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

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_{\ast }\sim 0.99$), a disk inclination of $i\sim 53^{\circ }$, a mass accretion rate of ${\dot{M}}_{\mathrm{BH}}\sim 15\%{\dot{\mathrm{M}}}_{\mathrm{Edd}}$, and an electron density of $n_{\mathrm{e}}\sim 10^{21}\mathrm{c}{\mathrm{m}}^{-3}$ to reproduce the observed reflection features. The model also yields a source distance of $D\sim 8.2\mathrm{kpc}$, slightly below the commonly adopted value of $10\mathrm{kpc}$ 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.

12 pages, 7 figures, 3 tables