On the timing behavior of PSR B1259-63 under the propeller torque from a transient accretion disc

The $\gamma$-ray pulsar binary system PSR B1259-63 flares in GeV after each periastron. The origin of those flares is still under debate. Recently, [2017ApJ...844..114Y] proposed a mechanism that might explain the GeV flares. In that model, a transient accretion disc is expected to be formed from the matter which was gravity-captured by the neutron star from the main sequence companion's circumstellar disc. The transient accretion disc exerts a spin down torque on the neutron star (propeller effect), which might be traceable via pulsar timing observation of PSR B1259-63. In this paper, we phenomenologically consider the propeller effect with a parameter $\chi$, which describes the coupling between the disc matter and the neutron star. Comparing the expected timing residuals against the recent observation in [2014MNRAS.437.3255S], we conclude that the angular momentum transfer is very weak (with the coupling parameter $\chi\le10^{-4}$).