  Quasi-spherical subsonic accretion onto slowly rotating magnetized NS is
considered, when the accreting matter settles down subsonically onto the
rotating magnetosphere, forming an extended quasi-static shell. The shell
mediates the angular momentum transfer to/from the rotating NS magnetosphere by
large-scale convective motions, which lead to an almost iso-angular-momentum
rotation law inside the shell. The accretion rate through the shell is
determined by the ability of the plasma to enter the magnetosphere due to
Rayleigh-Taylor instability while taking cooling into account. The settling
regime of accretion is possible for moderate X-ray luminosities L <4 10^36
erg/s. At higher luminosities a free-fall gap above the NS magnetosphere
appears due to rapid Compton cooling, and accretion becomes highly
non-stationary. From observations of spin-up/spin-down rates of wind accreting
equilibrium XPSRs with known orbital periods (GX 301-2, Vela X-1), the main
dimensionless parameters of the model and be determined and the NS magnetic
field can be estimated. For equilibrium pulsars with independent measurements
of the magnetic field the velocity of the stellar wind can be estimated without
the use of complicated spectroscopic measurements. For non-equilibrium pulsars,
a maximum possible value of the spin-down rate of the accreting neutron star
exists. From observations of the spin-down rate and the X-ray luminosity in
such pulsars (e. g. GX 1+4, SXP 1062 and 4U 2206+54) a lower limit on the
neutron star magnetic field is obtained, which in all cases turns out to be
close to the standard 10^12-10^13 G value, in agreement with cyclotron line
measurements. The model explains both the spin-up/spin-down of the pulsar
frequency on large time-scales and the irregular short-term frequency
fluctuations, which may correlate or anti-correlate with the X-ray luminosity
fluctuations.
