A precessing stellar disk model for superorbital modulations of the gamma-ray binary LS I+61$^{\circ}$ 303

Gamma-ray binary LS I+61$^{\circ}$ 303 consists of a neutron star orbiting around a Be star with a period of $P_{\rm orb}\simeq26.5\ {\rm d}$. Apart from orbital modulations, the binary shows long-term flux variations with a superorbital period of $P_{\rm sup}\simeq4.6\ {\rm yrs}$ as seen in nearly all wavelengths. The origin of this superorbital modulation is still not well understood. Under the pulsar wind-stellar outflow interaction scenario, we propose that the superorbital modulations of LS I+61$^{\circ}$ 303 could be caused by the precession of the Be disk. Assuming X-rays arise from synchrotron radiation of the intrabinary shock, we develop an analytical model to calculate expected flux modulations over the orbital and superorbital phases. The asymmetric two-peak profiles in orbital light curves and sinusoidal-like long-term modulations are reproduced under the precessing disk scenario. The observed orbital phase drifting of the X-ray peak and our fitting of long-term X-ray data indicate that the neutron star is likely orbiting around the star with a small eccentricity and periastron phase around $\Phi_{\rm p}\sim0.6$. We compare the Corbet diagrams of LS I+61$^{\circ}$ 303 with other Be/X-ray binaries and the linear correlation in the $P_{\rm sup}-P_{\rm orb}$ diagram suggests that the precession of the Be disk in LS I+61$^{\circ}$ 303 is induced by the tidal torque of its neutron star companion.