Assessing systematic uncertainties from spectral re-analysis of Cyg X-1 with different coronal geometries

TL;DR

This study reanalyzes NuSTAR and Suzaku spectra of Cyg X-1 to quantify systematic uncertainties in relativistic reflection modeling arising from coronal geometry. By comparing a phenomenological broken emissivity profile, a compact lamppost, and an extended disk-like corona (with height $h$ and radii $R_{ m in}$, $R_{ m out}$) and by allowing electron density to vary, the authors find that the disk-like corona provides a fit statistically comparable to the other geometries while yielding more physically consistent parameters, notably $i oughly 30^{\circ}$ and $n_{ m e} oughly 10^{20} m \,cm^{-3}$. Allowing density to vary broadens the allowed spin and inner-disk radius, yet the extended geometry remains a strongly motivated description in light of polarization constraints. Although lamppost models can fit well, polarimetric data favor extended corona scenarios, suggesting that a joint spectro-polarimetric approach is valuable for robustly constraining the corona and spin in Cyg X-1.

Abstract

In this work, we carry out a new spectral reanalysis of NuSTAR and Suzaku observations of the disk reflection spectra in the stellar-mass black hole X-ray binary Cyg~X-1. We compare three types of models: a broken power-law disk emissivity profile with no assumption about the coronal shape used in the previous work of the same observations, a compact lamppost corona, and an extended disk-like corona motivated by recent X-ray polarization results. Our goal is to measure the systematic uncertainties caused by the assumed geometry, with a focus on key parameters such as the black hole spin and the inclination of the inner accretion disk. We find that the disk-like corona gives a fit that is statistically similar to the broken power-law and lamppost models, but it leads to more physically reasonable results, such as a lower inclination angle of about $30^{\circ}$. By using a variable disk density model, we measure the disk density to be $n_{\rm e}\approx10^{20}$\,cm$^{-3}$, which is similar to earlier results. While the extended corona model infers a wider allowed parameter space for black hole spin and the inner radius of the disk-shaped coronal region, this reflects the additional physical freedom of the model. Even so, the disk-like corona remains a strong and physically well-motivated candidate for explaining the X-ray emission from Cyg~X-1.

Figures (11)

• Figure 1: Cartoon of the astrophysical system. The corona is described by an infinitesimal thin disk of inner radius of $R_{in}$, outer radius of $R_{out}$ at height $h$ above the the equatorial plane.
• Figure 2: In the upper panel, the black solid line corresponds to the total model and other lines correspond to its components. In the lower panel, ratio plots of Model 0 are given and red, blue, green, orange, brown, and magenta correspond to NuSTAR's FPMA, FPMB and Suzaku's XIS0, XIS1, PIN, GSO data respectively.
• Figure 3: Error bars represent the ratio plots (data/model) for the models in the denominator for each case (see upper left corner of each plot). The black broken solid lines show the ratios of different models, as indicated in the upper right corner of each plot. This allows us to clearly assess how each model in the numerator improves the fit of the model in the denominator. Since significant changes are observed primarily in the 4-10 keV energy range, the ratios are displayed within this range. Ratio plots with whole energy range (1-200 keV) for all model combinations are presented in Fig. \ref{['fig:ratio-full']}. Red, blue, faint green, and faint orange correspond to NuSTAR's FPMA/FPMB and Suzaku's XIS0/XIS1 data, respectively. The thick gray line is centered at the iron K$\alpha$ line (6.4 keV), with a width of 0.1 keV.
• Figure 4: One-dimensional confidence intervals for the spin parameter across the different models considered in this work. The green dashed line indicates the 90% confidence level ($\Delta \chi^2 = 2.706$).
• Figure 5: In the upper panel, the black solid line corresponds to the total model and other colourful lines correspond to its components. In the lower panel, ratio plots of Model 3 are given and red, blue, green, orange, brown, and magenta correspond to NuSTAR's FPMA, FPMB and Suzaku's XIS0, XIS1, PIN, and GSO data, respectively. See the text for more details.