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

TL;DR

The paper addresses the origin of optical polarization in LS I+61°303 within the pulsar binary framework by modeling Thomson scattering in the colliding-wind region. It advances the methodology by incorporating the finite angular size of the Be-star companion and including Be-disk scattering as a separate polarized component, then fits BVR polarization data with an MCMC approach to constrain wind and orbital parameters. The results yield $\eta\approx 0.18$, $e\approx 0.10$, and $\dot{M}_w/v_w\approx 1.55\times 10^{12}\,\mathrm{g\,cm^{-1}}$, with a Be-disk contribution of about $1.7\%$ to the polarization and a periastron phase $\nu_p\approx 0.54$, implying a magnetar-like NS with $B_{NS}\sim 1.5\times 10^{14}$ G. The work also discusses dispersion measure and potential radio-transparency windows, highlighting the utility of optical polarization as a diagnostic for the compact-object nature and wind geometry in gamma-ray binaries.

Abstract

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 $ν_{\rm p}=0.5-0.6$, 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 $η>0.1$, 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.

Figures (12)

• Figure 1: Left: Schematic picture of the colliding wind systems. The interaction between the pulsar wind from the pulsar (small filled circle) and outflow from the companion star (large filled circle) creates a shock (thick curved line) that wraps the pulsar. "I", "II" and "III" incinerates the regions of the free expanding stellar wind, the shock surface and the free expanding pulsar wind. "Z" indicates the direction of the orbital angular momentum. Right: Coordinate system applied in this study. The direction of the observer is represented by $n_{\rm o}$, where $\theta_{\rm o}$ and $\nu_{\rm o}$ are polar angle measured from Z-axis and azimuthal angle measured from X-axis, respectively. The X-axis directs toward the periastron. The $n_{disk}$ represents the axis of the Be disk that is perpendicular to the disk plane. By measuring from a scattering point, $P(r)$, the companion star convenes the sky with a solid angle of $\triangle \Omega=2\pi (1-\cos\theta_p)$, where $\theta_p$ is defined from $\cos\theta_p=\sqrt{1-R^2_*/r^2}$.
• Figure 2: Schematic illustration of the geometry of the binary system. The parameter $\nu$ represents the true anomaly (angle measured from the periastron) of the pulsar.
• Figure 3: Comparison between the P.D.s calculated with point source approximation (dashed line) and the finite size of the companion star (solid line). The circular orbit is assumed and the phase zero correspond to the direction of the observer measured from the companion star. The other model parameters are $D=0.1$ AU, $\dot{M}/v_{\rm w}=6.7\times 10^{11}~{\rm g~cm^{-1}}$ , $\theta_{\rm o}=45^{\circ}$ and $\eta=0.25$.
• Figure 4: Dependency of the P.D.s on $D/R_*$ for point source approximation (solid line) and finite size of the radiating star (dashed line). The minimum P.D. in an orbital cycle is displayed. The line of sigh corresponds to the point case for the solid line, and the dashed line represents the finite case. When $D/R_*=2$, $PD(\%)=0.045$ for point case and $PD(\%)=0.034$ for finite case; When $D/R_*=10$, $PD(\%)=0.009$ for point case and $PD(\%)=0.0087$ for finite case
• Figure 5: Orbital variation of P.D. for different momentum ratios. The dotted, solid, and dashed lines represent the cases of $\eta=0.01, 0.05$, and $0.25$, respectively. Other parameters are same as Figure \ref{['fig:point-vs-finite']}.