Period clustering of anomalous X-ray pulsars

The question of why the observed periods of anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) cluster in the range 2–12 s is discussed. The possibility that AXPs and SGRs are the descendants of high-mass X-ray binaries that have disintegrated in core-collapse supernova explosions is investigated. The spin periods of neutron stars in high-mass X-ray binaries evolve towards the equilibrium period, which is a few seconds, on average. After the explosion of its massive companion, the neutron star becomes embedded in a dense gaseous envelope, and accretion from this envelope leads to the formation of a residual magnetically levitating disk. It is shown that the expected mass of the disk in this case is 10^?7–10^?8 M_⊙, which is sufficient to support accretion at the rate 10¹⁴–10¹⁵ g/s over a few thousand years. During this period, the star manifests itself as an isolated X-ray pulsar with a number of parameters similar to those of AXPs and SGRs. The periods of such pulsars can cluster if the lifetime of the residual disk does not exceed the spin-down timescale of the neutron star.     

The spin-down mechanism of the X-ray pulsar 4U 2206+54

Observations of the X-ray pulsar 4U 2206+54 obtrained over 15 years show that its period, which is now 5555 ± 9 s, is increasing dramatically. This behavior is difficult to explain using traditional scenarios for the spin evolution of compact stars. The observed spin-down rate of the neutron star in 4U 2206+54 is in good agreement with the value expected in a magnetic-accretion scenario, taking into account that, under certain conditions, the magnetic field of the accretion stream can affect the geometry and type of flow. The neutron star in this case accretes material from a dense gaseous slab with small angular momentum, which is kept in equilibrium by the magnetic field of the flow itself. A magnetic-accretion scenario can be realized in 4U 2206+54 if the magnetic-field strength at the surface of the optical counterpart to the neutron star is higher than 70 G. The magnetic field at the surface of the neutron star is 4 × 10¹² G in this scenario, in agreement with estimates based on an analysis of X-ray spectra of the pulsar.     

Signs of magnetic accretion in X-ray pulsars

The spin-down mechanism of accreting neutron stars is discussedwith an application to one of the best studied X-ray pulsars GX301-2. We show that the maximum possible spin-down torque applied to a neutron star from the accretion flow can be evaluated as K _sd ^(t) = ??²/(r _m r _cor)^3/2. The spin-down rate of the neutron star in GX301-2 can be explained provided the magnetospheric radius of the neutron star is smaller than its canonical value. We calculate the magnetospheric radius considering the mass-transfer in the binary system in the frame of the magnetic accretion scenario suggested by V.F. Shvartsman. The spin-down rate of the neutron star expected within this approach is in a good agreement with that derived from observations of GX301-2.     

Long-period variations of pulsar emission and the dynamical ellipticity of neutron stars

Assuming that the observed periodic variations of pulsar emission are due to the free precession of the spin axis, we investigate the evolution of the rotation of a two-layer neutron star using the Hamiltonian method of Getino. We model the dynamical characteristics of a rotating neutron star using the observed variations of the emission of seven pulsars. We estimate the dependence of the period of the Chandler wobble, the period of precession of the spin axis, and the dynamical ellipticity of a neutron star on the model used to describe the super-dense neutron matter and the mass of the star.     

Acceleration of close binaries in supernova explosions

We investigate the orientation of the orbital planes of X-ray binary systems relative to the direction of the additional velocity acquired by the binary in a supernova explosion or as a result of radiative acceleration. In the second case, the acceleration occurs due to X-ray radiation during a stage of intense accretion onto the neutron star, which has an asymmetric magnetic field. Observational consequences that could enable estimation of the role of each acceleration mechanism are discussed. The results are also applicable to binary millisecond radio pulsars, assuming that they have gone through an accretion stage.     

A new look at anomalous X-ray Pulsars

We explore the possibility of explaining Anomalous X-ray Pulsars (AXPs) and Soft Gammaray Repeaters (SGRs) in a scenario with fall-back magnetic accretion onto a young isolated neutron star. The X-ray emission of the pulsar in this case originates due to the accretion of matter onto the surface of the neutron star from a magnetic slab surrounding its magnetosphere. The spin-down rate of the neutron star expected in this picture is close to the observed value. We show that such neutron stars are relatively young and are going through the transition from the propeller state to the accretor state. The pulsar’s activity in gamma-rays is connected with its relative youth, and is enabled by energy stored in a non-equilibrium layer located in the crust of the low-mass neutron star. This energy can be released due to the mixing of matter in the neutron star crust with super heavy nuclei approaching its surface and becoming unstable. The fission of nuclei in the low-density region initiates chain reactions leading to a nuclear explosion. Outbursts are probably triggered by instability developing in the region where the matter accreted by the neutron star accumulates in the magnetic polar regions.     

Formation of low-mass X-ray novae with black holes from triple systems

We apply a population synthesis technique to study the formation and evolution of low-mass X-ray binaries with black holes, observed as X-ray novae, from hierarchical triple systems. A scenario is suggested in which an inner close binary system evolves into an X-ray system with a large mass ratio. The high rate of accretion onto the neutron star leads to a common envelope stage, which may result in the formation of a Thorne-Zytkow (TZ) object. During its evolution, the envelope of the TZ object expands, encompassing the third star. The recurrent common-envelope stage decreases the size of the orbit of the third star, leading to the formation of a lowmass X-ray nova with a black hole. The dynamical stability of triple systems automatically ensures that only lowmass X-ray novae form. We also consider the possible formation of an X-ray nova from a binary in the case of asymmetrical core collapse during a supernova explosion.     

A spindown mechanism for short-period radio pulsars

It is shown that a model with accretion in a “quasi-propeller” mode can explain the observed spindown of pulsars with periods P<0.1 s. The mean accretion rate for 39 selected objects is \(\dot M = 5.6 \times 10^{ - 11} M_ \odot /year\). If \(\dot M\) is constant during the pulsar’s lifetime, the neutron star will stop rotating after 10⁷ years. The mean magnetic field at the neutron-star surface calculated in this model, \(\bar H_0 = 6.8 \times 10^8 G\), is consistent to an order of magnitude with the values of H₀ for millisecond pulsars from known catalogs. However, the actual value of H₀ for particular objects can differ from the catalog values by appreciable factors, and these quantities must be recalculated using more adequate models. The accretion disk around the neutron star should not impede the escape of the pulsar’s radiation, since this radiation is generated near the light cylinder in pulsars with P<0.1 s. Pulsars such as PSR 0531+21 and PSR 0833-45 have probably spun down due to the effect of magnetic-dipole radiation. If the difference in the braking indices for these objects from n=3 is due to the effect of accretion, the accretion rate must be of the order of 10¹⁸ g/s.     

Are anomalous X-ray pulsars and soft gamma-ray repeaters magnetars?

The magnetic fields of soft gamma-ray repeaters and anomalous X-ray pulsars have been estimated, taking into account the appreciable increase in the deceleration of the neutron star if it is embedded in a dense interstellar medium. These estimates yield the usual values of B?10¹² G.     

The formation of millisecond radio pulsars in close binary systems

An analysis of the basic parameters of a sample of radio and X-ray pulsars that are members of close binary systems is used to separate them into several families according to the nature of the pulsar companions and the previous evolution of the systems. To quantitatively describe the main parameters of close binaries containing neutron stars, we have performed numerical modeling of their evolution. The main driving forces of the evolution of these systems are the nuclear evolution of the donor, the magnetically coupled and radiation-induced stellar winds of the donor, and gravitational-wave radiation. We have considered donors that are low-mass stars in various stages of their evolution, nondegenerate helium stars, and degenerate stars. The systems studied are either the products of the normal evolution of close binaries with large initial component-mass ratios or result from inelastic collisions of old neutron stars with single and binary low-mass, main-sequence stars in the dense cores of globular clusters. The formation of single millisecond pulsars requires either the dynamical disruption of a low-mass (?0.1M_⊙) donor or its complete evaporation under the action of the X-ray radiation of the millisecond pulsar. The observed properties of binary radio pulsars with eccentric orbits combined with the bimodal spatial-velocity distribution of single radio pulsars suggest that it may be possible to explain the observed rotational and spatial motions of all radio pulsars as a result of their formation in close binaries. In this case, neutron stars formed from massive single stars or the components of massive wide binaries probably cannot acquire the high spatial velocities or rapid rotation rates that are required for the birth of a radio pulsar.     

Formation of planets during the evolution of single and binary stars

Current views of the origin and evolution of single and binary stars suggest that the planets can form aroundmain-sequence single and binary stars, degenerate dwarfs, neutron stars, and stellarmass black holes according to several scenarios. Planets can arise during the formation of a star mainly due to excess angular momentum leading to the formation of an accretion-decretion disk of gas and dust around a single star or the components of a binary. It is the evolution of such disks that gives rise to planetary systems. A disk can arise around a star during its evolution due to the accretion of matter from dense interstellar clouds of gas and dust onto the star, the accretion of mass froma companion in a binary system, and the loss of matter during the contraction of a rapidly rotating star, in particular, if the star rotates as a rigid body and the rotation accelerates with its evolution along the main sequence. The fraction of stars with planetary systems is theoretically estimated as 30–40%, which is close to the current observational estimate of ∼34%.     

Evolution of the masses of neutron stars in binary systems

We study the growth of the masses of neutron stars in binary systems due to the accumulation of mass from the optical donors accreted onto the neutron-star surface. Possible scenarios for this accretion are considered. The masses and magnetic-field strengths of radio pulsars derived using population-synthesis methods are compared to the observational data. The population-synthesis analysis indicates that a neutron star can increase its mass from the standard value of m _x ? 1.35M_⊙ to the Oppenheimer-Volkoff limit, m _x ? 2.5M_⊙, via accretion from a companion.     

The radio emission of anomalous pulsars

Previously developed methods for estimating the angle β between the spin axis of a neutron star and its magnetic moment together with observational data for anomalous X-ray pulsars (AXPs) indicate that these objects are nearly aligned rotators, and that the drift model can be applied to them. The magnetospheres of aligned rotators are appreciably more extended than in pulsars with large values of β. With such extents for the magnetosphere, the conditions for the generation of transverse waves via the cyclotron instability are satisfied. The expected spectrum of the resulting radiation is very steep (its spectral index is α > 3), consistent with the observed radio spectra of known AXPs (α > 2). A large magnetosphere also favors the appearance of appreciable pitch angles for relativistic electrons, and therefore the generation of synchrotron emission. The maximum of this emission falls in the microwave range. This mechanism provides appreciable fluxes at frequencies of tens of gigahertz and can explain the observed enhanced AXP radiation in this range.     

Differences in the parameters of radio pulsars with short and long periods

A comparative analysis of various parameters of pulsars with short (P < 0.1 s) and long (P > 0.1 s) periods is carried out. There is no correlation between the radio and gamma-ray luminosities of the pulsars and their surfacemagnetic fields, but there is a correlation between the X-ray luminosity and the surfacemagnetic field. A dependence of the X-ray and gamma-ray luminosities on the magnetic field at the light cylinder is also found. This result provides evidence for the formation of hard, non-thermal emission at the periphery of the magnetosphere. An appreciable positive correlation between the luminosity and the rate of rotational energy loss by the neutron star is observed, supporting the idea that all radio pulsars have the same basic source of energy. The efficiency of the transformation of rotational energy into radiation is significantly higher in long-period pulsars. The dependence of the pulse width on the pulsar period is steeper for pulsars with short periods than for those with long periods. The results obtained support earlier assertions that there are differences in the processes generating the emission in pulsars with P < 0.1 s and those with P > 0.1 s.     

A study of the X-ray pulsars X1845-024 and XTE J1858+034 based on INTEGRAL observations

We present an analysis of observations of the relatively unstudied X-ray pulsars X1845-024 and XTE J1858+034 carried out from May 2003 through November 2004 using the JEM-X and IBIS telescopes of the INTEGRAL international gamma-ray observatory at energies of 5-70 keV. The X-ray spectra and light curves of the pulsars are constructed. During the observation period, outbursts at 18-70 keV at levels of 13 mCrab and 111 mCrab were detected for X1845-024 and XTE J1858+034, respectively. We refined the rotational period of the neutron star in XTE J1858+034 (220.4 s), measured its acceleration during the outburst, and derived a probable value of the orbital period (?380 d).     

Accretion of neutral hydrogen and helium onto a neutron star. The X-ray and gamma-ray radiation of cool neutron stars

The accretion of neutral gas (hydrogen and helium) onto a neutron star is studied. The gas is gravitationally captured into the magnetosphere of the star, where it is ionized by thermal radiation from the stellar surface and accelerated by the electric field at the light cylinder and in a tube of open magnetic lines. Particles accelerated at light cylinder generate gamma-ray, some particles move to the star and heat its polar regions, resulting in the emission of X-rays. Our calculations of the model parameters of the X-ray and gamma-ray radiation indicate that the radiation intensities should be sufficient to be observed.     

The thermal evolution of Thorne-Zytkow objects

The evolution of stars with mass 5M _⊙ with an initially cool neutron core (Thorne-Zytkow objects) is computed numerically, taking into account the heating of the neutron star by flows of heat released during the accretion of a surrounding envelope. The temperature of the neutron core does not rise to values at which the system could become unstable to rapid increases in the neutrino luminosity. In other words, the heating of the neutron core does not lead to a rapid collapse of the initial configuration.     

Population synthesis for the luminosity functions of X-ray binaries made using the “Scenario Machine”

Using the “Scenario Machine” (a computer code based on the Monte-Carlo method, developed to calculate the evolution of a large ensemble of binaries), we have carried out population-synthesis calculations for X-ray binaries for the purpose of modeling the X-ray luminosity functions in various type galaxies. These calculations were focused on the evolution of magnetized neutron stars. The X-ray luminosity function is not universal, and depends on the star formation rate in the galaxy. In theoretical models, it is very important to take into account the evolution of the binaries and their lifetimes in their X-ray stages. We calculated the cumulative and differential X-ray luminosity functions in galaxies with a constant star formation rate, the cumulative luminosity functions for various time intervals since the peak star formation, and curves describing the evolution of the X-ray luminosity after a star formation burst in the galaxy.     

Parameters of radio pulsars in binary systems and globular clusters

The parameters of radio pulsars in binary systems and globular clusters are investigated. It is shown that such pulsars tend to have short periods (of the order of several milliseconds). Themagnetic fields of most of the pulsars considered are weak (surface fields of the order of 10⁸?10⁹ G). This corresponds to the generally accepted view that short-period neutron stars are spun up by angular momentum associated with the stellar wind from a companion. However, the fields at the light cylinders in these objects are two to three orders of magnitude higher than for the main population of single neutron stars. The dependence of the pulse width on the period does not differ from the corresponding dependences for single pulsars, assuming the emission is generated inside the polar cap, at moderate distances from the surface or near the light cylinder. The radio luminosities of pulsars in binary systems do not show the correlation with the rate of loss of rotational energy that is characteristic for single pulsars, probably due to the influence of accreting matter from a companion. Moreover, accretion apparently decreases the power of the emergent radiation, and can explain the observed systematic excess of the radio luminosity of single pulsars compared to pulsars in binary systems. The distributions and dependences presented in the article support generally accepted concepts concerning the processes occurring in binary systems containing neutron stars.     

Magnetic fields of radio pulsars

The mechanism of magnetodipole braking of radio pulsars is used to calculate new values of the surface magnetic fields of neutron stars. The angles β between the spin axes and magnetic moments of the neutron stars were estimated for 376 radio pulsars using three different methods. It is shown that small inclinations of magnetic axes dominate. The equatorial magnetic fields for the considered sample of pulsars are calculated using the β values obtained. As a rule, these magnetic fields are a factor of a few higher than the corresponding values in known catalogs.