[O iv]- and [Ne v]-weak Active Galactic Nuclei Hidden by Compton-thick Material in Late Mergers

We study “buried” active galactic nuclei (AGNs) almost fully covered by circumnuclear material in ultra/luminous infrared galaxies (U/LIRGs), which show weak ionized lines from narrow-line regions. Employing an indicator of a [O iv] 25.89 or [Ne v] 14.32 μm line to 12 μm AGN luminosity ratio, we find 17 buried AGN candidates that are [O iv]-weak (L [O IV]/L 12,AGN ≤ −3.0) or [Ne v]-weak (L [Ne V]/L 12,AGN ≤ −3.4) among 30 AGNs in local U/LIRGs. For the [O iv]-weak AGNs, we estimate their covering fractions of Compton-thick (CT; N H ≥ 1024 cm−2) material with an X-ray clumpy torus model to be fCT(spec)=0.55±0.19 on average. This value is consistent with the fraction of CT AGNs ( fCT(stat)=53%±12% ) among the [O iv]-weak AGNs in U/LIRGs and much larger than that in Swift/Burst Alert Telescope (BAT) AGNs (23% ± 6%). The fraction of [O iv]-weak AGNs increases from 27−10+13% (early) to 66−12+10% (late mergers). Similar results are obtained with the [Ne v] line. The [O iv]- or [Ne v]-weak AGNs in late mergers show larger N H and Eddington ratios (λ Edd) than those of the Swift/BAT AGNs, and the largest N H is ≳1025 cm−2 at logλEdd∼−1 , close to the effective Eddington limit for CT material. These suggest that (1) the circumnuclear material in buried AGNs is regulated by the radiation force from high-λ Edd AGNs on the CT obscurers, and (2) their dense material with large fCT(spec) (∼0.5 ± 0.1) in U/LIRGs is a likely cause of a unique structure of buried AGNs, whose amount of material may be maintained through merger-induced supply from their host galaxies.

(late mergers).Similar results are obtained with the [Ne V] line.The [O IV]-or [Ne V]-weak AGNs in late mergers show larger N H and Eddington ratios (λ Edd ) than those of the Swift/BAT AGNs, and the largest N H is 10 25 cm −2 at log 1 Edd l ~-, close to the effective Eddington limit for CT material.These suggest that (1) the circumnuclear material in buried AGNs is regulated by the radiation force from high-λ Edd AGNs on the CT obscurers, and (2) their dense material with large ( )  f CT

Introduction
Luminous infrared (IR) galaxies (LIRGs; with 8-1000 μm luminosities of L IR 10 11 L e ) and ultraluminous IR galaxies (ULIRGs; L IR 10 12 L e ) are mostly gas-rich mergers of galaxies (e.g., Kartaltepe et al. 2010) and hence are ideal laboratories to examine the evolution of supermassive black holes (SMBHs) induced by galaxy mergers.Although they are rare in the local Universe, they are the standard population constituting most of the cosmic IR background at z  1 (e.g., Casey et al. 2014;Coppin et al. 2015).Theoretical studies (e.g., Hopkins et al. 2006Hopkins et al. , 2008;;Blecha et al. 2018;Yutani et al. 2022) suggest that mergers enhance starburst and mass accretion onto SMBHs, identified as active galactic nuclei (AGNs).Indeed, multiwavelength AGN surveys have found that AGNs with moderate bolometric luminosities are usually found in nonmergers, whereas more luminous AGNs are commonly found in mergers (e.g., Treister et al. 2012).
The environment in the vicinity of the accreting SMBH is well understood for nonmergers, owing to a large sample size available in the local Universe.A key component for SMBH growth is circumnuclear material, which is fed to the central Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.black hole.Ricci et al. (2017b) made a systematic study of X-ray-luminous AGNs detected with Swift/Burst Alert Telescope (BAT), where the majority of the hosts are isolated galaxies, and found that about 70% of them are obscured by gas and dust with a hydrogen column density of N H 10 22 cm −2 .According to a simple, orientation-based AGN unification model (e.g., Antonucci 1993), if the survey has a high completeness level, the statistical fraction of obscured AGNs, ( )  f obs stat (10 22 cm −2 ), should be roughly equivalent to the "covering fraction" of the AGN.Ricci et al. (2017b) also found that the fraction of obscured AGNs in their sample is .This value of λ Edd corresponds to the threshold above which radiation pressure from the AGN on dusty gas with N H 10 22 cm −2 is larger than the gravitational force (e.g., Fabian et al. 2006Fabian et al. , 2008;;Ishibashi et al. 2018).As a result, they proposed a scenario that the covering fraction decreases with λ Edd due to the radiation pressure (see also Ricci et al. 2022).
It has been suggested that the AGNs in late mergers become heavily obscured by circumnuclear material.The optical and IR observations have found that the AGNs in U/LIRGs show weak ionized lines from narrow-line regions (NLRs), such as [O III] λ5007 and [O IV] 25.89 μm (e.g., Imanishi et al. 2006Imanishi et al. , 2008;;Yamada et al. 2019).This type of AGN is called "buried" AGNs, where no significant NLRs develop because the UV photons emitted from the accretion disk in almost all directions are absorbed by optically thick (A V  1 mag or N H  2 × 10 21 cm −2 ; Draine 2003) material.Performing a broadband X-ray study with the Nuclear Spectroscopic Telescope Array (NuSTAR) and Swift/BAT, Ricci et al. (2021) found that ( )  f obs stat (10 22 cm −2 ) reaches 90% for AGNs in local U/LIRGs.The difference in the fraction of Comptonthick (CT; with N H 10 24 cm −2 ) AGNs, CT stat obs stat = (10 24 cm −2 ), is more significant between late mergers (50%) and Swift/BAT sources (20%-30%; Ricci et al. 2015Ricci et al. , 2017b)).A multiwavelength study by Yamada et al. (2021) found that these AGNs in late mergers have high log Edd l (−2).How AGNs at high λ Edd , whose circumnuclear material should be affected by radiation pressure, get buried in dense obscurers remains an open question.Most of the buried AGNs in U/LIRGs at z  1 would be missed in observations at any wavelength.Hence, understanding the nature and evolution of "buried" AGNs may mean understanding a majority of the merger-induced AGNs in the Universe and thus the SMBH evolution in the context of cosmic history.
The first step in the study of buried AGNs is to identify the candidates and construct a sample set, followed by a more detailed study, including evaluating the relevant parameters and their relations, specifically the covering fraction and λ Edd .Yamada et al. (2019) found a good indicator for identifying whether an AGN is buried or not, which employs the [O IV] line to nuclear 12 μm luminosity ratio (L [O IV] /L 12,nuc ).A major downside in the method is the technical difficulty in measuring torus-originating L 12,nuc , which requires mid-IR observations with a high spatial resolution of subarcseconds to minimize the contamination from the host galaxy (Asmus et al. 2014(Asmus et al. , 2015)).Accordingly, the available samples to obtain the indicator are limited to nearby bright targets.
Moreover f obs spec (10 22 cm −2 ), for the individual AGNs in Swift/BAT sources and U/LIRGs, respectively.They performed X-ray spectroscopy with the X-ray torus model XCLUMPY (Tanimoto et al. 2019), which is one of the latest models based on the realistic geometries of clumpy tori (e.g., Krolik & Begelman 1988;Wada & Norman 2002;Hönig & Beckert 2007;Laha et al. 2020).XCLUMPY assumes Gaussian angular distributions of clumps (Nenkova et al. 2008a(Nenkova et al. , 2008b)), although we note that the ( )  f obs spec depends on the assumption of an X-ray torus model. 18For 28 Swift/BAT AGNs, Ogawa et al. (2021) estimated the values of ( )  f obs spec , which are well consistent with the values of ( ) f obs stat at each λ Edd bin reported by Ricci et al. (2017b).On the other hand, Yamada et al. (2021) found that the ( )  f obs spec (10 ).This is because the covering fractions of CT materials are less dependent on λ Edd than those of absorbers with 10 22 cm −2 among Swift/BAT AGNs; accordingly, we can reveal a different factor that determines the covering fraction of CT material (e.g., merger stages).
This work has two main goals.First, we establish useful diagnostics for identifying buried AGNs.Specifically, we employ a similar method to our previous work (Yamada et al. 2019) but using, together with [O IV], 12 μm AGN luminosities (designated as L 12,AGN ; e.g., Yamada et al. 2023) derived through spectral energy distribution (SED) analysis and also using [Ne V] 14.32 μm data as a supplement.The SED data are much more easily obtained than L 12,nuc .To evaluate the ( )  f obs spec for buried AGNs, we also compare the parameter with the ( ) f obs stat .Second, we discuss the physical mechanism of the buried structure of AGNs in U/LIRGs by using a covering fraction and λ Edd .Section 2 describes the sample we utilized.In Section 3, we establish the diagnostics for buried AGNs.Section 4 discusses the structure of buried AGNs.Section 5 summarizes the main results.The notations of N log H and L log mean the logarithms of hydrogen column density in cm −2 and luminosity in erg s −1 , respectively.All fractions are calculated by properly evaluating the binomial probability distribution with a beta function; we set the center value and its error range as the 50th and 16th-84th percentiles, respectively (Cameron 2011).All errors of the parameters are 1σ level, and upper/lower limits are 3σ level.Throughout the paper, we adopt a standard cosmology, H 0 = 70 km s −1 Mpc −1 , Ω M = 0.3, and Ω Λ = 0.7.

Sample and Data Description
For probing the buried AGNs with new diagnostics, we use two AGN samples in this work.One is a sample set of the AGNs in gas-rich mergers, selected from local U/LIRGs (Armus et al. 2009).The other is a sample of the X-ray-selected AGNs in nonmerging galaxies, detected with Swift/BAT (Ricci et al. 2017c).The AGNs contained in the two samples are exclusive. 18In XCLUMPY, the covering fraction of obscurers can be calculated by ), where σ X is the torus angular width and N H Equ is the equatorial hydrogen column density (see Figure 1 in Tanimoto et al. 2019; see also, e.g., Uematsu et al. 2021;Inaba et al. 2022;Nakatani et al. 2023).Tanimoto et al. (2018Tanimoto et al. ( , 2020Tanimoto et al. ( , 2022) ) and Buchner et al. (2019) report the difference in the X-ray spectral shape between the clumpy and smooth distribution of the obscurers.

GOALS Sample
Our base sample of U/LIRGs is the Great Observatories All-Sky LIRG Survey (GOALS; Armus et al. 2009).It consists of 202 U/LIRGs at z < 0.088, which are selected from fluxlimited IR sources detected with IRAS.Among these objects, Yamada et al. (2021) identified 57 U/LIRG systems that had been observed with hard X-rays, which totaled 84 individual nuclei in the optical band, and found significant hard X-ray detection from 40 AGNs from these nuclei.Yamada et al. (2023) performed hard-X-ray-to-radio SED decomposition for these 57 U/LIRGs (or 72 component sources resolved in the Herschel 70 μm band).They cataloged the intrinsic AGN luminosities for the 40 hard X-ray-detected AGNs in the multiwavelength bands, containing two Herschel-unresolved dual-AGN systems and 36 resolved single AGNs.The study further identified three AGN candidates through a significant test for two kinds of SED fits (with and without an AGN component) with a reduced Bayesian information threshold of equal to or more than 6.0 (i.e., posterior probability above 95%; Raftery 1995).The three AGN candidates should be CT AGNs on the basis of their 12 μm and X-ray luminosities (see Appendix A.1). Here, we exclude two unresolved dual-AGN systems (Mrk 266 and NGC 6240), two AGNs whose host galaxies have much smaller L IR (<10 11 L e ; NGC 6921 and NGC 7682) than those of the interacting pairs, and seven nonmerging sources (see Appendix A.2). Finally, our sample set consists of 30 sources, consisting of 27 hard X-ray-detected AGNs and three CT AGN candidates.Yamada et al. (2021) estimated the covering fractions of their cataloged sources with XCLUMPY and presented their SMBH masses and merger stages in four levels of A, B (early mergers), C, and D (late mergers), classified on the basis of their high-spatial-resolution optical/IR images.The [O IV] and [Ne V] fluxes were measured with Spitzer/InfraRed Spectrograph (IRS) (Inami et al. 2013; except for IC 4518, which is taken from Spoon et al. 2022).In Table 1, we summarize the main properties of the 27 AGNs and three AGN candidates in merging U/LIRGs.

Swift/BAT AGN Sample
We construct our sample set of X-ray-selected, Swift/BAT-Spitzer/IRS nonblazer AGNs from the 606 AGNs selected by Ichikawa et al. (2017) from the Swift/BAT 70 month catalog.The combined selection criteria by Ichikawa et al. (2017) and us are (i) galactic latitudes (|b| > 10°), (ii) spectroscopic redshifts being available, (iii) no interacting galaxies (Koss et al. 2012;Yamada et al. 2021), (iv) both [O IV] and [Ne V] line luminosities being constrained with Spitzer/IRS, (v) 12 μm AGN luminosity being constrained, and (vi) SMBH mass and Eddington ratios being presented in Koss et al. (2022).The resultant BAT-IRS sample contains 138 AGNs in nonmergers.Appendix B describes the detailed selection process.
So far, 27 of the 138 AGNs have been studied by our group using the XCLUMPY model.Thirteen AGNs are in Tanimoto et al. (2022), who systematically analyzed CT AGN candidates that may have dense circumnuclear material (see Section 4.1).Except for these AGNs, the covering fractions of the rest of the 14 non-CT AGNs studied in Ogawa et al. (2021) are available and are consistent with the relation between λ Edd and covering fraction derived from the obscured AGN fraction (Ricci et al. 2017b).Although the 14 AGNs are closer objects (z < 0.02) than the 138 AGNs (z ∼ 0.04 on average), they cover a wide range of log Edd l (−3 to 0).A Kolmogorov-Smirnov (K-S) test indicates that the difference in log Edd l between the BAT-IRS AGNs and 14 non-CT AGNs is not significant (p-value = 0.72).Thus, we treat the 14 non-CT AGNs studied  with XCLUMPY as representative ones (see also Section 3.1).Table 1 lists their properties.

Results
We

Definition of [O IV]-and [Ne V]-weak AGNs
We make a scatter plot of L [O IV] /L 12,AGN and ( )  f CT spec estimated for the X-ray data of our sample with XCLUMPY (left panel of Figure 1) to search for a potential correlation with the aim of using it as a tracer to evaluate the nature of potentially buried AGNs.We then perform regression analysis of the data, using the Bayesian maximum-likelihood method (Kelly 2007; see also Toba et al. 2019), which can handle even poorly constrained data with only upper limits determined, and find that the AGNs in U/LIRGs show a significant anticorrelation for the two quantities with a correlation coefficient of −0.48 ± 0.19.Its p-value is 0.0019, indicating that the correlation is significant at a >99% confidence level.This result supports that L [O IV] /L 12,AGN can be a useful tracer of ( ) f CT spec .Also, we find that the average values of and ( ) f CT spec of the 14 BAT-IRS AGNs (Section 2.2; gray diamond), −2.09 ± 0.45 and 0.27 ± 0.21, respectively, are within the typical range of the AGNs in U/LIRGs.
Similarly, we investigate a correlation between L [Ne V] / L 12,AGN and ( )  f CT spec (right panel of Figure 1).The correlation coefficient is −0.36 ± 0.24, and its p-value is 0.020 (i.e., a >95% confidence level).The average value of L log Ne V / L 12,AGN −3.4 for upper limits, which is technically more straightforward and is a viable option if the systematic uncertainty is small.

Cumulative N H Distribution for Buried AGNs
Under the definition of the [O IV] weakness in the previous subsection, 12 out of 27 hard X-ray-detected AGNs in U/LIRGs are classified into [O IV]-weak AGNs.For the [O IV]-weak ones, the median and average of ( )  f CT spec estimated with XCLUMPY are 0.48 ± 0.13 and 0.55 ± 0.19, respectively.These are significantly larger than the fraction of CT AGNs for Swift/BAT AGNs ( ( ) f 23% 6% CT stat =  ; Ricci et al. 2017b).This implies that a high fraction of [O IV]-weak AGNs are buried AGNs.
To assess the covering fractions estimated with XCLUMPY in an independent way, we compare the cumulative N H L log O IV /L 12,AGN −3.0 and −2.7 (the latter is for data points with only upper limits given), respectively.The vertical solid line and gray shaded area show the typical value with a 1σ dispersion for the Swift/BAT AGNs from Ricci et al. (2017b), assuming ( ) . The gray diamond is the average of the 14 BAT-IRS AGNs in Ogawa et al. (2021).The other symbols denote the merger stages as described in the legend at the top right corner.Right panel: the same as the left but for the [Ne V] line.Horizontal dashed and dotted lines are the thresholds of [Ne V]-weak AGNs for [ ] L log Ne V /L 12,AGN −3.4 and −3.1 (the latter is for upper limits), respectively.
distributions for [O IV]-weak and [O IV]-moderate AGNs in merging U/LIRGs in the left panel of Figure 2. We find that [O IV]-weak AGNs for sources without three AGN candidates (orange dashed-dotted line in Figure 2 = cosθ (θ: the half-opening angle), the structure of [O IV]-or [Ne V]-weak AGNs can be described in Figure 3.

Fraction of Buried AGNs
Since ( )  f CT spec depends on the assumption of the X-ray torus model (e.g., clumpy or smooth distribution), we examine the fraction of [O IV]-weak AGNs according to merger stages in U/LIRGs (left panel of Figure 4) and test the consistency between ( )  f CT spec and ( ) f CT stat should be ( ) f CT stat = 20%-40% and 30%-50% for early and late mergers, respectively.The values agree with the actual detection rates of CT AGNs at the respective merger stages,   line is also small (33% ± 11%; 5/16).A possible hypothesis for the origin of less obscured sources is that NLRs may not have been developed due to too short a time after a recent trigger of the AGNs.These AGNs may be contained in the U/LIRG sample, but the larger fraction of [O IV]-or [Ne V]-weak AGNs (Figure 4) and higher ( )  f obs stat (10 22 cm −2 ) in U/LIRGs suggest that the [O IV]-or [Ne V]-weak AGNs are likely different from those in the BAT-IRS sources.To unveil the origin of [O IV]-or [Ne V]-weak BAT-IRS AGNs, many of which are likely not buried, further studies are needed to draw a conclusion.
By contrast, the 10 obscured [O IV]-or [Ne V]-weak BAT-IRS AGNs with N H 10 22 cm −2 can be buried AGN candidates.Their properties are listed in Table 1.Six of these AGNs have N H 10 23 cm −2 , and their fractions of scattered light from the AGN with respect to the intrinsic AGN component are extremely small ( f scat < 0.5%; Ricci et al. 2017c; see also Ueda et al. 2007;Kawamuro et al. 2016).The estimates of f scat are 0.2%-0.3%(NGC 4992, ESO 297−18, Z147−20, ESO 506−27), 1.3% (NGC 7479), and 5.2% (Mrk 622), while f scat > 0.5% for the other four less obscured AGNs.The low-X-ray-scattering AGNs are difficult to find for U/LIRGs due to the contamination from hot gas and X-ray binaries in the starburst regions, while they were found in Swift/BAT AGNs (e.g., Yamada et al. 2019).The obscured AGNs with low f scat in soft X-rays are known to show on average smaller [O III] line to X-ray luminosity ratios (L [O III] /L X ) than the other (i.e., f scat 0.5%) obscured AGNs (Ueda et al. 2015;Gupta et al. 2021), the fact of which suggests that the former population of AGNs is buried in circumnuclear material with small opening angles.Therefore, the six AGNs are likely to be buried AGNs.The fraction of [O IV]-or [Ne V]weak AGNs with N H 10 23 cm −2 is only 5% ± 2% (6/138) for the BAT-IRS AGNs.Considering that the fraction is much smaller than that of buried AGNs in late mergers (66 12 10 -+ %), galaxy merging is likely to enhance the buried structure.We have finally found 23 buried AGN candidates containing 17 [O IV]-or [Ne V]-weak AGNs in merging U/LIRGs (where four are early mergers and 13 are late mergers) and six obscured ones in the nonmerging BAT-IRS AGNs.

How Do AGNs Get Buried in U/LIRGs?
For unveiling the origin of the buried structure in late mergers, we examine the effect of radiation pressure on the obscurers by focusing on the effective Eddington ratio ( Edd eff l ).
The ratio Edd eff l , calculated with the radiation pressure against the gravitational force by the SMBH, is an Eddington limit for dusty gas, in which the scattering cross section for UV photons is taken into account (e.g., Fabian et al. 2008).Ishibashi et al. (2018) calculate the Edd eff l , taking account of the effect of not only UV absorption by dusty gas but also their IR reradiation.Recent studies of Swift/BAT AGNs (Ananna et al. 2022;Ricci et al. 2022) found that the ( )  f obs stat (10 22 cm −2 ) decreases steeply , corresponding to Edd eff l for the obscurers with N H 10 22 cm −2 .This supports that their circumnuclear material is blown away by the radiation pressure when CT stat ~, which they argue may be mainly because the CT material at a location of a small elevation angle from the disk suffers a much smaller radiation pressure than that in regions closer to the polar angle and thus is not easily blown away and remains there, constituting the persistent CT region (e.g., Wada 2015).
In contrast, Yamada et al. (2021) found in their U/LIRG sample set that some AGNs in late mergers with log 2 Edd l - have larger ( )  f obs stat and ( ) f obs spec (10 22 cm −2 ) than those of Swift/ BAT AGNs with a similar λ Edd (Ricci et al. 2017b;Ogawa et al. 2021).Thus, these studies indicate that the AGNs in late mergers are not likely to follow the same trend regulated by the AGN-driven radiation pressure for obscurers with N H 10 22 cm −2 as for Swift/BAT AGNs.

Relation between the CT Covering Fraction and λ Edd
To understand the origin of the heavily obscured structure in buried AGNs, we examine the relation between ( )  f CT spec and λ Edd for merging U/LIRGs in Figure 5  The top panel of Figure 6 plots the N H -λ Edd diagram in a similar way as in Fabian et al. (2008).In the region below N H = 10 22 cm −2 (solid line) in the diagram, galactic dust lanes may become dominant in absorption.Part of the region above the threshold N H = 10 22 cm −2 and at a high λ Edd of close to 1 or above is the "outflow" region (pink shaded in the figure), where dusty clouds are blown away by radiation pressure.We also overlay a theoretical AGN evolution cycle curve adopted from Ishibashi et al. (2018;blue and orange solid curves).We superpose in the diagram the distribution of Swift/BAT AGNs in contours taken from Ricci et al. (2022) and also their proposed radiation-regulated unification model with arrows and number labels, which is concisely described below.When the AGN is neither very active nor obscured, accretion events enhance mass inflows and obscuration (region 1), and the AGN eventually transits to an obscured AGN (region 2).Once Edd eff l has increased beyond a certain threshold, depending on the amount of N H , which is usually N log H = 22-23 according to the theoretical prediction by Ishibashi et al. (2018; blue line in the figure) and at most 24, its circumnuclear material is blown away in a short time due to the radiation pressure (region 3).It soon becomes an unobscured AGN with high λ Edd (region 4) and transits to low N H and λ Edd .Most of AGNs in U/LIRGs are distributed on the contours of regions 2-4, while some AGNs in late mergers have larger N H and λ Edd .
In the bottom panel of Figure 6, we make a plot of the same diagram for the [O IV]-or [Ne V]-weak AGNs in late mergers, i.e., buried AGN candidates.We find that their distribution is mostly concentrated at a higher N H -λ Edd corner on the N H -λ Edd plane, unlike those for the Swift/BAT AGNs and the other AGNs in U/LIRGs.We also find that the highest N H is 10 25 cm −2 with Edd eff l close to the effective Eddington limit according to the prediction by Ishibashi et al. (2018) for the AGNs with N H 10 23 cm −2 and CT material (orange curve).The average of the six buried BAT-IRS AGNs (Section 3.3) shows a similar result, N log 23.9 0.2 H =  and log Edd l = 1.89 0.28 - .The two AGNs with log Edd l ∼ −0.5-0 in stage D mergers in and in the vicinity of the "outflow" region, Mrk 231 and IRAS F08572+3915, are known to have a kiloparsec scale and thus strong, ionized, and molecular outflows (Yamada et al. 2021).
The difference in the distributions of Swift/BAT AGNs and buried AGNs on the N H -λ Edd plane may originate in the difference in the amount of material supplied from the host galaxies.The circumnuclear material in Swift/BAT AGNs, most of which are nonmergers, is mostly surrounded by obscurers with N H 10 22 cm −2 , which would be blown away at log 2 Edd l - (e.g., Ricci et al. 2022Ricci et al. , 2023)), whereas the circumnuclear material in buried AGNs in late mergers may be shrouded in CT obscurers, which can be blown away at a higher threshold λ Edd of −1.In fact, a dramatic variability of N H has been discovered in an AGN with λ Edd ∼ −0.7 (stage D merger IRAS F05189−2524); its column density varied between non-CT (N H ∼ 8 × 10 22 cm −2 ) and CT (>2.3 × 10 24 cm −2 ) within ∼10 yr (see Figure 12 in Yamada et al. 2021).This is a distinctively larger variability than that in normal AGNs (e.g., Laha et al. 2020).Thus, these facts support that a larger amount of CT material in buried AGNs than in Swift/BAT AGNs causes a unique structure of buried AGNs in late mergers; hence, the variety of circumnuclear material may be uniformly regulated by the radiation pressure depending on λ Edd and the amount of material supplied, which is a key parameter of the difference between mergers and nonmergers.

Future Observations with X-Ray and IR Spectroscopy
A combination of deep X-ray and mid-IR spectroscopy would be crucial to reveal the fraction and structure of buried AGNs in U/LIRGs, which are the key population in the study of SMBH growth in obscured AGNs at z ∼ 1 and beyond (see Section 1).The James Webb Space Telescope (JWST), endowed with a supreme mid-IR spectroscopic capability and unprecedentedly high sensitivity, can identify rapidly growing SMBHs in U/LIRGs (e.g., Inami et al. 2022;Rich et al. 2023).JWST observations combined with high-quality X-ray observations would enable us to identify buried AGNs almost fully covered by dense circumnuclear material with high ( )  f CT spec at cosmic noon, the population of which is predicted to increase significantly toward higher redshifts (e.g., Ueda et al. 2014;Gilli et al. 2022), and would help us reveal the entire picture of growth of both obscured and unobscured SMBHs.

Conclusions
We established new mid-IR diagnostics employing L [O IV] /L 12,AGN or L [Ne V] /L 12,AGN for the buried AGNs almost fully covered by dense circumnuclear material.We evaluated the method by comparing it with the estimates of covering fractions derived from the X-ray spectral fitting with XCLUMPY.This study identified 17 buried AGN candidates in merging U/LIRGs and six from nonmerging BAT-IRS sources.
Constructing the cumulative N H distribution, we estimated the covering fraction of CT obscurers ( ) f 0.5 0.1 CT spec ~ for the buried AGNs in U/LIRGs, the result of which is consistent with the estimates with XCLUMPY.The ( )  f CT spec value is much larger than that for Swift/BAT AGNs ( AGNs with N H 10 23 cm −2 , plausible buried AGN candidates, is only 5% ± 2% (6/138).Considering that the fraction is much smaller than that of buried AGNs in late mergers (66 12 10 -+ %), most of which are obscured AGNs (90%), galaxy merging is likely to enhance the buried structure.
We also found that the [O IV]-or [Ne V]-weak AGNs in late mergers show larger N H and λ Edd than those of the Swift/BAT AGNs (Figure 6), and the largest N H is 10 25 cm −2 with log 1 Edd l ~-, close to the effective Eddington limit for CT  1).The (partial) horizontal line at N H = 10 22 cm −2 represents the effective Eddington limit for dusty gas, and the pink shaded area is the outflowing region expected according to Edd eff l (Fabian et al. 2008).The solid curve is the theoretical evolution path with Edd eff l for obscurers with N H larger (in orange) or smaller (in blue) than 10 23 cm −2 , in which the IR radiation trapping effect is considered (Ishibashi et al. 2018).All gray lines, arrows, and numbers are adopted from Ricci et al. (2022) and show their proposed recurrent evolution process of AGNs; the ellipse labeled as 1 demonstrates a hypothetical region for mostly unobserved AGNs, and the three levels of contour lines (in the regions with labels of 2, 3, and 4) show 50%, 68%, and 90% of the observed cumulative population among the BAT sources in the 3 log 0 Edd l -< < range (see legend at the top left and main text for details).The notations for the other symbols are the same as in Figure 1.Bottom panel: the same as the top but for 10 out of 13 [O IV]-or [Ne V]-weak AGNs in late mergers (Section 3.3), excluding three whose λ Edd are not constrained.material.These results suggest that (1) the circumnuclear material in buried AGNs is regulated by the radiation pressure from high-λ Edd AGNs on the CT obscurers, and (2) their dense material with large ( )  f CT spec (∼0.5 ± 0.1) in U/LIRGs is a likely cause of a unique structure of this type of buried AGN, and the amount of material may be maintained through merger-induced continuous supply from their host galaxies.Exploiting the [O IV] and [Ne V] weakness, buried AGNs at higher z, which may be a majority of the AGNs at z  1, can be identified with a combination of X-ray and mid-IR spectroscopy, particularly in the era of astronomy with JWST.
[O IV]-weak AGNs in U/ LIRGs and much larger than that in Swift/Burst Alert Telescope (BAT) AGNs (23% ± 6%).The fraction of [O IV]-weak AGNs increases from 27 , Ogawa et al. (2021) and Yamada et al. (2021) investigated the covering fractions based on the X-ray spectra, ( ) propose a new diagnostic method to determine to what degree individual AGNs are "buried," i.e., in what covering fraction ( ( ) f CT spec ) CT matter covers the central AGN, by using the ratio of the [O IV] luminosity to 12 μm AGN luminosity derived on the basis of IR SED analysis (L [O IV] /L 12,AGN ; see Section 1 and Yamada et al. 2023 for details).We define the [O IV]-weak AGNs and report their fraction in the AGNs in the GOALS and BAT-IRS samples.The ratio of the [Ne V] luminosity (L [Ne V] ) to L 12,AGN is also used as a tracer of buried AGNs.
AGN of the 14 BAT-IRS AGNs in Ogawa et al. (2021) is −2.58 ± 0.42.Although the significance of the correlation is not strong, the L [Ne V] /L 12,AGN can also be an indicator of ( ) f CT spec .To define the criteria of [O IV]-and [Ne V]-weak AGNs from the 138 BAT-IRS AGNs, we here focus on 86 AGNs whose [O IV] and [Ne V] fluxes and 1σ errors are measured.For the other BAT-IRS AGNs, the 3σ upper limits of the line fluxes are constrained.In the L [O IV] /L 12,AGN and L [Ne V] /L 12,AGN distributions for the 86 AGNs, the lower side of a 90% confidence interval corresponds to L [O IV] /L 12,AGN  −3.0 and L [Ne V] /L 12,AGN  −3.4,respectively.This threshold, however, should be an overestimate for the data points (i.e., AGNs) with only upper limits determined containing the other BAT-IRS AGNs.Since the typical 1σ error is ∼0.1 dex, we consider 0.3 dex as the systematic error, which is translated into the threshold of 12,AGN  −2.7 for those poorly determined data points.In consequence, we define AGNs with [ ] L log O IV /L 12,AGN −3.0 (or −2.7 if only upper limits are given for L [O IV] ) as [O IV]-weak and the others as [O IV]moderate.Similarly, we define [Ne v]-weak AGNs with [ ] L log Ne V /L 12,AGN −3.4 (or −3.1 for upper limits).Appendix C discusses the case of universal adoption of the threshold of [ ] L log O IV /L 12,AGN −3.0 and [ ]

Figure 1 .
Figure 1.Left panel: ( [ ] L log O IV /L 12,AGN ) vs. covering fraction of CT material ( ( ) f CT spec ).Horizontal dashed and dotted lines mark the thresholds of [O IV]-weak AGNs for [ ] 18) in early and late mergers, respectively.Similar results can be seen for [Ne V]- weak AGNs.The fractions of [Ne V]-weak AGNs are 35 18; late mergers), as shown in the right panel of Figure 4.These fractions in early and late mergers are larger than 18 138 for the [O IV] line) or 12% ± 3% (16/138 for the [Ne V] line) in the BAT-IRS AGNs.Adopting ( 6 (for [O IV]-weak) and 0.2-0.3(for the others), the expected fraction of CT AGNs (=sum of the fraction of [O IV]-weak/moderate AGNs times each ( ) f CT spec )

Figure 2 .
Figure 2. Left panel: cumulative N H distribution for (green dashed line) [O IV]-moderate AGNs, (orange dashed line) [O IV]-weak AGNs, and (orange solid line) [O IV]-weak AGNs plus three CT AGN candidates among merging U/LIRGs.Right panel: the same as the left but for the [Ne V] line.

Figure 3 .
Figure 3. Schematic picture of the structure of buried AGNs.The covering fractions of obscurers are very high, ( ( ) f 10 obs spec 22 cm −2 )  0.9 and al. (2017b) report that the covering fractions of CT material in the BAT AGNs hardly vary, . We overplot the typical relation in Swift/BAT AGNs ( ( ) f 0.23; CT stat ~Ricci et al. 2017b) and mean values of the 52 CT AGN candidates among them (∼0.2-0.5) in the four logλ Edd bins, the sample of which

Figure 4 .
Figure 4. Left panel: fraction of [O IV]-weak AGNs by merger stage.Orange circles indicate those for stages A-D and black stars those for early and late mergers.The gray solid and dashed lines mark the average with 1σ dispersion for 138 BAT-IRS AGNs.Right panel: the same as the left but for the [Ne V] line.

Figure 5 .
Figure 5. ( ) f CT spec derived from X-ray studies with XCLUMPY vs. λ Edd for merging U/LIRGs.The black solid curve and gray shaded area indicate the typical relation with a 1σ dispersion for Swift/BAT AGNs (Ricci et al. 2017b), assuming ( ) ( ) f f CT spec CT stat = .The vertical pink dashed line marks the Edd eff l for CT material (Ishibashi et al. 2018).Small blue diamonds with uncertainties show the mean values and standard errors in the four logλ Edd bins for the 52 CT AGN candidates, taken from Tanimoto et al. (2022; see text for details).The data points of the [O IV]-or [Ne V]-weak AGNs are circled in black.The notations for the other symbols are the same as in Figure 1.
. 2017b).Their large fraction of obscured AGNs with N H 10 22 cm −2 (90%) supports that the [O IV]-and [Ne V]weak AGNs are likely to be "buried," with the AGN not being able to develop an NLR due to optically thick material in almost all directions.The fraction of [O IV]-weak AGNs increases with merger stage from 27 mergers).Similar results are obtained with the [Ne V] line.For the BAT-IRS AGNs, the fraction of [O IV]-or [Ne V]-weak

Figure 6 .
Figure 6.Top panel: N H -λ Edd diagram for 26 AGNs in U/LIRGs whose Eddington ratios are constrained (Table1).The (partial) horizontal line at N H = 10 22 cm −2 represents the effective Eddington limit for dusty gas, and the pink shaded area is the outflowing region expected according to Edd 22 cm −2 ) of AGNs with log 2

Table 1
Main Properties of Host Galaxies and AGNs in Local U/LIRGs and Swift/BAT Sources ) have significantly larger N H than [O IV]-moderate ones as a whole (green dashed line).Moreover, among the 15 [O IV]-weak sources containing three plausible CT AGN candidates (see Appendix A.1), which are [O IV]-weak, the N H distribution becomes larger (solid orange line).Eight of them are CT AGNs, corresponding to a fraction of 53% ± 12% (8/15; i.e., 8 out of 15 AGNs).IV]-weak AGNs, the fraction of AGNs with N H 10 22 cm −2 is Although the number of [Ne V]-filtered buried AGNs might be somewhat larger than that of [O IV]-filtered, these imply that the populations of [O IV]and [Ne V]-weak AGNs have large CT covering fractions and are actually "buried" by optically thick (2 × 10 21 cm −2 ; see Section 1) material in almost all directions.
We also find that the fraction of the buried AGNs in U/LIRGs increases with the merger stage from ∼27% (early) to ∼66% (late mergers).The fraction of obscured AGNs among [O IV]-weak (or [Ne V]-weak) AGNs is very different between the merging U/LIRGs and BAT-IRS sources.The fraction of obscured AGNs among [O IV]-weak BAT-IRS AGNs is( ) + %; Section 3.2).The value for the [Ne V]