Spin-up/spin-down of neutron star in Be-X-ray binary system GX 304-1

We analyze spin-up/spin-down of the neutron star in Be X-ray binary system GX\,304-1 observed by \textit{Swift}/XRT and \textit{Fermi}/GBM instruments in the period of the source activity from April 2010 to January 2013 and discuss possible mechanisms of angular momentum transfer to/from the neutron star. We argue that the neutron star spin-down at quiescent states of the source with an X-ray luminosity of $L_x\sim 10^{34}$~erg s$^{-1}$ between a series of Type I outbursts and spin-up during the outbursts can be explained by quasi-spherical settling accretion onto the neutron star. The outbursts occur near the neutron star periastron passages where the density is enhanced due to the presence of an equatorial Be-disc tilted to the orbital plane. We also propose an explanation to the counterintuitive smaller spin-up rate observed at higher luminosity in a double-peak Type I outburst due to lower value of the specific angular momentum of matter captured from the quasi-spherical wind from the Be-star by the neutron star moving in an elliptical orbit with eccentricity $e\gtrsim 0.5$.