Quasispherical subsonic accretion in X-ray pulsars

A theoretical model is considered for quasispherical subsonic accretion onto slowly rotating magnetized neutron stars. In this regime, the accreting matter settles down subsonically onto the rotating magnetosphere, forming an extended quasistatic shell. Angular momentum transfer in the shell occurs via large-scale convective motions resulting, for observed pulsars, in an almost iso-angular-momentum $\omega \sim 1/R^2$ 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 instabilities, with allowance for cooling. A settling accretion regime is possible for moderate accretion rates $\dot M \lesssim \dot M_* \simeq 4\times 10^{16}$ g s$^{-1}$. At higher accretion rates, a free-fall gap above the neutron star magnetosphere appears due to rapid Compton cooling, and the accretion becomes highly nonstationary. Observations of spin-up/spin-down rates of quasispherically wind accreting equilibrium X-ray pulsars with known orbital periods (e.g., GX 301-2 and Vela X-1) enable us to determine the main dimensionless parameters of the model, as well as to estimate surface magnetic field of the neutron star. For equilibrium pulsars, the independent measurements of the neutron star magnetic field allow for an estimate of the stellar wind velocity of the optical companion without using complicated spectroscopic measurements. For nonequilibrium pulsars, a maximum value is shown to exist for the spin-down rate of the accreting neutron star. 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 can be put on the neutron star magnetic field, which in all cases turns out to be close to the standard value and which agrees with cyclotron line measurements. Furthermore, both explains the spin-up/spin-down of the pulsar frequency on large time-scales and also accounts for the irregular short-term frequency fluctuations, which may correlate or anticorrelate with the observed X-ray luminosity fluctuations.