BORUS02: AGN X-ray Reprocessor Model

• BORUS02 is a physically motivated X-ray reprocessor model for AGN that separately treats the line-of-sight continuum and the torus reprocessed emission.
• Its flexible parameterization—allowing independent constraints on covering factor, inclination, and average column density—enables detailed studies of both uniform and patchy obscuration.
• The model is widely compared with MYTorus and UXCLUMPY, proving essential for interpreting spectral features such as the Compton hump and fluorescent iron lines.

Borus02, commonly styled BORUS02, is a physically motivated X-ray reprocessor model for obscured active galactic nuclei (AGN) that describes the torus-reprocessed spectrum—specifically the Compton-scattered continuum and neutral fluorescent line emission—while treating the directly transmitted line-of-sight continuum separately. In the literature summarized here, it is used primarily for broadband X-ray spectroscopy of heavily obscured and Compton-thick AGN, where strong absorption below $10$ keV, a Compton hump around $\sim 20$–30 keV, and fluorescent iron emission dominate the observed spectrum. A defining feature of the model is that the average torus column density and covering factor are free parameters that can be constrained independently of the line-of-sight column density, making the model especially useful for testing whether the obscurer is homogeneous or patchy (Marchesi et al., 2018, Kayal et al., 2023, Pal et al., 25 Sep 2025).

1. Conceptual role in obscured-AGN spectroscopy

BORUS02 is used to model the global reprocessed emission from circumnuclear cold matter in AGN. In the papers considered here, this means the component produced when the intrinsic cutoff power-law continuum is intercepted by neutral obscuring material and re-emerges as Compton-scattered hard X-rays plus fluorescent line emission. The model is therefore applied where phenomenological absorbed power laws are inadequate, particularly in reflection-dominated or heavily obscured sources. One paper describes BORUS02 as “an updated and improved version of the widely used BNTorus model,” while another emphasizes that it is well suited to broad-band studies because it can fit the torus covering factor, the torus-average column density, and the inclination, rather than assuming a fixed covering geometry (Pal et al., 25 Sep 2025, Marchesi et al., 2018).

Within this framework, BORUS02 occupies an intermediate position between more rigid smooth-torus models and explicitly clumpy prescriptions. MYTorus and BORUS02 are repeatedly treated as conceptually similar in assuming uniform-density reprocessors, but BORUS02 differs in allowing the torus covering factor to vary. UXCLUMPY, by contrast, assumes a clumpy cloud distribution and is often preferred when the discussion turns to cloud-induced variability, although several studies still rely on BORUS02 for the main quantitative constraint on global covering factor or average torus column density (Kayal et al., 2023, Sengupta et al., 2023).

A recurrent use case is the separation of two physically distinct quantities: the line-of-sight column density $N_{\rm H,los}$, which governs attenuation of the direct continuum toward the observer, and the average/global torus column density $N_{\rm H,tor}$ or $N_{\rm H,avg}$, which is inferred from the reprocessed component. This separation underlies many of the model’s astrophysical inferences, especially the interpretation of obscuring media as inhomogeneous, patchy, or clumpy when $N_{\rm H,los}$ and $N_{\rm H,tor}$ differ substantially (Zhao et al., 2020, Torres-Albà et al., 2021, Silver et al., 2022).

2. Geometry and parameterization

In the cited studies, BORUS02 assumes a uniform-density spherical distribution with conical or biconical polar cut-outs, sometimes described as a spherical reprocessor with conical cavities and sometimes as a quasi-toroidal geometry with conical polar cutouts. The model covering factor is free over the interval $0.1$–$1.0$, corresponding to torus opening angles from $84^\circ$ to $\sim 20$0, with the standard relation

$\sim 20$1

or, equivalently,

$\sim 20$2

The inclination angle is also a formal model parameter; depending on the application it is either fitted or fixed to representative values such as $\sim 20$3 for type 2 AGN and $\sim 20$4 for type 1 AGN (Kayal et al., 2023, LaMassa et al., 2023, Pal et al., 25 Sep 2025).

The most commonly discussed BORUS02 parameters are the line-of-sight column density, the torus-average column density, the covering factor, the inclination angle, the photon index $\sim 20$5, and the normalization of the illuminating continuum. Several survey-style applications reduce degeneracies by linking line-of-sight and torus-average columns or by fixing covering factor when it is unconstrained, whereas pointed broadband studies often keep these quantities decoupled specifically to test for non-uniformity (Yan et al., 2023, Kayal et al., 2024).

Quantity	Role in BORUS02-based fits
$\sim 20$6	Column density attenuating the direct continuum
$\sim 20$7 or $\sim 20$8	Average/global torus column inferred from reprocessing
$\sim 20$9 or $N_{\rm H,los}$0	Covering factor of the obscurer
$N_{\rm H,los}$1	Torus opening angle
$N_{\rm H,los}$2 or $N_{\rm H,los}$3	Observer inclination
$N_{\rm H,los}$4	Photon index of the intrinsic continuum

This parameterization is central because it allows the same source to be Compton-thin along the line of sight yet embedded in a globally Compton-thick reflector, or conversely to have a Compton-thick line of sight through a torus whose average column is smaller. Multiple studies use exactly this distinction as the basis for interpreting AGN tori as structured rather than homogeneous (Silver et al., 2022, Torres-Albà et al., 2021, Marchesi et al., 2018).

3. Spectral decomposition and XSPEC implementation

A basic methodological point across the literature is that BORUS02 does not self-consistently include the line-of-sight transmitted component inside the same additive torus table. Instead, the direct intrinsic continuum is added separately and then attenuated by explicit absorption and Compton-loss terms, usually zphabs*cabs or ztbabs*cabs acting on a cutoff power law. The BORUS02 additive table then supplies the reprocessed torus continuum plus fluorescent emission. This architecture is the practical reason why $N_{\rm H,los}$5 can be decoupled from $N_{\rm H,los}$6 (Kayal et al., 2023, LaMassa et al., 2023).

Several papers give explicit XSPEC realizations. A frequently used form is

$N_{\rm H,los}$7

where Galactic absorption is applied externally, the direct continuum is the absorbed cutoffpl, borus02 represents the reprocessed torus component, and additional lines or contamination models account for residual soft-band structure or unresolved non-nuclear sources. Other studies adopt simpler survey or broadband forms such as

$N_{\rm H,los}$8

$N_{\rm H,los}$9

or

$N_{\rm H,tor}$0

all of which preserve the same decomposition into a reprocessed torus spectrum, an absorbed intrinsic continuum, and a soft scattered or leaked component (Yan et al., 2023, Pal et al., 25 Sep 2025, Cox et al., 30 Jan 2025).

In pointed observations, the model is often embedded in a larger broadband decomposition that includes thermal plasma emission, phenomenological Gaussian lines, cross-normalization constants, and source-specific contamination components. In survey-quality applications, by contrast, the parameter space is often simplified: line-of-sight and torus-average columns may be linked, the photon index may be given a prior such as $N_{\rm H,tor}$1, and redshift may be fixed or allowed to vary within photometric bounds (Yan et al., 2023, Kayal et al., 2024).

4. Diagnostic power and comparison with related torus models

The most consistent empirical claim attached to BORUS02 is that it is valuable because it can separate global torus structure from instantaneous line-of-sight obscuration. This is particularly important for Compton-thick AGN, where the line-of-sight attenuation and the global reprocessed spectrum can imply different column densities. Multiple studies explicitly use the contrast between $N_{\rm H,tor}$2 and $N_{\rm H,tor}$3 to argue for a patchy or clumpy obscurer, or at minimum for a medium that is not well represented by a single homogeneous column density (Kayal et al., 2023, Zhao et al., 2020, Marchesi et al., 2018).

Against MYTorus, BORUS02 is repeatedly said to offer its main added value through the free covering factor and average torus column density. MYTorus in coupled mode fixes the covering factor at $N_{\rm H,tor}$4, and even in decoupled mode its geometry is more rigid. Studies that fit the same sources with both models generally report strong agreement in $N_{\rm H,tor}$5 and $N_{\rm H,tor}$6, with increasing dispersion at the highest column densities, but use BORUS02 when the scientific question specifically concerns covering factor or torus-average opacity (Marchesi et al., 2018, Sengupta et al., 2023).

Against UXCLUMPY, BORUS02 usually yields line-of-sight column densities that are broadly consistent, but the two models are not directly equivalent because their geometries differ. UXCLUMPY is often preferred for detailed discussion of clumpiness because it assumes a clumpy distribution and can include an inner Compton-thick reflector, whereas BORUS02 remains the model of choice when the goal is to quantify a global covering factor within a smooth-density framework. Several comparative papers note that BORUS02 can classify slightly more sources as Compton-thick than MYTorus or UXCLUMPY, plausibly because its more flexible treatment of covering factor and torus morphology can shift borderline cases across the $N_{\rm H,tor}$7 threshold (Pal et al., 25 Sep 2025, Sengupta et al., 2023).

In survey work, BORUS02 also functions as a probabilistic obscuration classifier. One XMM-SERVS analysis uses the posterior probability distribution of $N_{\rm H,tor}$8 from BORUS02-based Bayesian fits to define heavily obscured and Compton-thick candidates, with

$N_{\rm H,tor}$9

and classifies sources as CT candidates when $N_{\rm H,avg}$0. In that setting the model is not used merely for best-fit spectroscopy, but for posterior-based source selection, intrinsic luminosity correction, and population-level inference of obscured fractions (Yan et al., 2023).

5. Empirical applications and characteristic results

BORUS02 has been applied in pointed multi-epoch studies, targeted local-AGN campaigns, and large survey analyses. In the multi-epoch Circinus analysis covering ten epochs from 1998 to 2020, joint fits with BORUS02 yielded a low covering factor $N_{\rm H,avg}$1, opening angle $N_{\rm H,avg}$2, nearly edge-on inclination $N_{\rm H,avg}$3, and a deeply Compton-thick average torus column $N_{\rm H,avg}$4, while the line-of-sight column varied from epoch to epoch within the Compton-thick regime. That combination was interpreted as evidence for a stable global torus geometry but variable line-of-sight obscuration caused by moving clouds (Kayal et al., 2023).

The model has also been used to show that line-of-sight Compton-thickness and global Compton-thickness are not identical classifications. In NGC 6300, simultaneous multi-epoch fitting gave a Compton-thin line of sight, $N_{\rm H,avg}$5, but a Compton-thick average torus column $N_{\rm H,avg}$6, with covering factor $N_{\rm H,avg}$7. In the radio-loud quasar 3C 223, BORUS02 found a Compton-thin line of sight $N_{\rm H,avg}$8 but a higher average torus column $N_{\rm H,avg}$9, although the fit required an unusually large scattered fraction, which the authors took as evidence for missing physics beyond the standard template (Sengupta et al., 2024, LaMassa et al., 2023).

In local hard-X-ray selected samples, BORUS02 has been used to derive broader statements about torus populations. An unbiased NuSTAR study of obscured AGN reported an average covering factor $N_{\rm H,los}$0 and argued that Compton-thin and Compton-thick AGN may share similarly Compton-thick average tori, with the observed distinction arising because they are seen through under-dense or over-dense regions. A separate systematic study of 35 nearby CT candidates measured covering factors directly and found that low-$N_{\rm H,los}$1 sources have, on average, larger offsets between $N_{\rm H,los}$2 and $N_{\rm H,los}$3 than high-$N_{\rm H,los}$4 sources, linking low covering factor to a “patchy torus” scenario (Zhao et al., 2020, Marchesi et al., 2018).

BORUS02 has also been deployed in moderate-count and survey-quality settings. In dust-obscured galaxies, it provided obscuration estimates broadly consistent with absorbed power-law fits but was preferred because it includes Compton scattering and reprocessing self-consistently; in that sample the BORUS02-derived $N_{\rm H,los}$5 values spanned $N_{\rm H,los}$6 to $N_{\rm H,los}$7, with one CT candidate. In XMM-SERVS, BORUS02-based Bayesian fitting of $N_{\rm H,los}$8 AGN yielded 22 representative CT candidates and 136 heavily obscured AGN, and the inferred CT fraction increased from $N_{\rm H,los}$9 at $N_{\rm H,tor}$0 to $N_{\rm H,tor}$1 at $N_{\rm H,tor}$2 (Kayal et al., 2024, Yan et al., 2023).

6. Limitations, caveats, and interpretive boundaries

A persistent caveat in the literature is that BORUS02 assumes a uniform-density reprocessor. When a source shows clear evidence of cloud-induced variability or structurally distinct reflecting zones, the model’s inferred covering factor and average torus column remain meaningful only within that smooth-medium assumption. Several authors therefore use BORUS02 to constrain average/global geometry but rely on explicitly clumpy models such as UXCLUMPY when discussing clumpiness in a more literal physical sense (Kayal et al., 2023, Sengupta et al., 2024).

Another important limitation is that a statistically acceptable BORUS02 fit may still encode physically implausible behavior. The 3C 223 analysis is the clearest example: the fit required a scattered fraction of $N_{\rm H,tor}$3, far above the $N_{\rm H,tor}$4–$N_{\rm H,tor}$5 usually found in AGN, and the photon index pegged at the model boundary $N_{\rm H,tor}$6. The authors therefore argued that the standard torus template was missing relevant physics, possibly extended reprocessing, an inner Compton-thick ring, or anisotropic illumination associated with the radio jet (LaMassa et al., 2023).

Parameter degeneracy is also a recurring issue. In low-count survey spectra or moderate-quality pointed observations, covering factor, inclination, and average torus column can be weakly constrained or effectively unconstrained. Many analyses respond by fixing $N_{\rm H,tor}$7, fixing $N_{\rm H,tor}$8 when the fit becomes implausibly flat, tying $N_{\rm H,tor}$9 to $0.1$0, or using simplified “BORUS02*” configurations in which geometry is frozen at representative values. These strategies stabilize $0.1$1 inference, but they reduce the model’s ability to diagnose torus geometry (Kayal et al., 2024, Cox et al., 30 Jan 2025).

A final interpretive boundary is classificatory. Several papers argue that once $0.1$2 and $0.1$3 are decoupled, the label “Compton-thick AGN” becomes ambiguous unless it is specified whether it refers to the line of sight or to the global reprocessor. BORUS02 has made that ambiguity explicit rather than resolving it away: the same source may be Compton-thin in transmission yet globally Compton-thick in reflection, or vice versa. This suggests that “Compton-thick” is not a single geometric state but a model-dependent descriptor of different parts of the obscuring medium (LaMassa et al., 2023, Silver et al., 2022).

In that sense, BORUS02 is best understood not as a complete physical theory of AGN tori, but as a flexible radiative-transfer framework that exposes the distinction between direct obscuration and global reprocessing. Its enduring significance in the recent literature lies precisely in this ability to quantify average torus structure while leaving room for the conclusion—often reached in practice—that the real circumnuclear medium is structured, anisotropic, or clumpy.