A theoretical model for quasi-spherical subsonic accretion onto slowly rotating magnetized neutron stars is constructed. In this model the accreting matter subsonically settles down onto the rotating magnetosphere forming an extended quasi-static shell. This shell mediates the angular momentum removal from the rotating neutron star magnetosphere during spin-down episodes by large-scale convective motions. The accretion rate through the shell is determined by the ability of the plasma to enter the magnetosphere. The settling regime of accretion can be realized for moderate accretion rates $\dot M< \dot M_*\simeq 4\times 10^{16}$ g/s. At higher accretion rates a free-fall gap above the neutron star magnetosphere appears due to rapid Compton cooling, and accretion becomes highly non-stationary. From observations of the spin-up/spin-down rates (the angular rotation frequency derivative $\dot \omega^*$, and $\partial\dot\omega^*/\partial\dot M$ near the torque reversal) of X-ray pulsars with known orbital periods, it is possible to determine the main dimensionless parameters of the model, as well as to estimate the magnetic field of the neutron star. We illustrate the model by determining these parameters for three wind-fed X-ray pulsars GX 301-2, Vela X-1, and GX 1+4. 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 can correlate or anti-correlate with the X-ray flux fluctuations in different systems. It is shown that in real pulsars an almost iso-angular-momentum rotation law with $\omega \sim 1/R^2$, due to strongly anisotropic radial turbulent motions sustained by large-scale convection, is preferred.Comment: 48 pages, 4 figures, accepted for publication in MNRA

Aims. We aim both to complement the existing data on the spin history of the peculiar accreting X-ray pulsar GX 1+4 with more past and current data from BeppoSAX, INTEGRAL, and Fermi and to interpret the evolution in the framework of accretion theory. Methods. We used source light curves obtained from BeppoSAX/WFC and INTEGRAL/ISGRI to derive pulse periods using an epoch-folding analysis. Fermi/GBM data were analysed by fitting a constant plus a Fourier expansion to background-subtracted rates, and maximizing the Y 2 statistic. We completed the sample with hard X-ray light curves from Swift/BAT. The data were checked for correlations between flux and changes of the pulsar spin on different timescales. Results. The spin-down of the pulsar continues with a constant change in frequency, i.e., an apparently accelerating change in the period. Over the past three decades, the pulse period has increased by about ∼50%. Short-term fluctuations on top of this long-term trend do show anti-correlation with the source flux. Possible explanations of the observed long-term frequency and its dependence on flux are discussed.

Accretion of matter onto the surface of a freely precessing neutron star with a complex non-dipole magnetic field can explain the change of X-ray pulse profiles of Her X-1 observed by RXTE with the phase of the 35-day cycle. We demonstrate this using all available measurements of X-ray pulse profiles in the 9-13 keV energy range obtained with the RXTE/PCA. The measured profiles guided the elaboration of a geometrical model and the definition of locations of emitting poles, arcs, and spots on the NS surface which satisfactorily reproduce the observed pulse profiles and their dependence on free precession phase. We have found that the observed trend of the times of the 35-day turn-ons on the O-C diagram, which can be approximated by a collection of consecutive linear segments around the mean value, can be described by our model by assuming a variable free precession period, with a fractional period change of about a few percent. Under this assumption and using our model, we have found that the times of phase zero of the neutron star free precession (which we identify with the maximum separation of the brightest spot on the neutron star surface with the NS spin axis) occur about 1.6 days after the the mean turn-on times inside each 'stable' epoch, producing a linear trend on the O-C diagram with the same slope as the observed times of turn-ons. We propose that the 2.5% changes in the free precession period that occur on time scales of several to tens of 35-day cycles can be related to wandering of the principal inertia axis of the NS body due to variations in the patterns of accretion onto the NS surface. The closeness of periods of the disk precession and the NS free precession can be explained by the presence of a synchronization mechanism in the system, which modulates the dynamical interaction of the gas streams and the accretion disk with the NS free precession period.

A review of wind accretion in high-mass X-ray binaries is presented. We focus on different regimes of quasi-spherical accretion onto a neutron star: supersonic (Bondi) accretion, which takes place when the captured matter cools down rapidly and falls supersonically towards the neutron-star magnetosphere, and subsonic (settling) accretion which occurs when the plasma remains hot until it meets the magnetospheric boundary. The two regimes of accretion are separated by a limit in X-ray luminosity at about 4 × 10 36 erg s −1 . In subsonic accretion, which works at lower luminosities, a hot quasi-spherical shell must form around the magnetosphere, and the actual accretion rate onto the neutron star is determined by the ability of the plasma to enter the magnetosphere due to the Rayleigh-Taylor instability. In turn, two regimes of subsonic accretion are possible, depending on the plasma cooling mechanism (Compton or radiative) near the magnetopshere. The transition from the high-luminosity regime with Compton cooling to the low-luminosity (L x 3 × 10 35 erg s −1 ) regime with radiative cooling can be responsible for the onset of the 'off states repeatedly observed in several low-luminosity slowly accreting pulsars, such as Vela X-1, GX 301-2 and 4U 1907+09. The triggering of the transition may be due to a switch in the X-ray beam pattern in response to a change in the optical depth in the accretion column with changing luminosity. We also show that in the settling accretion theory, bright X-ray flares (∼ 10 38 − 10 40 ergs) observed in supergiant fast X-ray transients (SFXT) may be produced by sporadic capture of magnetized stellar-wind plasma. At sufficiently low accretion rates, magnetic reconnection can enhance the magnetospheric plasma entry rate, resulting in copious production of X-ray photons, strong Compton cooling and ultimately in unstable accretion of the entire shell. A bright flare develops on the free-fall time scale in the shell, and the typical energy released in an SFXT bright flare corresponds to the mass of the shell.

This work considers a theoretical model for quasi-spherical subsonic accretion onto slowly rotating magnetized neutron stars. In this regime 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 neutron star magnetosphere by large-scale convective motions, which for observed pulsars lead to an almost so-angular-momentum rotation law with ω ∼ 1/R 2 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 while taking cooling into account. The settling regime of accretion is possible for moderate accretion ratesṀ Ṁ * ≃ 4 × 10 16 g/s. At higher accretion rates a free-fall gap above the neutron star magnetosphere appears due to rapid Compton cooling, and accretion becomes highly non-stationary. From observations of spin-up/spin-down rates of quasi-spherically wind accreting equilibrium X-ray pulsars with known orbital periods (like e.g. GX 301-2 and Vela X-1), it is possible to determine the main dimensionless parameters of the model, as well as to estimate the magnetic field on the surface of the neutron star. For equilibrium pulsars with independent measurements of the magnetic field, the model also allows us to estimate the velocity of the stellar wind from the companion without the use of complicated spectroscopic measurements. For non-equilibrium pulsars, it can be shown that there exists a maximum possible value of 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) we are able to estimate a lower limit on the neutron star magnetic field, which in all exemplified cases turns out to be close to the standard one and in agreement with cyclotron line measurements. The model further 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, seen in different systems.

We analyze spin-up/spin-down of the neutron star in Be X-ray binary system GX 304-1 observed by Swift/XRT and Fermi/GBM instruments in the period of the source activity from April 2010 to January 2013 and discuss possible mechanisms of angular momentum transfer to/from the neutron star. We argue that the neutron star spin-down at quiescent states of the source with an X-ray luminosity of L x ∼ 10 34 erg s −1 between a series of Type I outbursts and spin-up during the outbursts can be explained by quasi-spherical settling accretion onto the neutron star. The outbursts occur near the neutron star periastron passages where the density is enhanced due to the presence of an equatorial Be-disc tilted to the orbital plane. We also propose an explanation to the counterintuitive smaller spin-up rate observed at higher luminosity in a double-peak Type I outburst due to lower value of the specific angular momentum of matter captured from the quasi-spherical wind from the Be-star by the neutron star moving in an elliptical orbit with eccentricity e 0.5.

Abstract. A review of wind accretion in high-mass X-ray binaries is presented. We focus attention to different regimes of quasi-spherical accretion onto the neutron star: the supersonic (Bondi) accretion, which takes place when the captured matter cools down rapidly and falls supersonically toward NS magnetospghere, and subsonic (settling) accretion which occurs when plasma remains hot until it meets the magnetospheric boundary. Two regimes of accretion are separated by an X-ray luminosity of about 4 × 10 36 erg/s. In the subsonic case, which sets in at low luminosities, a hot quasi-spherical shell must be formed around the magnetosphere, and the actual accretion rate onto NS is determined by ability of the plasma to enter the magnetosphere due to Rayleigh-Taylor instability. We calculate the rate of plasma entry the magnetopshere and the angular momentum transfer in the shell due to turbulent viscosity appearing in the convective differentially rotating shell. We also discuss and calculate the structure of the magnetospheric boundary layer where the angular momentum between the rotating magnetosphere and the base of the differentially rotating quasi-spherical shell takes place. We show how observations of equilibrium X-ray pulsars Vela X-1 and GX 301-2 can be used to estimate dimensionless parameters of the subsonic settling accretion theory, and obtain the width of the magnetospheric boundary layer for these pulsars.

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