray Luminosity. The median and mean redshifts for our sample are 1.6 and 1.7 respectively. The points are color-coded by their flux bin. The blue dashed line corresponds to the mean Chandra 7Ms flux limit (Luo et al. 2017).

SAMPLE SELECTION
The sample discussed in this paper is derived from the deepest X-ray survey to date, the 7Ms exposure Chandra Deep Field South (CDFS) survey which covers a total area of 484.2 arcmin 2 (Luo et al. 2017, hereinafter L17). The 7Ms CDFS catalogue contains 1008 sources analyzed in three energy regimes: 0.5-7.0 keV (full), 0.5-2.0 keV (soft), and 2-7 keV (hard). We select 523 CDFS sources that have redshifts > 0.5, were detected in both the full band and hard band, and are labeled as AGN in the L17 catalog. We use the criterion of z > 0.5 to maximize the selection of objects in an epoch where we expect the greatest evolutionary effects. In L17, the sources are classified as AGN if they fulfill one of the photometric and/or spectroscopic criteria below: (a) A source with intrinsic luminosity L 0.5−7.0keV ≥ 3 × 10 42 ergs s −1 .
(b) A source with Γ ≤ 1.0, where Γ is the effective photon index and a value of ≤ 1.0 is indicative of an obscured AGN.
(c) A source with an X-ray to optical flux ratio of log(f X /f R ) > -1 where the X-ray flux is the FB and the R flux is provided in L17.
(d) A source with a factor of 3 or more X-ray emission over the level expected from pure star-formation as traced by the rest radio 1.4 GHz luminosity (Alexander et al. 2005).
(e) A source with broad emission and/or high-excitation emission lines in the optical spectrum via the cross-matched spectroscopically identified AGN catalogue in Szokoly et al. (2004), Mignoli et al. (2005), Silverman et al. (2010).
(f) A source with an X-ray to NIR flux ratio log(f X /f Ks ) > -1.2.
As noted in Xue et al. (2011) and L17, the above criteria are effective but not complete in identifying AGNs. In particular, these selection methods may not capture the lowest luminosity or most obscured AGN. Thus, there may be a fraction of sources classified as "Galaxies" in L17, which in actuality host an AGN. For the scope of this paper, we present our results on the galaxies classified as AGN only, but explore the objects classified as "Galaxies" in the Discussion.
We split the sample into four measured hard X-ray flux bins: The values of the first three bins were chosen to contain roughly equal numbers of objects, and the highest flux bin contains roughly 50 objects. We show the distribution of the hard Xray flux values as presented in L17 and the bin definitions used throughout this paper in Figure 1.
Since the main focus of this paper is to understand the nature of the low-flux sources in the context of AGN classification, we choose the highest energy X-ray band available because it should be least affected by obscuration, and thus, a more accurate indicator of the intrinsic AGN power. Furthermore, we apply an estimate of the intrinsic absorption as derived by L17 to the hard X-ray flux values. The hard Xray band fluxes as presented in L17 are not absorption corrected, but L17 provide an estimate of the intrinsic absorption which they apply to their full band luminosities, as follows.
The X-ray spectrum of an AGN can be described by a power law: the photon number density takes the form N (E) ∼ E −Γ where Γ is the photon index and E the photon energy. In L17, they estimate the power-law photon index Γ eff from the hard to soft band ratios, where Γ eff includes Galactic absorption. L17 then uses the Portable, Interactive, Multi-Mission Simulator (PIMMS, Mukai 1993) to estimate the intrinsic absorption. By assuming that the intrinsic power law spectrum has a fixed photon index of 1.8 modified by Galactic absorption, any value smaller is likely caused by intrinsic absorption (N H ). We then use the estimated N H tabulated in L17 to derive the intrinsic hard X-ray luminosity. Finally, we use PIMMS to recalculate the intrinsic hard X-ray luminosities over the rest 2-10 keV energy band which we define as L X,int, 2−10 keV . We modify the energy band so that our work may be directly comparable to similar studies. In Figure 2, we show the L X,int, 2−10 keV values as a function of redshift. The points are color-coded by their flux bin. The blue dashed line corresponds to the mean Chandra 7Ms flux limit derived in L17, 3.6×10 −17 erg s −1 cm −2 , re-calculated over the 2-10 keV energy range. In the following sections we describe the collection of the multiwavelength data we use in this work, with the aim of investigating the nature of the low-flux X-ray AGN sources.

Infrared Measurements
We cross-match our X-ray sample to IR catalogues to quantify the effect of varying levels of obscuration on our X-ray fluxes. We use Spitzer Infrared Array Camera (IRAC) (3.4 µm, 4.5 µm, 5.8 µm, 8.0 µm) data, the Spitzer peak-up imager (PUI) on the Infra-red Spectrograph (IRS) instrument (Houck et al. 2005) 16 µm data, Multi-band Imaging Photometer for Spitzer (MIPS) (24 µm) data, Herschel Photodetector Array Camera and Spectrometer (PACS) (100 µm, 160 µm) data. The Spitzer IRAC and Herschel data were taken from the GOODS-Herschel survey catalogue, where Herschel flux densities and uncertainties were obtained from point source fitting using Spitzer 24 µm detections positions as a prior . L17 provide the optical counter- parts to the CANDELS + 3DHST combined catalogue (Skelton et al. 2014). We cross-match our sources to the Elbaz et al. (2011) catalogue, which also provided associated GOODS counterpart coordinates, using the optical counterpart coordinates with a 1 arcsecond search tolerance. The Spitzer IRS PUI 16 µm detections were also found using the optical counterpart coordinates with a 1 arcsecond crossmatch search tolerance to the 16 µm GOODS-S catalogue (Teplitz et al. 2011). We find 169 Xray (32.3%) source matches in all four IRAC bands and MIPS 24 µm, 124 (24%) matches in Spitzer IRS PUI 16 µm data, and 76 (14.5%), 62 (11.9 %) objects have PACS 100 µm and 160 µm detections respectively.We note the majority of the analysis in section 3 is constrained to X-ray sources with IRAC bands and MIPS 24 µm detections.Within this X-ray, MIR sub-sample, over 50% of objects have both Herschel detections.

Optical Measurements
Another probe of AGN power is the strength of high ionization optical lines. L17 provide the counterparts to the CANDELS + 3DHST combined catalogue (Skelton et al. 2014). We use these coordinates from the L17 catalogue to perform a cross-match with a 0.2 arcsecond tolerance to the rest-frame color catalogue (Skelton et al. 2014), emission line catalogue (Momcheva et al. 2016), and ACS/WFC3IR images (Skelton et al. 2014). We have overlap with 167 objects with > 5σ detections with ACS F435W photometry, and 253 objects with > 5σ detections with WFC3-IR F160W photometry. In the emission line catalogue, we have 40 objects with > 2σ [Oiii] detections.

Radio Measurements
Radio emission is present in both AGN and star-forming dominated galaxies. The L17 catalogue provides 1.4 GHz fluxes via the Very Large Array (VLA) survey centered on the CDFS field. We find 94 objects above the 5σ flux density limit of 37 µJy. For the detected objects, we use the redshifts provided in L17 and calculate the rest frame luminosity for each object assuming a radio spectral index of α = 0.8 where α is defined as f ν ∝ ν −α . For the un-detected objects we calculate the upper limit using the limiting flux of the GOODS-S VLA survey (Miller et al. 2013), from which the upper limit fluxes are derived. In Figure 3, we show a summary of all the cross-matching results of our L17 subsample with the other wavelengths.

X-ray and Rest-Frame 5 µm Continuum
As stated in section 1, the combination of hard X-ray data and mid-infrared (MIR) data offers one of the best probes of obscuration in AGN host galaxies. X-ray emission is one of the most unambiguous signatures of AGN activity, and in obscured AGN, the material that attenuates the X-ray emission is expected to emit in the MIR. A measurement of a bright, un-obscured source in both the X-ray and MIR allows for empirical relationships to be derived between these quantities. The MIR contains features which can be attributed to AGN and/or SF processes. Between 3.2 µm to 5.7 µm, AGN torus emission dominates over MIR SF processes (Nenkova et al. 2008;Kirkpatrick et al. 2012;Lambrides et al. 2019). Previous studies have used SED decomposition or templates to calculate the restframe emission in this region (Mullaney et al. 2012;Stern 2015). Due to the uncertainties introduced with these methods, we instead take advantage of our large sample and its multiwavelength properties.
We infer the rest-frame 5 µm continuum region luminosities to directly measure the emission in this spectral region. For regions of redshift where 0.5 < z ≤ 1.5, 1.8 < z ≤ 3.1, and z ≥ 3.1, we use the observed IRAC 8 µm, IRS PUI 16 µm, and MIPS 24 µm luminosities respectively. This corresponds to rest-frame luminosities in the 3.2 µm to 5.7 µm continuum region, depending on the object's redshift, and refer to these luminosities as L Torus * for simplicity. We use the nomenclature Torus * because although we are not estimating the entirety of the IR Torus luminosity, we expect the AGN torus luminosity to dominate over SF processes in this wavelength regime.
We test the prediction of the AGN torus luminosity dominating the flux emission in the wavelengths used to calculate the L Torus * values on a local AGN and Starburst sample. Lambrides et al. (2019) uniformly analyzed all AGN and SF galaxy ever observed with the Spitzer Infrared Spectrograph (Houck et al. 2004). As similar studies have shown, Lambrides et al. S t e r n e t a l . 2 0 1 5  (2019) found, for even low-luminosity (L 24µm < 10 42 [erg s −1 ]) AGN, the PAH 6.2 µm equivalent width (EQW) is an excellent indicator of AGN contribution to the MIR: the lower the 6.2 µm EQW, the more the spectrum is dominated by an AGN component. The EQW classifier was able to separate highly star-forming Ultra-Luminous Infrared Galaxies with and without an AGN. Using the spectra and other crossmatched data provided in Lambrides et al. (2019), we calculate L Torus * using the same approach as in this work. We find L Torus * is as good as the 6.2 µm classifier. Performing a Spearman rank correlation on L Torus * (normalized by K band luminosity to account for mass difference) and PAH 6.2 µm EQW, we measure an anti-correlation (p-value < .001). We show the relationship between L Torus * and L X,int, 2−10 keV in Figure 4. The blue solid line is the luminosity dependent absorption corrected X-ray, νL ν (6 µm) relationship from Stern (2015), hereafter S15, which parametrizes the relationship as log L(2 − 10keV) = 40.981 + 1.024x−0.047x 2 where x ≡ log(νL ν (6 µm)). We chose the S15 relation due to the similar method in which they derived the equivalent L Torus * luminosity and the large luminosity range their sample covers. We find over 90% of our objects with the lowest X-ray fluxes, f X,2−7keV < 10 −16 erg s −1 cm −2 , are ≥ 2σ below the S15 rela-Y a n + 2 0 1 1 Sy 1 (Heckman+2005) Sy 2 (Heckman+2005) tion. The teal,pink, and gray triangles are the IRAC, IRS PUI, and MIPS upper-limits respectively. We calculate the upper-limits using the flux limits provided for the relevant MIR wavelength used in the L Torus * calculation. The flux limit for observed IRAC 8 µm, IRS PUI 12 µm, and MIPS 24 µm is 1.6 µJy, 65 µJy, and 20 µJy respectively. We test the effect of upper-limits by performing a censored regression analysis on each x-ray flux bin, and we find the L Torus * and L X,int, 2−10 keV relationship in each flux bin remains unchanged when upper-limits are taken into account. The tension between the X-ray and L Torus * for the lowest X-ray flux objects suggests that i) The low X-ray flux objects are intrinsically weak AGN with a non-AGN component contributing to the MIR luminosity, or ii) The low X-ray flux objects are moderately to heavily obscured AGN. With regards to scenario i), any non-AGN component in these systems would most likely arise from SF processes. In section 3.2, we compare the X-ray emission to a direct probe of AGN power that can be less effected by obscuration as compared to the X-rays: the [Oiii]λ5007 luminosity. In section 3.3 we test whether the excess MIR emission for the lowest flux sources can be attributed to a low-luminosity AGN in a host galaxy with extreme amounts of SF.

X-ray and [OIII]λ5007 Luminosities
The luminosity of emission lines formed in the narrow line region, such as [Oiii]λ5007, can be used as a quasi-isotropic indicator of AGN power (Brinchmann et al. 2004; Heckman et al.  The inconsistency between the X-ray and the [Oiii] emission observed for a substantial fraction of X ray sources strongly hints at them not being truly low-power AGN. In the next section, we follow-up on this hypothesis by checking whether these apparently underluminous X-ray sources have an extra component in the MIR due to an extremely large amount of star formation.
3.3. Do the low X-ray flux objects have significant SF?
Monochromatic continuum luminosity at 24 µm is commonly used to trace star-formation due to the warm dust associated with high-mass star-forming regions emitting at this wavelength (Calzetti et al. 2007). On the other hand, SF processes also contribute to the soft and hard X-ray components (Persic & Rephaeli 2002). X-ray emission in SF galaxies is predominately from gas in the ISM heated by stellar winds and supernova and point sources such as X-ray binaries. For star-forming galaxies, very high IR luminosities (L IR > 10 46 erg s −1 ) must be observed in order to correspond to L X,2−10 kev > 10 42 erg s −1 (Symeonidis et al. 2014). Conversely, for galaxies with an AGN, the 24 µm continuum luminosity may be significantly contaminated with reprocessed light from the central engine. Even more importantly, in AGN the X-ray emission tightly traces the power of the central engine, unless the central engine is obscured. Thus, the relationship between Xrays and the IR will vary significantly between SF and AGN dominated galaxies.
In Figure 6, we show the relationship between L X,int, 2−10 keV and the observed 24 µm luminosities for our sample. AGN studies quantifying this relation, or using other MIR continuum measurements, find an almost one to one relationship between these quantities, with minimal scatter (< 1 dex) (Gandhi et al. 2009;Asmus et al. 2015). The grey shaded region is the range of values for un-obscured AGN adapted from Asmus et al. (2015). The red solid and dashed lines is the X-ray to 24µm relationship for SF galaxies and ±2σ respectively for a sample of z ∼ 1 SF galaxies from Symeonidis et al. (2014). This relationship is adapted from Symeonidis et al. (2014) by converting the L 8−1000µm values to 24µm using the conversion presented in Calzetti et al. (2010). The points are colorcoded by redshift, and the points that are circled in red are the lowest-flux bin objects. Similarly to what we showed in the previous sections, we see an apparent inconsistency. A significant fraction of the X-ray sources appear to be under-luminous with respect to their observed 24 µm luminosity. For the redshift range spanned by our sources, the rest frame 24 µm wavelength ranges from 6 to 16 µm.
We test if there is a significant dependence between redshift and location of the points with respect to the Asmus et al. (2015) relation due to our usage of the observed 24 µm fluxes. We quantify the fraction of objects below the Asmus et al. (2015) relation in each redshift bin, and we find for 0.5 < z < 1.0: 61%, 1.0 < z < 1.5: 56%, 1.5 < z < 2.0: 55%, and 2.0 < z < 2.5: 71%, z > 2.5: 21%. For every redshift bin, excluding the highest bin, the fraction of sources 2σ below the Asmus et al. (2015) relation is between 50% and 60%. The lower fraction in the highest redshift bin is most likely due to the difference in sensitivity of the MIPS survey as compared to the 7Ms survey. In fact, as quantified in Elbaz et al. (2011), a z ∼ 3 galaxy, would need to be at least 1 × 10 46 erg s −1 in order to be 5 σ above the flux limit of 100 µJy in MIPS 24 µm, and our sample does not contain any such objects.
As seen in Figure 6, the objects that deviate the most from the Asmus et al. (2015) parameter space are the low-flux X-ray objects, but they are all at least 4σ above the SF relation. Furthermore, these very same objects are below the canonical X-ray relations with the L Torus * and optical line emission (see Figure 4, Figure 5).
In addition, we can estimate the contribution SF processes may have on L Torus * . Between 100µm to 160µm the dust spectrum can be approximated by a power law: f ν ∼ ν α . We use the observed 100µm and 160µm to calculate α, and extrapolate the 50µm luminosity. The ratio of L 50µm to L Torus * is smaller in galaxies where AGN dominate the 5µm emission. As shown in Brown et al. (2019), the peak AGN contamination is in the MIR, and red-wards of 30 µm, the contribution becomes less significant. We calculate the L 50µm to L Torus * ratios for our sample. In Figure 7, we show the distribution of our values. The solid and dashed red lines are the ratio values for the Kirkpatrick et al. (2012) featureless and silicate AGN templates respectively. The median L 50µm to L Torus * ratio for our sample is 1.1, and is roughly 3 times smaller than the expected SF value. Our results show that L Torus * is not significantly contaminated with SF emission. This corroborates the idea that our objects do not host intrinsically weak AGN, with a large star-forming component.

Chandra 7Ms Total Sample versus Spectrally Constrained Sample
As seen in sections 3.1, 3.2, and as will be seen in 4.3, the X-ray luminosities derived from simple assumptions are significantly underestimating the intrinsic luminosity of the low flux sources. On the other hand, Liu et al. (2017) performed a detailed spectral analysis on the X-ray bright AGN in the Chandra 7Ms sample. Their objects were selected from L17 only if they were classified as AGN and had at least 80 counts in the hard band. This threshold corresponds to a 2-7 keV flux of 2×10 −16 erg s −1 cm −2 . They performed a systematic X-ray spectral analysis, with emphasis on constraining intrinsic obscuration. We compare the X-ray properties derived from their 7Ms sub-sample, to the our L17 sub-sample. In Figure 8, we show a comparison of L X,int, 2−10 keV of our sample derived from L17 and L X,int, 2−10 keV derived from Liu et al. (2017). The blue colored points are the lowest X-ray flux bin objects (< 3× 10 −16 erg s −1 cm −2 ). We expect the higher flux bins to be the least affected by the X-ray underestimation in L17, and thus more consistent with the Liu et al. (2017) analysis. Therefore, the black solid line is the best fit relationship for all the objects excluding the two lowest flux bins. Of the 16 objects classified as Compton thick via Liu et al. (2017) and in our sample, the difference between L X,int, 2−10 keV derived in section 2 and the spectrally derived hard X-ray luminosities is on average −0.6 dex. It is important to point out that 44% of these Compton thick sources are in the lowest X-ray flux bins. We also note that over 78% of the lowest flux objects in the L17 sample were not spectrally analyzed in Liu et al. (2017) due to their low flux counts. We then compare the Liu et al. (2017) intrinsic hard band X-ray luminosities with L Torus * in Figure 9. The points are color-coded by the X-ray flux provided in L17. The blue solid line is the luminosity dependent relationship from S15.
No Absorption NH = 10 24 cm −2 "Galaxies" Figure 10. Non-absorption corrected luminosities vs L Torus * : The blue points have the lowest X-ray flux (< 3×10 −16 erg s −1 cm −2 ). As adapted by Hickox et al. (2017), the red shaded region indicates the range in intrinsic X-ray, 6 µm AGN luminosity relationships between Gandhi et al. (2009) andFiore et al. (2009). The blue shaded region indicates the same relationships but where the X-ray luminosity is absorbed by a column density of N H > 10 24 cm −2 (Lansbury et al. 2015). The open black circles are L17 classified "Galaxies" with z > 0.5 and with a detection in the HB.
sorption corrected luminosities bring these objects closer or to within 2σ of the S15 relationship. Thus, when a more sophisticated Xray analysis is available the intrinsic absorption estimation yields more accurate luminosities for sources with enough photon counts. The sources in our sample which have the greatest under-estimation of X-ray luminosity have insufficient X-ray counts to perform the above spectral analysis. Thus, when X-ray photon statistics are poor, X-ray vs multi-band diagnostics are necessary to approximate obscuration.

The Nature of Low X-ray Flux Sources
In section 3, we find a population of low Xray flux objects whose physical nature is unclear when taking into account the properties of MIR and optical emission. A classification of these sources based on their X-ray luminosity identifies these objects as low-luminosity AGN. However, when only considering the MIR and optical line emission, the same objects are classified as moderate to high luminosity AGN. More quantitatively, in subsection 3.1, we find 44% are at least 2σ below the expected S15 relationship. Of these objects, 90% are in the lowest X-ray flux bin. In subsection 3.2, we find 85% of our sample have [Oiii]λ5007 luminosities that are ≥ 2σ below their predicted L X,int, 2−10 keV values via the Yan et al. (2011) relationship. In subsection 3.3, we show that the tension between the X-ray luminosities and L Torus * cannot be explained by an unaccounted for SF component. Thus, we find strong evidence for a large population of obscured AGN disguising as low-luminosity AGN.
The multi-wavelength analysis of this work indicates that over 40% of our sample has underestimated intrinsic obscuration.We note that the lowest flux objects correspond to a mean Xray luminosity of 2.8 ×10 42 [ergs s −1 ]. Although in L17 there are multiple criteria that are used to differentiate an X-ray source as an AGN versus an SF galaxy, only one of the seven criteria need to be satisfied for a source to be determined as an AGN. The majority of the criteria, as noted in section 2, only capture moderate to high power AGN with the exception of the criterion that the Full band X-ray luminosity is greater than 10 42 [ergs s −1 ]. High power AGN are rare in the small volume that the CDFS field probes, and thus the most common criteria the X-ray sources satisfy in L17 is the X-ray luminosity threshold. Due to our results indicating that a large fraction of sources may have X-ray luminosities underestimated by at least an order of magnitude, the objects in L17 that are classified as galaxies may also be obscured AGN.
In the entirety of the L17 catalogue, 307 sources are classified as Galaxies. Of these 307 sources, we select objects with z > 0.5 and detections in the HB in order to be consistent with the L17 classified AGN sub-sample. We use these objects in the analysis moving forward, and label them as Galaxies. The Galaxies sub-sample consists of 28 sources, where 80% have a calculated rest-frame L Torus * values, 20% have uncorrected [OIII]5007λ luminosities greater than 10 42 [erg s −1 ], and 14% have VLA 1.4 GHz detections. Of the Galaxies L Torus * subsample, 62% have both Herschel PACS detections, and a mean, median 50 µm to 5 µm luminosity ratio of 1.26, 1.29 respectively. In the following sub-sections, we estimate the potentially unaccounted for obscuration and highlight some implications that might arise when one uses the most recent literature X-ray values for these objects.

Estimating the True Obscuration
We can estimate the level of obscuration by comparing the non-absorption corrected X-ray luminosities to empirical studies utilizing the MIR wavelength measurements. In Figure 10, we determine where the non-absorption corrected luminosities are located within empirically defined regions of non-obscured and heavily obscured sources, indicated by the shaded regions. For the un-obscured region, we use two different intrinsic X-ray -6 µm AGN luminosity relationships: i) The Gandhi et al. (2009) relationship, which was derived from a local sample of type 1 AGN, and careful decomposition of the nuclear 6 µm luminosity was performed to minimize host-galaxy contamination ii) The Fiore et al. (2009) relationship, which was derived from a sample that spanned a larger redshift and X-ray luminosity range as compared to Gandhi et al. (2009). The blue shaded region indicates the same relationships but where the X-  Figure 12. Radio/X-ray radio loudness parameter distribution: In the top panel, we plot the distribution (orange) of the radio-loudness diagnostic, as parametrized by Terashima & Wilson (2003). We calculate the radio upper limits using the limiting flux of the GOODS-S VLA survey (Miller et al. 2013) and show the distributions of the upper limit R X (grey). The dashed red line is the RL threshold as empirically found by Terashima & Wilson (2003). For comparison, the blue solid line is the mean R X value for a sample of bonafide RL sources, namely the 3CR sample with z > 1 (Wilkes et al. 2013). In the lower panel, we compute the predicted X-ray luminosities for X-ray under-luminous sources via the L Torus * values using the S15 relation. The black empty histogram is the distribution for L17 classified "Galaxies" with z > 0.5 and with a detection in the HB. ray luminosity is absorbed by a column density of N H = 10 24 cm −2 as presented in Lansbury et al. (2015). For the objects with f X < 3×10 −16 erg s −1 cm −2 , 100% are below the empirically shaded region for un-obscured AGN, and 74% are within or below the N H > 10 24 cm −2 parameter space. For these lowest flux objects, 70% of them have estimated N H values that are an order of magnitude greater then the values derived from L17.
We then correct our L X,int, 2−10 keV values to account for the underestimation in N H by assuming i) L Torus * is probing predominately AGN processes ii) The lower 2σ value of the S15 relationship is a sufficient upper limit of the true intrinsic hard X-ray luminosity. For all objects that are < 2σ below the S15 relation in Figure 4, we compute the predicted X-ray luminosity for a given L Torus * value using the S15 relationship referenced in section 3. We define these corrected luminosities as L X,int, 2−10 keV .
If our corrected luminosities are a better estimate of the intrinsic luminosity of these AGN, this implies the hardness ratio (HR =(FH-FS)/(FH+FS)) for the faintest sources does not provide a correct indication of obscuration. As detailed in Matt et al. (1997Matt et al. ( , 2000, a soft scattered component of heavily obscured AGN can dominate at rest energies < 10 keV. As we see in Figure 11, our most obscured sources live  Figure 13. R X as a function of f X, 2−7 keV : The red line is the RL threshold as empirically found by Terashima & Wilson (2003), and the upwards arrow indicates the region of radio-loudness. The open black circles are L17 classified "Galaxies" with z > 0.5 and with a detection in the HB.
in the parameter space of moderate to high hardness-ratios. As shown in , the classical hardness-ratio inference of heavily obscured sources may not be ideal. In L17, the majority of obscured sources do not have enough counts for detailed spectroscopic analysis, and thus, the HR is used to estimate the N H . In our work, we estimate how much the N H would need to be corrected in order to correspond to empirical X-ray-IR relationships. In Figure 11, we combine the hardness ratios, our estimated N H (labeled as "N H corrected"), and the X-ray to L Torus * ratio. We find a fraction of the sources with the highest corrected N H s, have HRs (0 − 0.5) consistent with X-ray spectra that have a soft-scattered component . In the following sections, we explore the effect of these newly derived X-ray luminosities on two important features that are often considered when investigating the nature and the evolution of AGN.

Implications for Radio-Loudness Determination
About 10% of AGN have radio emission that is at least 10 times higher than one would expect from SF or other physical processes typical of the majority of AGN (Kellermann et al. 1989). These objects are known as radio-loud (RL) AGN.
A wealth of studies have argued for a bimodality in the distribution of radio-loudness parameters between jetted RL and non-jetted radio-quiet (RQ) AGN (Kellermann et al. 1989;Terashima & Wilson 2003;Padovani et al. 2017). These parameters define radio-loudness as the ratio between the radio luminosity and another luminosity measurement within the spectral energy distribution. With the aim of assessing the presence of a RL population in our sample, we first use the radio-loudness parameter as parametrized by the relationship between the radio luminosity and X-ray luminosity (R X = νL ν,1.4GHz / L 0.5−7keV ) (Terashima & Wilson 2003). This is relevant to this work because sources that are observed as underluminous in the X-rays with respect to their radio power could be mistakenly identified as RL AGN. If the dimming of X-ray flux due to the hypothesis of extra obscuration is correct, a large fraction of objects in our sample would be erroneously classified as RL. In fact, a previous analysis of the 4Ms CDFS AGN sample (Tozzi et al. 2009), which included only AGN with L 2−10 > 10 42 erg s −1 , found that roughly 30% of their objects were RL.
The majority of our L17 sub-sample is not detected in the radio. In Figure 12, we show the distribution of the R X for the 94 sources that are detected at 1.4 GHz Luo et al. (2017). For ease of comparison to previous works, we calculate R X using the absorption corrected L 0.5−7keV values provided in L17. We calculate the radio luminosities assuming a radio spectral slope of α = −0.7 where f ν ∼ ν α . The dashed red- . q 24,obs as a function of redshift: The orange and blue circle represent the R X RL, R X RQ respectively.The dashed blue line is the lower 2 σ evolution of q 24,obs for M82 as plotted in Bonzini et al. (2012). The open pink cross is an object within the L17 classified "Galaxies" sub-set. We also plot for reference the high-z 3C objects (Wilkes et al. 2013).
line is the R X threshold for radio-loudness as empirically determined in Terashima & Wilson (2003). The solid blue line is the median R X value for the z ≈ 1 3C RL AGN sample (Wilkes et al. 2013), for reference. The 3C sample is used for comparison because these objects are bona-fide RL AGN with robust X-ray measurements. The grey histogram is the distribution of the upper limit R X for the sources in our sample with a radio upper limit. The radio upper limits are calculated using the limiting flux of the GOODS-S VLA survey (Miller et al. 2013). We also include the the "Galaxies" sub-sample as indicated by the black-edged, transparent histogram. According to the above assumptions, 56% of the radio detected objects are classified as RL. This is significantly greater than the expected 10% (Terashima & Wilson 2003). Furthermore, in Figure 13, we find the majority of objects posing as RL AGN are the sources in the two lowest flux bins.
Unless the X-ray measurements of our lowflux objects were not significantly underestimated, we would expect a radio-loudness analysis to yield similar number fractions found in other works. As seen in the lower panel of Figure 12, we find the percentage of objects that are classified as RL is significantly reduced when using L X,int, 2−10 keV : 13% out of the 38 objects with radio, MIR, and X-ray detections. We believe that this constitutes further indication that obscuration is present in a large fraction of these low X-ray flux sources, since this would explain the unreasonable fraction of RL objects observed if obscuration is not correctly taken into account.
We can also check radio loudness using a diagnostic that does not rely on the X-ray detections. There are well known correlations between the infrared and the radio (Sargent et al. 2010;Bonzini et al. 2012) that are expressed through the q 24 parameter, which is the logarithm of the ratio between the IR and the radio flux density. Bonzini et al. (2012) parametrize the q 24 parameter using the observed 24 µm flux density and observed 1.4 GHz radio flux density: q 24,obs = log 10 (S 24µm /S r ) where S 24µm is the observed 24 µm flux density from MIPS and S r is the observed 1.4 GHz flux density from the VLA. Observed flux densities are used, rather than rest-frame, due to insufficient data that is needed to derive bolometric values, and to avoid the high uncertainties that are introduced when modeling. Bonzini et al. (2012) assume the IR and radio properties of high-redshift star-forming galaxies are similar to local star-forming galaxies. Thus, a template of the prototypical starburst M82 is used to calculate q 24,obs as a function of redshift. We use the calculated M82 values as the star-forming galaxy locus via Bonzini et al. (2012), and classify objects that are RL as those with IR to radio fluxes that lie 2σ below the SF locus. In "Galaxies" Figure 15. Binned luminosity function analysis: We show the intrinsic hard X-ray as a function of redshift for all sources with the N H > 10 24 " cm −2 parameter space defined in Figure 10. The blue points are corrected for additional obscuration as defined by L X,int, 2−10 keV . The open black circles are L17 classified "Galaxies" . For comparison, we show the L X,int, 2−10 keV values (red crosses). The three rectangles are the three bins used in the luminosity function analysis. Figure 14, we color-code the q 24,obs values by whether they are classified as RL via R X . We find significant disagreement between R X and q 24,obs . Note that only 8% of our sample is classified as RL when q 24,obs is used. As seen in Figure 14, the objects that are classified as RL using L X,int, 2−10 keV (red circles), there is 100% overlap with the q 24,obs diagnostic. Surprisingly, we also find an object within the Galaxies sub-sample that is classified as RL AGN in both the corrected R X diagnostic and q 24,obs . In summary, without the assumption that there is a significant under-estimation of the X-ray luminosity, over half of our sample would be erroneously classified as RL.

Implications for Obscured AGN Space Density
The results discussed in this paper also have important bearings for cosmological studies. A major implication of our finding is in fact related to the space density of obscured AGN. We estimate the space density for the obscured sources in our sample with and without the corrected X-ray luminosities. We use a binned luminosity function, and define the three bins as: 10 42.5 < L X, 2−10 keV ≤ 10 43.5 , 10 43 < L X, 2−10 keV ≤ 10 44 , 10 43.3 < L X, 2−10 keV ≤ 10 44.3 and redshifts 0.5 < z ≤ 1.0, 1.0 < z ≤ 1.5, 1.5 < z ≤ 2.5 respectively, and where all luminosity units are in erg s −1 . In Figure 15, we show the intrinsic hard X-ray luminosity as a function of redshift for all sources with N H > 10 24 cm −2 as defined by being within or below the blueshaded region in Figure 10. The blue points are corrected for additional obscuration as defined by L X,int, 2−10 keV . The open black circles are L17 classified "Galaxies". For comparison, we show the L X,int, 2−10 keV values (red crosses). We choose the luminosity-redshift bins to maximize the number of sources included in the calculation, while minimizing the number of potential outliers. We immediately find that the difference between the L X,int, 2−10 keV and L X,int, 2−10 keV values would have a significant effect on space density calculations. Furthermore, we can quantify this effect by comparing the space density of our most obscured sources to model expectations.
We take all of our objects with an estimated N H > 10 24 cm −2 , and calculate the space density of our heavily obscured sources in the CDFS field. We present two space densities per luminosity, redshift bin. The first is the AGN sub-sample presented in Figure 4, and the second includes these sources plus the objects in "Galaxies" sub-sample. We use a binned luminosity function as parametrized by Ranalli et al. (2016). The differential luminosity function Φ is defined the number of objects N at co-moving volume V : We approximate the LF within a bin with luminosity boundaries L min,2−10keV , L max,2−10keV and redshift boundaries z min , z max as N/V probed where V probed is:  Figure 16. AGN Space Density: The solid colored three points are the heavily obscured AGN space densities for each luminosity-redshift bin, and their colors correspond to the theoretical model values for that bin. The points with red-circles are space density estimates including the L17 classified "Galaxies" sub-sample. The errors include model error and the upper and lower ends of the 68.3% confidence interval estimated using the Gehrels approximation (Gehrels 1986). The solid lines are the expected functions for three luminosity bins as modelled by Gilli et al. (2007).
In Figure 16, we show the space densities as a function of redshift for the three luminosityredshift bins. The AGN only sub-sample contains 19, 11, and 15 heavily obscured AGN candidates in the three redshift bins respectively. The estimated space density of these objects within the redshift and luminosity bins are be 6.9 ± 1.5 × 10 −5 Mpc −3 , 2.5 ± 0.9 × 10 −5 Mpc −3 , and 1.4±0.6×10 −5 Mpc −3 . The AGN + "Galaxies" combined sub-sample contains 29, 14, and 16 objects for the three redshift bins. The estimated space density of the "Galaxies" combined sub-sample within the redshift and luminosity bins are 12.8 ± 3.2 × 10 −5 Mpc −3 , 4.2 ± 0.9 × 10 −5 Mpc −3 , and 1.5 ± 0.6 × 10 −5 Mpc −3 . We find agreement with the predicted space density functions calculated using the X-ray background in Gilli et al. (2007). The errors include the upper and lower ends of the 68.3% confidence interval estimated using the standard Gehrels approximation (Gehrels 1986). We also estimate the N H > 10 24 cm −2 error by comparing the difference in space density estimates when using objects only below the below shaded region. We find a maximum 15% difference between including all of the objects in the blueshaded region versus only the objects below the blue-shaded region. We note that the x-axis errors represent the range of the redshift bin used in the space density calculation. Furthermore, the lowest and highest redshift bin space density enables us for the first time to make an accurate comparison with models in a parameter space poorly explored thus far. If we did not consider objects from the lowest X-ray flux bins as being obscured AGN, the estimated space density in the lowest redshift bin would drop by 50% and the highest redshift bin would drop by 40%. By taking into account the results of our work, we are able to probe a fainter luminosity bin then previously estimated in the literature, and we find both heavily obscured AGN space density calculations consistent with the X-ray background models.
Future work to test our estimation of the level of intrinsic obscuration can occur with not only future missions, but also with currently operating telescopes. Using a large ground based telescope, we can obtain more sensitive [Oiii] measurements, as well as other optical emission lines to further probe the AGN power. In addition, we can use ALMA to characterise the dustiness of the host galaxies. This would test whether the un-accounted for obscuration is truly located within parsecs of the SMBH versus host galaxy obscuration (see Circosta et al. 2019 for further examples of this possibility). Future X-ray missions, such as ATHENA, will enable more sensitive X-ray measurements. This would allow for more rigorous spectral analysis of the low X-ray flux sources. Finally, JWST will allow us to directly image the MIR flux on kpc scales. Thus, we could more robustly decouple SF from torus emission.
In conclusion, we find a significant fraction of the low flux population of Chandra 7Ms AGN are obscured AGN in disguise. This population is usually missed and/or mis-classified and should be taken into account when constructing AGN samples from deep X-ray surveys.