RELXILL: Relativistic X-ray Reflection Model

• RELXILL is a family of relativistic X-ray reflection models that self-consistently couples XILLVER with RELLINE to simulate emission from accretion disks under strong gravitational effects.
• It accurately fits broadened Fe K features, the Compton hump, and reflection continua, allowing constraints on black-hole spin, disk inclination, ionization, and coronal geometry.
• Variants of RELXILL address specific scenarios including lamp-post geometries, neutron-star illumination, and non-Kerr spacetimes, highlighting its adaptability for high-quality X-ray spectroscopy.

RELXILL is an angle-dependent relativistic X-ray reflection model constructed by self-consistently connecting the XILLVER reflection models with the relativistic blurring code RELLINE, in order to model the reflection spectrum from accretion disks in the strong-gravity region around compact objects (Garcia et al., 2013). In practice, it is used to fit broadened Fe K features, Compton humps, and associated reflection continua, and thereby to constrain quantities such as black-hole spin, disk inclination, ionization, iron abundance, emissivity structure, and coronal geometry (Choudhury et al., 2017). Over time, the name has come to denote a family of related models rather than a single kernel, with variants for lamp-post geometries, thermal Comptonization continua, neutron-star illumination, higher-density disks, and non-Kerr spacetimes (Sridhar et al., 2019, Garcia et al., 2021, 1908.10152).

1. Origins and physical rationale

Earlier reflection models used for accretion-disk spectroscopy provided angle-averaged solutions for the flux reflected at the disk surface, even though the emission angle changes over the disk because of relativistic light bending (Garcia et al., 2013). RELXILL was introduced specifically to overcome that simplification by using angle-dependent reflection spectra from XILLVER and mapping the actual emission angle at each disk location through relativistic ray tracing (Garcia et al., 2013).

The resulting architecture is explicitly hybrid. XILLVER computes the local ionized reflection spectrum from a plane-parallel slab, while RELLINE supplies the general relativistic transfer functions required to propagate that local emission to a distant observer in Kerr spacetime (Garcia et al., 2013). This removes the need to impose an external limb-darkening or limb-brightening law, because the angular distribution is computed rather than prescribed (Garcia et al., 2013).

The model is motivated by the standard disk-corona picture in which hard X-rays from a corona irradiate a thin, optically thick disk and generate fluorescent lines and a reflection continuum that are then distorted by Doppler shifts, gravitational redshift, and light bending (1908.10152). In this setting, the iron line region and the Compton hump are the principal diagnostics, but RELXILL is designed to fit the full reflection spectrum rather than a line profile alone (Choudhury et al., 2017).

2. Spectral ingredients and parameterization

RELXILL is commonly implemented to constrain the dimensionless spin parameter and disk ionization from relativistic reflection spectra (Choudhury et al., 2017). Across its variants, the core fitted parameters include spin, inclination, ionization, iron abundance, inner and outer disk radii, emissivity indices, photon index of the illuminating continuum, and a normalization of the reflected component (Ghosh et al., 2018).

A central thermodynamic quantity is the ionization parameter. In the notation used in the model applications, it is written as

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

or equivalently

$\xi = \frac{4\pi F_x}{n_e},$

depending on the illumination convention adopted in a given model flavor (Sridhar et al., 2019, Garcia et al., 2021). This parameter controls the ionization state of the reflecting gas and therefore the detailed shape of the reflection spectrum, including the Fe K complex and the Compton hump (Wang et al., 2017).

A second important quantity is the reflection fraction. In relxill, this was redefined from the older “reflection strength” to a more physical parameter, namely the ratio of the coronal intensity illuminating the disk to the coronal intensity that reaches the observer (Dauser et al., 2016). In lamp-post configurations this parameter is directly tied to accretion geometry: the strongest reflection is produced for low source heights and high spin, while a low-spin black hole is incapable of producing enhanced relativistic reflection (Dauser et al., 2016).

RELXILL also encodes the radial emissivity profile of the reflected emission, usually as a power law or broken power law. This is not a minor technicality. Several later applications and tests show that the inferred spin, inclination, and even metric constraints can depend sensitively on how the emissivity or intensity profile is parameterized (Zhang et al., 2019).

3. Model family and specialized variants

The RELXILL suite includes multiple flavors tailored to different assumptions about the compact object, the illuminating continuum, and the spacetime geometry (1908.10152, Garcia et al., 2021).

Flavor	Distinguishing assumption	Representative role
relxill / relxilllp	Kerr spacetime; power-law illumination; lamp-post available	Standard black-hole reflection modeling (Dauser et al., 2016)
relxilllpCp	Lamp-post geometry with thermal Comptonization continuum	Broadband BHXRB fitting with explicit continuum treatment (Sridhar et al., 2019)
relxillNS	Single-temperature blackbody illumination from NS surface or boundary layer	Reflection modeling for accreting neutron stars (Garcia et al., 2021)
RELXILL_NK	Non-Kerr stationary, axisymmetric, asymptotically flat spacetimes	Tests of the Kerr hypothesis and strong-field GR (1908.10152)

The neutron-star extension is structurally important because standard relxill assumes a power-law continuum, whereas relxillNS is built for systems in which the primary continuum is characterized by a single-temperature blackbody spectrum emitted either at the stellar surface or at the boundary layer (Garcia et al., 2021). The paper introducing relxillNS states that this differs significantly from the standard power-law-illuminated black-hole case and provides both xillverNS and relxillNS as public additions to the relxill suite (Garcia et al., 2021).

RELXILL_NK generalizes the relativistic sector beyond Kerr. It uses a general relativistic ray-tracing code for any well-behaved, stationary, axisymmetric, and asymptotically flat black-hole spacetime, while the local disk reflection is still handled through XILLVER (1908.10152). Its published flavors include relline_nk, relxill_nk, relxillCp_nk, relxillD_nk, rellinelp_nk, and relxilllp_nk (1908.10152).

Subsequent development has also pushed beyond the canonical point-like lamp-post. A later extension implemented a radially extended, ring-like primary source, with the lamp post recovered as the special case of zero ring radius (Nekrasov et al., 15 Oct 2025). This suggests that the RELXILL framework is best viewed as a relativistic reflection platform whose geometry can be modified while retaining the underlying reflection infrastructure.

4. Inference capabilities and fitting practice

A systematic NuSTAR simulation study found that RELXILL can recover both spin and ionization at 90% confidence, with improving constraints at higher reflection fraction, high spin, and low source height (Choudhury et al., 2017). The same study emphasized that the practical recovery of parameters depends strongly on how fits are performed around the starting parameters, because the model is sufficiently nonlinear that blind fitting can become trapped in local minima (Choudhury et al., 2017).

That methodological point carries directly into data analysis. The study advises careful stepping through nonlinear-behaving parameters such as $\log \xi$, binning according to detector resolution rather than only by minimum counts per bin, and using Poisson fit statistics such as Cash statistic when analyzing Poissonian data (Choudhury et al., 2017). A plausible implication is that disagreements between published RELXILL fits can arise not only from astrophysical differences but also from differences in fitting protocol.

The recovery of inclination has likewise been tested in dedicated simulations and multi-epoch fitting. In a broadband study of active galaxies using self-consistent RELXILL fits, inclination was found to be well-recovered at 90\% confidence, with improved constraints at higher reflection fraction and higher inclination; higher iron abundance and corona temperature tightened the constraints, while spin had little effect in reflection-based inclination measurements (Du et al., 2024). This places inclination among the parameters that can be robustly constrained when the reflection component is sufficiently dominant.

The same literature also makes clear that model self-consistency is not equivalent to model uniqueness. Inferences sharpen when more data are analyzed jointly, especially for multi-epoch broadband observations, but the decisive factor remains the strength and cleanliness of the reflection signal (Du et al., 2024).

5. Empirical applications across accreting compact objects

Broadband applications illustrate both the strengths of RELXILL and the dependence of its constraints on source geometry and spectral coverage. In MAXI J1535-571, broadband AstroSat spectroscopy showed prominent reflection signatures, including a broad Fe K$\alpha$ line at about 6.5 keV and a Compton hump near 30 keV; fitting with relxilllpCp constrained the spin to $a_* = 0.67^{+0.16}_{-0.04}$, while a joint fit with Kerrbb yielded a black-hole mass of $10.39_{-0.62}^{+0.61} M_{\odot}$ and a distance of $5.4_{-1.1}^{+1.8}$ kpc (Sridhar et al., 2019). The same analysis argued that a soft X-ray instrument alone cannot correctly characterize the Comptonizing component from the corona, thereby underscoring the importance of broadband reflection spectroscopy (Sridhar et al., 2019).

In the neutron-star low-mass X-ray binary 4U 1636-53, RELXILL and RELXILLLP both fit the spectra well, but they did not return equivalent geometric inferences (Wang et al., 2017). Standard RELXILL yielded an inclination of about $88^\circ$, at odds with the fact that the source shows no dips or eclipses, whereas RELXILLLP returned a reasonable inclination of about $56^\circ$ and lamp-post heights of $2.3$--$\xi = \frac{4\pi F_x}{n_e},$0 (Wang et al., 2017). This comparison is often cited because it shows that the assumed coronal geometry can determine whether a formally good fit is also physically plausible.

Active-galaxy applications highlight a different limitation. In the radio-loud narrow-line Seyfert 1 galaxy 1H 0323+342, relxill fitted the spectra above 3 keV and implied high black-hole spin, $\xi = \frac{4\pi F_x}{n_e},$1, with moderate reflection fraction $\xi = \frac{4\pi F_x}{n_e},$2, but it failed to predict the strong soft X-ray excess when fitted above 3 keV and extrapolated to lower energies (Ghosh et al., 2018). In that case, the best broadband description required blurred reflection together with intrinsic disk Comptonization and an additional steep power law associated with jet emission (Ghosh et al., 2018).

Another instructive case is MAXI J1836-194. Joint Suzaku and RXTE fitting with relxill required a steep inner emissivity profile, indicating a compact corona, whereas the lamp-post configuration relxilllp gave a worse fit and was excluded at 99\% confidence level compared to relxill (Dong et al., 2020). When two relativistic reflection components were used to mimic an ionization gradient, the inner emissivity flattened, suggesting that the ionization state of the disk is not constant (Dong et al., 2020).

RELXILL has also been used for spin determinations that disagree with other techniques. For XTE J1859+226, simultaneous fitting of seven RXTE spectra with relxill and relxillD yielded $\xi = \frac{4\pi F_x}{n_e},$3 and $\xi = \frac{4\pi F_x}{n_e},$4 at 90\% confidence, respectively, in marked tension with the much lower spin inferred from the relativistic precession model (Mall et al., 2023). This does not by itself resolve which method is correct, but it demonstrates that RELXILL-based spin estimates can be both precise and method-dependent.

6. Limitations, systematics, and ongoing development

RELXILL’s limitations are increasingly discussed in the context of next-generation X-ray missions. An accuracy study using simulated Athena/X-IFU and LAD observations found that the relativistic calculations recover the correct input parameters, but residuals appear when the emission from the inner part of the accretion disk is higher; these residuals disappear if the number of interpolation points on the disk in the integral of the transfer function is increased (Liu et al., 2024). The same study found that full reflection spectra require proper treatment of the emission angle, because the simplifying angle-averaged or radially averaged treatment becomes insufficient for very high-quality data (Liu et al., 2024).

Returning radiation is another identified boundary of the current framework. A model that computes the reflection spectrum at every point on the disk by using the actual spectrum of the incident radiation found that RELXILL with returning radiation cannot fit well the simulated data when the black-hole spin is very high and the coronal height and disk ionization parameter are low; some parameters can then be significantly overestimated or underestimated (Mirzaev et al., 2024). Better fits and correct parameter recovery were found as the spin decreases and the coronal height increases (Mirzaev et al., 2024).

Several astrophysical mismatches have also been documented. In the ultra-compact X-ray binary candidate SLX 1735-269, xillverCO was found to be an improvement over relxill or relxillns because the latter contain solar-like chemical abundances and could not reproduce the strong oxygen feature together with weak Fe K$\xi = \frac{4\pi F_x}{n_e},$5 emission (Moutard et al., 2024). In warped-disk simulations, single-component relxill fits produced biased spin and inclination estimates, while two-component relxill fits recovered the input values more accurately (Abarr et al., 2020). In tests of the Kerr hypothesis with GRS 1915+105, the choice of emissivity profile was found to be crucial, whereas changing between different RELXILL flavors had little effect once the intensity profile was modeled flexibly (Zhang et al., 2019).

These results do not negate the model’s utility. They show, more narrowly, that RELXILL is most reliable when its assumptions about geometry, composition, angular treatment, and irradiation are matched to the source class and the data quality. The current trajectory of development—non-Kerr metrics, neutron-star-specific illumination, higher-density disks, explicit treatment of returning radiation, and extended coronal geometries—suggests that the model family is evolving in response to precisely those domains where the standard implementation becomes a limiting approximation (1908.10152, Garcia et al., 2021, Nekrasov et al., 15 Oct 2025).