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Peer-reviewedCC BY 4.0The Astrophysical Journal

Energy-resolved Limits on Orbital X-Ray Polarization Modulation in Cygnus X-1

  • Sohee Chun1
  • Bert Vander Meulen2
  • Kun Hu1
  • Henric Krawczynski1
  1. 1Washington University in St. Louis
  2. 2European Space Agency (ESA)
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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 ( 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 1 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, 4–6, 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 nondetections 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.

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Cite

BibTeXRIS
BibTeX
@article{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},
  journal = {The Astrophysical Journal},
  year = {2026},
  month = oct,
  doi = {10.3847/1538-4357/aea617},
  url = {https://iopscience.iop.org/article/10.3847/1538-4357/aea617},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
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  - 2026/10/09
JO  - The Astrophysical Journal
DO  - 10.3847/1538-4357/aea617
UR  - https://iopscience.iop.org/article/10.3847/1538-4357/aea617
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 1 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, 4–6, 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 nondetections 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.
SN  - 0004-637X
SN  - 1538-4357
ER  -