Can a slowly rotating neutron star be a radio pulsar?

It is shown that the radius of curvature of magnetic field lines in the polar region of a rotating magnetized neutron star can be significantly less than the usual radius of curvature of the dipole magnetic field. The magnetic field in the polar cap is distorted by toroidal electric currents flowing in the neutron star crust. These currents close up the magnetospheric currents driven by the electron–positron plasma generation process in the pulsar magnetosphere. Owing to the decrease in the radius of curvature, electron–positron plasma generation becomes possible even for slowly rotating neutron stars, with   PB ^−2/3₁₂ < 10 s  , where P is the period of star rotation and   B ₁₂= B /10¹² G  is the magnitude of the magnetic field on the star surface.     

On the theory of annihilation lines in gamma-ray bursts

The mechanism of formation of an annihilation line 0.5 MeV in gamma-ray bursts due to electron-positron pair production in strong magnetic fields of neutron stars is discussed. Bremsstrahlung from a hot polar spot is supposed to be a source of gamma-quanta which produce the pairs. It is shown that a great part of radiation with the energyE>2mc ² per quantum (except for directions along or close to the magnetic field) is consumed by pair production and does not excape from the gamma-burster. This indicates a possible strong gap in continuum radiation at energies higher than 1 MeV. At the same time effective creation of pairs enables one to give a simple estimate of the expected annihilation line intensity in gamma-ray burst spectra. This estimate coincides with the available observational data.     

Thermal emission areas of heated neutron star polar caps

Observed hot spots on neutron stars are often associated with polar caps heated by the backflow of energetic electrons or positrons from accelerators on bundles of open magnetic field lines. Three effects are discussed that may be relevant to formation of hot spots and their areas. (1) The area of a polar cap is proportional to the ratio of the star’s surface dipole field to the local field at the polar cap. Because the field is coupled to the evolving spin of the superfluid core of the star, this ratio can depend on the stellar spin and its history. (2) The hot emission area may appear smaller to a distant observer when emitted X-rays propagate through electron-positron plasma created in the magnetosphere. The X-rays then change their energy spectrum because of cyclotron resonant scattering by pairs. (3) Hot spots may form on the star’s surface as a result of crust motions that are driven by the pull of core flux tubes pinned to the crust. Such motions twist the footprints of closed magnetic loops of the magnetosphere and induce an electric current in the loop, which will heat those footprints.     

Studies of accretion flows around rotating black holes – I. Particle dynamics in a pseudo-Kerr potential

We study the formation of the absorption features, called the cyclotron–annihilation lines, in the γ-spectra of the neutron stars (pulsars), owing to the fundamental quantum-electrodynamic effect of the one–photon pair creation in magnetized vacuum. As a result, we substantiate a new method for the determination of the neutron star magnetic fields B based on measuring the interval between the main annihilation and the first cyclotron–annihilation absorption lines. It is found that these lines may be easily resolved, and, consequently, the method is surely applicable if the following conditions are satisfied. (i) A γ-source has to be compact enough and located near a star, but not close to its magnetic poles. For instance, it may be a disc in the plane of a star magnetic equator with latitudinal angular width less than     and radial extent up to 25 per cent of the star radius. (ii) The source is to produce detectable γ-radiation at large angles ≳60° to the local magnetic field. Being situated in a closed field line region and having a broad radiation pattern, such a source is not what is usually considered in the context of the polar cap and outer gap models of the pulsar γ-emission dealing with open field lines only. (iii) Magnetic field strength must lie in a certain narrow interval with the centre at  ∼(3–4) × 10¹²  G. Its width depends on the star orientation and disc radial extend and in the most favourable case is about 20–30 per cent of its lower boundary. Finally, the influence of the star rotation on this method employment is considered and new possibilities arising from forthcoming polarization observations are briefly discussed.     

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).     

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 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.     

A numerical experiment relevant to line-tied reconnection in two-ribbon flares

The nonlinear evolution of a reconnecting magnetic field configuration similar to that occurring just before the onset of ‘post’-flare loops in two-ribbon flares is determined. The evolution, which is obtained by numerically solving the resistive MHD equations, shows two new features that have not yet been incorporated into contemporary models of ‘post’-flare loops. The first of these new features is the formation of a nearly stationary fast-mode shock above the region corresponding to the top of the loops. This fast-mode shock occurs just below the magnetic neutral line and between the slow-mode shocks associated with fast magnetic reconnection at the neutral line. The second new feature is the creation and annihilation of large-scale magnetic islands in the current sheet above the loops. The annihilation of the islands occurs very rapidly and appears to be a manifestation of the coalescence instability. The creation and annihilation of magnetic islands could be important in understanding the energetics of ‘post’-flare loops since the coalescence instability can produce an intermittent energy release more than an order of magnitude faster than that predicted by steady-state reconnection theories.     

On hard X-ray spectra of accreting neutron stars

Formation of the spectra of X-ray pulsars and gamma bursters is investigated. Interpretation of a hard X-ray spectrum of pulsars containing cyclotron lines is feasible on the basis of an isothermal model of a polar spot heated due to accretion to a neutron star. It has been ascertained that in the regions responsible for the formation of continuum radiation and lines the mode polarization is determined by a magnetized vacuum rather than by a plasma. Bearing this in mind, the influence of the magnetic field of a star on the wide wings of the cyclotron line and on its depth is discussed. The part played by the accreting column in the case of strong accretion (10¹⁹ el cm^–3) needed for long sustaining of the high level of X-rays from a neutron star-pulsar is studied. There occur the gaps in spectrum at frequencies close to the electron gyro-frequency and its harmonics due to the screening of the hot spot by the opaque gyro-resonant layers located within the accreting column. These gaps ensure the formation of cyclotron lines in absorption irrespective of the presence of such lines in the X-ray spectrum of a polar hot spot.The spectra of gamma-bursters recorded by Venus 11 and Venus 12 are interpreted in terms of a two-layer model of a polar hot spot. The estimates are given of the distance to some of the bursters, of the emission measure from a high-temperature layer responsible for continuum radiation and of the dispersion measure of a colder layer forming cyclotron lines in absorption. It is noted that the action of an accreting column leads generally to the radiation depression at frequencies below cyclotron lines. By the observed depression for one of the bursters the electron density of near-star accreting plasma during the burst has been directly estimated (4×10^–14 el cm^–3). Possible appearance of false cyclotron lines associated with cyclotron scattering in accreting column has been revealed.The problem of measuring the magnetic fields of neutron stars taking account of the gravitational redshift and the quantum recoil effect in emission and in absorption is discussed. Possibilty for a more precise measurement of the magnetic fields of those bursters whose spectrum contains both a cyclotron and an annihilation lines is noted.     

NuSTAR observations of the X-ray pulsar LMC X-4: A constraint on the magnetic field and tomography of the system in the fluorescent iron line

We present the results of the spectral and timing analysis of the X-ray pulsar LMC X-4 based on data from the NuSTAR observatory in the broad X-ray energy range 3–79 keV. Along with a detailed analysis of the source’s averaged spectrum, high-precision spectra corresponding to different phases of the neutron star spin cycle have been obtained for the first time. The Comptonization model is shown to describe best the source’s spectrum, and the evolution of its parameters as a function of the pulse phase has been traced. For all spectra (the averaged and phase-resolved ones) in the energy range 5–55 keV we have searched for the cyclotron absorption line. The derived upper limit on the optical depth of the cyclotron line τ ~ 0.15 (3σ) points to the absence of this feature in the given energy range, which provides a constraint on the magnetic field of the neutron star: B <3 × 10¹¹ or >6.5 × 10¹² G. The latter constraint is consistent with the magnetic field estimate obtained by analyzing the pulsar’s power spectrum, B ? 3 × 10¹³ G. Based on our analysis of the phase-resolved spectra, we have determined the delay between the emission peaks and the equivalent width of the fluorescent iron line. This delay depends on the orbital phase and is apparently associated with the travel time of photons between the emitting regions in the vicinity of the neutron star and the region where the flux is reflected (presumably in the inflowing stream or at the place of interaction between the stream and the outer edge of the accretion disk).     

New results of magnetic field measurements for BP Tau

We present measurements of the longitudinal magnetic field component B _‖ of the young star BP Tau in the He I 5876 emission line formation region, i.e., in the accretion flow near the stellar surface. The values obtained (?1.7 kG and ?1.0 kG in 2000 and 2001, respectively) agree with the results of similar measurements by other authors. At the same time, we show that the previously obtained field strength at the magnetic pole, B _p, and the inclination of the magnetic axis to the rotation axis, β, are untrustworthy. In our opinion, based on the B _‖ measurements available to date, it is not possible to conclude whether the star’s magnetic field is a dipole one or has a more complex configuration and to solve the question of whether this field is stationary. However, we argue that at least in the He I 5876 line formation region, the star’s magnetic field is not stationary and can be restructured in a time of the order of several hours. Nonstationary small-scale magnetic fields of active regions on the stellar surface and/or magnetospheric field line reconnection due to the twisting of these field lines as the star rotates could be responsible for the short-term magnetic field variability. It seems highly likely that there are no strictly periodic variations in brightness and emission line profiles in BP Tau due to the irregular restructuring of the star’s magnetic field.     

Non-LTE models of the accretion disks of UX Ori stars

The results of a non-LTE analysis of a number of spectral lines formed in the accreting envelopes of UX Ori stars are given. The accretion rate is estimated from an analysis of the first three lines of the Balmer series: M _a = 10^?8 ?10^?9 M _⊙ The gas temperature in this region is about 10,000 K. In the immediate vicinity of the star there is a hotter region, with T > 15,000 K, in which the 5876 Å line of neutral helium, observed in the spectra of these stars, is formed. The region of formation of this line has a small geometrical thickness, covers a small fraction of the star’s visible disk, and evidently consists of the site of contact of the accreting gas with the stellar surface. The low gas rotation rates in this region (150–200 km/sec) may mean that rapid rotation of the accreting gas is damped by the star’s magnetic field, which is strong enough to affect the gas stream. We estimate the magnetic field strength in this region to be about 150 G.     

On the origin and structure of stellar magnetic fields

Newly formed stars have magnetic fields provided by the compression of the interstellar field, and contrary to a widely accepted idea these fields are not destroyed by convective motions. For the same reason, the fallacy of ‘turbulent diffusion’, turbulent dynamo action is not possible in any star. Thus all stellar magnetic fields have a common origin, and persist throughout the lifetime of each star, including degenerate phases. This common origin, and a general similarity in stellar evolutionary processes, suggest that the fields may develop similar structural characteristics and MHD effects. This would open new possibilities of coordinating the studies of different types of stars and relating them to solar physics which has tended to become isolated from general stellar physics. As an initial step we consider three features of solar magnetic fields and their MHD effects. First, the solar magnetic field comprises two separate components: a poloidal field and a toroidal field. The former is a dipole field, permeating the entire Sun and closely aligned with the rotational axis; at the surface it is always concealed by much stronger elements of the toroidal field. The latter is probably wound from the former by differential rotation at latitudes below about 35°, where sections emerge through the solar surface and are then carried polewards. The second feature of solar magnetic fields is that all flux is concentrated into flux tubes of strength some kG, isolated within a much larger volume of non-magnetic plasma. The third feature is that the flux tubes are helically twisted into flux ropes (up to ?10²²Mx) and smaller elements ranging down to flux fibres (? 10¹⁸Mx). Some implications of similar features in other stars are discussed.     

On the electric field screening by electron–positron pairs in a pulsar magnetosphere

We present a steady one-dimensional model for a pulsar polar cap accelerator, where the field-aligned electric field and flow are solved self-consistently with a given current density. It is assumed that no particles return to the star. It is known that the space-charge-limited flow is accelerated to energies high enough to create electron–positron pairs if the assumed current density is high enough. We find that when pairs are created in such a space-charge-limited flow, the accelerating electric field is screened out within a short distance after pair creation, if the pair particle flux is larger than a critical value. We also find that a space charge density wave is excited in the screening region.
We find that a pair flux larger than the critical value M _c=10³–10⁵ must be reached in a layer with thickness equal to the braking distance for the decelerating component. Therefore, the required multiplicity – the number of pairs created by one primary particle – is too large to be realized in the actual pulsar magnetosphere. We suggest that in order to obtain a localized potential drop along the polar cap magnetic flux, one needs to take into account additional effects such as wave–particle interaction or quasi-periodic pair creation.     

The concentration of the large-scale solar magnetic field by a meridional surface flow

We calculate analytical and numerical solutions to the magnetic flux transport equation in the absence of new bipolar sources of flux, for several meridional flow profiles and a range of peak flow speeds. We find that a poleward flow with a broad profile and a nominal 10 m s^–1 maximum speed concentrates the large-scale field into very small caps of less than 15° half-angle, with average field strengths of several tens of gauss, contrary to observations. A flow which reaches its peak speed at a relatively low latitude and then decreases rapidly to zero at higher latitudes leads to a large-scale field pattern which is consistent with observations. For such a flow, only lower latitude sunspot groups can contribute to interhemispheric flux annihilation and the resulting decay and reversal of the polar magnetic fields.     

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.     

One-photon and two-photon annihilation lines in gamma-bursts,II

This paper, which is a continuation of Paper I (Zheleznyakov and Litvinchuk, 1985), studies the formation of a one-quantum annihilation line in the spectrum of gamma-ray bursts. The radiative transfer equation together with the positron density balance relation is solved, and the expected photon fluxes in the one- and two-quantum annihilation lines are calculated. The fractional luminosities of these lines versus source parameters are investigated. For a gamma-burst one-photon annihilation line, the luminosity is always much less than that for the two-photon line-i.e., the positron source power transforms almost entirely into radiation in the two-quantum annihilation line and the positron density depends solely on the specific source power and two-quantum annihilation probability. The flux of one-quantum annihilation quanta 1 MeV is estimated to be less than what modern detectors can resolve. This explains failure to detect the one-photon annihilation lines in gamma-bursts so far.     

Results of magnetic field measurements in young stars DO Tau, DR Tau, and DS Tau

The results of longitudinal magnetic field measurements B _z in the hot accretion spot in three classical T Tauri stars (CTTS) are reported. In all three stars the magnetic field is detected at a level above 2σ in the formation region of the narrow component of the He I 5876 Å emission line. In the case of DS Tau the longitudinal field B _z in the hot spot was also measured from the narrow emission components of the Na I D lines, implying +0.8 ± 0.3 kG, which is equal to the B _z field component measured from the He I 5876 Å line. Our results suggest that the 6-m telescope of the Special Astrophysical Observatory can be used to study magnetic fields in the hot spots of CTTS with magnitudes down to 13^m, making it possible to double the number of stars of this type with measured B _z values in the accretion zone.     

Modelling surface magnetic field evolution on AB Doradûs due to diffusion and surface differential rotation

From Zeeman–Doppler images of the young, rapidly-rotating K0 dwarf AB Doradûs, we have created a potential approximation to the observed radial magnetic field and have evolved it over 30 d subject to the observed surface differential rotation , meridional flow and various diffusion rates. Assuming that the dark polar cap seen in Doppler images of this star is caused by the presence of a unipolar field, we have shown that the observed differential rotation will shear this field to produce the observed high-latitude band of unidirectional azimuthal field. By cross-correlating the evolved fields with the initial field each day we have followed the decay with time of the cross-correlation function. Over 30 d it decays by only 10 per cent. This contrasts with the results of Barnes et al. , who show that on this time-scale the spot distribution of He699 is uncorrelated. We propose that this is due to the effects of flux emergence changing the spot distributions.