The bottom magnetic field and magnetosphere evolution of neutron star in low-mass X-ray binary

The accretion-induced neutron star (NS) magnetic field evolution is studied through considering the accretion flow to drag the field lines aside and dilute the polar-field strength, and as a result the equatorial field strength increases, which is buried inside the crust on account of the accretion-induced global compression of star crust. The main conclusions of model are as follows: (i) the polar field decays with increase in the accreted mass; (ii) the bottom magnetic field strength of about 10⁸ G can occur when the NS magnetosphere radius approaches the star radius, and it depends on the accretion rate as     ; and (iii) the NS magnetosphere radius decreases with accretion until it reaches the star radius, and its evolution is little influenced by the initial field and the accretion rate after accreting  ∼0.01 M_⊙  , which implies that the magnetosphere radii of NSs in low-mass X-ray binaries would be homogeneous if they accreted the comparable masses. As an extension, the physical effects of the possible strong magnetic zone in the X-ray NSs and recycled pulsars are discussed. Moreover, the strong magnetic fields in the binary pulsars PSR 1831−00 and PSR 1718−19 after accreting about  0.5 M_⊙  in the binary-accretion phase,  8.7 × 10¹⁰  and  1.28 × 10¹² G  , respectively, can be explained through considering the incomplete frozen flow in the polar zone. As an expectation of the model, the existence of the low magnetic field  (∼3 × 10⁷ G)  NSs or millisecond pulsars is suggested.     

Spin evolution of neutron stars in binary systems

I review our understanding of the evolution of the spin periods of neutron stars in binary stellar systems, from their birth as fast, spin-powered pulsars, through their middle life as accretion-powered pulsars, upto their recycling or “rebirth” as spin-powered pulsars with relatively low magnetic fields and fast rotation. I discuss how the new-born neutron star is spun down by electromagnetic and “propeller” torques, until accretion of matter from the companion star begins, and the neutron star becomes an accretion-powered X-ray pulsar. Detailed observations of massive radio pulsar binaries like PSR 1259-63 will yield valuable information about this phase of initial spindown. I indicate how the spin of the neutron star then evolves under accretion torques during the subsequent phase as an accretion-powered pulsar. Finally, I describe how the neutron star is spun up to short periods again during the subsequent phase of recycling, with the accompanying reduction in the stellar magnetic field, the origins of which are still not completely understood.     

Magnetic and spin evolution of neutron stars in close binaries

The evolution of neutron stars in close binary systems with a low-mass companion is considered, assuming the magnetic field to be confined within the solid crust. We adopt the standard scenario for the evolution in a close binary system, in which the neutron star passes through four evolutionary phases ('isolated pulsar'–'propeller'– accretion from the wind of a companion – accretion resulting from Roche-lobe overflow). Calculations have been performed for a great variety of parameters characterizing the properties of both the neutron star and the low-mass companion. We find that neutron stars with more or less standard magnetic field and spin period that are processed in low-mass binaries can evolve to low-field rapidly rotating pulsars. Even if the main-sequence life of a companion is as long as 10¹⁰ yr, the neutron star can maintain a relatively strong magnetic field to the end of the accretion phase. The model that is considered can account well for the origin of millisecond pulsars.     

The nature of the bimodal luminosity distribution of ultraluminous X-ray pulsars

The mechanism that can be responsible for the bimodal luminosity distribution of super-Eddington X-ray pulsars in binary systems is pointed out. The transition from the high to low state of these objects is explained by accretion flow spherization due to the radiation pressure at certain (high) accretion rates. The transition between the states can be caused by a gradual change in the accretion rate. The complex behavior of the recently discovered ultraluminous X-ray pulsars M 82 X-2, NGC 5907 ULX-1, and NGC 7793 P13 is explained by the proposed mechanism. The proposed model also naturally explains the measured spinup of the neutron star in these pulsars, which is slower than the expected one by several times.     

Period variation of X-ray pulsars and Kelvin-Helmholtz instability at the accretion disk boundary

We introduce between the magnetosphere of a neutron star and its accretion disk a sheared layer of finite thickness in which the velocity, density, pressure and magnetic field vary continuously and we discuss the Kelvin-Helmholtz instability of plane wave purturbations for the case of a compressible plasma. The results show that the K-H instability is still present and radial wave vector perturbation is the main mode of instability. We particularly considered the effect of the thickness of the sheared layer on the rotation of the neutron star, showing that by suitably adjusting the thickness we can explain the period changes in the X-ray pulsars. Application of this model to Her X-1 gave a good result.     

Neutron Stars in X-ray Binaries and their Environments

Neutron stars in X-ray binary systems are fascinating objects that display a wide range of timing and spectral phenomena in the X-rays. Not only parameters of the neutron stars, like magnetic field strength and spin period evolve in their active binary phase, the neutron stars also affect the binary systems and their immediate surroundings in many ways. Here we discuss some aspects of the interactions of the neutron stars with their environments that are revelaed from their X-ray emission. We discuss some recent developments involving the process of accretion onto high magnetic field neutron stars: accretion stream structure and formation, shape of pulse profile and its changes with accretion torque. Various recent studies of reprocessing of X-rays in the accretion disk surface, vertical structures of the accretion disk and wind of companion star are also discussed here. The X-ray pulsars among the binary neutron stars provide excellent handle to make accurate measurement of the orbital parameters and thus also evolution of the binray orbits that take place over time scale of a fraction of a million years to tens of millions of years. The orbital period evolution of X-ray binaries have shown them to be rather complex systems. Orbital evolution of X-ray binaries can also be carried out from timing of the X-ray eclipses and there have been some surprising results in that direction, including orbital period glitches in two X-ray binaries and possible detection of the most massive circum-binary planet around a Low Mass X-ray Binary.     

The neutron stars of Soft X–ray Transients

Summary. Soft X–ray Transients (SXRTs) have long been suspected to contain old, weakly magnetic neutron stars that have been spun up by accretion torques. After reviewing their observational properties, we analyse the different regimes that likely characterise the neutron stars in these systems across the very large range of mass inflow rates, from the peak of the outbursts to the quiescent emission. While it is clear that close to the outburst maxima accretion onto the neutron star surface takes place, as the mass inflow rate decreases, accretion might stop at the magnetospheric boundary because of the centrifugal barrier provided by the neutron star. For low enough mass inflow rates (and sufficiently short rotation periods), the radio pulsar mechanism might turn on and sweep the inflowing matter away. The origin of the quiescent emission, observed in a number of SXRTs at a level of , plays a crucial role in constraining the neutron star magnetic field and spin period. Accretion onto the neutron star surface is an unlikely mechanism for the quiescent emission of SXRTs, as it requires very low magnetic fields and/or long spin periods. Thermal radiation from a cooling neutron star surface in between the outbursts can be ruled out as the only cause of the quiescent emission. We find that accretion onto the neutron star magnetosphere and shock emission powered by an enshrouded radio pulsar provide far more plausible models. In the latter case the range of allowed neutron star spin periods and magnetic fields is consistent with the values recently inferred from the properties of kHz quasi-periodic oscillation in low mass X–ray binaries. If quiescent SXRTs contain enshrouded radio pulsars, they provide a missing link between X–ray binaries and millisecond pulsars. Received 4 November 1997; Accepted 15 April 1998     

Rotating black holes in neutron and quark stars: Phenomenon of pulsars

The phenomenon of pulsars is considered as the evidence for existence of black holes in neutron and quark stars. Within the framework of the degenerated star model with black-hole interior the existence of millisecond pulsars withP<0.5 ms and single pulsars with negative derivative of the period were predicted. The anisotropic accretion of neutron (or quark) star matter on to a rotating black hole leads to the formation of directed radiation (projector), which makes heat spots at surface (volcanos), that explains the nature of pulsating radiation and the complicated structure of impulses. This model gives both the mechanism of self-acceleration of degenerated star rotation (mass accretion on to the internal black hole) producing millisecond pulsars and also the mechanism of significant deceleration of rotation (ejection of neutral mass through a volcanic crater), leading to long-periodic X-ray pulsars. The black hole produces high densities and temperatures of the degenerated star mass that transforms gradually the neutron star into quark star (Cygnus X-3).     

Radius of the neutron star magnetosphere during disk accretion

The dependence of the spin frequency derivative \(\dot \nu \) of accreting neutron stars with a strongmagnetic field (X-ray pulsars) on the mass accretion rate (bolometric luminosity, L_bol) has been investigated for eight transient pulsars in binary systems with Be stars. Using data from the Fermi/GBM and Swift/BAT telescopes, we have shown that for seven of the eight systems the dependence \(\dot \nu \) (L_bol) can be fitted by the model of angular momentum transfer through an accretion disk, which predicts the relation \(\dot \nu \) ～ L^6/7_bol. Hysteresis in the dependence \(\dot \nu \) (L_bol) has been confirmed in the system V 0332+53 and has been detected for the first time in the systems KS 1947+300, GRO J1008-57, and 1A 0535+26. Estimates for the radius of the neutron star magnetosphere in all of the investigated systems have been obtained. We show that this quantity varies from pulsar to pulsar and depends strongly on the analytical model and the estimates for the neutron star and binary system parameters.     

A Two—Temperature Supernova Fallback Disk Model for Anomalous X—ray Pulsars

We present a case study of the relevance of the radially pulsational instability of a two-temperature accretion disk around a neutron star to anomalous X-ray pulsars (AXPs). Our estimates are based on the approximation that such a neutron star disk with mass in the range of 10^-6-10^-5M⊙ is formed by supernova fallback. We derive several peculiar properties of the accretion disk instability: a narrow interval of X-ray pulse periods; lower X-ray luminosities; a period derivative and an evolution time scale. All these results are in good agreement with the observations of the AXPs.     

Studying millisecond pulsars in X-rays

Millisecond pulsars represent an evolutionarily distinct group among rotation-powered pulsars. Outside the radio band, the soft X-ray range (～0.1–10 keV) is most suitable for studying radiative mechanisms operating in these fascinating objects. X-ray observations revealed diverse properties of emission from millisecond pulsars. For the most of them, the bulk of radiation is of a thermal origin, emitted from small spots (polar caps) on the neutron star surface heated by relativistic particles produced in pulsar acceleration zones. On the other hand, a few other very fast rotating pulsars exhibit almost pure nonthermal emission generated, most probably, in pulsar magnetospheres. There are also examples of nonthermal emission detected from X-ray nebulae powered by millisecond pulsars, as well as from pulsar winds shocked in binary systems with millisecond pulsars as companions. These and other most important results obtained from X-ray observations of millisecond pulsars are reviewed in this paper, as well as results from the search for millisecond pulsations in X-ray flux of the radio-quite neutron star RX J1856.5-3754.     

Flux-Vortex Pinning and Neutron Star Evolution

G. Srinivasan et al. (1990) proposed a simple and elegant explanation for the reduction of the neutron star magnetic dipole moment during binary evolution leading to low mass X-ray binaries and eventually to millisecond pulsars: Quantized vortex lines in the neutron star core superfluid will pin against the quantized flux lines of the proton superconductor. As the neutron star spins down in the wind accretion phase of binary evolution, outward motion of vortex lines will reduce the dipole magnetic moment in proportion to the rotation rate. The presence of a toroidal array of flux lines makes this mechanism inevitable and independent of the angle between the rotation and magnetic axes. The incompressibility of the flux-line array (Abrikosov lattice) determines the epoch when the mechanism will be effective throughout the neutron star. Flux vortex pinning will not be effective during the initial young radio pulsar phase. It will, however, be effective and reduce the dipole moment in proportion with the rotation rate during the epoch of spindown by wind accretion as proposed by Srinivasan et al. The mechanism operates also in the presence of vortex creep.     

On the theory of X-ray pulsar radiation

The origin of hard X-ray spectrum (continuum and cyclotron lines) of pulsars in binary systems is discussed. A model of the polar region of a neutron star consisting of a hot spot in a dense plasma atmosphere with a quasi-homogeneous magnetic field and an extended accreting column in an inhomogeneous dipolar field is investigated. In the hot spot bremsstrahlung and Thomson scattering form continuum radiation, while bremsstrahlung and cyclotron scattering produce the absorption cyclotron lines. By the observed continuum intensity one can estimate the maximum distances to pulsars. Cyclotron scattering in gyro-resonant layers localized in the accreting column leads to a general attenuation of the radiation of a hot spot, but is unable to ensure the formation of cyclotron lines. For strong accretion the hot spot radiation becomes insignificant, the lines disappear and the pulsating component of an X-ray pulsar is produced by the accreting column bremsstrahlung transformed by Thomson scattering.     

Bimodality of anomalous pulsars?

At present, it is widely believed that anomalous X-ray pulsars (AXPs), soft gamma-ray repeaters (SGRs), rotational radio transients (RRATs), compact central objects (CCOs) in supernova remnants, and X-ray dim isolated neutron stars (XDINSs) belong to different classes of anomalous objects in which the central bodies are isolated neutron stars. Previously, we have shown that AXPs and SGRs can be described in terms of the drift model for parameters of the central neutron star typical of radio pulsars (rotation periods P ～ 0.1–1 s and surface magnetic fields B ～ 10¹¹–10¹³ G). Here, we show that some of the peculiarities of the sources under consideration can be explained by their geometry (in particular, by the angle β between the rotation axis and the magnetic moment). If β ? 10° (an aligned rotator), the drift waves in the outer layers of the neutron star magnetosphere can account for the observed periodicity in the radiation. For large β (a nearly orthogonal rotator), the observed modulation of the radiation and its short bursts can be explained by mass accretion from the ambient medium (e.g., a relic disk).     

X-ray binaries

Summary The various types and classes of X-ray binary are reviewed high-lighting recent results. The high mass X-ray binaries (HMXRBs) can be used to probe the nature of the mass loss from the OB star in these systems. Absorption measurements through one orbital cycle of the supergiant system X1700-37 are well modelled by a radiation driven wind and also require a gas stream trailing behind the X-ray source. In Cen X-3 the gas stream is accreted by the X-ray source via an accretion disk. Changes in the gas stream can cause the disk to thicken and the disk to obscure the X-ray source. How close the supergiant is to corotation seems to be as much a critical factor in these systems as how close it is to filling its Roche lobe. In the Be star X-ray binaries a strong correlation between the neutron stars rotation period and its orbital period has been explained as due to the neutron star being immersed in a dense, slow moving equatorial wind from the Be star. For the X-ray pulsars in the transient Be X-ray binaries a centrifugal barrier to accretion is important in determining the X-ray lightcurve and the spin evolution. The X-ray orbital modulations from the low mass X-ray binaries, LMXRBs, include eclipses by the companion and/or periodic dipping behaviour from structure at the edge of the disk. The corresponding optical modulations show a smooth sinusoidal like component and in some cases a sharp eclipse by the companion. The orbital period of the LMXRB XB1916-05 is 1% longer in the optical compared to that given by the X-ray dip period. The optical period has been interpreted as the orbital period, but this seems inconsistent with the well established view of the origin of the X-ray modulations in LMXRB. A new model is presented that assumes the X-ray dip period is the true orbital period. The 5.2 h eclipsing LMXRB XB2129+47 recently entered a low state and optical observations unexpectedly reveal an F star which is too big to fit into the binary. This is probably the first direct evidence that an X-ray binary is part of a hierarchical triple. Finally the class of X-ray binaries containing black hole candidates is reviewed focusing on the value of using X-ray signatures to identify new candidates.     

Warping modes in discs around accreting neutron stars

The origin and stability of a thin sheet of plasma in the magnetosphere of an accreting neutron star are investigated. First, the radial extension of such a magnetospheric disc is explored. Then a mechanism for magnetospheric accretion is proposed, reconsidering the bending wave explored by Agapitou, Papaloizou & Terquem, that was found to be stable in ideal magnetohydrodynamics. We show that this warping becomes unstable and can reach high amplitudes, in a variant of Pringle's radiation-driven model for the warping of active galactic nucleus accretion discs. Finally, we discuss how this mechanism might give a clue to explain the observed X-ray kilohertz quasi-periodic oscillation of neutron star binaries.     

Millisecond Pulsars,their Evolution and Applications

Millisecond pulsars (MSPs) are short-period pulsars that are distinguished from “normal” pulsars, not only by their short period, but also by their very small spin-down rates and high probability of being in a binary system. These properties are consistent with MSPs having a different evolutionary history to normal pulsars, viz., neutron-star formation in an evolving binary system and spin-up due to accretion from the binary companion. Their very stable periods make MSPs nearly ideal probes of a wide variety of astrophysical phenomena. For example, they have been used to detect planets around pulsars, to test the accuracy of gravitational theories, to set limits on the low-frequency gravitational-wave background in the Universe, and to establish pulsar-based timescales that rival the best atomic-clock timescales in long-term stability. MSPs also provide a window into stellar and binary evolution, often suggesting exotic pathways to the observed systems. The X-ray accretion-powered MSPs, and especially those that transition between an accreting X-ray MSP and a non-accreting radio MSP, give important insight into the physics of accretion on to highly magnetized neutron stars.     

Interaction of the X-ray source radiation with the atmosphere of the normal star in close binary systems

The structure of the stellar atmosphere irradiated by an X-ray source is calculated. On the basis of these numerical calculations an approximate theory of the X-ray reprocessing is formulated. The interaction of X-rays with the stellar atmosphere induces a considerable stellar wind. However, the main part of the X-ray energy is reemitted.The optical appearances of the close binary system including an X-ray source are discussed. The light curve of such a system is obtained. The mass-loss rate of a star with the size close to that of its Roche lobe is evaluated in the isothermal approximation. Most likely, the accretion of matter on to a neutron star, or a black hole, is the cause of the X-ray luminosity. The accreting matter is supplied with the mass outflow from the normal component induced by X-rays. The X-ray luminosity is shown to have an upper limit stipulated by the outflow saturation.The model of HZ Her=Her X1 system is constructed which accounts for the observed light curve. The optical appearances of the system are due to the X-ray heating of the face of the X-ray source area of the normal star. The radiation of this hot area is partly reflected by the surface of the disc around the X-ray source. The thin disc is formed by the accretion of matter by the X-ray source. The effective reflection of hard X-rays (hv15–30 keV) by the stellar surface is considered. This phenomenon makes it possible to detect those X-ray pulsars whose beam does not intercept the Earth.The model of Sco X1 as a black hole in a close binary system is discussed.     

Accretion magnetar in the close binary system 4U 2206+54

The magneto-rotational evolution of a neutron star in the massive binary system 4U 2206+54 is discussed in light of the recent discovery of its 5555 s rotational period and its average rate of spin-down. We show that this behavior of the neutron star means that its magnetic field exceeds the quantum mechanical critical limit and it is an accretion magnetar. The system’s evolution is explained by wind driven mass transfer without formation of an accretion disk. The constant character of the x-ray source indicates a steady rate of accretion and raises anew the question of the stability of the boundary of the magnetosphere of a star undergoing spherical accretion. A solution to this problem is also a key to determining the mechanism for the slowing down of the star’s rotation.     

A possible detection mechanism for pre-low-mass X-ray binaries

This work presents a possible detection mechanism for close, detached, neutron star–red dwarf binaries, which are expected to be the evolutionary precursors of low-mass X-ray binaries (LMXBs). Although this pre-low-mass X-ray binary (pre-LMXB) phase of evolution is predicted theoretically, as yet no such systems have been identified observationally. The calculations presented here suggest that the X-ray luminosity of neutron star wind accretion in a pre-LMXB system can be expected to exceed the intrinsic X-ray luminosity of the red dwarf secondary star. Furthermore, the temperature of the radiation emitted from the neutron star wind accretion process is expected, within the confines of a reasonable set of conditions, to lie within the detection range of X-ray satellites. Sources with X-ray luminosities greater than that expected for a red dwarf star, but the positions of which coincide with that of a red dwarf star, are then candidate pre-LMXB systems. These candidate systems should be surveyed for the radial velocity shifts that would occur as a result of the orbital motion of a red dwarf star within a close binary system containing a high-mass compact object.