X-ray polarization in the soft state of Cyg X-1

Abstract

We aim to identify the physical mechanism responsible for the observed X-ray emission and polarization of Cyg X-1 in the soft state. We perform a detailed spectral analysis of X-ray data obtained by NICER, NuSTAR, and INTEGRAL during observations simultaneous with IXPE on 2023 June 20, supplemented at higher energies with archival CGRO data. We develop a new model, retBB, that describes thermal disk emission and its returning reflection, and apply it together with accurate models of Comptonization and relativistically broadened reflection. Using the resulting spectral solution, we compute the expected polarization signal and compare it with the IXPE measurements. Our spectropolarimetric modeling shows that the observed polarization is produced by Comptonization in a corona undergoing a semi-relativistic outflow with a velocity of ~0.3c. Our spectral solutions admit either low or high black-hole spin values, depending on the adopted model setup. However, the observed polarization strongly favors a low spin. At high spin, the polarization angle would inevitably rotate significantly across the energy band, which is not consistent with the observations. Apart from this rotation of the polarization angle, general relativistic effects do not play a significant role in producing the observed polarization. In particular, we find that, at most, returning disk radiation contributes only a minor amount.

Figures (14)

• Figure 1: Spectropolarimetric properties of radiation Comptonized in a slab geometry representing the disk-corona system. (a) Energy dependence of the PD as observed at inclination $i = 35\degr$ for the outflow velocities $v = 0$ (solid) and $v=0.3c$ (dashed) and two values of the blackbody temperature of seed photons, $kT_{\rm seed} = 0.05$ keV (black) and 0.25 keV (red), corresponding to the color temperatures in our fitted disk model at $\simeq 100 R_{\rm g}$ and $\simeq 10 R_{\rm g}$, respectively. In all cases, the Comptonization parameters are $kT_{\rm e} = 25$ keV and $\tau = 0.75$, corresponding to the corona parameters found in Sect. \ref{['sect:results']}. (b) The corresponding energy spectra.
• Figure 2: Geometries considered in this work and the main spectral components produced close to the black hole. (a) Geometry considered in models 1 and 2. (b) Geometry with an additional warm corona considered in model 3. (c) 'No-corona' geometry considered in model 4.
• Figure 3: Spectral energy distribution of Cyg X-1. Top: the NICER (cyan), NuSTAR (black and red), INTEGRAL (green) and CGRO (blue) unfolded spectra for model 2. The dot-dashed (green), dotted (magenta), and solid (cyan) curves show the absorbed Comptonized component (including unscattered seed photons from the thermal disk), coronal reflection from accretion disk, and static reflection, respectively; see Table \ref{['tab:models']} for the definition of spectral components. The spectral components are normalized to NICER. Bottom: the data-to-model ratios.
• Figure 4: Unabsorbed spectral components and polarization properties of model 2 involving a rapidly rotating black hole. Polarization is calculated neglecting an outflow (i.e., $v=0$). The orange points in panels (b) and (c) show the average PD and PA measured by IXPE in the soft state of Cyg X-1 2025AA...701A.115K. (a) The total spectrum (solid black curve) and individual spectral components of model 2; the direct thermal disk emission, reflected returning radiation, hybrid Comptonized emission, and its reflection are shown by dashed red, dashed blue, dot-dashed green, and dotted magenta curves, respectively. (b) The polarization degree. The solid black curve shows the net PD resulting from the combined polarization signals of all components, while the colored curves show the contributions of the polarized part of each component to the total flux. (c) The polarization angle, measured counterclockwise from celestial North. For the PA calculation, we assume that the disk rotates clockwise and that the disk axis is aligned with the radio jet, adopting a position angle of $-23\fdg5$. The line styles and colors in panels (b) and (c) correspond to those used in panel (a).
• Figure 5: Same as Fig. \ref{['fig:components2']} but for model 3 with $a=0$ and including an outflow with $v=0.3c$. The red dashed curves are for the thermal disk spectrum modified by warm-corona Comptonization.