Measuring black hole spins with x-ray reflection spectroscopy: A GRMHD outlook

X-ray reflection spectroscopy has evolved as one of the leading methods to measure black hole spins. However, the question is whether its measurements are subjected to systematic biases, especially considering the possible discrepancy between the spin measurements inferred with this technique and those from gravitational wave observations. In this work, we use general relativistic magnetohydrodynamic (GRMHD) simulations of thin accretion disks around spinning black holes for modeling the accretion process, and then we simulate NuSTAR observations to test the capability of modern reflection models in recovering the input spins. For the first time, we model the electron density and ionization profiles from GRMHD-simulated disks. Our study reveals that current reflection models work well only for fast-rotating black holes. We model the corona as the base of the jet and we find that reflection models with lamppost emissivity profiles fail to recover the correct black hole spins. Reflection models with broken power-law emissivity profiles perform better. As we increase the complexity of the simulated models, it is more difficult to recover the correct input spins, pointing toward the need to update our current reflection models with more advanced accretion disks and coronal geometries.

💡 Research Summary

This paper presents a comprehensive assessment of systematic uncertainties in black‑hole spin measurements obtained through X‑ray reflection spectroscopy. The authors employ state‑of‑the‑art general relativistic magnetohydrodynamic (GRMHD) simulations of geometrically thin (H/r≈0.05) accretion disks around Kerr black holes with three dimensionless spin values (a* = 0.5, 0.8, 0.98). A magnetic field seed is used to launch a jet, which the authors identify as the hot corona. The simulations include a radiative cooling prescription that keeps the disk thin and realistic.

From the time‑averaged simulation data, the authors perform relativistic ray‑tracing to generate synthetic spectra for two observer inclinations (30° and 70°). For each cell of the simulated disk they compute the local reflection spectrum using the xillver code, explicitly incorporating the radial profiles of electron density and ionization parameter that naturally emerge from the GRMHD run. This approach departs from the usual assumption of constant density and ionization in standard reflection models.

The resulting full‑disk reflection spectra are then folded through the NuSTAR response matrix to create mock 30 ks observations, complete with realistic statistical noise and instrumental effects. These synthetic data sets are fitted with the latest families of relativistic reflection models—relxill, relxill_nk, reltrans, and kyn—using two emissivity prescriptions: the traditional lamppost geometry and a broken power‑law profile. The authors also explore the impact of including or excluding reflection from the plunging region inside the ISCO, and of fixing versus varying the density/ionization profiles.

Key findings are as follows. For the high‑spin case (a* ≈ 0.98) all models recover the input spin to within ≈5 % and the fits are especially good at high inclination (70°), where relativistic broadening is strongest. In the intermediate‑spin case (a* ≈ 0.8) the lamppost emissivity leads to a systematic under‑estimation of the spin (Δa* ≈ ‑0.15) and a markedly larger χ², whereas the broken power‑law emissivity reduces the bias to ≈0.1 and improves the fit quality. For the low‑spin case (a* ≈ 0.5) both emissivity prescriptions exhibit large biases, and the inclusion of plunging‑region reflection further destabilises the spin recovery. This behavior reflects the reduced sensitivity of the reflection features to the ISCO radius when the ISCO lies farther from the black hole.

Incorporating the realistic electron‑density and ionization gradients from the GRMHD simulations modestly improves the fits, but the residual systematic errors indicate that the assumption of a uniform density/ionization profile remains a limiting factor. Moreover, the current reflection models do not fully account for emission from the plunging region, non‑Keplerian orbital motion, or the finite thickness of the disk, all of which become important for moderate and low spins.

The authors conclude that present‑day X‑ray reflection spectroscopy is reliable for rapidly rotating black holes observed at moderate to high inclinations, but it can suffer significant systematic biases for slower spins or for more complex corona geometries such as jet‑like bases. They advocate the development of next‑generation reflection models that embed GRMHD‑derived disk structure, variable density/ionization, realistic coronal geometries, and plunging‑region physics. Such models, combined with upcoming high‑resolution missions like XRISM and Athena, will be essential for reconciling spin measurements from X‑ray spectroscopy with those obtained via gravitational‑wave observations.