REFLIONX: X-ray Reflection Model

• REFLIONX is an X-ray reflection model for optically thick, ionized accretion disks that computes both the reflected continuum and line emissions from a constant-density slab.
• It is implemented in spectral and timing models by convolving its rest-frame outputs with relativistic transfer kernels to account for Doppler shifts and gravitational redshift.
• Compared with models like XILLVER, REFLIONX reveals systematic differences in soft X-ray absorption and enables high-density diagnostics that affect inferred iron abundances and geometrical parameters.

Searching arXiv for recent and relevant papers on REFLIONX and its use in reflection and reverberation modeling. REFLIONX is a non-relativistic X-ray reflection model for optically thick, ionized accretion-disc material illuminated by an external continuum. In the literature summarized here, it is consistently treated as a rest-frame reflection code that computes the reflected continuum and line emission from a constant-density slab, and is then either convolved with a relativistic transfer kernel for spectroscopy or embedded in reverberation frameworks for timing analyses. Across active galactic nuclei, black-hole X-ray binaries, and neutron-star comparisons, REFLIONX functions both as a widely used baseline model and as a source of identifiable systematics relative to XILLVER-based and RELXILL-based alternatives, especially in the soft X-ray band and in high-density regimes (Khanthasombat et al., 2024).

1. Definition and physical scope

REFLIONX, in the usage described across these studies, computes the spectrum produced when a power-law X-ray continuum illuminates a constant-density, optically thick slab representing the disc surface. It includes continuum reflection, photoelectric absorption edges, fluorescent emission lines, and Compton scattering, and it is commonly described as a model for ionized reflection from a semi-infinite slab (Waddell et al., 2019). In the AGN reverberation literature, it is the reflection engine underlying kynrefrev, where it supplies the rest-frame reflection spectrum subsequently processed by relativistic transfer functions and timing calculations (Khanthasombat et al., 2024).

The model is parameterized by the ionization parameter $\xi$, iron abundance $A_{\rm Fe}$, the photon index $\Gamma$ of the illuminating continuum, and a normalization; in several applications the high-energy cutoff is fixed at $300\,\mathrm{keV}$ or represented through a tied Comptonization continuum (Waddell et al., 2019). The ionization parameter is written in the supplied studies as either

$\xi = \frac{L}{n r^2}$

or

$\xi = \frac{4\pi F_{\rm X}}{n_e},$

with the notation varying by paper but the physical meaning unchanged: $\xi$ measures the ratio of ionizing flux to gas density (Waddell et al., 2019, Jia et al., 2023, Kumar, 2024).

Several papers emphasize two structural assumptions. First, REFLIONX is based on a constant-density slab rather than a vertically stratified atmosphere (Waddell et al., 2019). Second, it is angle-averaged rather than angle-resolved, so inclination dependence is typically introduced by an external relativistic convolution such as kerrconv, relconv, or relconv_lp (Waddell et al., 2019, Tripathi et al., 2020). This differs from XILLVER-based frameworks, which are described as angle-dependent and built on a richer atomic database (Tripathi et al., 2020).

2. Implementation in spectral and reverberation models

In relativistic spectroscopy, REFLIONX is not itself a relativistic model. It is convolved with transfer kernels that impose Doppler shifts, gravitational redshift, and disc geometry. In the Mrk 478 multi-epoch analysis, the exact XSPEC construction is

$$\texttt{tbabs} \times \texttt{const\_1} \times \big[\texttt{zgauss} + (\texttt{cflux} \times \texttt{cutoffpl}) + (\texttt{const\_2} \times \texttt{cflux} \times \texttt{kerrconv} \times \texttt{reflionx})\big],$$

where cutoffpl represents the primary continuum, kerrconv supplies relativistic blurring, and const_2 encodes the reflection fraction (Waddell et al., 2019). In black-hole binary work, analogous constructions use relconv*reflionx_hd, relconv*reflionx_hdv2, or relconv_lp*reflionx_HD_nthcomp_v2, tying the illuminating continuum parameters between the direct and reflected components (Kumar, 2024, Chakraborty et al., 2021).

In reverberation studies, REFLIONX enters through public lamp-post timing codes. In kynrefrev, the workflow described in the data is: assume a lamp-post corona at height $h$ above a Novikov–Thorne disc, compute the rest-frame reflection spectrum with REFLIONX, apply relativistic ray-tracing and time delays through the KYN transfer function, integrate over soft and hard bands, and compute lag-frequency spectra from the Fourier cross-spectrum (Khanthasombat et al., 2024). In the general-relativistic spectral–timing model of Chainakun and collaborators, REFLIONX is used locally on each disc zone after computing the incident flux and local ionization, and the blurred reflected spectra are propagated to the observer to generate both mean spectra and lag-energy spectra (Chainakun et al., 2016).

The timing formalism uses

$$C(f) = S^*(f)\,H(f), \qquad \tau(f) = \frac{\arg C(f)}{2\pi f},$$

with dilution handled through the reflection fraction in each band (Khanthasombat et al., 2024). Because REFLIONX fixes the shape and relative strength of the reflected spectrum in the soft and hard bands, it directly affects the inferred reverberation lag amplitudes and the mapping between observed delays and geometry (Khanthasombat et al., 2024, Chainakun et al., 2015).

3. REFLIONX in comparison with XILLVER and RELXILL

A recurring theme is that REFLIONX and XILLVER-based models can fit similar datasets while implying different physical interpretations. The most systematic comparison is the AGN reverberation study of kynrefrev versus kynxilrev, where the only intended difference is the underlying reflection code: kynrefrev uses reflionx.mod, whereas kynxilrev uses xillverD-5.fits (Khanthasombat et al., 2024). That work attributes their timing differences chiefly to soft-band spectral differences: XILLVER is described as more absorbed below $A_{\rm Fe}$0 keV, implying a lower soft-band reflection fraction and stronger lag dilution for the same geometry (Khanthasombat et al., 2024).

The same issue appears in simultaneous spectral–timing analyses of Mrk 335. There, REFLIONX and XILLVER both fit the Fe K band and hard reverberation lags well, but they extrapolate differently below 2 keV. The authors state that the soft-excess mismatch between revb ⊗ reflionx and revb ⊗ xillver is attributable to differences in atomic data and low-energy absorption, and that these systematic differences exceed the statistical uncertainties (Chainakun et al., 2015). In that study, for a constant-density disc, REFLIONX and XILLVER yield markedly different combinations of black-hole mass and source height for otherwise similar-quality fits, reinforcing the claim that inferred geometry can be model-dependent (Chainakun et al., 2015).

Spectral fitting studies reach comparable conclusions. In Mrk 478, REFLIONX and RELXILL both fit the X-ray data statistically well, but REFLIONX implies a low-ionization, power-law-dominated solution with $A_{\rm Fe}$1–$A_{\rm Fe}$2, whereas RELXILL implies a highly ionized, reflection-dominated solution with $A_{\rm Fe}$3–$A_{\rm Fe}$4 (Waddell et al., 2019). The authors judge the REFLIONX interpretation to be more consistent with the source’s normal $A_{\rm Fe}$5, showing that the two models encode different disc ionization regimes and different balances between direct and reflected emission (Waddell et al., 2019).

The contrast persists in broader benchmarking. In the study of GRS 1915+105 and MCG–6–30–15, RELCONV$A_{\rm Fe}$6REFLIONX, RELCONV$A_{\rm Fe}$7XILLVER, and RELXILL yield similar parameters for the simpler stellar-mass case, but differ significantly for the AGN case, where REFLIONX tends to prefer lower spin and lower inclination and gives worse overall fits (Tripathi et al., 2020). In the AGN-host alignment study, however, simulations show that the inclination difference induced by switching between RELXILL and REFLIONX is usually only a few degrees, with mean rms deviations of $A_{\rm Fe}$8, $A_{\rm Fe}$9, and $\Gamma$0 for input inclinations of $\Gamma$1, $\Gamma$2, and $\Gamma$3 respectively (Middleton et al., 2016). This suggests that model dependence is observable but context dependent: it is small for some inclination measurements, yet substantial for ionization, reflection fraction, mass, height, and soft-band interpretation.

A recent broadband Seyfert analysis sharpens this point further. For PG 1426+015, high-density REFLIONX-based models fit the soft excess, Fe K complex, and Compton hump without ad hoc modification, whereas XILLVER-based models fail unless the O VIII feature is artificially suppressed (Walton et al., 16 Sep 2025). The authors attribute the divergence to a stronger soft continuum and weaker O VIII line in REFLIONX, partly linked to different resonant-line transfer treatments (Walton et al., 16 Sep 2025). This suggests that, in bare Seyferts with strong soft excesses, the choice between REFLIONX and XILLVER is not merely technical but can determine whether a reflection-only interpretation remains viable.

4. High-density extensions and the iron-abundance problem

A major development in REFLIONX usage is the introduction of high-density variants such as reflionx_hd, reflionx_hdv2, and reflionx_HD_nthcomp_v2, motivated by the inadequacy of standard low-density reflection grids for black-hole binaries (Jia et al., 2023, Kumar, 2024). These models extend the electron density well above the canonical $\Gamma$4 used in standard reflection tables and permit explicit tests of the degeneracy between iron abundance and density (Jia et al., 2023).

In MAXI J0637-430, standard relxillCp requires $\Gamma$5, even when density is allowed to rise to $\Gamma$6 within the high-density RELXILL grid (Jia et al., 2023). Replacing that with relconv*reflionx_hd, fixing iron abundance to solar, and allowing the density to vary yields logN = 22.0_{-0.6}^*, corresponding to $\Gamma$7, with a good fit quality $\Gamma$8 and no need for extreme iron enrichment (Jia et al., 2023). The authors interpret this as evidence that the supersolar iron abundance inferred from low-density models is an artifact of the density assumption, while the black-hole spin remains robust across model choices (Jia et al., 2023).

The same pattern appears in XTE J2012+381. Low-density RELXILL fits produce $\Gamma$9, and even high-density relxillCp at $300\,\mathrm{keV}$0 still demands $300\,\mathrm{keV}$1 (Kumar, 2024). In contrast, relconv*reflionx_HD_nthcomp_v2 yields $300\,\mathrm{keV}$2 with $300\,\mathrm{keV}$3 in one configuration, and $300\,\mathrm{keV}$4 with $300\,\mathrm{keV}$5 in another (Kumar, 2024). The paper therefore uses REFLIONX primarily as a density diagnostic rather than as the primary spin-measurement tool (Kumar, 2024).

In MAXI J1348-630, REFLIONX-based high-density models again reduce the required iron abundance to around solar while returning densities of $300\,\mathrm{keV}$6 (Chakraborty et al., 2021). The preferred reflionx_hdv2 implementation yields $300\,\mathrm{keV}$7–$300\,\mathrm{keV}$8 across most epochs, with $300\,\mathrm{keV}$9–$\xi = \frac{L}{n r^2}$0 except for one higher value in E3, and tracks a physically plausible evolution of inner radius and ionization through the outburst (Chakraborty et al., 2021). In Cygnus X-1, a modified variable-density reflionx_hd gives the especially clear result

$\xi = \frac{L}{n r^2}$1

while removing the need for iron abundances of $\xi = \frac{L}{n r^2}$2 or $\xi = \frac{L}{n r^2}$3 times solar required by standard RELXILL and REFLIONX fits (Tomsick et al., 2018).

These studies converge on a common inference. High density changes the reflected continuum through enhanced free–free heating and associated soft excess, modifies line and edge strengths, and can mimic the effects otherwise ascribed to extreme $\xi = \frac{L}{n r^2}$4 (Jia et al., 2023, Chakraborty et al., 2021, Tomsick et al., 2018). A plausible implication is that low-density reflection fits in bright black-hole binaries can systematically bias iron abundance and, through parameter degeneracies, bias inner radius and inclination as well.

5. Reverberation, dilution, and model-dependent geometry

REFLIONX has a distinct role in reverberation analyses because timing constraints are sensitive not only to light-travel time but also to the spectral partition between direct and reflected flux. In the comparative KYN study, both REFLIONX-based kynrefrev and XILLVER-based kynxilrev reproduce the observed lag–mass relation by construction, but the inferred coronal properties differ (Khanthasombat et al., 2024). For the REFLIONX-based fits, the lag–height relation is given as

$\xi = \frac{L}{n r^2}$5

with $\xi = \frac{L}{n r^2}$6, while the preferred source heights cluster around $\xi = \frac{L}{n r^2}$7–$\xi = \frac{L}{n r^2}$8 with a typical value near $\xi = \frac{L}{n r^2}$9 (Khanthasombat et al., 2024). REFLIONX also yields a strong correlation between source height and luminosity, with Spearman $\xi = \frac{4\pi F_{\rm X}}{n_e},$0, a trend absent in the XILLVER-based model (Khanthasombat et al., 2024).

The authors interpret the main difference as a dilution effect. Because XILLVER is more absorbed in the $\xi = \frac{4\pi F_{\rm X}}{n_e},$1–$\xi = \frac{4\pi F_{\rm X}}{n_e},$2 keV band, soft reverberation lags are more diluted, forcing the XILLVER-based timing model toward lower heights and lower black-hole masses to match the same lag-frequency observables (Khanthasombat et al., 2024). REFLIONX, having less soft-band absorption in this comparison, can accommodate larger intrinsic heights while remaining consistent with the observed lag amplitudes and phase-wrapping frequencies (Khanthasombat et al., 2024).

The simultaneous spectral–timing modeling of Mrk 335 reaches a related conclusion. There, REFLIONX and XILLVER fit the hard band comparably, but the soft band and therefore the Fe L lag interpretation diverge (Chainakun et al., 2015). More generally, the AGN reverberation model of 2016 uses REFLIONX to compute the local reflection spectrum on each disc element, then derives the energy-dependent response function $\xi = \frac{4\pi F_{\rm X}}{n_e},$3 and reflected response fraction $\xi = \frac{4\pi F_{\rm X}}{n_e},$4, which together determine the lag-energy spectrum including dilution (Chainakun et al., 2016). The model shows that ionization gradients encoded through REFLIONX can naturally produce lag-energy dips around 3 keV and 7–10 keV if the inner disc is highly ionized and the source height exceeds $\xi = \frac{4\pi F_{\rm X}}{n_e},$5 or the disc becomes colder at larger radii (Chainakun et al., 2016).

This establishes a technical point of broader importance. In reverberation work, REFLIONX is not merely a spectral ingredient. It sets the band-dependent reflection fractions that enter the diluted light curves and therefore the mapping from timing data to source geometry (Khanthasombat et al., 2024, Chainakun et al., 2016). Consequently, model-dependent differences in low-energy opacity and line strengths can propagate into fitted masses, heights, and scaling relations even when the relativistic transfer formalism is identical.

6. Limitations, revisions, and broader model context

The supplied literature repeatedly identifies REFLIONX as foundational but simplified. Its principal limitations are the constant-density slab assumption, angle-averaged output, and older or more limited atomic data relative to XILLVER-based families (Tripathi et al., 2020, Huang et al., 14 Dec 2025). In the DAO benchmark study, REFLIONX is contrasted with DAO and XILLVER as one of the standard non-relativistic reflection models, but it is noted to rely on a Gaussian-approximated Compton redistribution function and a custom atomic dataset rather than the newer XSTAR-based infrastructure used in XILLVER and DAO (Huang et al., 14 Dec 2025). The same paper states that REFLIONX is angle-averaged and that classic tables are less flexible with respect to arbitrary illuminating spectra (Huang et al., 14 Dec 2025).

At the same time, REFLIONX has been modified in several directions. High-density extensions have already been noted. Another important modification appears in the returning-radiation study, where the underlying REFLIONX code, rather than its public power-law tables, is used with the actual incident spectrum at each radius: the sum of lamp-post illumination and returning radiation (Mirzaev et al., 2024). That work shows that standard relativistic models modified only to read REFLIONX tables, while still assuming simple power-law illumination, can misestimate spin, height, ionization, and iron abundance when returning radiation is strong, especially for very high spin and low coronal height (Mirzaev et al., 2024). The central lesson is that REFLIONX as a microphysical solver is more general than many public tables imply, but relativistic fitting frameworks may still inherit biases if they simplify the local illumination spectrum (Mirzaev et al., 2024).

The neutron-star reflection paper adds another contextual refinement. It treats REFLIONX as a workhorse model originally designed for black-hole systems illuminated by cutoff power laws, and argues that neutron-star soft states require blackbody-illuminated reflection instead (Garcia et al., 2021). New models such as xillverNS and relxillNS are presented there as successors for that regime, while REFLIONX-based blackbody variants remain useful comparators (Garcia et al., 2021). This suggests that the domain of validity of REFLIONX depends not only on geometry and density but also on whether the assumed form of the illuminating continuum matches the astrophysical source.

Across the supplied studies, the most stable conclusion is not that REFLIONX is invalid, but that it is model-defining: it encodes specific assumptions about density, angular structure, incident spectrum, and atomic microphysics that materially affect inferred quantities. It remains one of the most widely used reflection models in relativistic X-ray spectroscopy, yet the modern literature treats its outputs as subject to cross-checking against alternative reflection families and to reinterpretation when high-density, soft-band, or returning-radiation physics is important (Khanthasombat et al., 2024, Waddell et al., 2019, Tripathi et al., 2020, Huang et al., 14 Dec 2025).