DAO: A New and Public Non-Relativistic Reflection Model

TL;DR

DAO addresses rest-frame X-ray disk reflection by coupling XSTAR for atomic physics with the Feautrier radiative-transfer framework, and by using the exact Compton redistribution function averaged over a relativistic Maxwellian. It handles arbitrary illumination with a plane-parallel, constant-density slab and solves a two-boundary problem via a Λ-iteration until convergence, yielding more accurate Comptonization and line features than prior models. The main contributions include up-to-date atomic data, exact redistribution for Compton scattering, and flexible illumination, demonstrated through comparisons with reflionx and xillver and a detailed study of ionization, incidence angle, and density effects. These improvements enhance the physical realism and applicability of X-ray reflection modeling for XRBs and AGNs and pave the way for extensions to higher densities, disk-blackbody bottom illumination, non-uniform structure, polarization, and CLOUDY integration.

Abstract

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.

Figures (19)

• Figure 1: Reflection spectra generated by our model (DAO, red solid line), compared with those from reflionx (blue dashed line) and xillvercp (green dotted line). The incident nthcomp spectrum from xillvercp (refl_frac=0, $\Gamma$ = 2, $kT_E$ = 60 keV) is depicted by the grey dash-dotted line, iron abundance is set at 1.32 for DAO and xillver to account for different abundance tables. Other parameters are set at default their value as shown in Table \ref{['model parameters']}. To compare fairly with reflionx and xillver, we also run DAO using the Gaussian approximation. Left column: Gaussian-approximated redistribution function. Right column: exact redistribution function. All spectra are normalized by their integral of energy, $EJ_\mathrm{norm}(E) = EJ(E)/\int EJ(E)dE$.
• Figure 2: Ions fraction of Fe and Ni for reflection shown in Figure \ref{['Comparsion different model with nthcomp incident']}
• Figure 3: Same as Figure \ref{['Comparsion different model with nthcomp incident']}, but with different nthcomp incident spectra obtained from xillvercp by setting refl_frac = 0, $kT_{\rm e} = 60$ keV, and $\Gamma = 1.4$ (top panel) and $\Gamma = 2.4$ (bottom panel). The ionization parameter is set to $\log\xi = 3.0$ for all spectra.
• Figure 4: Comparison of angle-averaged reflection spectra computed using the exact (red solid line) and Gaussian (green dashed line) redistribution functions. The incident cut-off power-law spectrum is shown as a grey dashed line. The parameters are $\Gamma = 1.4$, $A_{\mathrm{Fe}} = 5.0$, and $\log\xi = 3.5$, with varying cut-off energies of $E_\mathrm{cut} = 10$ keV (top), 100 keV (middle), and 1000 keV (bottom). Other parameters are set at their default value. The lower sub-panel in each plot displays the ratio of the spectrum computed with the exact redistribution to that computed with the Gaussian approximation.
• Figure 5: Angle-averaged reflection spectra for various ionization parameters ($\log\xi$), distinguished by color. The nthcomp incident spectra are obtained from xillvercp by setting refl_frac = 0 and $kT_E = 60$ keV, with $\Gamma = 1.4$ (top panel) and $\Gamma = 2.4$ (bottom panel). Other parameters are set at their default values. The shape of incident spectrum is shown as a black dashed line for comparison.