Compton-thick vs. Compton-thin States in AGN

• Compton-thick and Compton-thin states in AGN are defined by the hydrogen column density, dictating the level of X-ray obscuration and spectral appearance.
• Key spectral signatures like the Fe Kα line and Compton hump differentiate the regimes, with thick states showing a suppressed continuum and pronounced reflection features.
• Monte Carlo models, such as MYTORUS and borus02, reveal the complex, clumpy structures of the obscuring medium and help disentangle global from line-of-sight absorption.

Compton-thick and Compton-thin states are fundamental regimes describing the obscuration of X-ray sources, particularly active galactic nuclei (AGN), by interposing material characterized by its hydrogen column density, $N_{\rm H}$. This distinction governs the observed X-ray spectral properties, the accessibility of the intrinsic continuum, fluorescent line and Compton reflection features, and ultimately the census of black hole growth within galaxies. Demarcation between these regimes is set by the electron (Thomson) scattering optical depth, $\tau_T = \sigma_T N_{\rm H}$, with $\sigma_T = 6.65 \times 10^{-25}\,\mathrm{cm}^2$ the Thomson cross section. Compton-thin states are present when $N_{\rm H} < 10^{24}\,\mathrm{cm}^{-2}$ ($\tau_T \lesssim 0.66$), and Compton-thick states when $N_{\rm H} \geq 10^{24}\,\mathrm{cm}^{-2}$ ($\tau_T \gtrsim 0.66$) (Marchesi et al., 2018, Malizia et al., 2010).

1. Physical Definitions and Spectral Consequences

The line-of-sight hydrogen column density ($N_{\rm H,LOS}$) quantifies the degree of obscuration toward the nuclear X-ray source:

• Compton-thin regime: $N_{\rm H,LOS} < 10^{24}\,\mathrm{cm}^{-2}$. Below this threshold, photoelectric absorption dominates at $E \lesssim 10$ keV, with only modest Compton scattering. The observed continuum above a few keV remains detectable, possibly with a low-energy cut-off (Lanzuisi et al., 2018, Traina et al., 2021).
• Compton-thick regime: $\tau_T = \sigma_T N_{\rm H}$0. Here, $\tau_T = \sigma_T N_{\rm H}$1 and multiple Compton scatterings strongly suppress the direct continuum up to $\tau_T = \sigma_T N_{\rm H}$2 keV. The transmitted emission is either absent or highly attenuated, with the spectrum dominated by reflected/scattered emission and fluorescent line features (Marchesi et al., 2018, Piconcelli et al., 2011).

Observable signatures differ sharply:

Regime	$\tau_T = \sigma_T N_{\rm H}$3 Range	Photoelectric Cut-off	Compton Scattering	Fe K$\tau_T = \sigma_T N_{\rm H}$4 EW	Compton Hump
Compton-thin	$\tau_T = \sigma_T N_{\rm H}$5	Below $\tau_T = \sigma_T N_{\rm H}$6 keV	Weak	100–200 eV	Absent/shallow
Compton-thick	$\tau_T = \sigma_T N_{\rm H}$7	$\tau_T = \sigma_T N_{\rm H}$820 keV blocked	Strong, multi	$\tau_T = \sigma_T N_{\rm H}$91 keV	Strong, $\sigma_T = 6.65 \times 10^{-25}\,\mathrm{cm}^2$0–$\sigma_T = 6.65 \times 10^{-25}\,\mathrm{cm}^2$1 keV

The strong Fe K$\sigma_T = 6.65 \times 10^{-25}\,\mathrm{cm}^2$2 line ($\sigma_T = 6.65 \times 10^{-25}\,\mathrm{cm}^2$3 keV) arises via fluorescence, with an equivalent width (EW) typically exceeding $\sigma_T = 6.65 \times 10^{-25}\,\mathrm{cm}^2$4 keV in reflection-dominated (CT) spectra (Yaqoob et al., 2010). The "Compton hump" at $\sigma_T = 6.65 \times 10^{-25}\,\mathrm{cm}^2$5–$\sigma_T = 6.65 \times 10^{-25}\,\mathrm{cm}^2$6 keV is produced by energy down-scattering of harder photons.

2. Monte Carlo Spectral Models and Geometrical Considerations

The radiative transfer within obscuring media of AGN is modeled with physically-motivated, finite-column-density geometries:

• MYTORUS (Murphy & Yaqoob 2009): Azimuthally symmetric torus ($\sigma_T = 6.65 \times 10^{-25}\,\mathrm{cm}^2$7 half-opening), self-consistent modeling of transmitted ("zeroth-order") continuum, Compton-scattered reflection, and self-consistent Fe K$\sigma_T = 6.65 \times 10^{-25}\,\mathrm{cm}^2$8/K$\sigma_T = 6.65 \times 10^{-25}\,\mathrm{cm}^2$9 lines. "Decoupled" configuration fits $N_{\rm H} < 10^{24}\,\mathrm{cm}^{-2}$0 (direct continuum) and $N_{\rm H} < 10^{24}\,\mathrm{cm}^{-2}$1 (global mean affecting reflection/lines) independently, revealing patchiness or clumpiness (Marchesi et al., 2018, Traina et al., 2021).
• borus02 (Baloković et al. 2018): Spherical shell torus with polar cutouts, free covering factor $N_{\rm H} < 10^{24}\,\mathrm{cm}^{-2}$2, and average torus column density. Both the covering factor and global $N_{\rm H} < 10^{24}\,\mathrm{cm}^{-2}$3 impact the observed fraction of CT sources (Traina et al., 2021).

Monte Carlo calculations both resolve degeneracies between spectral curvature (photon index $N_{\rm H} < 10^{24}\,\mathrm{cm}^{-2}$4 vs. $N_{\rm H} < 10^{24}\,\mathrm{cm}^{-2}$5) and allow separate estimation of line-of-sight and global column densities. These models enable constraints on AGN geometry, covering factors, and the spatial distribution of obscuring gas (Yaqoob, 2012).

3. Variability, Patchiness, and Dual Column Diagnostics

CT and Compton-thin states are not absolute properties; patchy/clumpy torus models reveal:

• Different $N_{\rm H} < 10^{24}\,\mathrm{cm}^{-2}$6 and $N_{\rm H} < 10^{24}\,\mathrm{cm}^{-2}$7: AGN can be Compton-thin along the line of sight but globally Compton-thick, as monitored in NGC 3081 ($N_{\rm H} < 10^{24}\,\mathrm{cm}^{-2}$8, $N_{\rm H} < 10^{24}\,\mathrm{cm}^{-2}$9) or Mkn 3 ($\tau_T \lesssim 0.66$0, $\tau_T \lesssim 0.66$1) (Traina et al., 2021, Yaqoob et al., 2015). "Changing-look" phenomena, where $\tau_T \lesssim 0.66$2 transitions between thin and thick states over months, reflect cloud motion within the torus (Marchesi et al., 2022).
• Variability timescales: Transit times for obscuring clouds correspond to distances from accretion disk corona ($\tau_T \lesssim 0.66$3) to torus scale ($\tau_T \lesssim 0.66$4 pc), implying a dynamic, multi-phase, clumpy medium (Marchesi et al., 2022).
• Global vs. line-of-sight classification: Spectral fitting via "decoupled" torus models quantifies both columns, establishing true covering factors and revealing that a significant fraction of Compton-thin AGN by LOS are globally Compton-thick (Tzanavaris et al., 2021).

These complexities require both $\tau_T \lesssim 0.66$5 and $\tau_T \lesssim 0.66$6 to be measured for accurate AGN population synthesis and cosmic X-ray background (CXB) modeling.

4. Empirical Measurements and Population Fractions

Large hard X-ray surveys—Swift-BAT, INTEGRAL/IBIS, NuSTAR, and Chandra COSMOS Legacy—provide:

• Observed CT fractions: Typically $\tau_T \lesssim 0.66$7–$\tau_T \lesssim 0.66$8\% in local ($\tau_T \lesssim 0.66$9) flux-limited samples (Swift-BAT 100-month, INTEGRAL/IBIS 20–40 keV). However, correcting for hard X-ray selection bias (suppression at high $N_{\rm H} \geq 10^{24}\,\mathrm{cm}^{-2}$0) indicates intrinsic CT fractions of $N_{\rm H} \geq 10^{24}\,\mathrm{cm}^{-2}$1%–$N_{\rm H} \geq 10^{24}\,\mathrm{cm}^{-2}$2\% locally; among Seyfert 2s, up to 40–45% (Malizia et al., 2010, Ricci et al., 2016, Marchesi et al., 2018).
• Luminosity and redshift dependence: Intrinsic CT fraction diminishes with increasing AGN luminosity ($N_{\rm H} \geq 10^{24}\,\mathrm{cm}^{-2}$3=$N_{\rm H} \geq 10^{24}\,\mathrm{cm}^{-2}$4 for $N_{\rm H} \geq 10^{24}\,\mathrm{cm}^{-2}$5–$N_{\rm H} \geq 10^{24}\,\mathrm{cm}^{-2}$6, $N_{\rm H} \geq 10^{24}\,\mathrm{cm}^{-2}$7 for $N_{\rm H} \geq 10^{24}\,\mathrm{cm}^{-2}$8–$N_{\rm H} \geq 10^{24}\,\mathrm{cm}^{-2}$9). At high redshift ($\tau_T \gtrsim 0.66$01), COSMOS-Legacy finds $\tau_T \gtrsim 0.66$1 rising from $\tau_T \gtrsim 0.66$2 to $\tau_T \gtrsim 0.66$3 when rescaled to $\tau_T \gtrsim 0.66$4 (Lanzuisi et al., 2018).
• Covering factors: Compton-thick AGNs exhibit higher mean covering factors ($\tau_T \gtrsim 0.66$5) compared to less obscured AGN ($\tau_T \gtrsim 0.66$6–1.0) (Tanimoto et al., 2022). The apparent dichotomy suggests CT AGN tori are gas-rich, structurally distinct from lower-column systems.

Incompleteness due to observational biases is a dominant limitation; multiwavelength selection (mid-IR, [OIV] lines) is essential to reveal CT AGNs missed in X-ray surveys (LaMassa et al., 2019, Yaqoob et al., 2010).

5. Diagnostics: Spectral, Line, and Multiwavelength Criteria

Classification between Compton-thin and Compton-thick is achieved through:

• Fe K$\tau_T \gtrsim 0.66$7 line equivalent width (EW): EW $\tau_T \gtrsim 0.66$8–$\tau_T \gtrsim 0.66$9 eV is consistent with Compton-thin; EW $N_{\rm H,LOS}$0–$N_{\rm H,LOS}$1 eV (with strong Compton shoulder) signals CT and reflection-dominated spectra (Yaqoob et al., 2010, Piconcelli et al., 2011).
• Compton hump: A distinct upturn peaking at $N_{\rm H,LOS}$2–$N_{\rm H,LOS}$3 keV is a hallmark of CT obscuration (Lanzuisi et al., 2018, Marchesi et al., 2018).
• Reflection-dominated continuum: Flat spectral slope $N_{\rm H,LOS}$4 in $N_{\rm H,LOS}$5–$N_{\rm H,LOS}$6 keV, lack of transmitted component, and strong Fe K$N_{\rm H,LOS}$7 signal CT regimes (Piconcelli et al., 2011).
• Flux ratios (“T” parameter): $N_{\rm H,LOS}$8, with $N_{\rm H,LOS}$9 (after de-reddening) typical of CT, $N_{\rm H,LOS} < 10^{24}\,\mathrm{cm}^{-2}$0 for Compton-thin (Piconcelli et al., 2011).
• Broadband fitting: High signal-to-noise NuSTAR/XMM/Chandra spectra in conjunction with physically-motivated torus codes (MYTORUS, borus02, XCLUMPY) break degeneracy between $N_{\rm H,LOS} < 10^{24}\,\mathrm{cm}^{-2}$1 and $N_{\rm H,LOS} < 10^{24}\,\mathrm{cm}^{-2}$2, enabling robust classification (Marchesi et al., 2018, Marchesi et al., 2019, Tanimoto et al., 2022).
• Infrared/X-ray diagnostics: Despite common use of $N_{\rm H,LOS} < 10^{24}\,\mathrm{cm}^{-2}$3 as a CT proxy, MC simulations show this ratio is more sensitive to continuum slope ($N_{\rm H,LOS} < 10^{24}\,\mathrm{cm}^{-2}$4) and covering factor ($N_{\rm H,LOS} < 10^{24}\,\mathrm{cm}^{-2}$5) than $N_{\rm H,LOS} < 10^{24}\,\mathrm{cm}^{-2}$6 (Yaqoob et al., 2010).

6. Broader Astrophysical and Survey Implications

The fraction and identification of Compton-thick AGN are central for:

• CXB synthesis: CT AGN are required to account for the $N_{\rm H,LOS} < 10^{24}\,\mathrm{cm}^{-2}$7 keV CXB peak; population synthesis models adopt intrinsic CT fractions of 15–30%, in accord with bias-corrected X-ray surveys (Ricci et al., 2016, Malizia et al., 2010).
• Growth of SMBHs: Heavily obscured accretion is hypothesized as a rapid SMBH growth phase. Accurate demographics constrain both mass build-up and IR background production via reprocessing (Ricci et al., 2016).
• AGN unification: Luminosity and Eddington ratio dependencies in covering factor (declining $N_{\rm H,LOS} < 10^{24}\,\mathrm{cm}^{-2}$8 with $N_{\rm H,LOS} < 10^{24}\,\mathrm{cm}^{-2}$9 or $E \lesssim 10$0) support the "receding torus" model; transitions between CT and CTN states ( “changing look" AGN) reflect torus dynamics, cloud distributions, and feedback cycles (Marchesi et al., 2022).
• Host-galaxy properties: CT AGN at $E \lesssim 10$11 are preferentially found in merging/interacting hosts, with the merger fraction rising with both luminosity and redshift, at least a factor $E \lesssim 10$2–$E \lesssim 10$3 higher than in Compton-thin AGN (Lanzuisi et al., 2018).

Continued improvements in spectral sensitivity, multi-epoch monitoring, and physically motivated modeling are vital for progressing toward a complete census of Compton-thick and Compton-thin AGN, refining our understanding of obscured accretion, and interpreting the cosmic X-ray and infrared backgrounds.