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Quasi-spherical subsonic accretion can be realized in slowly rotatingwind-fed X-ray pulsars (XPSRs) at X-ray luminosities <4 10^{36} erg/s. In thisregime the accreting matter settles down subsonically onto the rotatingmagnetosphere, forming an extended quasi-static shell. The shell mediates theangular momentum removal from the rotating NS magnetosphere by shear turbulentviscosity in the boundary layer or via large-scale convective motions. In thelast case the differential rotation law in the shell is close toiso-angular-momentum rotation. The accretion rate through the shell isdetermined by the ability of the plasma to enter the magnetosphere due toRayleigh-Taylor instabilities while taking cooling into account. Measurementsof spin-up/spin-down rates of quasi-spherically wind accreting XPSRs inequilibrium with known orbital periods (like e.g. GX 301-2 and Vela X-1) enabledetermination of the main dimensionless parameters of the model and the NSmagnetic field. For equilibrium pulsars with independent measurements of themagnetic field, the stellar wind velocity from the companion can be estimatedwithout the use of complicated spectroscopic measurements. For non-equilibriumpulsars, a maximum possible spin-down torque exerted on the accreting NSexists. From observations of the spin-down rate and X-ray luminosity in suchpulsars (GX 1+4, SXP 1062, 4U 2206+54, etc.) a lower limit on the NS magneticfield is derived, which in all cases turns out to be close to the standard oneand in agreement with cyclotron line measurements. The model explains theexistence of super slowly rotating XPSRs without the need to hypothesize onadditional accretion properties and magnetar-like magnetic fields in accretingneutron stars.

Quasi-spherical accretion in low-luminosity X-ray pulsars: Theory vs. observations