Symbiotic X-ray binaries (SyXBs) comprise a rare class of low-mass X-ray binaries. We study the Galactic SyXBs, which we consider as detached binaries composed of low-mass giants and wind-fed neutron star (NS) companions, by simulation of the interaction of a magnetized NS with its environment and utilizing a population synthesis code. We focus mainly on the parameters that influence the observational appearance of an SyXB: the donor wind velocity (vw) and the angular momentum distribution in the shell of matter settling on to an NS. We estimate the birthrate of SyXBs as ∼4.1 × 10−5 to ∼6.6 × 10−6 yr−1 and their number in the Galaxy as ∼100–1000. The assumed stellar wind velocity from cool giants is the input parameter that influences the model SyXB population most.
Among known SyXBs or candidate systems, 4U 1954+31 and IGR J16358−4724 in which the NSs have very long spin periods may host quasi-spherically accreting NSs. GX 1+4 has a peculiar long-term spin behaviour and it may also be a quasi-spherical wind-accreting source. We cannot identify whether there are wind-fed accretion discs in 4U 1700+24, Sct X-1, IRXS J180431.1−273932 and 2XMM J174016.0−290337.