The properties of wind accretion in symbiotic X-ray binaries (SyXBs) consisting of red-giant and magnetized neutron star (NS) are discussed. The spin-up/spin-down torques applied to NS are derived based on a hydrodynamic theory of quasi-spherical accretion onto magnetized NSs. In this model, a settling subsonic accretion proceeds through a hot shell formed around the NS magnetosphere. The accretion rate onto the NS is determined by the ability of the plasma to enter the magnetosphere.Due to large Reynolds numbers in the shell, the interaction of the rotating magnetosphere with plasma initiates a subsonic turbulence. The convective motions are capable of carrying the angular momentum through the shell. We carry out a population synthesis of SyXBs in the Galaxy with account for the spin evolution of magnetized NS. The Galactic number of SyXBs with bright (M_v<1) low-mass red-giant companion is found to be from sim 40 to 120, and their birthrate is sim 5times 10^{-5}-10^{-4} per year. According to our model, among known SyXBs, Sct X-1 and IRXS J180431.1-273932 are wind-fed accretors. GX 1+4 lies in the transition from the wind-fed SyXBs to SyXBs in which the giants overflow their Roche lobe. The model successfully reproduces very long NS spins (such as in IGR J16358-4724 and 4U 1954+31) without the need to invoke very strong magnetic fields.
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