Energy-Resolved Limits on Orbital X-ray Polarization Modulation in Cygnus X-1
Abstract
Reflection off the companion star and its focused stellar wind is predicted to modulate the X-ray polarization of black hole X-ray binaries at half the orbital period (Porb/2), with an energy-dependent amplitude. We test this prediction against all publicly available IXPE observations of Cygnus X-1, comprising 26 time bins of up to one day from 12 observation IDs spanning 2022-2024. Since the normalized Stokes parameters correlate linearly with the spectral hardness ratio in all three energy bands (2-4, 4-6, and 6-8 keV), we employ a simultaneous harmonic regression that decouples spectral variability from orbital modulation at both Porb/2 and Porb, complemented by direct fitting of 3D Monte Carlo radiative transfer stellar companion and wind-scattering templates. After removing the spectral hardness trend, neither approach reveals statistically significant orbital modulation: permutation tests yield p > 0.01 in all bands, with 99% confidence upper limits of 0.25%, 0.63%, and 1.96% on the Porb amplitude and 0.42%, 0.97%, and 2.78% on the Porb/2 amplitude in the 2-4 keV, 4-6 keV, and 6-8 keV bands, respectively. The best-fit stellar companion and wind-scattering amplitude scaling factors in the three bands of A = 0.67 ± 0.85, 0.97 ± 0.62, and −1.06 ± 1.11 are consistent with a null result. These non-detections are sensitivity-limited, as the predicted stellar companion and wind-scattering RMS amplitudes in the three bands of ≈0.10%, ≈0.33%, and ≈0.49% lie below the statistical noise floor of ∼0.18%, ∼0.38%, and ∼1.01%. We quantify the additional exposure required to detect the predicted signal and constrain the wind physics.
Versions
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BibTeX
@misc{chun2026energyresolved,
title = {{Energy-Resolved Limits on Orbital X-ray Polarization Modulation in Cygnus X-1}},
author = {Sohee Chun and Bert Vander Meulen and Kun Hu and Henric Krawczynski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.30894},
eprint = {2606.30894},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.30894},
}
RIS
TY - UNPB
TI - Energy-Resolved Limits on Orbital X-ray Polarization Modulation in Cygnus X-1
AU - Sohee Chun
AU - Bert Vander Meulen
AU - Kun Hu
AU - Henric Krawczynski
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2606.30894
UR - https://arxiv.org/abs/2606.30894
AB - Reflection off the companion star and its focused stellar wind is predicted to modulate the X-ray polarization of black hole X-ray binaries at half the orbital period (P_orb/2), with an energy-dependent amplitude. We test this prediction against all publicly available IXPE observations of Cygnus X-1, comprising 26 time bins of up to one day from 12 observation IDs spanning 2022-2024. Since the normalized Stokes parameters correlate linearly with the spectral hardness ratio in all three energy bands (2-4, 4-6, and 6-8 keV), we employ a simultaneous harmonic regression that decouples spectral variability from orbital modulation at both P_orb/2 and P_orb, complemented by direct fitting of 3D Monte Carlo radiative transfer stellar companion and wind-scattering templates. After removing the spectral hardness trend, neither approach reveals statistically significant orbital modulation: permutation tests yield p > 0.01 in all bands, with 99% confidence upper limits of 0.25%, 0.63%, and 1.96% on the P_orb amplitude and 0.42%, 0.97%, and 2.78% on the P_orb/2 amplitude in the 2-4 keV, 4-6 keV, and 6-8 keV bands, respectively. The best-fit stellar companion and wind-scattering amplitude scaling factors in the three bands of A = 0.67 ± 0.85, 0.97 ± 0.62, and −1.06 ± 1.11 are consistent with a null result. These non-detections are sensitivity-limited, as the predicted stellar companion and wind-scattering RMS amplitudes in the three bands of ≈0.10%, ≈0.33%, and ≈0.49% lie below the statistical noise floor of ∼0.18%, ∼0.38%, and ∼1.01%. We quantify the additional exposure required to detect the predicted signal and constrain the wind physics.
ER -