Constraining the Corona Geometry of Cyg X-1 with Broad Band Spectrum and Polarimetric Analysis Based on Observations in May 2022

TL;DR

The study tackles the high polarization degree observed in Cyg X-1 during its May 2022 hard state by performing a joint broad-band spectral and X-ray polarimetric analysis with IXPE, NuSTAR, and NICER. It demonstrates that a two-Comptonization corona, with two optical depths and a cooler disk seed temperature around $kT_{in}\sim0.15$ keV, provides a better fit than a single-Comptonization model and naturally yields a higher PD than standard expectations. Monte Carlo simulations of slab-like (sandwiching) and wedge-shaped coronae show that a slab geometry reproduces the observed PD energy dependence and PA behavior, supporting a two-component coronal picture, though the absolute PD remains underpredicted by the models. The results imply a complex corona with different optical depths, a truncated/separated disk geometry, and point toward further refinement of seed photon distributions and reflection effects in the polarization modeling.

Abstract

Cygnus X-1 (Cyg X-1) exhibited a low hard state in 2022, observed by several missions. The IXPE reported that the polarization angle is aligned with the radio jet and gave a polarization degree approximately 4 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, and NICER data. By investigating the time variability of the spectrum, we find that the two-Comptonization components model can better reproduce the data than the one-Comptonization component 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.

Figures (11)

• Figure 1: Light curves of observation 1 and 2. We exhibit the light curves of Cyg X-1 observed by, IXPE (red), NuSTAR (blue) and NICER (pink). The left panel shows the light curves of observation 1 and the right panel shows those of observation 2. The upper and lower panels are the light curves below and above 4 keV. Scale factors are applied to make count rates of different missions compatible with each other and that of IXPE is fixed to 1. Alt text: Four light curves for Cyg X-1 observations in 2022.
• Figure 2: Light curves of Cyg X-1 observation 1 of IXPE and NICER. The upper panel shows the light curve of IXPE in 2 -- 8 keV and the lower panel shows that of NICER in 0.3 - 15 keV band The shades with different colors are the selected time periods closed to the negative dip and positive spike in the IXPE light curve (summarized in table \ref{['name']}). Alt text: Two light curves of Cyg X-1 observation 1.
• Figure 3: The fitting results of time periods i and vi with different models. The upper panel shows the fitting spectrum and data-to-model ratio of one-Comptonization component model for period i (left) and vi (right), respectively. The lower panel presents those of two-Comptonization components model. Systematic uncertainties are already taken into account. Alt text: Four spectrum and data-to-model ratio plots of the selected data of Cyg X-1 observation 1.
• Figure 4: The hardness ratio of IXPE observations 1. The figure shows the hardness ratio of observation 1. The green and red parts are the relatively hard and soft parts, respectively. The blue parts represent the very hard part, corresponding to the negative dips shown in figure \ref{['LCnicerixpe']}. Alt text: Hardness ratio plot of Cyg X-1 observation 1.
• Figure 5: Simultaneous fitting of IXPE, NuSTAR, and NICER of time period A. We fit time period A with the double Comptonization components model of IXPE (green), NuSTAR (red), and NICER (black). The spectrum show high consistency with MBPO correction applied to them. Alt text: One spectrum and data-to-model ratio plot of time period A.