The First Polarimetric View on Quasi-Periodic Oscillations in a Black Hole X-ray Binary

We present the first polarimetric analysis of Quasi-Periodic Oscillations (QPO) in a black hole binary utilizing \textit{IXPE} data. Our study focuses on Swift J1727.8--1613, which experienced a massive outburst that was observed by various telescopes across different wavelengths. The \textit{IXPE} observation we studied was conducted during the Hard-Intermediate state. The polarization degree (PD) and polarization angle (PA) were measured at 4.28$\pm$0.20\% and $1.9^{\circ}\pm1.4^{\circ}$, respectively. Remarkably, significant QPO signals were detected during this observation, with a QPO frequency of approximately 1.34 Hz and a fractional root-mean-square (RMS) amplitude of about 12.3\%. Furthermore, we conducted a phase-resolved analysis of the QPO using the Hilbert-Huang transform technique. The photon index showed a strong modulation with respect to the QPO phase. In contrast, the PD and PA exhibit no modulations in relation to the QPO phase, which is inconsistent with the expectation of the Lense-Thirring precession of the inner flow. Further theoretical studies are needed to conform with the observational results.