Orbital variability of the optical linear polarization of the \(\gamma\)-ray binary LS I +61 303 and new constraints on the orbital parameters

We studied the variability of the linear polarization and brightness of the \(\gamma\)-ray binary LS I +61 303. High-precision BVR photopolarimetric observations were carried out with the Dipol-2 polarimeter on the 2.2 m remotely controlled UH88 telescope at Mauna Kea Observatory and the 60 cm Tohoku telescope at Haleakala Observatory (Hawaii) over 140 nights in 2016--2019. We determined the position angle of the intrinsic polarization \(\theta \simeq 11^\circ\), which can either be associated with the projection of the Be star's decretion disk axis on the plane of sky, or can differ from it by \(90^\circ\). Using the Lomb-Scargle method, we performed timing analyses and period searches of our polarimetric and photometric data. We found statistically significant periodic variability of the normalized Stokes parameters \(q\) and \(u\) in all passbands. The most significant period of variability, \(P_\text{Pol} = 13.244 \pm 0.012\) d, is equal to one half of the orbital period \(P_\text{orb} = 26.496\) d. Using a model of Thomson scattering by a cloud that orbits the Be star, we obtained constraints on the orbital parameters, including a small eccentricity \(e