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

Abstract

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).

Towards Precision Measurements of Accreting Black Holes Using X-Ray Reflection Spectroscopy

“…They note that the data quality around 10 keV is crucial for distinguishing between the effects of returning radiation and super-solar abundance. Riaz et al (2021) also find that in the most extreme cases (in particular, for maximally rotating BHs and for very centrally concentrated emissivities) the returning radiation systematically affects the fitted parameters, e.g. the BH spin.…”

“…The recent work of Riaz et al (2021) does not support this possibility, but their study is limited to non-ionized disks. They find that increasing the iron abundance and the increasing contribution of returning radiation produce very different spectral distortions of the low energy part of the Compton hump (which is reduced by the former and enhanced by the latter effect).…”

“…Note, however, that Connors et al (2020) interpret the spectrum of XTE J1550-564, which is thought to be a slow-rotating BH (a * ≈ 0.5, Steiner et al 2011), with a reflection component affected by returning radiation. The returning radiation should be important for a small height (at most a few r g ; Niedźwiecki & Zdziarski 2018) of the X-ray source in the lamppost geometry and for a steep radial emissivity in phenomenological models (Riaz et al 2021). For the radial thermal emissivity of a standard accretion disk (i.e., described by the Novikov-Thorne model) the contribution from the inner disk is relatively weak and, therefore, the effect of the returning radiation gives only a small correction, but it can be strongly increased if the non-zero stress inner boundary condition is applied (Dabrowski et al 1997, Agol & Krolik 2000.…”

“…Blue dotted curves represent the differences between the red solid and black dashed curves. From Riaz et al (2021). ©AAS.…”

“…Fig.13Fraction of radiation returning to the disk as a function of the emissivity index q of the power-law irradiation profile for various values of the BH spin parameter a * . FromRiaz et al (2021). ©AAS.…”