Reflecting the Reflection: Impact of Returning Radiation in Black Hole X-ray Binary Spectra

X-ray reflection spectroscopy is a powerful tool for exploring the innermost regions of accreting black hole systems. The X-ray spectra of black hole X-ray binaries (XRBs) typically consist of three components: thermal emission from the accretion disk, Comptonized emission from a hot corona, and a reflection component resulting from the illumination of the disk by the corona. Modeling the reflection features provides key information about the black hole’s spin and disk's parameters.

A phenomenon known as returning radiation (i.e., disk emission that is bent back onto itself by the black hole’s strong gravity) can significantly affect the reflection spectra, particularly for sources in the high-soft state. However, current XSPEC reflection models do not fully account for this effect.
We present a new reflection model that self-consistently includes returning radiation. To isolate its effects, we adopt a standard disk–corona configuration but disable the corona, allowing the reflection spectrum to arise solely from returning radiation, including higher-order reflections. Compared to widely used models such as relxillNS, our model naturally produces a harder high-energy reflection spectrum without requiring a Comptonized component. Our results demonstrate that returning radiation alone can account for the observed reflection features of XRBs in the soft state
and should therefore be considered an important component. Including returning radiation in spectra modeling also enables us to explore its impact on black hole spin measurements and test General Relativity in the strong-field regime.