The drift model of “magnetars”

It is shown that the drift waves near the light cylinder can cause the modulation of emission with periods of order several seconds. These periods explain the intervals between successive pulses observed in AXPs, SGRs and radio pulsars with long periods. The model under consideration gives the possibility to calculate real rotation periods P of host neutron stars. It is shown that P≤1 s for the investigated objects. The magnetic fields at the surface of the neutron star are of order 10¹¹–10¹³ G and equal to the fields usual for the known radio pulsars.      

Relationship between the nonstationary radio-luminosity variations of the Crab Nebula and the activity of its pulsar

Based on the half-century-long history of radio observations of the Crab Nebula, we investigate the evolution of its radio luminosity. We found a secular decrease in the radio luminosity; it has decreased by 9% since the discovery of the radio source in 1948. Apart from the secular decrease in the luminosity of the Crab Nebula, we identified two time intervals, 1981–1987 and 1992–1998, when radio bursts with energy release ～10⁴¹ erg took place. In these years, the spectral indices of the instantaneous spectra decreased significantly due to the increase in the flux densities at short (centimeter and millimeter) wavelengths. These events were preceded by sudden increases in the pulsar’s rotation rates, the largest of which, with an amplitude of ΔΩ/Ω = 3 × 10^?8, occurred in 1975 and 1989. We show that the magnetospheric instability mechanism that accompanies strong glitches can provide the energetics of the excess luminosity of the Nebula through the ejection of relativistic electrons with a total energy higher than 6 × 10⁴² erg from the pulsar’s magnetosphere.     

Neutron stars in globular clusters: Formation and observational manifestations

Population synthesis is used to model the number of neutron stars in globular clusters that are observed as low-mass X-ray sources and millisecond radio pulsars. The dynamical interactions between binary and single stars in a cluster are assumed to take place only with a continuously replenished “background” of single stars whose properties keep track of the variations in parameters of the cluster as a whole and the evolution of single stars. We use the hypothesis that the neutron stars forming in binary systems from components with initial masses of ～8–12 M _⊙ during the collapse of degenerate O-Ne-Mg cores through electron captures do not acquire a high space velocity. The remaining neutron stars (from single stars with masses >8 M _⊙ or from binary components with masses >12 M _⊙) are assumed to be born with high space velocities. According to this hypothesis, a sizeable fraction of the forming neutron stars remain in globular clusters (about 1000 stars in a cluster with a mass of 5 × 10⁵ M _⊙). The number of millisecond radio pulsars forming in such a cluster in the case of accretion-driven spinup in binary systems is found to be ～10, in agreement with observations. Our modeling also reproduces the observed shape of the X-ray luminosity function for accreting neutron stars in binary systems with normal and degenerate components and the distribution of spin periods for millisecond pulsars.     

Energetics of galactic nuclei

A model of compact galactic nuclei in statistical equilibrium was developed in [L. Sh. Grigorian and G. S. Sahakian, Astrofizika (in press)]. It was shown that they should consist predominantly of neutron stars (pulsars) and white dwarfs. The problem of the energy reserves of galactic nuclei is discussed in terms of this concept. The mechanism of conversion of a white dwarf into a neutron star due to the accretion of interstellar matter is considered. This means that a galactic nucleus has an energy reserve of some 5·10⁶⁰ N₈ erg (N is the number of stars in the nucleus). It is shown that galactic nuclei are powerful sources of hard γ radiation [power L » 2·10⁴⁴µ₃₀N₈(Ω/50)^17/7 erg/sec, where µ is the magnetic moment and Ω is the angular rotation rate of a neutron star ] due to curvature radiation from relativistic electron fluxes flowing along channels of open magnetic field lines of pulsars. The x-ray and ultraviolet emission are due to synchrotron emission from the same electron fluxes in the magnetic field of the galactic nucleus (L » 10⁴²-10⁴⁴ erg/sec). The optical (visible and infrared) and radio emission are due to bremsstrahlung from electrons in the interstellar medium [L » 6·10⁴⁶N ₈ ² (5/R_pc)³ erg/sec, where R is the radius of the galactic nucleus]. An equation is obtained for the magnetic moment of a pulsar: µ ≈ 3.4·10^-5L_γP^17/7, where P is the pulsar’s period and L_03B3; is the luminosity of the pulsar’s y radiation.     

Radio precursors to neutron star binary mergings

We discuss a possible generation of radio bursts preceding final stages of binary neutron star mergings which can be accompanied by short gamma-ray bursts. Detection of such bursts appear to be advantageous in the low-frequency radio band due to a time delay of ten to several hundred seconds required for radio signal to propagate in the ionized intergalactic medium. This delay makes it possible to use short gamma-ray burst alerts to promptly monitor specific regions on the sky by low-frequency radio facilities, especially by LOFAR. To estimate the strength of the radio signal, we assume a power-law dependence of the radio luminosity on the total energy release in a magnetically dominated outflow, as found in millisecond pulsars. Based on the planned LOFAR sensitivity at 120 MHz, we estimate that the LOFAR detection rate of such radio transients could be about several events per month from redshifts up to z∼1.3 in the most optimistic scenario. The LOFAR ability to detect such events would crucially depend on exact efficiency of low-frequency radio emission mechanism.     

Evolution of Pulsars with Energy Release in the Superfluid Core of a Neutron Star

The effect of a neutron-proton vortex system on the rotation dynamics of neutron stars is examined. The dynamics of the motion of a two component superfluid system in the core of a neutron star yields an equation for the evolution of the pulsar's rotation period. The spin down of the star owing to energy release at the core boundary, which is associated with a contraction of the length of the neutron vortex as it moves radially and magnetic energy of the vortical cluster is released, is taken into account. Evolutionary curves are constructed for pulsars with different magnetic fields and stellar radii. For certain values of the coefficient of friction between the superfluid and normal components in the core of the neutron star, at the end of its evolution a radio pulsar may become an anomalous x-ray pulsar or a source of soft gamma radiation with a period on the order of 10 seconds.     

The nature of radio emission from pulsars

It is shown that radio emission from pulsars is unlikely to be of coherent synchrotron origin if the surface magnetic field of the central neutron star is greater than 10⁸ G.     

Heating of the polar caps of old radio pulsars

The X-ray luminosity and temperature of the polar cap heated by the back flux of positrons from a radio pulsar with a period P ～ 1 s and a magnetic field B ~ 10¹² G have been estimated. An additional source of X-ray emission—a thin, hotter semiring on the polar-cap periphery—is shown to also exist. It is heated by the back flux of electrons from the light cylinder. Furthermore, the electric field near the hot semiring accelerates the ions of the surface layer that leave the neutron-star magnetosphere. The semiring area is smaller than the polar-cap area approximately by a factor of 100, i.e., at the same luminosity the temperature is higher by a factor of 3. The observed X-ray emission from old radio pulsars is the emission from thin hot polar-cap semirings. The emission from the polar caps themselves is strongly attenuated by interstellar absorption.     

On timing and spectral characteristics of the X-ray pulsar 4U 0115+63: Evolution of the pulsation period and the cyclotron line energy

An overview of the results of observations for the transient X-ray pulsar 4U 0115+63, amember of a binary system with a Be star, since its discovery to the present day (～40 years) based on data from more than dozen observatories and instruments is presented. An overall light curve and the history of change in the spin frequency of the neutron star over the entire history of its observations, which also includes the results of recent measurements made by the INTEGRAL observatory during the 2004, 2008, and 2011 outbursts, are provided. The source’s energy spectra have also been constructed from the INTEGRAL data obtained during the 2011 outburst for a dynamic range of its luminosities 10³⁷?7 × 10³⁷ erg s^?1. We show that apart from the fundamental harmonic of the cyclotron absorption line at energy～11 keV, its four higher harmonics at energies ?24, 35.6, 48.8, and 60.7 keV are detected in the spectrum. We have performed a detailed analysis of the source’s spectra in the 4–28 keV energy band based on all of the available RXTE archival data obtained during bright outbursts in 1995–2011. We have confirmed that modifying the source’s continuum model can lead to the disappearance of the observed anticorrelation between the energy of the fundamental harmonic of the cyclotron absorption line and the source’s luminosity. Thus, the question about the evolution of the cyclotron absorption line energy with the luminosity of the X-ray pulsar 4U 0115+63 remains open and a physically justified radiation model for X-ray pulsars is needed to answer it.     

How rapidly do neutron stars spin at birth? Constraints from archival X-ray observations of extragalactic supernovae

Traditionally, studies aimed at inferring the distribution of birth periods of neutron stars are based on radio surveys. Here we propose an independent method to constrain the pulsar spin periods at birth based on their X-ray luminosities. In particular, the observed luminosity distribution of supernovae (SNe) poses a constraint on the initial rotational energy of the embedded pulsars, via the     correlation found for radio pulsars, and under the assumption that this relation continues to hold beyond the observed range. We have extracted X-ray luminosities (or limits) for a large sample of historical SNe observed with Chandra , XMM and Swift , which have been firmly classified as core-collapse SNe. We have then compared these observational limits with the results of Monte Carlo simulations of the pulsar X-ray luminosity distribution for a range of values of the birth parameters. We find that a pulsar population dominated by millisecond periods at birth is ruled out by the data.     

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).     

Space distribution and birth-rate of pulsars

Using the data of the 321 pulsars so far known the Galactic distribution and the luminosity function of pulsars have been investigated. The total number of pulsars in our Galaxy is found to be 9 × 10⁴. If the mean age of pulsars is 1.8 × 10⁶ years, the birth-rate of pulsars in the Galaxy will be one every 20 years. This rate is not in contradiction with the birth-rate of supernovae.     

Pulsar radio emission

The theory of pulsar radio emission has been developed in a series of our papers since 1992. It was shown that pulsar radio emission is produced in the lower part of a channel of open magnetic field lines, in a region with a height h ≈ 1.1-10⁷ μ ₃₀ ^1/3 /P^4/21 cm above a magnetic cap of the neutron star (P is the pulsar’s period and μ is the star’s magnetic moment). Here, owing to vigorously occurring processes (the production of photons of curvature radiation and their annihilation into e⁺e^- pairs), two ultrarelativistic particle fluxes are formed: an electron flux moving upward and a positron flux falling onto the star’s magnetic cap. These main fluxes are accompanied by narrow strips of positron and electron fluxes of relatively low energy, the curvature emission from which is a strong coherent radio source. The present paper is a review of earlier papers, and important additions and refinements are also made. Equations are offered for the radio luminosity of a pulsar, the solid angle of the radio beam, and the magnetic moment and moment of inertia of the pulsar’s neutron star. Translated from Astrofizika, Vol. 43, No. 1, pp. 147-169, January–March, 2000.     

On the differential rotation of the polar caps of neutron stars

The model of a magnetized rotating neutron star with an electric current in the region of its fluid polar magnetic caps is considered. The presence of an electric current leads to differential rotation of the magnetic caps. The rotation structure is determined by the electric current density distribution over the surface. In the simplest axisymmetric configuration, the current flows in one direction near the polar cap center and in the opposite direction in the outer ring (the total current is zero for the neutron star charge conservation). In this case, two rings with opposite directions of rotation appear on the neutron star surface, with the inner ring always lagging behind the star’s main rotation. The differential rotation velocity is directly proportional to the electric current density gradient along the polar cap radius. At a width of the region of change in the electric current from 1 to 10² cm and a period ～1 s and a magnetic field B ～ 10¹² G typical of radio pulsars, the linear differential rotation velocity is ～10^?2–10^?4 cm s^?1 (corresponding to a revolution time of ～0.1–10 yr).     

A new look at pulsar statistics — Birthrate and evidence for injection

We make a statistical analysis of the periodsP and period-derivativesP of pulsars using a model independent theory of pulsar flow in theP-P diagram. Using the available sample ofP andP values, we estimate the current of pulsars flowing unidirectionally along theP-axis, which is related to the pulsar birthrate. Because of radio luminosity selection effects, the observed pulsar sample is biased towards lowP and highP. We allow for this by weighting each pulsar by a suitable scale factor. We obtain the number of pulsars in our galaxy to be 6.05_−2.80 ^+3.32 × 10⁵ and the birthrate to be 0.048_−0.011 ^+0.014 pulsars yr⁻¹ galaxy⁻¹. The quoted errors refer to 95 per cent confidence limits corresponding to fluctuations arising from sampling, but make no allowance for other systematic and random errors which could be substantial. The birthrate estimated here is consistent with the supernova rate. We further conclude that a large majority of pulsars make their first appearance at periods greater than 0.5 s. This ‘injection’, which runs counter to present thinking, is probably connected with the physics of pulsar radio emission. Using a variant of our theory, where we compute the current as a function of pulsar ‘age’ (1/2P/P), we find support for the dipole braking model of pulsar evolution upto 6 × 10⁶ yr of age. We estimate the mean pulsar braking index to be 3.7_−0.8 ^+0.8.     

Soft gamma repeaters activity in time

In this short note I discuss the hypothesis that bursting activity of magnetars evolves in time analogously to the glitching activity of normal radio pulsars (i.e. sources are more active at smaller ages), and that the increase of the burst rate follows one of the laws established for glitching radio pulsars. If the activity of soft gamma repeaters decreases in time in the way similar to the evolution of core‐quake glitches (∝t^5/2), then it is more probable to find the youngest soft gamma repeaters, but the energy of giant flares from these sources should be smaller than observed 1044–1046 erg as the total energy stored in a magnetar's magnetic field is not enough to support thousands of bursts similar to the prototype 1979 March 5 flare. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Statistics of neutron stars at the stage of a supersonic propeller

We analyze the statistical distribution of neutron stars at the stage of a supersonic propeller. An important point of our analysis is allowance for the evolution of the angle of inclination of the magnetic axis to the spin axis of the neutron star for the boundary of the transition to the supersonic propeller stage. We have determined the spin period distributions of pulsars at the propeller stage for two models: the model with hindered particle escape from the stellar surface and the model with free particle escape. As a result, we have shown that consistent allowance for the evolution of the inclination angle in the region of extinct radio pulsars for the two models leads to an increase in the total number of neutron stars at the supersonic propeller stage. This increase stems from the fact that when allowing for the evolution of the inclination angle χ for neutron stars in the region of extinct radio pulsars and, hence, for the boundary of the transition to the propeller stage, this transition is possible at shorter spin periods (P ～ 5–10 s) than assumed in the standard model.     

Determination of the parameters of the neutron stars in pulsars

It is shown that knowing the energy flux density of the radio emission, the rate of increase in the period, and the distance of a pulsar enables one to calculate all the rest of its most important characteristics (the solid angle of the radio emission beam, the radio luminosity, the solid angle of the beam of γ rays, the energy flux density of the g-ray emission, and the magnetic moment, moment of inertia, and mass of the neutron star). Equations from which these pulsar characteristics can be calculated are given at the end of the paper. The results of calculations for a number of pulsars are given in Tables 2 and 3 as an illustration. Translated from Astrofizika, Vol. 43, No. 2, pp. 277-291, April–June, 2000.     

Nucleosynthesis in supernova outbursts and the chemical composition of the envelopes of neutron stars

The formation of chemical elements in the envelopes of neutron stars is considered at the densities ?=10⁷ to 10¹³ g cm^?3. It is shown, that the compression of cold and hot matter leads to different chemical compositions. The compression of cold matter is accompanied by a decrease of atomic weightA, up to ?≈3×10¹² g cm^?3. One may distinguish the following stages during the compression of hot matter: quasi-equilibrium, when there exists both nuclear equilibrium and kinetic equilibrium in β-processes; and limited equilibrium, when the total number of nuclei is constant. It is shown that a nonequilibrium chemical composition may be formed in the envelopes of neutron stars where there is an excess of neutrons in the presence of superheavy nuclei. The nuclear energy, stored in the neutron star envelope may be sufficient to support neutron star luminosity at a level of ～ 10³⁶ erg s^?1 over a period of ～ 10⁵ yr. Possible applications to the problem of X-ray sources and pulsars are discussed. The formation of the heavy nuclei in Supernovae explosions is considered briefly. Rough estimates are made for the differences in chemical composition of ejected matter during the explosions of stars of different masses and Supernovae of different types.     

Distribution of free electrons in the galactic plane

A method is proposed for constructing a map of the electron density distribution in the galactic plane. Data on the dispersion measures DM of more than 1500 pulsars and their distances, found by an independent method, are used. The independent distances of the pulsars are estimated using an empirical relation of the form L=γP ^α Ṗ ^β W ^δ between the radio luminosity L of the pulsars and their periods P, the rate of change Ṗ. of their periods, and the half width W of their pulses. A map of the electron density distribution in the galactic plane within a ±400 pc layer is provided. __________ Translated from Astrofizika, Vol. 49, No. 2, pp. 277–287 (May 2006).