The strong Fe K line and spin of the black-hole X-ray binary MAXI J1631-479

We study the transient black hole binary MAXI J1631–479 in its soft spectral state observed simultaneously by the NICER and NuSTAR instruments. Its puzzling feature is the presence of a strong and broad Fe K line, while the continuum consists of a strong disk blackbody and a very weak power-law tail. The irradiation of the disk by a power-law spectrum fitting the tail is much too weak to account for the strong line. Two solutions were proposed in the past. One invoked an intrinsic Fe K disk emission, and the other invoked disk irradiation by the returning blackbody emission. We instead find that the strong line is naturally explained by the irradiation of the disk by the spectrum from Comptonization of the disk blackbody by coronal relativistic electrons. The shape of the irradiating spectrum at $\lesssim$10 keV reflects that of the disk blackbody; it is strongly curved and has a higher flux than that of a fit with a power-law irradiation. That flux accounts for the line. While this result is independent of the physical model used for the disk intrinsic emission, the value of the fitted spin strongly depends on it. When using a Kerr disk model for a thin disk with a color correction, the fitted spin corresponds to a retrograde disk, unlikely for a Roche-lobe overflow binary. Then, a model accounting for both the disk finite thickness and radiative transfer yields a spin of $a_*\approx0.8$–0.9, which underlines the strong model-dependence of X-ray spin measurements.

💡 Research Summary

The authors present a comprehensive spectral analysis of the transient black‑hole X‑ray binary MAXI J1631‑479 during a soft‑state observation obtained simultaneously with NICER and NuSTAR. The source exhibits a classic soft‑state spectrum: a dominant multi‑temperature disk blackbody and an unusually weak high‑energy tail. Despite the weakness of the tail, the data reveal a strong, broad Fe K emission line with an equivalent width of ≈180–210 eV, a feature that cannot be produced by the modest power‑law tail if one assumes a standard power‑law illumination of the disk.

Two earlier explanations for this puzzling line have been proposed. The first suggested that the line is intrinsic to the disk, arising from radiative transfer of deep‑layer blackbody photons. The second invoked returning radiation: blackbody photons emitted by the disk are bent by strong gravity back onto the disk surface and reflected. Both ideas face difficulties: detailed vertical radiative‑transfer calculations for standard thin disks do not predict strong Fe K features, and the returning‑radiation model double‑counts the same blackbody component.

In this work the authors introduce a third, physically motivated scenario: the disk photons are up‑scattered by a hot, relativistic corona, producing a Comptonized spectrum that illuminates the disk. The crucial point is that the Comptonized spectrum is strongly curved below ≈10 keV, retaining a high photon flux in the Fe K band compared with a simple power‑law extrapolation. Moreover, relativistic beaming (Ghisellini et al. 1991) enhances the fraction of coronal photons directed toward the disk. Together, these effects generate a reflected spectrum that naturally reproduces the observed Fe K line strength and shape.

To test this hypothesis the authors employ a self‑consistent fitting framework (Zdziarski et al. 2025) that convolves the Comptonization model (comppsc) with a relativistic reflection kernel (xilconv) and applies relativistic blurring (relconv). The Comptonization is modeled with a hybrid electron distribution: a thermal Maxwellian characterized by electron temperature kT_e and optical depth τ_T, plus a high‑energy non‑thermal tail with a steep power‑law index p. The reflection strength R is left free, and the Fe abundance is allowed to vary.

Two disk models are examined. The first, kerrbb, assumes a geometrically thin, optically thick disk with a fixed color‑correction factor f_col = 1.7. When coupled with the reflection component, kerrbb yields a statistically acceptable fit but drives the dimensionless spin parameter to a retrograde value a_* ≈ −0.4. Such a retrograde spin is highly implausible for a Roche‑lobe overflow low‑mass X‑ray binary, suggesting that the thin‑disk, fixed‑color‑correction assumption is inadequate in this regime.

The second model, slimbh, incorporates finite disk thickness, the dependence of the scale height on the Eddington ratio, and realistic atmosphere spectra derived from full radiative‑transfer calculations (Davis & Hubeny 2006). In slimbh the color correction is effectively computed (f_col = −1), and the viscosity parameter is set to α = 0.1. Using slimbh, the joint NICER–NuSTAR fit yields a high spin a_* ≈ 0.86 ± 0.03, a mass M ≈ 10.7 M_⊙, an inclination i ≈ 30°–35°, and a reflection strength R ≈ 2–3. The coronal covering fraction (the fraction of the disk surface illuminated) is modest (f_cov ≈ 0.3–0.6), and the Comptonizing electron temperature is kT_e ≈ 8–18 keV with optical depth τ_T ≈ 0.2–0.7, consistent with a soft‑state corona.

The authors also address instrumental systematics: a small cross‑calibration slope (plabs) is required between NICER and the two NuSTAR modules, and a narrow energy band (7.00–7.37 keV) in NuSTAR‑B is excluded due to an artificial dip likely caused by detector geometry and Sun‑proximity effects. Fractional rms analysis shows negligible variability in the 2–10 keV band (disk‑dominated) and strong variability only above 15 keV, confirming that the high‑energy tail carries the bulk of the rapid fluctuations.

Overall, the paper demonstrates that in soft‑state black‑hole binaries the Fe K line can be powered predominantly by reflection of the Comptonized disk emission rather than by a weak power‑law tail or intrinsic disk processes. It also highlights the extreme model dependence of spin measurements: a thin‑disk, fixed‑color‑correction model yields an unphysical retrograde spin, whereas a more realistic slim‑disk model provides a high, physically plausible spin. This work therefore underscores the necessity of employing physically self‑consistent disk and corona models when interpreting reflection features and deriving black‑hole spins from X‑ray spectroscopy.