Population synthesis for symbiotic X-ray binaries

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 similar to 4.1 x 10-5 to similar to 6.6 x 10-6?yr-1 and their number in the Galaxy as similar to 1001000. 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.