In this paper we report strong evidence for a ~304-day periodicity in the spin history of the accretion-powered pulsar GX 1+4 that is very likely to be a signature of the orbital period of the system. Using BATSE public-domain data, we show a highly-significant periodic modulation of the pulsar frequency from 1991 to date which is in excellent agreement with the ephemeris proposed by Cutler, Dennis & Dolan in 1986, which were based on a few events of enhanced spin-up that occurred during the pulsars spin-up era in the 1970s. Our results indicate that the orbital period of GX 1+4 is 303.8+-1.1 days, making it by far the widest low-mass X-ray binary system known. A likely scenario for this system is an elliptical orbit in which the neutron star decreases its spin-down rate (or even exhibits a momentary spin-up behavior) at periastron passages due to the higher torque exerted by the accretion disk onto the magnetosphere of the neutron star.
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