The Cygnus X-1 Puzzle: Implications of X-ray Polarization Measurements in the Soft and Hard States on the Properties of the Accretion Flow and the Emission Mechanisms

TL;DR

This work synthesizes X-ray polarization measurements of Cygnus X-1 in soft and hard states to probe accretion-flow geometry and energy dissipation. By comparing compact near-ISCO and extended corona models, it finds the compact corona energetically favored, though extended configurations cannot be excluded, and highlights the need for energy transport mechanisms beyond simple radiative cooling. A central proposal is a mildly relativistic, electron-positron pair layer enveloping the disk that moves away from the disk, producing high polarization parallel to the jet via Comptonization and Compton-rocket effects in both states. The results imply that magnetically driven dissipation and outflows significantly shape X-ray spectra and polarization, challenging conventional spin- and geometry-based interpretations and motivating further multi-state spectro-polarimetric modeling and observations.

Abstract

In this paper, we summarize key observational constraints of the accretion flow on the black hole X-ray binary Cygnus X-1 (Cyg X-1). The discussion highlights the flows of energy close to the black hole and the importance of the distance range from which the radiating zone draws its energy. For the hard state, we examine compact and extended corona models. We find that compact corona models are energetically favored, but extended models cannot be fully excluded. We discuss the high linear polarization of the Cyg X-1 X-rays in the soft and hard states, parallel to the direction of the radio jet. We propose the presence of a pair layer enveloping the accretion disk moving at approximately half the speed of light away from the disk for both the soft and the hard state. In the soft state, the pairs cool to the Compton temperature of the disk emission. In the hard state, the pairs acquire thermal and bulk motion allowing them to Comptonize the emission to produce the observed power law emission. In both emission states, the bulk motion away from the disk leads to a net polarization parallel to the radio jet. We emphasize that the geometry of the accretion flow in the hard state is still not well constrained, and that observed spectral (including the relativistically broadened Fe K-$α$ line) and spectro-polarimetric signatures depend strongly on the plasma processes responsible for energy dissipation in the plasma.

Figures (5)

• Figure 1: Efficiency $\eta_{\rm grav}(r_1=r,r_2=\infty)$ between the conversion of gravitational energy to free energy when mass moves on Keplerian orbits from $r\rightarrow\infty$ to $r$.
• Figure 2: The observed X-ray fluxes set a lower limit on the energy density $U_{\rm rad}$ of X-rays in the corona. The energy has to be supplied by magnetized plasma with the energy density $U_{\rm B}$, by soft radiation with energy density $U_{\rm soft}$, or bulk motion of plasma with energy density $U_{\rm matter}$ streaming into the corona, each with its characteristic velocity.
• Figure 3: We propose to explain the soft state emission from Cyg X-1 with a new model in which the geometrically thin, optically thick accretion disk is covered with a layer of mildly relativistically moving pair plasma. This figure shows the result from simple radiation transport simulations showing the spectral energy distribution (SED, top) and Stokes $Q$ energy spectrum (bottom) for models with different bulk flow velocities $\beta$ in units of speed of light. The purple line is for $\beta\,=\,0$, the green line is for constant $\beta\,=\,0.36$, and the red line is for the $\beta$-profile of Fig. 3 in AB98 with $\beta$ varying from 0.36 to 0.705 along the flow. The SEDs have been normalized to 1 at their peak. Positive $Q$-values correspond to a PA parallel to the surface of the atmosphere, negative $Q$-values correspond to a PA parallel to the surface normal.
• Figure 4: Same as Fig. \ref{['f:outflow1']} but for the model with the $\beta$-profile from Figure 3 of AB98 for different inclinations.
• Figure 5: Same as Fig. \ref{['f:outflow1']} with the $\beta$-profile of Figure 3 of AB98 with most of the atmosphere being at 0.3 keV, but with the uppermost layer being at 150 keV to produce an SED similar as during the IXPE soft state observations of Cyg X-1. The different curves are for different uppermost layer optical depths $\Delta t_{\rm z}$.