The High Energy X-ray Probe (HEX-P): The Circum-nuclear Environment of Growing Supermassive Black Holes

Ever since the discovery of the first Active Galactic Nuclei (AGN), substantial observational and theoretical effort has been invested into understanding how massive black holes have evolved across cosmic time. Circum-nuclear obscuration is now established as a crucial component, with almost every AGN observed known to display signatures of some level of obscuration in their X-ray spectra. But despite more than six decades of effort, substantial open questions remain: How does the accretion power impact the structure of the circum-nuclear obscurer? What are the dynamical properties of the obscurer? Can dense circum-nuclear obscuration exist around intrinsically weak AGN? How many intermediate mass black holes occupy the centers of dwarf galaxies? In this paper, we showcase a number of next-generation prospects attainable with the High Energy X-ray Probe (https://hexp.org) to contribute towards solving these questions in the 2030s. The uniquely broad (0.2--80 keV) and strictly simultaneous X-ray passband of HEX-P makes it ideally suited for studying the temporal co-evolution between the central engine and circum-nuclear obscurer. Improved sensitivities and reduced background will enable the development of spectroscopic models complemented by current and future multi-wavelength observations. We show that the angular resolution of HEX-P both below and above 10 keV will enable the discovery and confirmation of accreting massive black holes at both low accretion power and low black hole masses even when concealed by thick obscuration. In combination with other next-generation observations of the dusty hearts of nearby galaxies, HEX-P will hence be pivotal in paving the way towards a complete picture of black hole growth and galaxy co-evolution.

The Compton-thick fraction is often inferred to be similarly substantial to the obscured AGN population across cosmic time (see discussion in e.g., Comastri et al. 2015;Civano et al. 2023), even after considering the non-trivial dependence with the nature of the intrinsic X-ray-emitting corona and/or accretion flow (e.g., Gandhi et al. 2007;Vasudevan et al. 2016;Kammoun et al. 2023;Piotrowska et al. 2023).For example, the latest population synthesis models from Ananna et al. (2019) constrain the abundance of Compton-thick AGN to be 50 ±9% within z = 0.1 and 56 ± 9% within z = 1 of all AGN.
Theoretical models of supermassive black hole growth additionally suggest that enhanced circum-nuclear obscuration is intricately linked to not just supermassive black hole accretion (e.g., Fabian 1999), but also galaxy-supermassive black hole co-evolution (e.g., Anglés-Alcázar et al. 2021) and galaxy-galaxy interactions as a whole (e.g., Springel et al. 2005;Hopkins et al. 2006;Pfeifle et al. 2023).Although it is still uncertain as to the exact role the dense circum-nuclear obscurer plays, some viable options include a feeding reservoir for the central black hole (e.g., Storchi-Bergmann and Schnorr-Müller 2019), or a by-product of the central engine itself (e.g., Wada 2012).Compton-thick AGN are hence pertinent targets to unveil the drivers of galaxy growth and understand the co-evolution between supermassive black holes and galaxies, as highlighted in the Astro2020 Decadal Survey 3 .However, Compton-thick AGN are one of the most difficult classes of AGN to detect and study (Hickox and Alexander, 2018;Asmus et al., 2020;Brandt and Yang, 2022).For energies E < 10 keV, the intrinsic X-ray flux from the corona is mostly extinguished via the photoelectric effect and only a few percent of the intrinsic flux escapes (Gupta et al., 2021).Some flux survives in the form of narrow X-ray fluorescent lines at specific energies, with those arising from neutral iron K at 6.4 keV (rest frame) typically being the strongest.The remaining AGN flux observed is dominated by X-ray photons that have undergone Compton recoil in one or multiple scatterings and escaped the obscurer, giving rise to the underlying Compton-scattered continuum.At ∼ 20 -40 keV, the continuum peaks into a broad Compton hump with overall shape determined by the geometry of the obscurer (e.g., Matt et al. 2000;Murphy and Yaqoob 2009;Buchner et al. 2019).
The ability for accurate and precise inference from circum-nuclear obscuration models with everincreasing numbers of fit parameters is currently met by substantial challenges.The first is exploring the degenerate and multi-modal (i.e.non-identifiable) parameter spaces inherent to the spectral model libraries that result from ray tracing simulations.A typical model to explain the 0.2 -80 keV spectra of obscured AGN can consist of ≳ 10 parameters describing the intrinsic X-ray spectrum, the geometric prescription of the surrounding circum-nuclear obscurer and other contaminating soft X-ray emissions.The corresponding multi-dimensional parameter spaces are very complex and do not necessarily lead to unique spectral solutions when compared with alternative geometric models of the obscurer (e.g., Saha et al. 2022;Kallová et al. 2023).As such, parameter exploration, model verification and model comparison are all non-trivial and can be exceedingly expensive to compute with increased numbers of fit parameters (e.g., van Dyk et al. 2001;Buchner et al. 2014;Buchner and Boorman 2023).Increased complexity of obscuration models will also require more ray-tracing simulations to compute.Due to the corresponding trade-off between exploring fewer geometries versus coarser parameter grid resolution, the conventional use of multi-dimensional tables and grid interpolation to fit spectra may become obsolete entirely.A promising alternative is emulation, which has been shown to accelerate the computation time associated with radiative transfer simulations (Kerzendorf et al., 2021;Rino-Silvestre et al., 2022) and avoid the requirement for coarse gridding of parameters into multi-dimensional tables entirely (Matzeu et al., 2022).
The second challenge is the observational requirement for high quality broadband spectroscopy of Compton-thick AGN to test complex physical models.Valuable insights have been attained with focusing Xray optics < 10 keV, typically capable of isolating the Fe Kα complex and underlying reflection continuum from contaminating non-AGN spectral features (e.g., Risaliti et al. 1999;Brightman and Nandra 2011a;LaMassa et al. 2017).But without similar sensitivities > 10 keV, strong ambiguity still remains relating to the shape of the Compton hump (see discussion in Brightman et al. 2015;LaMassa et al. 2019LaMassa et al. , 2023)).Hard X-ray sensitivities provided by coded aperture masks have limited previous studies to higher observed X-ray fluxes (e.g., Yaqoob 2012;Gandhi et al. 2013Gandhi et al. , 2015;;Ricci et al. 2017b), and reduced spectral resolution that is insufficient to strongly constrain geometrical properties of the circum-nuclear environment (see discussion in e.g., Baloković 2017;Tanimoto et al. 2022).
In X-rays, an inhomogeneity in the circum-nuclear material can vary (i) the accretion luminosity and/or (ii) obscuration level.Such changes can be detected and disambiguated with sufficiently sensitive timeresolved X-ray spectroscopy with a wide-enough passband (Ricci and Trakhtenbrot, 2022).For line-of-sight column density variations ∆ N H ≲ 10 23 cm −2 , the photoelectric turnover ≲ 10 keV has been used to robustly confirm obscuration variations (e.g., Risaliti et al. 2002Risaliti et al. , 2005;;Markowitz et al. 2014).However, for variations ∆ N H ≳ 10 23 − 10 24 cm −2 sensitive broadband spectroscopy is advantageous to provide constraints on the underlying absorbed spectrum < 10 keV as well as the reprocessed spectrum > 10 keV to avoid the strong degeneracy between the spectral slope, obscuration level and amount of reprocessing (e.g., Walton et al. 2014;Rivers et al. 2015;Lefkir et al. 2023).Decoupling such large changes in obscuration from intrinsic flux variations exclusively in Compton-thick AGN is currently even less represented in the literature, owing in part to the observational demand for observing variations in the Compton hump that are non-trivial to disentangle ≳ 10-20 keV in all but the brightest targets (e.g., Puccetti et al. 2014;Marinucci et al. 2016;Nardini 2017;Zaino et al. 2020;Kayal et al. 2023).
Column density variations are expected to occur over periods of time from ∼1 day up to several months, assuming a typical range of obscuring cloud filling factors, velocities and distances from the accreting black hole (e.g, Nenkova et al., 2008).Tentative column density variability timescales on the order of years also exist (e.g., Gandhi et al. 2017;Masini et al. 2017;Laha et al. 2020;Torres-Albà et al. 2023), but additional sensitive monitoring is required to quantify its prevalence in the obscured AGN population.Thus X-ray obscuration variability is a powerful tool for providing reliable constraints on the location of obscuring clouds and their distances from the accreting supermassive black hole (Markowitz et al., 2014;Buchner et al., 2019).By combining numerous epochs of broadband X-ray observations with physical obscuration models, the global properties of the circum-nuclear environment (such as covering factor and average column density) can be decoupled from the epoch-dependent variable components to provide the tightest constraints on obscurer properties in the heavily obscured AGN population currently known (e.g., Ricci et al. 2016;Baloković et al. 2018;Pizzetti et al. 2022;Marchesi et al. 2022;Torres-Albà et al. 2023;Kayal et al. 2023).For such observations, simultaneous observations from ∼ 0.2 -80 keV are essential.These are challenging to achieve, currently requiring coordination of complementary missions (e.g., XMM-Newton and NuSTAR), which has limited the sample size for such studies (see Section 4).

The Circum-Nuclear Environment at Low Accretion Power
Volume-limited multi-wavelength surveys have revealed that the majority of supermassive black holes in the nearby Universe are underfed (e.g., Ho 1997Ho , 2008;;Baldi et al. 2018Baldi et al. , 2021b,a;,a;Williams et al. 2022).This implies that the majority of local galaxies host low-luminosity AGN, often parameterised to have bolometric luminosities L bol ≲ 10 42 erg s −1 , and/or Eddington-scaled bolometric luminosities (also known as the Eddington ratio) of λ Edd = L bol / L Edd ≲ 10 −3 (e.g., Elitzur 2006;Hönig and Beckert 2007;Kawamuro et al. 2016).However, our understanding of the circum-nuclear environment in AGN at low luminosities and accretion powers is currently very incomplete.

Accreting Intermediate Mass Black Holes
Large numbers of intermediate mass black holes with masses M BH ∼ 10 2 -10 5 M ⊙ are required to exist throughout cosmic history to give rise to the ∼ 10 9 M ⊙ supermassive black holes observed within mere hundreds of million years from the Big Bang (e.g., Bañados et al. 2018) up to the present day.A large ongoing challenge however, is to observationally identify intermediate mass black holes and to understand how they were formed (Greene et al., 2020).Dwarf galaxies are useful to search for intermediate mass black holes.To explain their low masses, dwarf galaxies are expected to have undergone fewer mergers than more massive galaxies which in turn restricts the availability of fuel for the central black holes to grow.Dwarf galaxies in the local Universe are hence expected to contain the seeds of the first supermassive black holes, and the dwarf galaxy black hole occupation fraction is a crucial piece of the puzzle (e.g., Volonteri et al. 2008;Volonteri 2010;Greene 2012;Reines 2022).
A useful strategy is to search for intermediate mass black hole signatures during episodes of accretion in dwarf galaxy AGN.The difficulty is that any biases imposed on selecting accreting supermassive black holes in AGN are exacerbated in the case of intermediate mass black holes in low-mass galaxies.Dwarf galaxies often have high levels of star formation which can be significantly stronger than the optical emission associated with the accretion disc surrounding accreting intermediate mass black holes (e.g., Moran et al. 2014;Trump et al. 2015).Optical spectroscopy has proven a useful tool for identifying unobscured dwarf AGN signatures (e.g., Greene andHo 2004, 2007;Reines et al. 2013;Baldassare et al. 2018).However, this technique requires that host galaxy dilution be minimal and that the AGN be largely unobscured while accreting at high rates, close to the Eddington limit.X-ray observations are less affected by host galaxy contamination but soft X-rays can be readily absorbed leading to the same biases encountered for more massive black holes in AGN (e.g., Brandt and Alexander 2015;Hickox and Alexander 2018).Broadband X-ray observations including hard X-rays are hence crucial to disentangle obscured accreting massive black holes from individual host galaxy X-ray binaries that often have different predicted hard X-ray spectral shapes (see discussion in e.g., Lehmer et al. 2023).Detailed broadband X-ray spectroscopic studies of obscured massive black holes in low-mass galaxies are currently rare though due to the requirement for sufficient sensitivities (e.g., Ansh et al. 2023;Mohanadas and Annuar 2023).

The HEX-P Perspective
The High-Energy X-ray Probe (HEX-P; Madsen et al. 2023) is a probe-class mission concept that offers sensitive coverage (0.2 − 80 keV) of the X-ray spectrum with exceptional spectral, timing and angular capabilities.It features two high-energy telescopes (HET) that focus hard X-rays, and soft X-ray coverage with a low-energy telescope (LET).
The LET (0.2 -25 keV) consists of a segmented mirror assembly coated with Ir on monocrystalline silicon that achieves a half power diameter of 3.5", and a low-energy DEPFET detector, of the same type as the Wide Field Imager (WFI; Meidinger et al. 2020) onboard Athena (Nandra et al., 2013).It has 512 × 512 pixels that cover a field of view of 11.3' × 11.3'.It has an effective passband of 0.2 -25 keV, and a full frame readout time of 2 ms, which can be operated in a 128 and 64 channel window mode for higher count-rates to mitigate pile-up and achieve faster readout.Pile-up effects remain below an acceptable limit of ∼ 1% for fluxes up to ∼ 100 mCrab in the smallest window configuration (64w).Excising the core of the PSF, a common practice in X-ray astronomy, will allow for observations of brighter sources, with a typical loss of up to ∼ 60% of the total photon counts.
The HETs (2 -80 keV) consist of two co-aligned telescopes and detector modules.The optics are made of Ni-electroformed full shell mirror substrates, leveraging the heritage of XMM-Newton (Jansen et al., 2001), and coated with Pt/C and W/Si multilayers for an effective passband of 2 -80 keV.The high-energy detectors are of the same type as those onboard NuSTAR (Harrison et al., 2013), and they consist of 16 CZT sensors per focal plane, tiled 4 × 4, for a total of 128 × 128 pixel spanning a field of view slightly larger than for the LET, of 13.4' × 13.4'.
The unique improvements yielded by HEX-P will provide significant advancements in the study of supermassive black hole growth.Enhanced sensitivity above 10 keV relative to NuSTAR will enable detailed modelling constraints of the faintest Compton-thick AGN currently known (see Section 5 and Pfeifle et al. 2023), as well as the completion of the local AGN census which is predominantly restricted by our ability to uncover Compton-thick AGN (Asmus et al., 2020).The strictly simultaneous broadband coverage will also remove any ambiguity associated with spectral component variability which can significantly affect the inference of key system parameters (see discussion in Baloković et al. 2018Baloković et al. , 2021;;Torres-Albà et al. 2023 and Section 4).Lastly, the extended passband of the LET up to energies of ∼ 25 keV will provide sensitive overlapping X-ray spectroscopy in all three HEX-P cameras.The energy range ∼ 5 -8 keV contains the iron K lines which hold enormous diagnostic value for the structure of the circum-nuclear obscurer when combined with the underlying continuum ≳ 10 keV (e.g., Baloković et al. 2018).Having three individual instruments across this wavelength range will also provide independent verification for blue-shifted absorption features arising from outflowing material that have proven difficult to detect in heavily obscured AGN to-date (e.g., Matzeu et al. 2019).At higher energies, the passband between ∼8 -25 keV encompasses the first inflection point of the Compton hump which holds exciting potential as a fingerprint-like identifier for the circum-nuclear obscurer(s) surrounding AGN (see e.g., Buchner et al. 2019Buchner et al. , 2021)).
The paper is organised as follows.Section 2 presents the latest compilation of published Compton-thick AGN within ∼ 400 Mpc confirmed in part by NuSTAR observations.To our knowledge, this is the largest compilation of local Compton-thick AGN constructed to date which combines sources selected at a variety of different wavelengths.In Section 3 we present a detailed X-ray spectral analysis of local megamaser AGN, highlighting the prospects for HEX-P and next-generation obscuration models to study the effects of radiative feedback from AGN. Section 4 showcases the future possibilities with multi-epoch studies attainable with high-sensitivity, strictly simultaneous, broadband X-ray spectroscopy.The current and future prospects behind the behaviour of dense AGN obscurers at extremely low luminosities are discussed in Section 5 followed by the prospects for detecting faint obscured AGN in dwarf galaxies in Section 6.We then provide a quantitative estimate of the volume accessible by HEX-P for robust characterisation of Compton-thick obscuration and compare to the current state-of-the-art in Section 7. We present our summaries in Section 8.
All the HEX-P simulations presented in this work were produced with a set of response files that represent the observatory performance based on current best estimates (v07 -17-04-2023; see Madsen et al. 2023).The effective area is derived from a ray-trace of the mirror design including obscuration by all known structures.The detector responses are based on simulations performed by the respective hardware groups, with an optical blocking filter for the LET and a Be window and thermal insulation for the HET.The LET background was derived from a GEANT4 simulation (Eraerds et al., 2021) of the WFI instrument, and the one for the HET from a GEANT4 simulation of the NuSTAR instrument, both positioned at L1.

THE DATABASE OF COMPTON-THICK AGN (DOCTA)
To understand the Compton-thick AGN population uncovered to-date, and as a natural starting point for our HEX-P simulations, we construct a comprehensive list of Compton-thick AGN identified in the literature.To ensure accurate modelling of the underlying Compton scattered continuum in such sources, we limit our search to targets confirmed with spectral modelling that included NuSTAR data.Whilst other X-ray missions such as Suzaku/Hard X-ray Detector, Swift/Burst Alert Telescope and INTEGRAL instruments have provided hard X-ray spectroscopic constraints for some Compton-thick AGN (e.g., Yaqoob 2012;Vasylenko et al. 2013;Gandhi et al. 2013Gandhi et al. , 2015;;Ricci et al. 2015), we limit ourselves to the requirement for NuSTAR due to its 100-fold increase in sensitivity > 10 keV relative to previous missions (Harrison et al., 2013).The resulting Database of Compton-thick AGN (DoCTA) was created as follows: 1. Literature search: We first identify a list of peer-reviewed publications with a NASA ADS7 search query for any refereed paper containing the phrase 'Compton-thick' and 'NuSTAR' somewhere in its main body of text.The search returned 690 refereed publications.2. Literature refinement: We manually filtered through the list of publications identified in Step 1, finding ∼90 publications that use AGN X-ray spectroscopic modelling with NuSTAR (often but not always complemented by soft X-ray spectroscopy from a different instrument) to constrain line-of-sight column density via obscuration models of some form.
3. Line-of-sight column density 8 : We sought to extract the line-of-sight column density of each system for every acceptable model fit presented per publication.Our reasoning behind this strategy was to be as complete of the literature as possible, enabling inclusion of sources that are classified as Compton-thick with a specific model setup, but not in others.A number of sources have line-of-sight column density measurement upper bounds consistent with the Compton-thick limit, but to be conservative we only consider sources with at least one line-of-sight column density measurement lower 90% confidence bound above the Compton-thick threshold of 1.5×10 24 cm −2 .4. Computing unabsorbed luminosities: To understand the fundamental demographics of the sample, we next estimated intrinsic luminosity.Given the inevitably large number of local AGN selected, a large number of redshift-independent distances are available for the sources.We cross-matched the initial set of objects from Step 3 with the NASA Extragalactic Database9 using sexagesimal coordinates to remove duplicates arising from different published identifiers.We then downloaded all redshift-independent distances per source and used the median distance where more than five distance measurements were available.To overcome possible effects from discrepant distance estimates to a given source, we additionally store the distances used by each work and manually correct intrinsic 2 -10 keV luminosities into fluxes when intrinsic fluxes are not provided.We use the median redshiftindependent distance listed on NED where available, otherwise the luminosity distance is calculated assuming the cosmological parameters H 0 = 70.0km s −1 Mpc −1 , Ω Λ = 0.7 and Ω M = 0.3.
DoCTA contains 66 Compton-thick AGN candidates, with a wide range of possible scientific applications.The primary focus for this work is to assess the ability of current circum-nuclear obscuration models paired with modern broadband X-ray spectral sensitivity to provide unique solutions for intrinsic luminosity and line-of-sight column density, in the absence of considerable source variability (see Figure 3 & Section 4 for more information on this assumption).
Figure 1 presents the distance vs. unabsorbed 2 -10 keV X-ray luminosity for every intrinsic 2 -10 keV luminosity measurement of every source in DoCTA.The left panel shows that DoCTA is limited to ≲ 100 Mpc for the conventional Seyfert definition with unabsorbed 2 -10 keV luminosity, L 2−10 keV > 10 42 erg s −1 .Beyond ∼ 250 Mpc, only quasars (L 2−10 keV > 10 44 erg s −1 ) have been found as Compton-thick.But overall there is a significant range of published intrinsic luminosities per source, with some estimates ranging over > 3 orders of magnitude in the most extreme cases.This trend is shown in Figure 1, which marks the range in intrinsic luminosity reported in the spectral fits included in DoCTA.Under the assumption of negligible source variability (c.f. Figure 3), such variation can arise from choosing different circum-nuclear obscuration models.This also leads to a significant systematic uncertainty in parameter inference (i.e.unabsorbed luminosity, but also line-of-sight column density and covering factors).It is concerning that this occurs even in the local Universe where the observing conditions are optimal (e.g., bright fluxes thanks to source proximity and spatial separation of nearby nuclear contaminants).Some sources, particularly at larger distances, appear to show little luminosity variation.However, this may be because those targets have been studied in fewer publications than famous nearby sources (e.g., the Circinus Galaxy, NGC 4945).
Figure 2 presents distance vs. line-of-sight column density from the literature for every available measurement of every source in DoCTA.Similarly to Figure 1, we find a significant range of measured line-of-sight column densities.Such a range can arise from subtle differences in the physical properties of the obscurer assumed in different models.For example, line-of-sight column density is inextricably linked to predicted intrinsic luminosity since an increase in line-of-sight column density requires an increase in intrinsic luminosity to explain the additional absorption.Alternatively, parameter differences across obscuration models can arise from how the parameters are represented in the corresponding table models used in the spectral fitting (e.g., the number of parameter grid points).A primary effect of such confusion is that a significant number of sources have published measured line-of-sight column densities both above and below the Compton-thick limit (horizontal dashed line) to 90% confidence.Such uncertainty can clearly have fundamental model-dependent effects on measurements of the Compton-thick AGN abundance, for example.A subset of the DoCTA sources are known Changing-Obscuration AGN (Ricci and Trakhtenbrot, 2022), in which the line-of-sight column density varies both below and above the For most sources the reported luminosities vary over one to two orders of magnitude, in some extreme cases over three orders of magnitude.The colour coding is used to distinguish between different sources, and does not correspond to a physical parameter.
Compton-thick threshold (e.g., NGC 1358; Marchesi et al. 2022).However, Compton-thick Changing-Obscuration events are currently observationally rare meaning that the wide range in line-of-sight column densities are not expected to be dominated by Changing-Look AGN.
A large number of different model prescriptions for the obscuration-based reprocessed spectrum in AGN are available in the literature today as well as different bespoke setups that incorporate those models.A prime example of the latter is the use of decoupled models, in which the global average properties of the reprocessor are decoupled from the reprocessing effects along the line-of-sight (see Yaqoob 2012 for an detailed review of such techniques).On the practical side, decoupled model fitting often improves the fit due to the larger range of spectral shapes attainable.On the theoretical side, it can be interpreted as flux variability, or line-of-sight column density variations arising from a clumpy obscurer.As such, decoupled model setups can often include an overall scaling of the intrinsic continuum relative to the reprocessed one.LaMassa et al. ( 2019) have shown the effect of manually altering the contribution from reprocessing in the broadband spectral fitting of NGC 4968, finding that an increase in reprocessed flux corresponds to an overall decrease in intrinsic continuum flux, as expected.
Many obscured AGN are variable in hard X-rays (e.g., Torres-Albà et al. 2023), including bright Comptonthick AGN (e.g., Puccetti et al. 2014;Marinucci et al. 2016;Marchesi et al. 2022).To understand the high-energy (E > 10 keV) spectral constraints for the DoCTA population, and to qualitatively understand the possibility of variability impacting the ranges shown in Figures 1 & 2, we extracted all archival  1, apart from the reported line-of-sight column density is shown on the vertical axis.The Compton-thick threshold adopted for this work is shown with a horizontal dashed line.The large range between reported line-of-sight log N H values per source in the Compton-thick regime highlights the challenge with current models to constrain the upper boundary of column density for Compton-thick AGN.The large range is due to modelling degeneracies remaining in low signal-to-noise ratio hard X-ray data and variability in time relative to the complementary soft X-ray observations.Both issues will be directly addressed with HEX-P.
NuSTAR data available per source with > 10 ks of net exposure time in both FPMA and FPMB.While intra-observation variability is not unheard of in Compton-thick AGN (e.g., Puccetti et al. 2014), it is currently rare in the literature, so we choose to extract epoch-averaged spectra.The NuSTAR data for both FPMA and FPMB were processed using the NuSTAR Data Analysis Software package within HEAsoft.The task nupipeline was used to generate cleaned event files.Spectra and corresponding response files were generated using nuproducts with circular source regions of 20 pixels (∼49") and background regions as large as possible on the same detector as the target.Each spectrum was then binned using the optimal binning scheme of Kaastra and Bleeker (2016).
Figure 3 presents residuals in the form of (data -model) / error for every extracted NuSTAR spectrum after fitting a simple zcutoffpl model in PyXspec to only the first observed spectrum per source in the 3 -78 keV band.The figure is organised vertically into bins of NuSTAR/FPMA 3 -78 keV signal-to-noise ratio, increasing from the bottom to top row.A number of interesting features are visible from Figure 3. Firstly there is a large diversity in shapes of the Fe K complex (rest frame 6.4 keV is marked with a vertical line in each panel) and Compton hump across the sample.A number of factors can contribute to observed spectral diversity in heavily obscured AGN, whether it be from contamination in the Fe K band and softer energies (E ≲ 8 keV) arising from competing spectral components (e.g., Annuar et al. 2015;Reynolds et al. 2015;Farrah et al. 2016;Gandhi et al. 2017) or due to the structure of the obscurer itself at E ≳ 8 keV (e.g., Buchner et al. 2019Buchner et al. , 2021)).As noted by Bauer et al. 2015, it is physically unlikely for a single column density obscurer to surround AGN and a plausible alternative could be a continuous distribution of obscurers with varying column densities and other geometric parameters, consistent with Galactic molecular cloud studies (e.g., Goodman et al. 2009).
Most of the highest signal-to-noise ratio Compton-thick AGN on the top row of Figure 3 display significant spectral variability with NuSTAR (Puccetti et al., 2014;Marinucci et al., 2016;Marchesi et al., 2022;Kayal et al., 2023).Only a small number of targets have been selected for NuSTAR follow-up because of known variability; with sufficient sensitivity, repeated observations of others may well show that obscurer-based variability is ubiquitous amongst Compton-thick AGN.For the remainder of the DoCTA population, there are either insufficient NuSTAR epochs to search for variability (see panels with N obs = 1 in the figure) or the visual difference in the observed reflection spectra is small.Furthermore, the lowest third of DoCTA sources in terms of signal-to-noise ratio have insufficient data quality to reveal any spectral variability in detail (see Section 4 for further discussion).
HEX-P is optimised in many ways to guide the future development of X-ray spectral models.First, the improved broadband sensitivity achieved by reducing the background level will result in a significant improvement in the observed signal-to-noise ratio for the bulk of the Compton-thick AGN population present in DoCTA.Such improvements will fundamentally decrease the number of possibilities for nonunique spectral fits in which parameter posteriors are significantly different.Second, the extended range of the LET to energies > 10 keV means that there will be three instruments in total providing sensitive spectra over the energy range corresponding to the inflection point of the Compton hump.Detailed spectral modelling of Compton hump diversity is currently an under-used resource for constraining the covering factor of material with different column densities surrounding the central engine (e.g., Buchner et al. 2019).Lastly, the simultaneous broadband focusing capabilities of HEX-P are a novel concept amongst previous, current and future planned X-ray missions.Broadband coverage removes any possible issues that can arise from variability or significantly mis-matched data quality in the soft and hard X-ray bands.

DEVELOPING NEXT-GENERATION MODELS OF THE CIRCUM-NUCLEAR ENVIRONMENT
All physical obscurer models feature multiple geometric degrees of freedom that are unique to the geometry assumed (e.g., some combination of line-of-sight column density, global obscurer column density, inclination angle, covering factors, etc.).However, the relative importance for each parameter in a given model fit is often non-trivial with many inter-parameter dependencies and multi-modal solutions to consider.Studies of the obscuration properties of AGN have shown that the covering factor is related to the Eddington-scaled accretion rate (e.g., Fabian 1999;Fabian et al. 2008;Ricci et al. 2017c), meaning that the geometry of the obscurer may be inherently related to the intrinsic properties of the central engine itself.
An optimal sample of AGN to observe in X-rays for the development of future obscuration models would hence include (1) Compton-thick obscuration to ensure the reprocessed emission dominates the observed spectrum, (2) known inclination to remove a geometrical degree of freedom, and (3) precise measurements of black hole mass and multi-wavelength coverage to provide an independent estimate of Eddington-scaled accretion rate.
Disk megamasers satisfy all three criteria.The 22 GHz radio emission line emitted by water vapour is produced by maser amplification10 , and requires highly inclined sight lines to be detected (e.g., Zaw et al. 2020).In agreement with the unified model of AGN (Antonucci, 1993;Urry and Padovani, 1995;Netzer, Figure 3. Every Compton-thick AGN in DoCTA confirmed by NuSTAR.Each panel plots the relative residual for a simple cutoffpl fit to each NuSTAR spectrum with > 10 ks of data, and is coloured by the signal-to-noise ratio in the 3 -78 keV band.2015), megamasers are thus often found in Compton-thick AGN in which highly inclined lines-of-sight lead to the highest column densities toward the central engine (e.g., Greenhill et al. 2008;Masini et al. 2016;Panessa et al. 2020).Accurate Very Long Baseline Interferometry maser mapping additionally provides one of the most precise estimates of the central black hole mass currently known, enabling accurate measurements of Eddington-scaled accretion rate as long as robust bolometric luminosity estimates are available (Brightman et al., 2016).We additionally note that under the unified model, the privileged inclination angles required for 22 GHz water megamaser detection would be purely an orientation effect, with the circum-nuclear obscurer being somewhat similar in all AGN.Thus future astrophysical surveys of megamasers may be an extremely useful tool not just for studying the circum-nuclear properties of obscured AGN, but the entire AGN population.
In the following sections, we analyse a sample of confirmed Compton-thick AGN with detected water megamaser emission as a basis for developing the next generation of physically-motivated obscuration models for HEX-P.

NuSTAR-confirmed Compton-thick megamasers
As a basis for our simulations, we selected a sample of ten Compton-thick AGN in DoCTA with confirmed 22 GHz megamaser in the literature (Masini et al., 2016;Panessa et al., 2020).We additionally included NGC 2960 from Masini et al. (2016) since the target was one of the lowest signal-to-noise ratio sources in their analysis, providing an interesting comparison for HEX-P.The sample considered is shown in Table 1.To ensure accurate spectral simulations, we then complemented the longest NuSTAR exposure per source with the closest Chandra observations in time available.Each Chandra observation was reprocessed using the chandra repro command in CIAO (Fruscione et al., 2006), before creating circular source + background and annular background-only regions centred on the target with each level 2 event file.Owing to the poorer angular resolution of NuSTAR compared to Chandra, we additionally created circular source + background regions for all clearly visible off-nuclear sources that were within the NuSTAR extraction region.Spectra and response files were then produced using the specextract command.The breakdown of the sample in terms of source properties and X-ray observations are shown in Table 1.The level of flux contaminating the NuSTAR spectra from extracted off-nuclear sources was found to be negligible compared to all AGN apart from NGC 5643.The source has a well-studied ultra luminous X-ray source that needed to be accounted for in our spectral analysis (Annuar et al., 2015).We note that at a separation of ∼ 50", the AGN and ultra luminous X-ray source would be easily resolved by the HETs and LET onboard HEX-P (see Section 5.1).
For X-ray spectral fitting, we use BXA v2.9 which connects the PyMultiNest nested sampling algorithm (Feroz et al., 2009;Buchner et al., 2014) to the Python wrapper for the X-ray spectral fitting environment Xspec (Arnaud, 1996).We chose to fit each AGN component with the UXCLUMPY model and its associated omni-directional Thomson scattered emission table.Since we primarily require a good enough description of the observed Chandra + NuSTAR spectra to perform HEX-P simulations, we did not test additional physically-motivated models.UXCLUMPY does however include two unique geometrical parameters that describe the covering factor of material in the obscurer; TORsigma, the angular dispersion of the cloud distribution and CTKcover, the covering factor of an additional inner ring of Compton-thick clouds surrounding the AGN.Our spectral model for the AGN in Xspec parlance was as follows: We assumed non-informative priors for line-of-sight column density, intrinsic power-law exponential cut-off, intrinsic power-law normalisation, the omni-directional scattered fraction, Compton-thick inner ring covering factor, cosine of the obscurer dispersion, thermal soft-excess temperature and its associated normalisation.For the intrinsic power-law photon index, we assumed a Gaussian prior with mean 1.8 and standard deviation 0.15 in agreement with numerous X-ray surveys (e.g., Ricci et al. 2017b).Finally for cross-calibrations between Chandra and FPMB relative to FPMA we assumed log-Gaussian priors with mean 0 and standard deviation 0.03, consistent with the values of Madsen et al. (2015).In total, there were 11 free parameters in the UXCLUMPY AGN model.We find all sources to have column densities in excess of 10 24 cm −2 to 90% confidence.Interestingly, this includes NGC 2960 for which we find a line-of-sight column density solution of N H > 1.5 × 10 24 cm −2 to 98.2% confidence by fitting the combined Chandra and NuSTAR data.Previous works that analysed the NuSTAR data alone consistently found N H < 10 24 cm −2 using the MYtorus obscuration model (Masini et al., 2016).Due to our Compton-thick solution, we include NGC 2960 in DoCTA ex post facto.Figure 3 shows that the NuSTAR spectra of NGC 2960 are amongst the lowest signal-to-noise in the 3 -78 keV band of all other Compton-thick AGN studied with NuSTAR to date.Its low signal-to-noise ratio spectrum thus makes NGC 2960 a challenging and very conservative example to showcase the spectral constraints attainable with HEX-P.

Simulating the Faint Megamaser NGC 2960
We simulate a grid of NuSTAR and HEX-P/HET×2 + LET spectra to quantify the relative improvement in physical parameter inference attainable with HEX-P observations of NGC 2960.Whilst the Compton-thick solution for NGC 2960 that we report here was acquired with the inclusion of Chandra data, we restrict our simulations to purely NuSTAR due to the relative scarcity of simultaneous observations publicly available (see Figure 6) and as an extrapolation for the discovery space in hard X-rays of new Compton-thick AGN previously missed.In total, we simulate a range of exposures between 10 ks and 100 ks with ten realisations per exposure.Each simulated spectrum had the same starting spectrum -namely the maximum a posteriori spectral fit acquired with Chandra + NuSTAR.However, we additionally increased the obscurer dispersion to 60 • and Compton-thick inner ring covering factor to 30% to provide a more substantial covering factor of material to simulate.
The results of the NGC 2960 simulation grid are shown in Figure 4 in terms of 90% posterior parameter constraints on Eddington ratio (top panel) and line-of-sight column density (bottom panel) as a function of exposure time.For Eddington ratio error propagation, we sample from the black hole mass and associated uncertainties in Table 1.However, for the bolometric correction we use the Compton-thick bolometric correction from Brightman et al. (2016) that focused on Compton-thick megamasers.To focus on the improvements attainable purely from X-ray spectral fitting as opposed to other systematics, we assume zero uncertainty on bolometric correction.We justify this choice by assuming the plethora of next-generation multi-wavelength observatories that are coming online over the next decade that will provide precise photometric data across the electromagnetic spectrum for accurate measurements of bolometric output.
Even for the low signal-to-noise ratio challenge that NGC 2960 poses, HEX-P is able to achieve Eddington ratio uncertainties comparable to the uncertainties on black hole mass for exposures ≳ 30 ks.In contrast, NuSTAR does not reach a similar uncertainty regime for the entire range of exposures considered in the simulations.HEX-P is additionally able to classify the target as Compton-thick to 90% confidence for exposures ≳ 25 ks -a feat that is not possible from purely NuSTAR spectroscopy in our simulated range of exposures.We note that the remaining posterior uncertainty above the Compton-thick limit at all exposures with HEX-P arises from the stability of the Compton-scattered component in UXCLUMPY.The overall shape of the reprocessed component does not change substantially for line-of-sight column densities N H ≳ 5 × 10 24 cm −2 , such that constraining line-of-sight column densities to more than a lower limit is currently difficult.The top axes of Figure 4 shows the measured signal-to-noise ratio in the 10 -25 keV band for NuSTAR and HEX-P.The reduced background and simultaneous coverage from three different instruments is able to boost the signal-to-noise ratio by factors of ∼ 4 relative to that of NuSTAR.In the case of NGC 2960, the boost in observed signal-to-noise ratio means that a 10 ks exposure with HEX-P would require ≫ 100 ks of NuSTAR exposure to reach an equivalent 10 -25 keV spectral quality.The 10 -25 keV energy band holds a plethora of information, not only regarding the line-of-sight column density but also the overall structure of the circum-nuclear obscurer (see e.g., Buchner et al. 2019Buchner et al. , 2021)).HEX-P is able to constrain the intrinsic luminosity, and hence accretion rate, to comparable precision of the black hole mass for exposures ≳ 30 ks.The top axes show the average measured signal-to-noise ratio in the 10 -25 keV band for NuSTAR and HEX-P, which is found to be ∼ 4× higher than NuSTAR on average.

Prospects for a New Era of Spectral Models
From the signal-to-noise ratio improvements highlighted in Figure 4 and the exceedingly low signal-tonoise ratio of the NuSTAR data for NGC 2960, it is clear that every known Compton-thick AGN will benefit greatly from modest HEX-P observations.Next we simulate our sample of Compton-thick megamasers for 100 ks with both NuSTAR and HEX-P to visually showcase the spectral improvements attainable, which will allow the development of next-generation spectral models.In Figure 5 we present a like-for-like comparison between NuSTAR (left column) and HEX-P (right column), ordered from bottom to top by observed 2 -10 keV flux.A number of crucial improvements are visible.
Hard X-ray Sensitivity: Whether it be due to the overall spectral slope, high-energy cut-off, structural properties of the obscurer or some combination of each, every AGN has a very distinctive spectral shape > 10 keV that is clearly detected with HEX-P.In contrast, a large number of the simulated NuSTAR spectra are not well-detected ≳ 20 keV.These improvements offer a number of useful avenues for model constraints and development.(1) Extending the range of detectable energies to ≳ 50 keV with HEX-P will enable a dramatic reduction in confusion arising from different model components.For example, the high-energy exponential cut-off associated with the intrinsic coronal emission can be extremely difficult to disentangle from the turnover of the Compton hump (e.g., Baloković et al. 2019;Kammoun et al. 2023).Furthermore the covering factor is very dependent on Compton hump shape, and reducing the measurement uncertainties ≳ 20 keV will greatly advance our ability to detect it.
Spectral Resolution: From Figure 5, it is clear that the spectral resolution arising from the LET is superior to that of NuSTAR.By combining high spectral resolution measurements of the Fe K region (including the Fe Kα and Fe Kβ lines) with sensitive measurements of the underlying reflection continuum up to energies ≳ 20 keV will enable detailed studies of fluorescence emission in heavily obscured AGN, including metallicities, dynamics and emission origins.
Simultaneous Soft X-ray Coverage: Figure 5 clearly shows the vast range in predicted spectral shapes from our broadband Chandra + NuSTAR fitting that are not accessible with NuSTAR.Whilst quasi-simultaneous soft X-ray coverage is a common strategy for NuSTAR observations, exposure times and corresponding signal-to-noise ratios are often not consistent across instruments (see Figure 6), leading to discrepant measurements of line-of-sight column density (e.g., Marchesi et al. 2018).With HEX-P, well-matched sensitivities with 100% observing simultaneity will enable broadband X-ray spectral fitting effectively devoid of mismatched signal-to-noise ratio issues.

UNCOVERING THE DYNAMICS OF THE THICKEST OBSCURERS
Multi-epoch X-ray observations have proven to be a powerful tool for constraining the structure and dynamics of the obscurer.The ability to determine the amount of obscuring material along the line-of-sight as a function of time can be used to place constraints on the sizes of obscuring clumps as well as their distance from the supermassive black hole (e.g., Elvis et al., 2004;Risaliti et al., 2009;Markowitz et al., 2014).Even for sources with sparsely-sampled light curves, changes in line-of-sight column density as a function of time can be used to gain insight into the general scales associated with the obscurer (e.g., Laha et al., 2020).
Since the launch of NuSTAR, broadband X-ray coverage has allowed the use of complex reflector models, which in turn can constrain global properties of the obscurer such as obscuring covering factor (parameterised as the fraction of sky covered when viewed from the perspective of the corona), inclination angle, and the global obscuring column density out of the line-of-sight; (e.g., Baloković et al., 2018;Marchesi et al., 2019b;Buchner et al., 2019;Baloković et al., 2021;Zhao et al., 2021).Some works have suggested a correlation between the global properties of the obscurer and the characteristic change in line-of-sight column density as a function of timescale (e.g.Pizzetti et al., 2022;Torres-Albà et al., 2023).An advantage of multi-epoch fitting is that parameters unexpected to vary over the relatively short timescales associated with the observations (e.g., the obscurer covering factor, or global obscurer column density out of the line-of-sight) can be tied across observing epochs.Such an approach typically leads to more precise constraints on obscurer parameters since there are typically fewer regions of the parameter space compatible with multiple spectra than a single epoch-averaged spectrum (see e.g., Baloković et al. 2018;Pizzetti et al. 2022;Marchesi et al. 2022;Torres-Albà et al. 2023).
HEX-P, with its capability to simultaneously observe the soft and hard X-ray bands to greatly improved sensitivity limits, will prove a key instrument for time domain studies (e.g., Brightman et al. 2023), including the time-resolved characterisation AGN obscuration in X-rays.Non-simultaneous soft and hard band observations impose significant difficulty in disentangling intrinsic coronal luminosity variability from obscuration-related variability.For example, Torres-Albà et al. ( 2023) found that for ∼57% of 12 nearby obscured AGN with confirmed long-term X-ray variability.However the two variability options could not be distinguished due to non-simultaneous soft and hard X-ray observations.
With the results of Torres-Albà et al. ( 2023) in mind, we sought to assess the current availability of multi-epoch broadband X-ray observations amongst the obscured AGN population.We queried the High Energy Astrophysics Science Archive Research Center11 for targeted NuSTAR observations of any AGN in the 70-month BAT catalogue with line-of-sight column densities N H > 10 22 cm −2 according to the X-ray spectral fitting catalogues of Ricci et al. (2017b).We then searched for soft X-ray coverage from any of XMM-Newton, Swift/XRT, or Chandra for each of the 372 obscured AGN with NuSTAR observations available (439 NuSTAR observations in total).Figure 6 quantifies the frequency of joint soft + NuSTAR observations in the obscured AGN sample as a function of ever-increasing hard X-ray observation simultaneity window.To be conservative, we consider any NuSTAR observation with > 20% of its total exposure with joint soft exposure within each considered time window to be 'joint'.Even by liberally considering the non-simultaneous scenario of soft observations within one year of the NuSTAR observations, only ∼ 25% have > 20% of their exposure coincident with NuSTAR exposure.We additionally note that having considerably different NuSTAR and soft X-ray exposure times can give rise to dramatically different data quality across the spectral passband.Data quality mis-matches have been shown to influence measurements of obscuration parameters in heavily obscured AGN (e.g., Marchesi et al. 2018;Tanimoto et al. 2022.HEX-P will clearly revolutionise the field, providing 100% strictly simultaneous broadband coverage for all observations.
In the sections that follow, we quantify the advances HEX-P will make towards multi-epoch observations of obscured AGN with detailed simulations.

Case study I: Non-Compton-thick Obscured AGN
First we consider an obscured but not Compton-thick AGN (line-of-sight N H ≲ 10 24 cm −2 ) which presents both intrinsic luminosity and line-of-sight obscuration variability over three epochs of observation.To make our simulations conservative, we normalise the source flux to NGC 835 -the faintest AGN in the sample of Torres-Albà et al. (2023) with confirmed line-of-sight column density variability.We Figure 6.The percentage of hard X-ray observations with overlapping soft X-ray exposure available for NuSTAR vs. HEX-P.To be conservative, in each time window (shown along the horizontal axis) we consider any hard X-ray observation with > 20% of its total exposure overlapping with a soft X-ray observation to be 'joint'.Archival NuSTAR observations were considered for any Swift/BAT AGN from the 70-month compilation of Ricci et al. (2017b) obscured with line-of-sight column density N H > 10 22 cm −2 .Clearly, the complimentary data provided by the LET + HETs onboard HEX-P will, for the very first time, provide complete simultaneous coverage across the hard and soft X-ray bands.
parameterise the obscurer with the borus02 model (Baloković et al., 2018) in decoupled mode, in which the obscurer properties were tuned to match the properties derived by Zhao et al. (2021) for a sample of ∼ 100 obscured AGN.We simulate and fit with the same model to avoid any systematic uncertainties associated with the a-priori unknown obscurer that could be more dramatic for the less sensitive NuSTAR data than HEX-P (i.e.fewer model spectra can accommodate a given HEX-P spectrum than NuSTAR with reduced sensitivities and passband -see e.g., Saha et al. 2022).We consider three different line-of-sight column densities, namely N H = 1, 3, 6 × 10 23 cm −2 .To model additional flux variability, we include a cross-normalisation constant to the intrinsic AGN emission to simulate 50%, 100% and 200% flux variability for each of the three observational epochs, respectively.We then pair line-of-sight column densities with different flux variability constant values per observational epoch such that the observed fluxes remain as similar as possible -e.g., the lowest obscuration with the highest intrinsic luminosity, etc.We then run spectral simulations of 20 ks exposure times with NuSTAR and HEX-P before re-fitting to quantitatively compare each mission's ability to disentangle the two separate forms of variability we consider.
Figure 7 shows the results of our simulations.The left panel presents the simulated HEX-P spectra, in which the variations in column density from the photo-electric turnover and intrinsic flux from the overall normalisations are clearly visible.The right panel shows the resulting constraints in terms of intrinsic flux and line-of-sight column density for both HEX-P and the equivalent simulated NuSTAR spectra.Overall we find uncertainties ∼ 3 -4 times larger with NuSTAR than with HEX-P.The NuSTAR constraints can only place upper limits on the lowest line-of-sight column density scenario we considered, primarily due to its lack of simultaneous soft-band coverage encompassing the photo-electric turnover at soft energies.At higher column densities, the remaining two scenarios are consistent within 99% confidence in terms of both line-of-sight column density constraints and intrinsic flux.In contrast, even for a short 20 ks snapshot HEX-P has no issue in disentangling intrinsic flux variability from line-of-sight column density variability for the full range of column densities considered.The broader passband is crucial, enabling proper characterisation of obscuration changes visible through the photoelectric turnover that are degenerate with intrinsic flux changes at harder energies.

Case study II: Compton-thick AGN
As discussed in Section 1, there have been comparatively few detailed multi-epoch broadband spectroscopic studies of Compton-thick AGN to date, and are dominated by the brightest sources known (e.g., Puccetti et al. 2014;Marinucci et al. 2016).An additional limitation with observing variability in Compton-thick AGN is that eclipsing events or intrinsic flux variations are more likely to manifest at ≳10 keV, where the effects of photoelectric absorption are reduced and Compton scattering dominates providing excess detectable flux (e.g., Marinucci et al. 2016;Zaino et al. 2020).The improved sensitivity at >10 keV with HEX-P will lead to new insights into broadband variability characteristics of Compton-thick AGN that have not been possible to date.To simulate the prospects attainable with HEX-P, we use the faintest Compton-thick AGN with a published multi-epoch NuSTAR-based campaign to date as a baseline.The nearby Seyfert 2 galaxy NGC 1358 (z = 0.0134) was subject to a multi-epoch monitoring campaign with NuSTAR and XMM-Newton between 2017 -2022, and was found to be highly variable in line-of-sight column density by Marchesi et al. (2022).
For our HEX-P simulations we use decoupled borus02 and choose a range of line-of-sight column densities consistent with those measured for NGC 1358 by Marchesi et al. (2022) which varied above and below the Compton-thick limit in a changing-look scenario.The specific line-of-sight column densities we considered were N H = 0.8, 1.4, 2×10 24 cm −2 .To make our simulations applicable to the wider AGN population we choose a value of Γ = 1.8, consistent with the broader population of lowredshift Seyfert galaxies (e.g., Ricci et al. 2017b).The Thomson-scattered flux fraction is set to 2%, which is again conservative considering the latest relations between scattered fraction and line-of-sight column density from Gupta et al. (2021).We additionally include a thermal apec component (with temperature kT = 0.3 keV) to model the remaining soft excess flux that the Thomson-scattered power-law does not account for.The global obscuring column density out of the line-of-sight is assumed to be N H = 3.2×10 23 cm −2 with a covering factor of 15% within the borus02 model.
We simulate one 30 ks HEX-P observation for each line-of-sight column density state mentioned above.The line-of-sight column density is recovered to high accuracy with relative uncertainties ≤ 20%.Owing to the strong advantage of linking parameters that are not expected to vary between epochs, the global column density is precisely recovered with uncertainties < 0.3 dex, and the obscuration covering factor is correctly found to be < 20% to high confidence.Our simulations thus clearly show that a HEX-P monitoring campaign would allow us to characterise the properties of the clumpy obscuring medium in heavily obscured AGN with unprecedented quality to far fainter flux levels than are attainable with current X-ray observatories.Such capabilities are critical for constraining the dynamics of the obscurer in the wider Compton-thick AGN population that is currently impossible.

THE CIRCUM-NUCLEAR OBSCURER OF AGN AT LOW ACCRETION POWER
Our knowledge of the obscurer surrounding low accretion power AGN is currently severely incomplete.A root cause is the considerable challenge to select and classify true low accretion power AGN, especially at high line-of-sight column densities.NuSTAR has provided an unprecedented view into the hard X-ray properties of the circum-nuclear environment of low-luminosity AGN for the first time (Ursini et al., 2015;Annuar et al., 2017;Young et al., 2018;Younes et al., 2019;Annuar et al., 2020;Diaz et al., 2020;Baloković et al., 2021;Diaz et al., 2023).NuSTAR has also led to the discovery and classification of a few low-luminosity Compton-thick AGN (e.g., Annuar et al., 2017;Brightman et al., 2018;Da Silva et al., 2021), providing exciting evidence suggesting AGN can sustain a significant obscuration structure at low luminosities.However current observational studies of Compton-thick low-luminosity AGN are often hindered by the requirement for deep integration times to obtain sufficient counts for detailed X-ray spectral modelling (e.g., Annuar et al., 2020).
Given the current scarcity of bona-fide low-luminosity Compton-thick AGN confirmed by broadband X-ray studies including hard X-ray observations with NuSTAR, we sought to investigate the prospects attainable with HEX-P for identifying, classifying and studying this elusive population in the nearby Universe.We tuned our simulations to the properties of four bona-fide low-luminosity AGN with heavy obscuration in the literature; M 51a (Brightman et al., 2018), NGC 660 (Annuar et al., 2020), NGC 1448 (Annuar et al., 2017) and NGC 2442(Da Silva et al., 2021).We note all sources have column density classifications based in part with NuSTAR.Also, all are confirmed Compton-thick apart from NGC 660 which has both Compton-thick and sub-Compton-thick (but still heavily obscured) solutions in Annuar et al. (2020).With this in mind, for the remainder of this Section, we refer to this sample of four sources as the low-luminosity Compton-thick AGN sample.

Selecting and classifying low-luminosity Compton-thick AGN
A major challenge for studies of low-luminosity AGN is confidently associating detected sources with accretion onto a supermassive black hole, as opposed to off-nuclear accretion onto lower-mass compact objects such as ultra luminous X-ray Sources, other individual X-ray binaries or jetted emission (see Bachetti et al. 2023;Lehmer et al. 2023;Connors et al. 2023;Marcotulli et al. 2023 for the HEX-P perspective on ultra luminous X-ray sources, other extragalactic accreting compact objects and resolved AGN jets).A major advantage arises from spectral coverage at ≳ 10 keV in which the spectral curvature from accreting supermassive black holes can be dramatically different from that of lower-mass accreting compact objects.However, an additional difficulty with classification is being able to resolve emission components into individual sources to confidently ascertain the spectral parameters of the central AGN.Given the dramatic improvement in X-ray angular resolution of HEX-P compared to both XMM-Newton and NuSTAR, we sought to test HEX-P's ability to resolve contaminating sources in the host galaxy from low-luminosity AGN.
We base our simulations on the central region of M 51 which is known to host a Compton-thick lowluminosity AGN as well as a number of bright off-nuclear X-ray sources (Brightman et al., 2018).Our main consideration here was that of 'ULX-3', which is situated ∼ 30" from the central AGN and is the closest spatial contamination of all four sources in the Compton-thick low-luminosity AGN sample.Though spatially resolved with Chandra, the close separation led to strong contamination with NuSTAR which must be accounted for by simultaneously fitting both datasets to infer spectral parameters of the central AGN and ULX-3.
To demonstrate HEX-P's unique capability to spatially-resolve closely separated sources in both the soft and hard X-ray energy bands, we compare current constraints from Chandra and NuSTAR to that of HEX-P with simulations.We simulate HEX-P soft (< 10 keV) and hard (> 10 keV) X-ray imaging of M 51a and the nearby ultra luminous X-ray source (ULX-3, Brightman et al., 2018) using the Simulated Observations of X-ray Sources (SOXS ZuHone et al., 2023) and Simulation of X-ray Telescopes (SIXTE Dauser et al., 2019) software suites.We rely upon SOXS for creating SIMulated inPUT (SIMPUT) files, which incorporates our spectral and spatial models for individual targets.For simplicity, we choose all emission to have energies > 2 keV, in order to exclude any softer extended X-ray emission from the simulation and to enable a more direct study of the resolving power of HEX-P.
We used point source models to simulate the spatial morphology of M 51a and ULX-3.For spectral modelling, we fit the Chandra spectra for M 51a and ULX-3 simultaneously with the unresolved NuSTAR spectrum of both sources using the same UXCLUMPY-based model described in Section 3 combined with the ultra luminous X-ray source model used to fit NGC 5643.We allow the AGN model to vary for the M 51a Chandra spectrum and combined NuSTAR spectrum and vice-versa for ULX-3.The individual AGN and ULX-3 maximum a-posteriori models found with BXA were then used in conjunction with the spatial model to generate a SIMPUT file.Next, we used SIXTE to produce the telescope event files, energy-filtered imaging, and spectroscopic data products.In order to compare HEX-P's capabilities with current facilities, we also simulated event files for Chandra ACIS-S (0.1-8 keV) and NuSTAR FPMA + FPMB (3 -78 keV).
We show the simulated HEX-P / LET and HET imaging in Figure 8, juxtaposed with the simulated Chandra and NuSTAR imaging of the same sources.Despite resolving the AGN and ultra luminous X-ray source well, Chandra is only able to study the targets below 8 keV.As discussed throughout this paper, this limitation considerably restricts the ability for physical inference of the obscurer.It is also clear from the figure that while NuSTAR has access to soft (< 10 keV) and hard (> 10 keV) X-ray energies, it cannot spatially-resolve the X-ray sources well on these spatial scales.HEX-P provides a unique combination of high spatial resolution broadband observations, enabling a new era of spatially-resolved closely-separated nuclear sources.These simulations showcase the power and complementary nature of HEX-P / LET and HET imaging to provide enhanced searches of heavily obscured low-luminosity AGN in our nearby galactic neighbourhood.

The nature of the obscurer at low accretion powers
The covering factor of the obscurer at low accretion powers is currently very uncertain, due in part to the difficulty associated with selecting heavily obscured low-luminosity AGN relative to their less obscured counterparts.Here we investigate the ability of HEX-P to study the covering factor of Compton-thick AGN via detailed spectral modelling of individual sources.
To provide a firm basis for our simulations, we begin from all archival Chandra and NuSTAR data available for NGC 660, NGC 2442 and NGC 1448.For NGC 2442, there were two archival NuSTAR and two archival Chandra observations.We extracted spectra following the same criteria as throughout this paper, before manually checking for significant variability between observations.Due to a lack of strong variability, we then co-added all NusTAR / FPMA, NuSTAR / FPMB and Chandra spectra individually to provide ∼49.5 ks of total Chandra exposure and ∼112 ks of NuSTAR exposure.For NGC 1448 and NGC 660, we extract the Chandra and NuSTAR data following the methods from Annuar et al. (2017) and Annuar et al. (2020), respectively.We additionally include the same absorbed power-law model components from Annuar et al. (2017) for two off-nuclear contaminants inevitably included in the NGC 1448 NuSTAR extraction region that were resolved by Chandra.The two contaminant model components were kept frozen to their best-fit values from Annuar et al. (2017) for all fitting that involved NuSTAR.However given the results of Section 5.1, HEX-P would easily resolve these contaminants from the AGN such that any spectral simulations and corresponding fitting of HEX-P spectra only considered the AGN component in NGC 1448.
We then performed spectral modelling using the UXCLUMPY model (Buchner et al., 2019) which included emission from a clumpy obscurer, as well as soft X-ray excess emission from an omni-present warm mirror as well as a thermal component with apec.We experimented with a number of spectral fitting setups, but due to the low signal-to-noise ratio of the observed spectra, a number of unphysical parameter constraints had to be avoided.One example is the tendency for the fit to prefer a low covering-factor obscurer (i.e. the TORsigma parameter in UXCLUMPY tended towards its minimum) in exchange for a hard X-ray photon index and overall unobscured spectrum.Similar degeneracies are well documented in the literature (e.g., Brightman et al. 2015) and as such we opted to freeze TORsigma to a fiducial value of 60 • for the spectral fitting of archival data.Interestingly, the resulting parameter posteriors indicated a diversity in CTKcover between sources, suggesting a diversity in Compton hump shapes across the three sources fit here12 .From each acquired modal posterior model spectrum, we simulated corresponding HEX-P / LET and HEX-P / HET×2 spectra with 100 ks exposures before re-running the same spectral fits with TORsigma additionally left free to vary.Given the distribution of column densities assigned to clouds in the UXCLUMPY model (Buchner et al., 2019), it is difficult to parametrically calculate a covering factor for a particular cloud configuration.We instead used pre-tabulated calculations of covering factor for all material with N H > 10 22 cm −2 and N H > 10 24 cm −2 for a two-dimensional grid of TORsigma and CTKcover values.We used grid interpolation to propagate all posterior uncertainties from TORsigma and CTKcover into posteriors for both of these column density regimes.
To investigate HEX-P's ability to probe precise relations between accretion power and covering factor in Compton-thick low-luminosity AGN, we required an estimate of Eddington ratio for each target.The black hole masses we used were log M BH / M ⊙ = 7.35 ± 0.50 (Annuar et al., 2020) 13 , 7.28 ± 0.33 (Davis et al., 2014) and 6.0 +0.1 −0.5 (Annuar et al., 2017) for NGC 660, NGC 2442 and NGC 1448, respectively.We then used the bolometric correction relation determined by Nemmen et al. (2014) for low-luminosity AGN to estimate the posterior distribution on the bolometric correction.
The corresponding two-dimensional contours shown in Figure 9 give the posteriors on Eddington ratio vs. covering factor for material with N H > 10 22 cm −2 and N H > 10 24 cm −2 in the left and right panels, respectively.HEX-P spectroscopy is thus able to constrain the covering factor to within ≲ ± 20% in the lowest-luminosity Compton-thick AGN currently known.Such observations are critical to understand the presence and corresponding importance of circum-nuclear obscuration in the low luminosity regime.

AN INTERMEDIATE MASS BLACK HOLE CONFIRMED WITH MEGAMASER EMISSION
To explore the parameter space attainable with HEX-P in the search for obscured intermediate mass black holes, we start from the work of Chen et al. (2017) who selected a sample of ten low-mass AGN from the 40-month NuSTAR serendipitous survey.Of this sample, IC 750 has a confirmed 22 GHz water megamaser signature in the literature (Zaw et al., 2020) placing a tight upper bound on the central black hole mass in the intermediate mass range of M BH < 1.4×10 5 M ⊙ .As discussed in Section 3 megamasers are ideal targets for HEX-P to aid the development of future circum-nuclear obscuration models, and hence IC 750 provides an extension to the black hole mass range of known megamaser AGN.Furthermore, Chen et al. (2017) performs phenomenological X-ray spectral fitting to an ∼30 ks Chandra spectrum of IC 750, finding the source to be heavily obscured with line-of-sight N H ∼ 1.2×10 23 cm −2 .As discussed by Chen et al. (2017) and throughout this work, X-ray spectral fitting to a predominantly soft-band spectrum without sensitive broadband coverage can give rise to wide systematic uncertainties on the properties of the obscurer.
We downloaded and reprocessed all archival Chandra datasets of IC 750 using the chandra repro command available in CIAO (Fruscione et al., 2006).The level 2 event files were then used to create circular source + background and annular background-only regions centered on the target.We made sure to make the source + background regions small enough to remove as much contamination as possible from the E < 2 keV diffuse extended emission reported by Chen et al. (2017).The background regions were created to be as large as possible whilst avoiding off-nuclear sources and chip gaps.Source + background, background and response spectral files were then produced using the specextract command.
After a variety of different tests of significant spectral variability, we chose to co-add the six individual X-ray spectra using the ftool command addspec.The resulting co-added spectrum contained a net exposure of 177 ks with 441 source counts detected in the 0.5 -8 keV band (see the left panel of Figure 10).As an initial assessment of the spectrum, we fit a similar model to Chen et al. (2017); namely an absorbed power-law with an additional thermal component provided by apec and a narrow Gaussian line to represent the Fe K complex.The corresponding folded spectrum with shaded posterior and two-dimensional posterior between observed 0.5 -8 keV luminosity and Fe K equivalent width are shown in the left and right panels of Figure 10, respectively.Despite the observed (i.e.absorption-uncorrected) 0.5 -8 keV luminosity being consistent with ultra luminous X-ray sources (e.g., Earnshaw et al. 2019), the observed Fe K equivalent width is enormous with values >2 keV at >99% confidence.Such large equivalent widths are rare but not unheard of in the Compton-thick AGN population (Levenson et al., 2002;Boorman et al., 2018), and strongly indicative of a deeply buried accreting massive black hole.

Inferring the obscuration geometry with HEX-P
To provide a basis for HEX-P simulations, we next turned to physically-motivated spectral models of obscuration.To test the distinguishing power of broadband X-ray spectroscopy, we fit the existing co-added Chandra spectrum with two distinctive physical X-ray obscuration models: BNsphere (Brightman and Nandra, 2011a), representing a spherical distribution of matter and UXCLUMPY (Buchner et al., 2019), representing a clumpy distribution of matter.Despite using the BNsphere model, we include a soft X-ray excess component in both model fits that is often attributed to a small fraction of intrinsic X-ray flux escaping through less-obscured sight-lines.Though unlikely in a spherical model (i.e.there are no less-obscured sight-lines when surrounded by fully-covering obscuration), by allowing a small amount of flux to escape we approximately reproduce a leaky-sphere geometry akin to that described in Greenwell et al. (2022).Some contribution to the soft X-ray excess in obscured AGN may still come from larger scales than the circum-nuclear obscurer (see discussion in Gupta et al. 2021), such that our approximation is justified.Both physically-motivated obscurer model setups are assumed to be coupled (i.e. the line-of-sight obscuration is assumed to be the same as the global obscuration level out of the line-of-sight).
The line-of-sight column density vs. intrinsic luminosity posterior distributions from the spectral fits to the existing Chandra data are shown in the left panel of Figure 11 with light shading, encompassed by a dashed line.BNsphere and UXCLUMPY find IC 750 to have line-of-sight column density in excess of the Compton-thick limit to ∼85% and ∼99% probability14 , making IC 750 a firm Compton-thick accreting intermediate mass black hole candidate.However as shown in the right panel of Figure 11, the existing soft band Chandra spectral coverage is incapable of distinguishing the two obscuration models.This means that the true range of the intrinsic luminosity posterior we have derived from the spectral fitting spans ∼ 4 dex, and the properties of the obscurer cannot be constrained (see e.g., LaMassa et al. 2017LaMassa et al. , 2019 for more discussion on this).We next simulate HEX-P/LET and HET×2 spectra from the modal posterior parameter values derived by fitting the Chandra data, using exactly the same exposure as the co-added Chandra spectrum for both models and re-fit with BXA.The resulting posterior contours and simulated spectra unfolded with the best-fitting model posteriors are shown with transparent white contours encompassed by thick borders in the left and right panels of Figure 11, respectively.Clearly the broadband coverage provided by HEX-P is able to dramatically decrease the luminosity degeneracy of the BNsphere model fit, as well as definitively constrain the line-of-sight column density as Compton-thick.The dramatic difference between the two model fits in the right panel at energies > 10 keV is crucial, since HEX-P can not only precisely measure intrinsic luminosities and line-of-sight column densities but also distinguish between obscuration geometries.
HEX-P is hence well poised to find, classify and study the obscured accretion onto intermediate mass black holes.Gaining access to spectroscopic information of sufficient sensitivity at > 10 keV is additionally crucial to decipher genuine intermediate mass black hole accretion from other lower mass compact object accretion in the host galaxy.

THE DISCOVERY SPACE FOR COMPTON-THICK AGN
The Compton-thick population remains extremely elusive and uncertain, not just in X-ray surveys of the distant Universe but even in our nearest cosmic volumes < 100 Mpc (Ricci et al., 2015;Asmus et al., 2020;Torres-Albà et al., 2021).A big open question is the volume for which we can reliably classify AGN as Compton-thick and whether the spectral data is sufficient to constrain the morphology of the circum-nuclear Left, center and right panels correspond to exposure times of 20 ks, 100 ks and 500 ks, respectively.Across all panels, each curve shows the combination of distance (horizontal axis) and unabsorbed X-ray luminosity in the 2 -10 keV band (vertical axis) that gives an observed signal-to-noise ratio of 8 in the hard 10 -25 keV band.The simulations detailed in Figure 4 show that this requirement on signal-to-noise is sufficient to correctly classify an AGN as Compton-thick to 90% confidence.By increasing the volume for discovery and detailed study by an order of magnitude relative to NuSTAR, HEX-P will open up a new era in the pursuit of a complete AGN census.
obscurer.Here, we demonstrate the much larger search volume accessible with HEX-P than NuSTAR for the detailed study of Compton-thick AGN.
We build upon the simulations of NGC 2960 detailed in Section 3.2 and shown in Figure 4, and characterise the luminosity and distance space that can be accessed with a given exposure time.We created a large grid of spectral simulations for a Compton-thick AGN UXCLUMPY model with line-of-sight column density N H = 1.5 × 10 24 cm −2 and a ∼ 50% covering factor of material with N H > 10 22 cm −2 .We simulate spectra with 20 ks, 100 ks and 500 ks exposures for a grid of distance and unabsorbed 2 -10 keV luminosities.For each grid point, we generate ten realisations to estimate the scatter arising from statistical fluctuations.For each exposure time and each luminosity, we identify the distance out to which line-of-sight column densities N H < 1.5 × 10 24 cm −2 can be ruled out to 90% significance based on the 10 -25 keV signal-to-noise ratio (as per Figure 4).
HEX-P will double the distance out to which Compton-thick AGN can be securely discovered, over what was possible with NuSTAR.This is demonstrated in Figure 12, in three separate panels for each exposure considered.Each panel plots the unabsorbed 2 -10 keV luminosity as a function of distance.We note that for Compton-thick column densities, the corresponding observed 2 -10 keV luminosities would be ∼ 1 -2 dex lower, dependent upon the choice of spectral model.We choose a fiducial unabsorbed 2 -10 keV luminosity of 2 × 10 43 erg s −1 to define the limiting distance for Compton-thick AGN classifications in our simulations.Figure 12 shows that irrespective of exposure time, HEX-P can provide detailed spectral classifications of Compton-thick AGN to ≳ 2× the distance of NuSTAR, increasing the available volume and number of target sources by ∼ 8 -10×.Even for the shortest exposure considered of 20 ks, HEX-P would provide full characterisation of the Compton-thick AGN population with unabsorbed 2 -10 keV luminosities L 2−10 keV > 10 42 erg s −1 within 100 Mpc.This encompasses the current volume cut of the highly-complete multi-wavelength selected Local AGN Survey which predicts 362 +145 −116 AGN within the volume with 61 AGN previously unidentified (LASr; Asmus et al. 2020).
For very long exposures ≳ 300 ks, the effective volume for sensitive HEX-P spectral modelling of the Compton-thick population extends to ∼ 1 Gpc for Seyfert-luminosity AGN with unabsorbed 2 -10 keV luminosities L 2−10 keV ≳ 10 43 erg s −1 .The corresponding large accessible volume for detailed spectral modelling is testament to the vast jump in sensitivity provided by HEX-P.This will be pivotal in probing the dusty hearts of galaxies such as mergers, Ultra/Luminous Infrared Galaxies and Compact Obscured Nuclei that have been suggested to host deeply buried Compton-thick AGN (e.g., Iwasawa et al. 2011;Torres-Albà et al. 2018;Aalto et al. 2019;Ricci et al. 2021;Falstad et al. 2021;Pfeifle et al. 2023.Together with the planned HEX-P extragalactic surveys (Civano et al., 2023), and a wide array of multi-wavelength facilities, detailed studies of Compton-thick AGN will pave the way towards a complete census of black hole growth across cosmic time.

SUMMARY
In this paper, we detail many aspects of heavily obscured AGN studies performed in the literature todate with an extrapolation to the prospects attainable with the next-generation HEX-P concept.We begin by compiling an up-to-date and highly complete catalogue of Compton-thick AGN confirmed with spectroscopic fitting that incorporated NuSTAR (The Database of Compton-thick AGN, DoCTA; see Section 2).We show that there is an enormous range of measured line-of-sight column density and intrinsic luminosity for the targets, highlighting the need for improved broadband spectroscopy paired with next-generation multi-wavelength models of the circum-nuclear obscurer.
The key findings from our HEX-P simulations are as follows: • The development of future AGN models with HEX-P: with the findings of DoCTA in mind, we present an analysis of archival NuSTAR + Chandra data for ten Compton-thick megamaser AGN.Megamasers have some of the best constrained black hole masses with known inclinations that would help create physically-motivated models of the obscurer that depend on accretion power.We showcase HEX-P simulations for the faintest megamaser in our sample, finding that an exposure of 25 ks suffices to classify the target as Compton-thick to better than 90% confidence and to measure the intrinsic accretion rate precisely.
• Strictly simultaneous broadband X-ray spectroscopy: HEX-P will provide highly sensitive and strictly simultaneous X-ray spectroscopic observations in the 0.2 -80 keV passband for the first time.We show that future HEX-P monitoring campaigns of heavily obscured AGN will disentangle obscurationbased variations from intrinsic flux variations to much greater precision than is possible with current instruments.
• The nature of the circum-nuclear environment at low accretion power: It is currently extremely difficult to constrain the geometry of circum-nuclear obscuration at low intrinsic AGN power.We show that the enhanced sensitivities and angular resolution of HEX-P are essential for (1) disentangling true low-luminosity AGN from off-nuclear compact objects and (2) constraining the covering factor of the obscurer in sources with L bol ≲ 10 42 erg s −1 .
• The obscured growth of intermediate mass black holes: Current estimates of the black hole occupation fraction rely on the detection of dwarf AGN that are biased towards unobscured sources.We show detailed HEX-P simulations of one candidate Compton-thick intermediate mass AGN in the literature.We show that sensitive broadband spectroscopy from HEX-P is sufficient to not only constrain the Frontiers line-of-sight column density into the Compton-thick regime, but to differentiate between alternative physical prescriptions for the geometry of the obscurer.
• A new discovery space for Compton-thick AGN: We determine the accessible volume for accurate characterisation of Compton-thick AGN.We find the improved sensitivities provided by HEX-P will more than double the distance and increase the accessible volume by up to an order of magnitude relative to NuSTAR.

APPENDIX A. 1. Tabulated covering factors in UXCLUMPY
In Table 2, we provide the tabulated covering factors in UXCLUMPY for all material with N H > 10 22 cm −2 and N H > 10 24 cm −2 as a function of TORsigma and CTKcover.We note that for each covering factor column density boundary to apply, the nH parameter in UXCLUMPY must be above the corresponding column density boundary.The covering factors plotted as a function of TORsigma and CTKcover are shown in Figures 13 and 14, coloured by the alternative parameter respectively.(2) -Compton-thick inner ring covering factor in UXCLUMPY.(3) -Corresponding covering factor of material with N H > 10 22 cm −2 .(4) -Corresponding covering factor of material with N H > 10 24 cm −2 .The covering factors shown in columns (3) and ( 4) are only valid if the corresponding nH parameter is above 10 22 cm −2 and 10 24 cm −2 , respectively.This work made use of data from the NuSTAR mission, a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory, and funded by the National Aeronautics and Space Administration.We thank the NuSTAR Operations, Software and Calibration teams for support with the execution and analysis of these observations.This research has made use of the NuSTAR Data Analysis Software (NuSTARDAS) jointly developed by the ASI Science Data Center (ASDC, Italy) and the California Institute of Technology (USA).This research has made use of data obtained from the Chandra Data Archive and the Chandra Source Catalog, and software provided by the Chandra X-ray Center (CXC) in the application packages CIAO and Sherpa.

Figure 1 .
Figure 1.(Left) Distance vs. intrinsic (i.e.unabsorbed) 2 -10 keV luminosity reported in the literature for all local Compton-thick AGN.We only include Compton-thick classifications that included NuSTAR data in the spectral analysis.Multiple reported luminosities are connected by a vertical dashed line.(Right) Same as the left panel, with vertical bars indicating the range in best-fit luminosities for each source.For most sources the reported luminosities vary over one to two orders of magnitude, in some extreme cases over three orders of magnitude.The colour coding is used to distinguish between different sources, and does not correspond to a physical parameter.

Figure 2 .
Figure2.Left and right panels are the same as in Figure1, apart from the reported line-of-sight column density is shown on the vertical axis.The Compton-thick threshold adopted for this work is shown with a horizontal dashed line.The large range between reported line-of-sight log N H values per source in the Compton-thick regime highlights the challenge with current models to constrain the upper boundary of column density for Compton-thick AGN.The large range is due to modelling degeneracies remaining in low signal-to-noise ratio hard X-ray data and variability in time relative to the complementary soft X-ray observations.Both issues will be directly addressed with HEX-P.

Figure 4 .
Figure 4. Simulated parameter constraints for one of the faintest Compton-thick AGN candidates known; NGC 2960.Bottom panel: Line-of-sight column density posterior 90% quantile range as a function of exposure time for NuSTAR (grey hatched region) and HEX-P (orange filled region).HEX-P is able to stringently confirm the target as Compton-thick (horizontal dotted line) with a modest ∼ 25 ks exposure, which is not possible with NuSTAR alone.Top panel: same as bottom, but for constrained Eddington ratio.HEX-P is able to constrain the intrinsic luminosity, and hence accretion rate, to comparable precision of the black hole mass for exposures ≳ 30 ks.The top axes show the average measured signal-to-noise ratio in the 10 -25 keV band for NuSTAR and HEX-P, which is found to be ∼ 4× higher than NuSTAR on average.

Figure 5 .
Figure 5. Simulating the spectral prospects attainable with NuSTAR (left) and HEX-P (right) with 100 ks observations of the Compton-thick megamasers considered in this work.Both panels show the folded simulated spectra from each telescope, normalised by their respective effective areas.Clearly HEX-P offers a greatly expanded passband, with improved sensitivities up to the highest energies ∼ 80 keV and much higher spectral resolution than NuSTAR.

Figure 7 .
Figure 7. Left panel: HEX-P/LET + 2×HET spectra simulated with 20 ks exposures from the model described in Section 4.1, based on NGC 835 as a baseline.Colours correspond to the different combinations of line-of-sight column density and intrinsic flux scaling.Right panel: Corresponding 99% confidence contours between intrinsic flux scaling vs. line-of-sight column density derived from HEX-P (filled) and NuSTAR (empty).The crosses represent the best-fit values.

Figure 8 .
Figure8.Comparing the energy coverage and spatial resolution of Chandra, NuSTAR, and HEX-P for the case of M 51a and the nearby ULX-3.Each row represents Chandra, HEX-P / LET, HEX-P / HET and NuSTAR), from top to bottom, respectively.Each column represents an effective increase in observing energy passband, with left showing 2 keV < E < 10 keV, middle 10 keV < E < 25 keV and right E > 25 keV, respectively.For instruments without access to a specific energy passband, the panel is marked as 'inaccessible'.Clearly, Chandra can spatially resolve M 51a and ULX-3, but does not have access to harder X-ray energies (> 10 keV).In contrast, NuSTAR has broadband coverage (3 − 78 keV), but lacks the angular resolution to resolve the two sources.HEX-P will provide spatially-resolved measurements of M 51a and ULX-3 in both the 2 -25 keV passband with LET as well as the 2 -80 keV passband with HET.

Figure 9 .
Figure 9. HEX-P 100 ks simulation contours for NuSTAR-confirmed low-luminosity Compton-thick AGN.The posterior contours show Eddington ratio vs. covering factor for material in the UXCLUMPY geometry with Left: N H > 10 22 cm −2 and Right: N H > 10 24 cm −2 .Note due to the overall similar correlations between TORsigma, CTKcover and the global covering factors of material with N H > 10 22 cm −2 and N H > 10 24 cm −2 (see Section 8), the propagated uncertainties in global covering factor have similar shapes.Performing similar spectral fitting to archival NuSTAR + Chandra data was insufficient to break degeneracies associated with the covering factor, photon index and line-of-sight column density -see Section 5.2 for details.

Figure 10 .
Figure 10.(Left) Co-added Chandra spectrum of IC 750, fit with a phenomenological model.(Right) Posterior 2D contour between observed 0.5 -8 keV luminosity and Fe K equivalent width derived from the spectral fit shown in the left panel.

Figure 11 .
Figure 11.(Left) Posterior 2D contours between intrinsic 2 -10 keV luminosity and line-of-sight column density derived with the BNsphere and UXCLUMPY physically-motivated obscuration models.The posterior contours derived from fitting the archival Chandra data are shown with light shading bounded by a dashed line.The constraints from fitting simulated HEX-P spectra are shown with transparent white contours bounded by thick lines.HEX-P can easily constrain the target to be Compton-thick with high confidence as well as precisely measure the intrinsic luminosity of the buried X-ray corona.(Right) Simulated HEX-P spectra with posterior range derived from spectral fitting.The soft X-ray band covered by archival Chandra spectroscopy is insufficient to distinguish spectral models.In contrast, the broad passband of HEX-P encompasses stark spectral differences in the Compton hump, enabling geometrical constraints on the obscurer.

Figure 12 .
Figure 12.Sensitivity curves for the discovery and detailed study of Compton-thick AGN in hard X-rays.Left, center and right panels correspond to exposure times of 20 ks, 100 ks and 500 ks, respectively.Across all panels, each curve shows the combination of distance (horizontal axis) and unabsorbed X-ray luminosity in the 2 -10 keV band (vertical axis) that gives an observed signal-to-noise ratio of 8 in the hard 10 -25 keV band.The simulations detailed in Figure4show that this requirement on signal-to-noise is sufficient to correctly classify an AGN as Compton-thick to 90% confidence.By increasing the volume for discovery and detailed study by an order of magnitude relative to NuSTAR, HEX-P will open up a new era in the pursuit of a complete AGN census.

Figure 13 .
Figure 13.Relation between the obscurer dispersion (TORsigma) and the global covering factor of material with N H > 10 22 cm −2 (left) and N H > 10 24 cm −2 (right) in UXCLUMPY.The colourbar shows the corresponding covering factor of the Compton-thick inner ring (CTKcover).The corresponding relation assuming TORsigma to be a strict boundary to the obscurer opening is shown with a grey dashed line.

Figure 14 .
Figure14.Same as in Figure13with the horizontal axis and colourbar parameters swapped.

Table 1 .
Megamaser sample properties and X-ray observations used in this work.

Table 2 .
Tabulated UXCLUMPY covering factors as a function of TORsigma and CTKcover.