Modeling X-ray reflection spectra from returning radiation: application to 4U 1630$-$47

TL;DR

This work addresses the impact of returning radiation on X-ray reflection spectra in black hole X-ray binaries, a regime often neglected by standard XSPEC models. The authors develop zijiRetRad, a self-consistent XSPEC table model that isolates reflection produced by self-irradiation of the disk by disabling the corona and computing iterative returning-reflection spectra around a Kerr black hole with a Novikov-Thorne disk. Applied to the soft-state NuSTAR data of 4U 1630--47, the model favors a near-maximal spin $(a_*\ o0.99)$, a moderate disk inclination $(i\approx53^{\circ})$, high electron density $(n_e\sim10^{21}\,\mathrm{cm^{-3}})$, and a mass accretion rate of about $(15\%\dot{M}_{\rm Edd})$, with a derived distance $D\approx8.2$ kpc. Compared to relxillNS, zijiRetRad naturally produces a harder high-energy reflection tail without invoking an additional Comptonized component, highlighting the significance of returning-radiation effects in the high-soft state and motivating future extensions to include a weak corona self-consistently and to broaden the parameter space.

Abstract

Returning radiation is thought to play a key role in disk illumination of black hole X-ray binaries in the high-soft state, yet it has not been fully incorporated into XSPEC reflection models. We present a new table model for reflection spectroscopy that, for the first time, self-consistently accounts for the returning radiation. To isolate this effect, we adopt the standard disk-corona configuration but disable the corona, allowing the reflection spectrum to be produced solely by self-irradiation of the disk. Applying our model to the black hole X-ray binary 4U 1630$-$47, we report a rapidly spinning black hole ($a_* \sim 0.99$), a disk inclination of $i \sim 53^\circ$, a mass accretion rate of $\dot{M}_{\rm BH} \sim 15\% \, {\rm \dot{M}_{Edd}}$, and an electron density of $n_{\rm e} \sim 10^{21} \,\mathrm{cm^{-3}}$ to reproduce the observed reflection features. The model also yields a source distance of $D\sim 8.2 \, {\rm kpc}$, slightly below the commonly adopted value of $10 \, {\rm kpc}$ in the literature. Compared to the widely used relxillNS, our model naturally produces a harder high-energy reflection spectrum, fitting the data without invoking a Comptonized component.

Figures (7)

• Figure 1: Schematic illustration of (a) a black hole-disk-corona model including thermal, Compton, and reflection components, and (b) a black hole-disk model with reflection component from self-irradiation of the disk (thermal returning) and iterative reflection (reflection returning). The color gradient in the disk indicates that the temperature increases towards the black hole.
• Figure 2: Reflection spectra (solid lines) produced by returning radiation (3rd iteration) and black-body spectra (dashed lines) from the ziji code for a $10{\rm \, M_\odot}$ black hole, showing the impact of spin (a), mass accretion rate (b), electron density (c), and inclination angle (d) on the spectra.
• Figure 3: Returning radiation flux profile in the rest frame of the disk for a $10{\rm \, M_\odot}$ black hole and for different values of the spin parameter.
• Figure 4: Ratio plots for the different models utilized during model build-up using zijiRetRad. The respective models are shown in the upper part of each panel. The lower panel shows the bets-fit model alongside the reduced $\chi^2$ obtained. Blue and orange colors correspond to FPMA and FPMB respectively.
• Figure 5: Model components (upper panels) and $\Delta \chi={\rm (data-model)/error}$ (lower panels) for the best-fit models obtained with zijiRetRad (left panels with $D$ free and middle panels with $D = 10\,{\rm kpc}$) and with relxillNS (right panels). The green, magenta, red, and black curves correspond to the blackbody, reflection, Comptonization, and total spectra, respectively. In the upper left and middle (right) panels, the reflection and blackbody components correspond to zijiRefl (relxillNS) and zijiBB (kerrbb), while the Comptonization component (nthComp) is present only in the relxillNS panel. The total model is indicated at the bottom of each upper panel.