A XRISM View of Relativistic Reflection in Cygnus X-1

TL;DR

XRISM Resolve provides the first high-resolution view of relativistic Fe K line emission in Cygnus X-1, enabling a decisive separation of broad relativistic features from the continuum and narrow line/components. Through comprehensive modeling of the Fe K region with relativistic reflection and distant reprocessing components, the study derives a black hole spin of $a \simeq 0.98$ and an inner-disk inclination of $\theta \simeq 63^\circ$, with the spin consistent with previous reflection-based measurements and the inclination suggesting inner-disk misalignment. The analysis demonstrates that the red wing of the Fe line robustly constrains spin and that high-resolution data help mitigate degeneracies with gas physics that affect the blue wing, while energy coverage of the Compton hump further refines other reflection parameters. The results underscore XRISM’s capability to disentangle spectral components, refine measurements of BH spin and disk geometry in X-ray binaries, and motivate joint multi-mission studies (e.g., with NuSTAR and Xtend) to robustly assess systematic uncertainties in the relativistic reflection method.

Abstract

We present the first high-resolution XRISM/Resolve view of the relativistically broadened Fe K line in Cygnus X-1. The data clearly separate the relativistic broad line from the underlying continuum and from narrow emission and absorption features in the Fe band. The unprecedented spectral resolution in the Fe K band clearly demonstrates that the flux excess can be attributed to a single, broad feature, as opposed to a superposition of previously unresolved narrow features. This broad feature can be best interpreted as emission consistent with an origin near the innermost stable circular orbit around a rapidly rotating black hole. By modeling the shape of the broad line, we find a black hole spin of $a\simeq0.98$ and an inclination of the inner accretion disk of $θ\simeq63^\circ$. The spin is consistent with prior reflection studies, reaffirming the robustness of past spin measurements using the relativistic reflection method. The measured inclination provides reinforcing evidence of a disk-orbit misalignment in Cygnus X-1. These results highlight the unique abilities of XRISM in separating overlapping spectral features and providing constraints on the geometry of accretion in X-ray binaries.

Figures (6)

• Figure 1: Top: Light curve of Cygnus X-1 as seen by XRISM Resolve during ObsID 300049010. The black, blue, and red indicate the light curves in the 2-10 keV, 5-10 keV, and 2-5 keV bands, respectively. The bottom axis shows the MJD of the observation, while the top axis shows the orbital phase of Cygnus X-1. The light curve was binned so that each point corresponds to a 300s interval. The vertical magenta and cyan lines indicate orbital phases 0.9 and 1, respectively. The vertical black lines indicate the duration of the NuSTAR observation used in this analysis. Bottom: Hardness ratio computed by dividing the 5-10 keV light curve in the top panel by the 2-5 keV light curve.
• Figure 2: Spectra (top panels) and residuals produced when fitting the spectra from the first half (left) and second half (right) of the XRISM Resolve observation of Cygnus X-1 with a power-law model (middle panels) and with our best-fit model (lower panels). The solid line represents our best-fit model, while the dashed line shows the underlying power law component. The spectra in the figure were rebinned for visual clarity to have a minimum significance of 50$\sigma$ per bin, or to combine a maximum number of 20 spectral bins.
• Figure 3: Focused look in the 6.25-7.15 keV (top) and 6.3-6.5 keV (bottom) at the XRISM Resolve observation of Cygnus X-1, during the first (left) and second (right) halves of the observation. The solid red lines represent our best-fit models. The dashed blue lines show the un-blurred MYTorus component, illustrating that the Fe K$\alpha$ complex is resolved in the data. The spectra were not rebinned for visual purposes, and display the spectral bins produced by the "optimal" binning scheme used in the analysis.
• Figure 4: The top panel shows the XRISM Resolve spectrum from the first half of the observation (black) compared with simultaneous NuSTAR FPMA (red) and FPMB (blue) spectra. The bottom panels show ratio of data/model for the XRISM and NuSTAR spectra when all parameters in the spectral model are linked (panel b), and when the parameters of the reflection component are allowed to vary independently (panel c). All parameters produce agreement within $1\sigma$ between the spectra from the two instruments.
• Figure 5: Ratio of spectra from the first half of the XRISM observation of Cygnus X-1 to a power law model (black line), showing the shape of the relativistically broadened Fe line. The red line in both panels shows the best-fit model, obtained with a BH spin of $a=0.975$ and an inclination of $\theta=62^\circ$. The different colored dashed lines represent the models with different BH spins (left) and different viewing inclinations (right), when the other parameter is held at the best-fit value. The models were shifted to match the flux at the peak of the line, around 7 keV, and do not represent the results of spectral fits. Lower BH spins under-predict the red wing of the Fe line in the left panel, whereas higher spins over-predict both the blue and red wings of the line. Similarly, different inclinations (right panel) fail to capture the profile of the line.