XILLVER: X-ray Reflection in Accretion Disks

• XILLVER is a non-relativistic X-ray reflection code that models reprocessed emission from an optically thick accretion-disk atmosphere irradiated by a hard X-ray continuum.
• It employs self-consistent radiative-transfer, ionization, and thermal balance calculations using methods like the Feautrier technique and lambda iteration to simulate key spectral features such as fluorescent lines, absorption edges, and the Compton hump.
• The code serves as the foundational local reflection engine for the RELXILL family and has been extended to high-density, neutron-star, and C/O-rich scenarios, influencing both spectral fitting and timing analyses.

XILLVER is a non-relativistic X-ray reflection code for computing the rest-frame spectrum produced when an external continuum irradiates an optically thick accretion-disk atmosphere. In the standard formulation, it models a Compton-thick, plane-parallel slab intended to represent the surface layers of an accretion disk, and solves the coupled radiative-transfer, ionization-balance, and thermal-balance problem self-consistently. Within modern reflection spectroscopy, XILLVER occupies a foundational position: it provides the local reflection microphysics for the RELXILL family, while relativistic packages add Doppler boosting, gravitational redshift, light bending, and transfer through curved spacetime on top of the XILLVER rest-frame spectrum (Garcia et al., 2013, Dauser et al., 2016, 1908.10152).

1. Definition and physical scope

XILLVER models the reprocessed emission from an accretion-disk atmosphere illuminated from above by a hard X-ray continuum. The emergent spectrum contains the canonical signatures of X-ray reflection: fluorescent lines, absorption edges, and the Compton hump. In its standard use, the illuminating spectrum is a power law, and the code is intended for regimes in which the thermal disk flux is faint compared to the incident power-law flux; the 2013 public grid was explicitly described as suitable for active galactic nuclei and stellar-mass black holes in the hard state (Garcia et al., 2013).

The code is non-relativistic in the specific sense that it computes the local disk-frame reflection spectrum rather than the observed spectrum after propagation through the strong-gravity region. In the terminology adopted in later RELXILL work, XILLVER is the “flat-disk” or nonrelativistic reflection model: the disk microphysics is retained, but strong-field blurring is absent. This separation is central to the architecture of modern reflection modeling, because it allows the reflection physics and the spacetime transport to be treated as distinct layers of the calculation (Dauser et al., 2016, 1908.10152).

A common misconception is that XILLVER itself is a relativistic reflection model. It is not. The relativistic model is RELXILL or one of its extensions, whereas XILLVER supplies the local reflection spectrum later used by those frameworks (Dauser et al., 2016, Garcia et al., 2013).

2. Radiative-transfer and atomic framework

The standard XILLVER calculation treats the disk atmosphere as a constant-density, plane-parallel slab and iteratively solves three coupled problems: radiative transfer, ionization balance, and thermal balance. The radiative transfer is solved with the Feautrier method and lambda iteration, while the local ionization and atomic state are obtained from XSTAR. In the 2013 release, the transfer equation was rewritten in terms of total optical depth,

$d\tau = \chi(E)\,dz,$

with $\chi(E)=\alpha_{\rm kn}(E)+\alpha_a(E)$, where $\alpha_{\rm kn}$ is the Klein–Nishina scattering opacity and $\alpha_a$ the absorption opacity. That implementation used 200 spatial zones, Thomson depth from $10^{-4}$ to $10$, and about 100 iterations for convergence (Garcia et al., 2013).

The same release introduced a substantially updated incident continuum prescription. Earlier versions had used a pure power law over a broad band, whereas the updated model adopted a power law that breaks at $100\ \mathrm{eV}$, has an exponential low-energy cutoff below that energy, extends to $1\ \mathrm{MeV}$, and imposes a high-energy cutoff at $300\ \mathrm{keV}$. The motivation was twofold: for steep spectra, a pure power law overpopulates low-energy photons, and for hard spectra, the high-energy extension strongly affects heating and Compton broadening (Garcia et al., 2013).

Atomic completeness is a defining feature of XILLVER. The 2013 library incorporated a richer XSTAR database including Fe M-shell unresolved transition arrays, K-shell data for Mg, Si, S, Ar, Ca, Al, and Ni, updated radiative and dielectronic recombination rates, improved Fe photoionization cross sections at high energies, and photoionization cross sections for metastable states of low-charge Fe ions. The inclusion of metastable-state cross sections was specifically identified as correcting a too-weak Fe K line at low ionization in earlier calculations (Garcia et al., 2013).

Two later upgrades substantially altered the hard- and high-density regimes. First, a 2020 revision replaced the approximate Gaussian Compton redistribution with an exact angle-averaged thermal Compton kernel based on the differential Klein–Nishina cross section and its thermal average. The new source term was written schematically as

$j_{\rm sc}(E') = \int R(E,E')\,I(E)\,dE,$

with $\chi(E)=\alpha_{\rm kn}(E)+\alpha_a(E)$0 constructed from the exact Compton kernel rather than a Thomson-limit approximation. This upgrade was motivated by the inaccuracy of the older treatment above roughly $\chi(E)=\alpha_{\rm kn}(E)+\alpha_a(E)$1 and at relativistic electron temperatures, and it primarily reshaped the Compton hump and high-energy turnover rather than the low-energy line-rich spectrum (García et al., 2020).

Second, the 2024 high-density update propagated new XSTAR atomic rates into XILLVER 3.5. The most consequential change was dielectronic recombination suppression at high density, included through fits from Nikolić et al. (2013); the paper identified changes in recombination rates as the dominant reason the new model differs from earlier versions. The updated microphysics also included continuum lowering, expanded atomic data, and fixes to earlier XSTAR issues. The revised code, using XSTAR 2.59 and ATDB23, was described as extending the reliable density treatment from the older $\chi(E)=\alpha_{\rm kn}(E)+\alpha_a(E)$2 regime up to about $\chi(E)=\alpha_{\rm kn}(E)+\alpha_a(E)$3 (Ding et al., 2024).

3. Public grids, parameters, and normalization

The 2013 public release provided a complete library of 720 synthetic reflection spectra packaged as a single FITS table for XSPEC atable use. Each spectrum is parameterized by the photon index $\chi(E)=\alpha_{\rm kn}(E)+\alpha_a(E)$4 of the illuminating continuum, the surface ionization parameter $\chi(E)=\alpha_{\rm kn}(E)+\alpha_a(E)$5, and the iron abundance $\chi(E)=\alpha_{\rm kn}(E)+\alpha_a(E)$6 relative to solar. The published grid covered

$\chi(E)=\alpha_{\rm kn}(E)+\alpha_a(E)$7

with fixed hydrogen density $\chi(E)=\alpha_{\rm kn}(E)+\alpha_a(E)$8 and energy range $\chi(E)=\alpha_{\rm kn}(E)+\alpha_a(E)$9 to $\alpha_{\rm kn}$0 (Garcia et al., 2013).

The ionization parameter is defined in the standard XILLVER form,

$\alpha_{\rm kn}$1

where $\alpha_{\rm kn}$2 is the illuminating X-ray flux and $\alpha_{\rm kn}$3 the electron density. Physically, $\alpha_{\rm kn}$4 measures the ratio of incident ionizing flux to density, and therefore controls the thermal and ionization structure of the illuminated skin. At low $\alpha_{\rm kn}$5, the spectrum is line- and edge-rich; at high $\alpha_{\rm kn}$6, the atmosphere becomes highly ionized and the reflected continuum is less strongly modified (Garcia et al., 2013).

Normalization became a separate issue once XILLVER was embedded in relativistic modeling. In the nonrelativistic limit, models such as PEXRAV and XILLVER assume a simple normalization in which the incident and observed coronal intensities are directly comparable. In 2016, the RELXILL work replaced the older “reflection strength” with a geometry-based “reflection fraction,” defined as the ratio of coronal intensity illuminating the disk to coronal intensity reaching the observer,

$\alpha_{\rm kn}$7

This parameter was implemented in all flavors of RELXILL and in the nonrelativistic XILLVER model, under the name refl_frac, beginning with version v0.4a on 18 January 2016 (Dauser et al., 2016).

The same work stressed that reflection fraction and reflection strength are distinct quantities. Reflection strength $\alpha_{\rm kn}$8 was defined observationally in the $\alpha_{\rm kn}$9–$\alpha_a$0 band as a reflected-to-incident flux ratio near the Compton hump, whereas $\alpha_a$1 is intended as a geometry-based quantity tied to coronal illumination. In the nonrelativistic semi-infinite slab limit, $\alpha_a$2 corresponds to equal coronal intensity illuminating the disk and reaching the observer; in relativistic lamp-post configurations, light bending and photon capture break that trivial correspondence (Dauser et al., 2016).

4. Angular dependence and relativistic coupling

A major advance in the XILLVER program was the move from angle-averaged reflected flux to angle-dependent emergent specific intensity. In the 2013 angular-treatment paper, the radiation field in a slab with $\alpha_a$3 and $\alpha_a$4 was solved using the Feautrier variables

$\alpha_a$5

leading to

$\alpha_a$6

The reflected intensity was tabulated on ten angular bins,

$\alpha_a$7

This was introduced because the reflected spectrum is not isotropic: the effective optical depth scales as $\alpha_a$8, so grazing-angle emission experiences different absorption and scattering than near-normal emission (Garcia et al., 2013).

The paper showed that the difference between the true angle-dependent local spectrum and an angle-averaged approximation can reach factors of $\alpha_a$9 locally and up to $10^{-4}$0 in the integrated reflected spectrum. It also found that XILLVER predicts limb brightening, but not the simple empirical angular laws often assumed in earlier relativistic blurring models. These angle-dependent spectra were then coupled self-consistently to RELLINE to create RELXILL, removing the need for an ad hoc limb-darkening or limb-brightening prescription (Garcia et al., 2013).

In RELXILL and its descendants, the division of labor is explicit: XILLVER computes the local disk-frame reflection spectrum, and the relativistic layer computes the observer-frame transport. This architecture was generalized in RELXILL_NK, where XILLVER remained the non-relativistic local disk reflection engine while ray tracing was extended from Kerr to generic stationary, axisymmetric, asymptotically flat spacetimes for tests of the Kerr hypothesis (1908.10152).

The same rest-frame role is visible in timing applications. The reverberation model revb for Mrk 335 used XILLVER to generate the reflected spectrum entering both the time-averaged fit and the lag response functions, with measured lags derived from

$10^{-4}$1

That analysis emphasized full dilution, in which both soft and hard bands contain mixtures of direct continuum and reflection, and noted that inferred black-hole mass and coronal height are model-dependent because XILLVER and REFLIONX differ significantly below $10^{-4}$2 (Chainakun et al., 2015).

A closely related issue appears in AGN reverberation population studies. The public lamp-post reverberation code kynxilrev uses XILLVER tables, specifically xillverD-5.fits, whereas kynrefrev uses REFLIONX. The 2024 comparison found that XILLVER-based reverberation produces smaller lag amplitudes than REFLIONX-based reverberation for the same source height because the XILLVER soft band is more absorbed, increasing dilution. In the accepted lag–mass-scaled mock samples, kynxilrev systematically preferred lower black-hole mass and lower coronal height than kynrefrev, especially for low-spin systems (Khanthasombat et al., 2024).

5. Variants and specialized model families

XILLVER has been repeatedly adapted to physical environments not captured by the original power-law-illuminated, solar-composition grid. Three prominent branches are summarized below.

Model	Distinguishing assumption	Target systems
XILLVER	Power-law illumination; non-relativistic disk reflection	AGN and black-hole binaries in the hard state
XILLVER$10^{-4}$3	C/O-rich, H/He-poor composition; blackbody lower boundary included	Ultra-compact X-ray binaries
xillverNS	Single-temperature blackbody illumination	Accreting neutron stars

XILLVER$10^{-4}$4 was introduced to model reflection from the oxygen-rich disks of ultra-compact X-ray binaries such as 4U 0614+091 and 4U 1543-624, where the donor is inferred to be a CO or ONeMg white dwarf. The modified code allowed the carbon and oxygen abundances to vary together through $10^{-4}$5, mimicked H/He depletion by increasing the abundances of all elements except He, C, and O by a factor of 10 relative to Lodders (2003), included an intrinsic disk blackbody at the lower boundary with temperature $10^{-4}$6, and used a slab density $10^{-4}$7. The illumination-strength parameter was defined as

$10^{-4}$8

This O-rich version naturally produced a strong O VIII Ly$10^{-4}$9 line near $10$0 and an O VIII K-edge at $10$1, allowing the observed $10$2 feature to be interpreted as a combination of disk reflection and Ne I absorption rather than requiring an extreme neutral neon abundance (Madej et al., 2014).

xillverNS and relxillNS extended the framework to accreting neutron stars, where the irradiating continuum is often a blackbody from the stellar surface or boundary layer rather than a coronal power law. The xillverNS grid assumes a plane-parallel slab, total optical depth 10, incidence angle $10$3, no bottom illumination, and solar abundances except for variable iron abundance. Its parameter ranges were given as $10$4–$10$5, $10$6–$10$7, $10$8–$10$9, and $100\ \mathrm{eV}$0–$100\ \mathrm{eV}$1 solar. These models were released publicly within relxill version 1.5.0 (Garcia et al., 2021).

High-density XILLVER calculations form another specialized branch rather than a new model name. The 2024 update argued that luminous accretion disks should reach densities of $100\ \mathrm{eV}$2–$100\ \mathrm{eV}$3, high enough that plasma effects become important. With the updated rates, even highly ionized high-density slabs were found to produce strong iron resonance features in the $100\ \mathrm{eV}$4–$100\ \mathrm{eV}$5 band and strong oxygen resonance structure in the $100\ \mathrm{eV}$6–$100\ \mathrm{eV}$7 band. A plausible implication is that some earlier inferences of supersolar iron abundance partly reflected incomplete high-density atomic physics rather than true composition (Ding et al., 2024).

6. Comparative assessments, applications, and systematic uncertainties

XILLVER has been benchmarked extensively against PEXRAV, REFLIONX, Monte Carlo calculations, and newer public codes. In the nonrelativistic regime, the 2016 normalization study reported that XILLVER, PEXRAV, and a Monte Carlo simulation give broadly similar reflection strengths, with modest discrepancies traceable to abundance sets and XILLVER’s approximate Compton-scattering treatment; that paper also stated that the older XILLVER treatment is reliable up to roughly $100\ \mathrm{eV}$8 (Dauser et al., 2016). Later, the DAO comparison retained XILLVER as a principal benchmark and found broad agreement over $100\ \mathrm{eV}$9–$1\ \mathrm{MeV}$0, while attributing soft-band discrepancies mainly to different XSTAR and atomic-database versions and hard-band discrepancies to exact versus Gaussian Compton redistribution (Huang et al., 14 Dec 2025).

The comparison with REFLIONX is recurrent because both codes are widely used yet not interchangeable. In the original 2013 grid paper, XILLVER and REFLIONX agreed qualitatively in soft spectra and low-ionization cases but diverged in intermediate ionization and in the high-ionization soft X-ray continuum, partly because REFLIONX suppresses many Fe K$1\ \mathrm{MeV}$1 lines from second-row Fe ions through Auger-resonant-destruction assumptions (Garcia et al., 2013). Later observational studies showed that these spectral differences propagate into parameter inference. For Mrk 335, simultaneous spectral and lag fitting produced markedly different preferred source height and black-hole mass depending on whether XILLVER or REFLIONX was used below $1\ \mathrm{MeV}$2 (Chainakun et al., 2015). For GRS 1915+105, by contrast, RELCONV$1\ \mathrm{MeV}$3XILLVER and RELXILL yielded nearly identical results and differences from REFLIONX were modest, whereas for MCG-6-30-15 the model choice affected inferred spin, inclination, ionization, and iron abundance much more strongly (Tripathi et al., 2020).

A further systematic issue is geometry ambiguity. In low-accretion-rate AGN, XILLVER has been used as the disk-reflection counterpart to the torus model BORUS02. Broadband fits to a BASS/DR2 sample of 17 LLAGN found that reflection is statistically required in 14 of 17 sources, but XILLVER and BORUS02 were often statistically indistinguishable. In that setting, XILLVER constrained disk ionization, reflection fraction, inclination, $1\ \mathrm{MeV}$4, and $1\ \mathrm{MeV}$5, yet the analysis concluded that current data do not always uniquely identify whether the dominant reflector is an inner disk or distant torus (Díaz et al., 2022).

The soft X-ray oxygen band has emerged as a specific point of tension. In PG 1426+015, broadband XMM-Newton and NuSTAR fits showed that XILLVER could reproduce the soft excess together with the Fe K feature and Compton hump only if the O VIII line at $1\ \mathrm{MeV}$6 was phenomenologically suppressed with a relativistically blurred narrow gabs component. The paper reported that the equivalent width of this oxygen feature in XILLVER is about a factor of 3 larger than in REFLIONX, and the absolute line flux about a factor of 2 larger when the models are normalized to the same flux at $1\ \mathrm{MeV}$7. Once suppressed, the XILLVER fit reached $1\ \mathrm{MeV}$8 and implied $1\ \mathrm{MeV}$9 and $300\ \mathrm{keV}$0, but the authors emphasized that such spin constraints remain model-dependent because they rely on a reflection-dominated interpretation of the soft excess (Walton et al., 16 Sep 2025).

Taken together, these results define the current status of XILLVER. It is the standard non-relativistic reflection engine underlying much of contemporary relativistic spectroscopy and reverberation analysis; it has been progressively upgraded in angular resolution, Compton scattering, and high-density atomic physics; and it has been extended to chemically exotic disks and neutron-star illumination geometries. At the same time, the literature consistently treats its low-energy spectral structure, density dependence, and coupling to specific relativistic frameworks as active sources of systematic uncertainty rather than settled details (Garcia et al., 2013, García et al., 2020, Ding et al., 2024).