Constraining the corona geometry of Cyg X-1 with broad-band spectrum and polarimetric analysis based on observations in 2022 May

Abstract Cygnus X-1 (Cyg X-1) exhibited a low hard state in 2022, observed by several missions. The Imaging X-ray Polarimetry Explorer (IXPE) reported that the polarization angle (PA) is aligned with the radio jet and gave a polarization degree (PD) approximately four times higher than the general expectations of $1\%$ through the analysis of the time-integrated data with a simple spectral model, indicating that the disk inclination is higher than a canonical value of about $30^{\circ }$. Many subsequent theoretical studies employed a non-standard model to explain this high PD. Here, we revisit the disk/corona spectrum through a detailed joint analysis using IXPE, NuSTAR (Nuclear Spectroscopic Telescope Array), and NICER (Neutron star Interior Composition Explorer) data. By investigating the time variability of the spectrum, we find that the two-component Comptonization model can better reproduce the data than the one-component Comptonization model originally adopted. We observed a lower disk photon temperature of about $0.15$ keV. Detailed simulation suggests that lowering the disk temperature by a factor of 2 increases the PD by roughly 2 percentage points in the IXPE 2–$8$ keV band for a slab-like corona geometry, helping to reconcile the observed high PD with theoretical predictions. However, the simulated PDs are still significantly lower than the observed ones—even for a rather high $60^{\circ }$ inclination. We also investigated the polarization properties of a simple wedge-shaped corona with a truncated disk and a sandwiching slab corona. We find that the slab corona predicts an apparent energy dependence in PD while PA remains constant in the IXPE band, in agreement with the observed polarization. Therefore, we suggest that Cyg X-1 in 2022 May exhibits a two-Comptonization coronal emission with different optical depths, and the hard one is in a sandwiching slab geometry. We also discuss how the polarization is affected by other parameters of the black hole and the corona.