Investigation for binary characteristics of LS I+61303 with optical polarization

We investigate the optical linear polarization caused by Thomson scattering of the stellar radiation for gamma-ray binary \lsi61, which likely contains a young pulsar. Based on the pulsar binary scenario, we model the interaction between the pulsar wind and stellar wind from the massive companion star, which creates a shock. To accurately compute the resulting polarization of the stellar wind, we develop a method for the Thomson scattering that accounts for the finite size of the companion star. By fitting the optical polarization data, we constrain the system parameters, such as eccentricity, the momentum ratio of the two winds, and mass-loss rate from the companion star. We find that (i) the predicted eccentricity $e\sim 0.1$ is smaller than the values derived from the radial velocity curve and (ii) the orbital phase of the periastron is $\nu_{\rm p}=0.5-0.6$, which is consistent with the previous polarization study of Kravtsov et al. Additionally, we estimate the mass-loss rate from the companion star and the momentum ratio of two winds as $\dot{M}\sim 2\times 10^{-6}\rm M_{\odot}~{\rm year^{-1}}$ and $\eta>0.1$, respectively. Assuming that the pulsar wind carries the spin-down energy, the spin-down magnetic field of the putative pulsar inferred from these parameters is of the order of $B\sim 10^{14}\mathrm{G}$, which may support the highly-B pulsar or magnetar scenario for the compact object of $\rm{LS\ I} +61^{\circ}303$. We also discuss the dispersion measure under the predicted orbital geometry and provide a corresponding interpretation of the pulsed radio signal detected by FAST.