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

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.