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

TL;DR

MAXI J1631--479 exhibits a strong, broad Fe K line alongside a soft disk-dominated spectrum with a weak tail. The authors employ a self-consistent, convolution-based approach to model both disk Comptonization and disk reflection, using two relativistic disk models (kerrbb and slimbh) to measure spin in the soft state. The key finding is that the Fe K line can be naturally explained by irradiation from the spectrum produced by Comptonization of disk photons, which is curved and more luminous than a simple power-law irradiation would imply. Spin measurements are highly model-dependent: Kerrbb favors a retrograde or negative spin, while slimbh yields a high prograde spin, $a_*=0.84\pm0.03$, with a mass $M\approx9\,M_\odot$, distance $D\approx4.9$ kpc, and inclination $i\approx33^{\circ}$; this underscores the importance of disk physics (finite thickness and radiative transfer) in spin inferences and motivates independent mass/distance constraints for robust tests in BH X-ray binaries.

Abstract

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.

Figures (4)

• Figure 1: The NICER 2--10 keV and NuSTAR 3--10 and 10--60 keV light curves, and the NuSTAR hardness ratio during the studied observations. The zero time corresponds to the start of the NuSTAR observation, and the vertical dashed lines show the end of Part I (red) and the beginning of Part II (black; see Table \ref{['log']}).
• Figure 2: The data to model ratios for the model fitted with slimbh to the NuSTAR data alone and without the reflection component for Part I (left) and Part II (right). We see patterns characteristic of Compton reflection.
• Figure 3: The NICER (green) and NuSTAR FPM A and B (black and red, respectively) unfolded spectra (top panels) and data-to-model ratios (bottom panels) for the joint fit using slimbh. The Part I and II results are shown in the left and right panels, respectively. The total model spectra and the unabsorbed ones are shown by the solid black and blue curves, respectively. The unscattered parts of the disk emission, scattering alone, and reflection are shown by the magenta, green, and red curves, respectively. Their sums equal the total unabsorbed spectra (in blue).
• Figure 4: The hybrid electron distributions corresponding to the joint best fit using comppsc and slimbh, see Figure \ref{['spectrum']} and Table \ref{['fits']}. The distributions for Part I and II are shown by the red and blue solid curves, respectively. The dashed cyan and magenta curves show the corresponding Maxwellian spectra. The normalization is arbitrary.