A Two-stage Kick Scenario for the Peculiar Low-mass X-Ray Binary GX 1+4

The low-mass X-ray binary (LMXB) GX 1+4 stands out with its unique properties. Despite being an old system, it hosts a strongly magnetized neutron star (NS), a trait usually linked to younger systems. Its exceptionally long orbital period (1160 days) and low eccentricity (0.101) imply that the NS formed with minimal mass loss and a weak natal kick. These features collectively point toward the NS having formed through the accretion-induced collapse (AIC) of a white dwarf. However, GX 1+4’s unusually high peculiar velocity (∼189.36 km s −1 ) defies standard AIC explanations. To address this discrepancy, we propose a two-stage kick scenario within the AIC framework: an initial natal kick followed by a delayed electromagnetic “rocket effect” kick. Our Monte Carlo simulations indicate that while the natal kick (≲100 km s −1 ) can generate a wide range of orbital eccentricities, the subsequent rocket kick (∼240–480 km s −1 ) explains both the high systemic velocity and low eccentricity. This two-stage kick mechanism naturally reproduces the observed characteristics of GX 1+4, provided that the NS’s initially buried magnetic field reemerges after the acceleration process ends. Our study represents the first attempt to quantitatively constrain the kick velocities in GX 1+4 and underscores the importance of possible rocket kicks in forming such peculiar LMXB systems.