DAO: A New and Public Non-Relativistic Reflection Model

We present a new non-relativistic reflection model, DAO, designed to calculate reflection spectra in the rest frame of accretion disks in X-ray binaries and active galactic nuclei. The model couples the XSTAR code, which treats atomic processes, with the Feautrier method for solving the radiative transfer equation. A key feature of DAO is the incorporation of a high-temperature corrected cross section and an exact redistribution function to accurately treat Compton scattering. Furthermore, the model accommodates arbitrary illuminating spectra, enabling applications across diverse physical conditions. We investigate the spectral dependence on key physical parameters and benchmark the results against the widely used reflionx and xillver codes.

💡 Research Summary

The manuscript introduces DAO, a new publicly available non‑relativistic reflection code designed to compute the rest‑frame reflection spectra of accretion disks in X‑ray binaries and active galactic nuclei. DAO builds upon the mathematical framework of the widely used xillver model but replaces several approximations that limit the accuracy of existing tables. The core of DAO is a tight coupling between the XSTAR atomic physics package (version 2.59) and the Feautrier method for solving the second‑order radiative‑transfer equation in a plane‑parallel, constant‑density slab.

A major innovation is the implementation of a high‑temperature corrected Compton scattering cross‑section and an exact redistribution function, following García et al. (2020). Unlike reflionx, which uses the Fokker‑Planck (Kompaneets) approximation, and xillver, which adopts a Gaussian redistribution kernel, DAO treats Compton scattering with the full quantum‑mechanical kernel appropriate for a relativistic Maxwellian electron distribution. This allows the code to correctly capture Klein‑Nishina effects and the asymmetric energy exchange that become important at photon energies ≳ keV or electron temperatures ≳ keV.

DAO’s input parameters are highly flexible. Users can select among several standard illumination spectra – a simple power law, a cut‑off power law, the thermal Comptonisation model nthComp, a black‑body, or an arbitrary user‑provided file. The illumination is normalised via the ionisation parameter ξ = 4πF_X/n_H, and a bottom illumination option (black‑body from the disk mid‑plane) is also available, which is particularly relevant for hot disks in X‑ray binaries. The default slab has a column density of 10²⁴ cm⁻², hydrogen density 10¹⁵ cm⁻³, and solar abundances except for iron, which can be varied independently.

The numerical grid comprises 200 logarithmic optical‑depth points (τ = 10⁻⁴–10), 5000 linearly spaced energy points from 0.1 eV to 1 MeV, and 10 cosine‑angle bins (µ = 0.05–0.95). Convergence is achieved with 15 outer iteration cycles (N_main) and up to 200 radiative‑transfer sub‑iterations (N_RTE). At each depth the code iterates between (i) XSTAR calculations of emissivity j(E) and absorption α(E), (ii) Feautrier solution for the mean intensity u(z,µ,E) and flux h(z,µ,E), (iii) evaluation of the Compton‑scattered mean intensity J_c(E) using the exact redistribution kernel, and (iv) updating the temperature profile to enforce thermal equilibrium.

Benchmarking against the publicly available reflionx and xillver tables shows overall agreement in the soft‑X‑ray band, but significant deviations appear above ~30 keV. DAO’s spectra display a slightly steeper high‑energy tail and subtle shifts in the Fe Kα line centroid and width, reflecting the more accurate treatment of multiple scatterings and Klein‑Nishina suppression. When complex illumination (e.g., nthComp plus a black‑body) is employed, DAO can directly ingest the user‑defined spectrum, something not possible with the pre‑computed xillver tables.

DAO is released under an open‑source license on GitHub and Zenodo, with all source files, redistribution kernels, and example scripts provided. It uses the same atomic database (ATDB 2024) as XSTAR, ensuring that future atomic data updates propagate automatically. While the current implementation assumes a constant‑density, plane‑parallel slab, the modular code structure permits extensions to include density gradients, magnetic fields, or full relativistic ray‑tracing to produce the final observed spectrum (i.e., a full relxill‑type model).

In summary, DAO resolves two longstanding limitations of non‑relativistic reflection modeling: (1) the inaccurate Compton scattering approximations that compromise high‑energy predictions, and (2) the inflexibility of pre‑computed illumination spectra. By delivering a physically rigorous, highly configurable, and openly distributed tool, DAO stands to become the reference platform for next‑generation X‑ray reflection studies, especially in the era of high‑resolution missions such as XRISM and Athena.