Impact of the Returning Radiation on the Analysis of the Reflection Spectra of Black Holes

A fraction of the electromagnetic radiation emitted from the surface of a geometrically thin and optically thick accretion disk of a black hole returns to the disk because of the strong light bending in the vicinity of the compact object (returning radiation). While such radiation clearly affects the observed spectrum of the source, it is often neglected in theoretical models. In the present paper, we study the impact of the returning radiation on relativistic reflection spectra. Assuming neutral material in the disk, we estimate the systematic uncertainties on the measurement of the properties of the system when we fit the data with a theoretical model that neglects the returning radiation. Our NICER simulations show that the inclination angle of the disk and the black hole spin parameter tend to be overestimated for low viewing angles, while no clear bias is observed for high viewing angles. The iron abundance of the disk is never overestimated. In the most extreme cases (in particular, for maximally rotating black holes), the returning radiation flattens the radial emissivity beyond a few gravitational radii. In such cases, it also produces residuals that cannot be compensated for by adjusting the parameters of models that neglect the returning radiation. This may be an important issue for the interpretation of data from future X-ray missions (e.g., Athena). When we simulate some observations with NuSTAR and fit data above 10 keV, we find that some conclusions that are valid for the NICER simulations are no longer true (e.g., we can obtain a high iron abundance).

Automated summary

This paper studies the impact of returning radiation on relativistic reflection spectra from black hole accretion disks, finding systematic uncertainties in measurement properties when neglecting returning radiation; NICER simulations show overestimation of disk inclination and black hole spin parameter at low viewing angles, with no bias at high viewing angles, and consistent iron abundance estimation. In extreme cases, returning radiation flattens radial emissivity and produces uncompensated residuals, potentially affecting interpretation of data from future X-ray missions. NuSTAR observations above 10 keV show different conclusions from NICER simulations, such as the ability to obtain a high iron abundance.