X-Ray Polarization from the Gamma-Ray Binary LS I +61 303

Technical Summary: X-Ray Polarization from the Gamma-Ray Binary LS I +61◦303

Problem and Context
Gamma-ray binaries are stellar systems comprising a compact object and a massive star, emitting radiation above 100 MeV. The high-energy emission implies the presence of highly relativistic particles accelerated at the intrabinary shock formed by the interaction of the compact object's relativistic wind and the massive star's wind. While X-ray emission in these systems is understood to be synchrotron radiation, the magnetic field configuration within the acceleration region remains a subject of investigation. Previous observations of the gamma-ray binary PSR B1259–63 by the Imaging X-ray Polarimetry Explorer (IXPE) detected X-ray polarization aligned with the shock cone axis, suggesting a magnetic field oriented perpendicular to that axis. However, it remains unknown whether this magnetic field geometry is universal for gamma-ray binaries. Furthermore, the orbital parameters of LS I +61◦303 (hereafter LS61) are not well-constrained, leading to ambiguity in interpreting the electric vector polarization angle (EVPA) relative to the binary geometry.

Methodology
The authors present IXPE observations of LS61 conducted over two successive orbits, covering orbital phases 0.74 to 1.05. Data were collected from three detector units (DUs) using the 2–8 keV energy band. Standard reduction procedures were applied, including background filtering based on count rates and source extraction from a 60″ radius region.

The analysis employed two primary approaches:

1. Model-Independent Analysis: A calculation of polarization degree (PD) and EVPA using weighted event counts without background subtraction, followed by a correction for background utilizing the additive nature of Stokes parameters.
2. Spectropolarimetric Analysis: Generation of Stokes $I$, $Q$, and $U$ spectra binned by energy, modeled using an absorbed power law with constant polarization.

To interpret the EVPA, the authors compared the measured angle against the projected orbital motion of the compact object on the sky. They utilized four distinct sets of orbital elements derived from different techniques:

• Radial velocity measurements (Casares et al. 2005; Aragona et al. 2009).
• High-precision optical photo-polarimetry (Kravtsov et al. 2020), with two solutions (one with free longitude of ascending node $\Omega$, one constrained).
• Modeling of keV/TeV light curves (Chen & Takata 2022).

For solutions lacking direct inclination ($i$) constraints, the authors assumed $i = 75^\circ$ based on mass function constraints, while also testing lower inclinations ($40^\circ$–$60^\circ$).

Key Results

• Polarization Detection: X-ray polarization was detected with a significance of $4.2\sigma$. After background subtraction, the average polarization degree in the 2–8 keV band is $13.1\% \pm 3.0\%$. The electric vector position angle (EVPA) is $-23.8^\circ \pm 6.6^\circ$ (measured anticlockwise from north in the equatorial coordinate system).
• Spectral Consistency: The spectropolarimetric analysis yielded consistent results ($PD = 11.4\% \pm 2.8\%$, $EVPA = -24.1^\circ \pm 7.1^\circ$) and a photon index of $\Gamma = 1.46 \pm 0.03$, consistent with previous measurements.
• Orbital Phase Stability: No statistically significant difference in polarization was found between the two observed orbits or between high and low flux intervals.
• Geometric Alignment:
  • Radial Velocity Solutions: When using orbital elements from Casares et al. (2005) or Aragona et al. (2009), the measured EVPA is misaligned with the compact object-massive star axis by approximately $26^\circ$ to $28^\circ$. This offset increases for lower inclinations.
  • Kravtsov Solutions: The solution with a free $\Omega$ (K20B) yields a small offset ($\sim 10^\circ$) but requires a high inclination ($i = 87^\circ$), which the authors note may be biased by noise. The solution with a constrained $\Omega$ (K20A) suggests a perpendicular orientation ($\sim 90^\circ$ offset).
  • Chen & Takata Solution: The orbital elements derived from modeling the keV/TeV light curves show good alignment between the X-ray EVPA and the compact object-massive star axis (offset $\sim 2.5^\circ$ to $5^\circ$), assuming an inclination of $60^\circ$–$75^\circ$.

Significance and Conclusions
This work represents the second detection of X-ray polarization from a gamma-ray binary. The detection of a $13.1\%$ polarization degree implies that the magnetic field in the particle acceleration region possesses a significant ordered component, estimated to be roughly $20\%$ of the total field energy, though this is considered a lower bound due to potential geometric effects.

The primary contribution of the paper is the use of X-ray polarimetry to test orbital models of LS61. The authors find that if the physical situation mirrors that of PSR B1259–63 (where the shock cone axis aligns with the binary axis), the orbital elements derived from keV/TeV light curve modeling (Chen & Takata 2022) are favored. Conversely, if the radial velocity-based orbits are correct, the $\sim 30^\circ$ misalignment between the EVPA and the binary axis suggests that Coriolis forces induced by binary motion deflect the shocked flows, creating an asymmetric shock region.

The paper concludes that X-ray polarimetry offers a new method to break degeneracies in orbital solutions for gamma-ray binaries. If the true orbit can be independently determined, the X-ray position angle could serve as a direct probe of the intrabinary shock formation dynamics. The authors do not claim to have definitively resolved the orbital parameters of LS61 but highlight the tension between different models and the potential for future polarimetric observations to clarify the system's geometry.