Accretion And Propeller Torque In The Spin-down Phase Of Neutron Stars: The Case Of Transitional Millisecond Pulsar PSR J1023+0038

The spin-down rate of PSR J1023+0038, one of the three confirmed transitional millisecond pulsars, was measured in both radio pulsar (RMSP) and X-ray pulsar (LMXB) states. The spin-down rate in the LMXB state is only about 27 % greater than in the RMSP state (Jaodand et al. 2016). The inner disk radius, r_in, obtained recently by Ertan (2017) for the propeller phase, which is close to the co-rotation radius, r_co, and insensitive to the mass-flow rate, can explain the observed torques together with the X-ray luminosities, Lx . The X-ray pulsar and radio pulsar states correspond to accretion with spin-down (weak propeller) and strong propeller situations respectively. Several times increase in the disk mass-flow rate takes the source from the strong propeller with a low Lx to the weak propeller with a higher Lx powered by accretion on to the star. The resultant decrease in r_in increases the magnetic torque slightly, explaining the observed small increase in the spin-down rate. We have found that the spin-up torque exerted by accreting material is much smaller than the magnetic spin-down torque exerted by the disk in the LMXB state.