Evidence of residual Doppler shift on three pulsars, PSR B1259-63, 4U1627-67 and PSR J2051-0827

Abstract

The huge derivative of orbital period observed in binary pulsar PSR B1259-63, the torque reversal displaying on low mass X-ray binary, 4U1627-67 and the long term change of orbital period of PSR J2051-0827, seem totally unrelated phenomena occurring at totally different pulsar systems. In this paper, they are simply interpreted by the same mechanism, residual Doppler shift. In a binary system with periodic signals sending to an observer, the drift of the signal frequency actually changes with the varying orbital velocity, projected to line of sight at different phases of orbit. And it has been taken for granted that the net red-shift and blue-shift of an full orbit circle be cancelled out, so that the effect of Doppler shift to the signal in binary motion cannot be accumulated over the orbital period. However, taking the propagation time at each velocity state into account, the symmetry of the velocity distribution over the orbital phase is broken. Consequently, the net Doppler shift left in an orbit is non-zero. Understanding this Newtonian second Doppler effect not only makes pulsars better laboratory in the test of gravitational effects, but also allows us to extract the angular momentum of the pulsar of PSR J2051-0827, $\leq 2\times 10^{43}gcm^2$; and the accretion disc of 4U 1627-67, $7\times 10^{50} gcm^2/s$, respectively, which are of importance in the study of structure of neutron stars and the physics of accretion disc of X-ray binaries.