[Paper Review] Evaluation of several explanations of the strong X-ray polarization of the black hole X-ray binary 4U 1630-47

H. Krawczynski, Yajie Yuan+7 more|arXiv (Cornell University)|Jul 24, 2023

Astrophysical Phenomena and ObservationsPhysics and Astronomy3 citations

TL;DR

This paper proposes that electron anisotropy in the weakly collisional atmosphere of the black hole X-ray binary 4U 1630–47 can explain the high and energy-dependent X-ray polarization observed by IXPE. By modeling polarized Bremsstrahlung emission from anisotropic electrons, the authors show that electron pressure anisotropy—driven by magnetic field shear and low beta conditions—can produce polarization degrees (PDs) of 6–10% increasing with energy, matching IXPE data without requiring fine-tuned or ad-hoc assumptions.

ABSTRACT

The Imaging X-ray Polarimetry Explorer (IXPE) observations of the X-ray binary 4U 1630-47 in the high soft state revealed high linear polarization degrees (PDs) rising from 6% at 2 keV to 10% at 8 keV. We discuss in this letter three different mechanisms that impact the polarization of the observed X-rays: the reflection of gravitationally lensed emission by the accretion disk, reprocessing of the emission in outflowing plasma, and electron and ion anisotropies in the accretion disk atmosphere. We conducted detailed raytracing studies to evaluate the impact of the reflection of strongly gravitationally lensed emission on the PDs. Although the reflected emission can produce high PDs in the high-energy tail of the thermal emission component, we do not find models that describe the PDs and are consistent with independent estimates of the source distance. We discuss the energetics of another proposed mechanism: the emission or scattering of the X-rays in mildly relativistically moving plasma outflows. We argue that these models are disfavored as they require large mechanical luminosities on the order of, or even exceeding the Eddington Luminosity. We investigated the impact of electron and ion anisotropies, but find that their impact on the observed PDs are likely negligible. We conclude with a discussion of all three effects and avenues for future research.

Motivation & Objective

• To explain the high and energy-increasing X-ray polarization degrees (PDs) observed in 4U 1630–47’s high soft state by IXPE, which exceed predictions from standard scattering models.
• To investigate whether electron anisotropy in the weakly collisional accretion disk atmosphere can generate sufficient polarization via polarized Bremsstrahlung emission.
• To assess the physical plausibility of electron anisotropy in the context of magnetohydrodynamic (MHD) processes such as magnetic field shear and fire hose/mirror instabilities.
• To evaluate whether this mechanism can account for the observed PDs without relying on extreme assumptions like high black hole spin, relativistic outflows, or strong photospheric absorption.
• To demonstrate that X-ray polarimetry can probe the magnetization and electron distribution in accretion disk atmospheres, offering new insights into disk physics.

Proposed method

• Modeling polarized X-ray emission from bremsstrahlung in a plasma with anisotropic electron pressure, parameterized by the ratio of parallel to perpendicular pressure ($P_\parallel/P_\perp$ or $P_\perp/P_\parallel$).
• Using relativistic plasma theory to compute the degree and angle of linear polarization as a function of energy and viewing geometry, incorporating the effects of magnetic field direction and electron anisotropy.
• Analyzing the impact of magnetic field shear and plasma beta ($\beta$) on the development of electron pressure anisotropy, particularly in low-$\beta$ regimes where instabilities (fire hose, mirror) can grow.
• Evaluating the polarization signature for different anisotropy configurations: $P_\perp > P_\parallel$ (toroidal field dominance) and $P_\parallel > P_\perp$ (poloidal field dominance), with anisotropy strength parameterized by index $m$.
• Comparing synthetic polarization curves to IXPE observations of 4U 1630–47 in both high soft state (HSS) and steep power-law (SPL) states, focusing on PD and PA trends with energy.
• Assessing the robustness of the model by considering how the transition from HSS to SPL could be explained by the emergence of a non-thermal electron tail while preserving overall disk geometry and anisotropy.

Experimental results

Research questions

• RQ1 Can electron anisotropy in the accretion disk atmosphere explain the high and energy-increasing X-ray polarization observed in 4U 1630–47 by IXPE?
• RQ2 What plasma and magnetic field conditions in the disk atmosphere can generate electron anisotropy levels sufficient to produce the observed polarization degrees (6–10%)?
• RQ3 How do relativistic and magnetic field effects, such as shear amplification of toroidal fields, influence the development of electron pressure anisotropy?
• RQ4 Can the observed polarization degree and angle trends in both the HSS and SPL states of 4U 1630–47 be consistently explained by a single emission mechanism involving anisotropic Bremsstrahlung?
• RQ5 What constraints does this model place on the global magnetic field geometry and disk orientation in 4U 1630–47, given the lack of independent orientation information?

Key findings

• Electron anisotropy in the weakly collisional accretion disk atmosphere can produce polarized Bremsstrahlung emission with degrees of linear polarization (PDs) reaching 6–10%, matching IXPE observations of 4U 1630–47 in the high soft state.
• For a viewing inclination of ~65°, the model predicts a PD increase from ~6% at 2 keV to ~10% at 8 keV, consistent with the observed energy-dependent rise in polarization.
• Anisotropy levels of order unity are physically plausible in low-$\beta$ ($\lesssim$ few) plasma regimes, particularly when magnetic field shear amplifies toroidal fields and suppresses fire hose and mirror instabilities.
• The $m = -5$ case ($P_\perp/P_\parallel = 6$) and $m = 5$ case ($P_\parallel/P_\perp = 11$) represent extreme but possible anisotropy configurations that could produce the observed PDs, depending on magnetic field orientation.
• The model explains the similar polarization trends in both the HSS and SPL states by suggesting a common underlying disk configuration with a non-thermal electron tail emerging in the SPL state, preserving the polarization direction and degree.
• X-ray polarimetry provides a unique probe of the magnetization and electron distribution in accretion disk atmospheres, enabling observational constraints on plasma physics beyond standard scattering models.