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.      

Hydrogen molecular ion in the magnetic field of a neutron star

A two-dimensional potential energy surface of an H ₂ ⁺ molecular ion is calculated for the case of the strong magnetic field of the neutron starB=10¹¹–10¹³ G. It is shown that the dependence of the potential energy from the angle between the magnetic field direction and the internuclear axis becomes very sharp as the magnetic field increases. The obtained potential energy surfaces can be used for studying the vibrational-rotational structure of the H ₂ ⁺ spectrum in a strong magnetic field and the development of the observational methods for the determination of the magnetic field of a neutron star.     

Electromagnetic bursting of a rapidly rotating magnetized neutron star in a close binary system

We examine a possible manifestation of the electromagnetic activity of a magnetized, rotating neutron star in a binary system. Accreting matter from the companion is initially accumulated at the magnetosphere. When the accumulated mass is such that the inflow can start, together with the accretion flare there will be a burst due to the closure of electric currents. The luminosity associated to the latter effect may be as large as 10⁴² erg/s, if a neutron star possesses the following characteristics: massM =M , period of rotationP = 5 ms, magnetic fieldB ₀ = 10¹² G, and radiusr ₀ = 10⁶ cm. The electromagnetic activity might be relevant for understanding soft gamma ray repeaters.     

Nuclear reactions on accreting neutron star surface

The production of X-rays and gamma-rays in bursts is believed to be due to the rapid burning of matter accreted onto a neutron star surface from its companion, most probably a giant star. The accreted matter consists mainly of hydrogen and helium and a very small amount of heavy elements. Due to the infall of matter, the temperature at the bottom layers is raised to a value of the order of 10⁸ K. The neutron star surface density is>10⁷ g cm^–3. As hydrogen burning is a slow process under any temperature and density conditions, we consider the helium-burning reactions as the source of gamma-rays in the neutron star surface. Under high-density conditions the ordinary laboratory reaction rates should become modified. At high-density conditions, the strong screening effect due to the polarising cloud of electrons around the ions become important and enhances the reaction rates considerably. The helium-burning reactions are calculated under such conditions. The abundances of helium-burning products such as¹²C, 1¹⁶O, and²⁰Ne, etc., are computed. Under high-density and temperature conditions carbon is found to be more abundant than oxygen. Neon is completely absent in almost all the relevant physical conditions in which a strong screening effect is operative. It is suggested that explosive burning of accreted helium of 10^–13 M will account for the observed energy of gamm-ray burst.     

Expansion of neutron star matter and its final nuclear composition

The final nuclear composition of the matter expanding from the density of a neutron star is investigated. It is assumed that starquakes cause the cracks which penetrate the neutron star crust and that the neutron star fluid can flow out through the cracks into space. The change with time of the nuclear composition of this matter is calculated by use of the compressible nuclear mass formula, and the hydrodynamics of the system is followed by the effect of nuclear transformation with time of the second fission of heavy neutron-rich nuclei, which is followed by a rapid rise to above 10⁹ K. If the value of the -strength function exceeds about 10^–5.5 MeV^–1 s^–1, the system proceeds to a state of nuclear equilibrium in the later expansion stage and the nuclear composition is reshuffled, finally to be transformed into neutron-excess, stable nuclei within the atomic mass region 80A120. It also becomes clear that if the strength function has a value smaller than the above critical value, then the neutron-rich nuclides withA[200, 400] are copiously produced. These results will also be applied in the cases of a neutron-star-black-hole collision and the explosion of a neutron star associated with the catastrophic phase transition within the neutron star core. The astrophysical implications are briefly discussed.     

Toroidal magnetic field of a superfluid neutron star in a postnewtonian approximation

The effect of proton superconductivity on the generation of a toroidal magnetic field inside a neutron star is examined. It is shown that including the entrainment of superconducting protons by superfluid neutrons does not change the previously obtained results. Proton superconductivity does influence the structure of the generated magnetic field since, over a time on the order of 10⁴–10⁵ years, the magnetic field increases linearly with time and can exceed the first critical field for proton superconductivity. The distribution of the stationary toroidal magnetic field inside a neutron star is also found.     

Neutrinooszillationen in Neutronensternmaterie

According to the suggestion of T. J. Mazurek (1979) neutrino oscillations occuring during the dynamic stellar collapse (M ≥ 10M) could be result in a transfer of leptonic zero-point energy to baryons. Then the adiabatic index increases above γ ≥ 4/3, and such an increase is necessary to reverse the collapse. From the theory of neutrino oscillations of B. Pontekorvo (1967) we derive the oszillation length L of neutrinos in vacuum and the characteristic oscillation lengh L^* of neutrinos taking into consideration the refraction index n_e of neutron star matter. The comparison of both oscillation lenghts shows that for electron densities, characteristically of neutron star matter, the oscillation lenght L is considerable larger than the oscillation lenght L^*. Therefore neutrino oscillations cannot influence the scenario for neutrino emission of the neutron star.     

Ohm’s law for plasma in general relativity and Cowling’s theorem

The general-relativistic Ohm’s law for a two-component plasma which includes the gravitomagnetic force terms even in the case of quasi-neutrality has been derived. The equations that describe the electromagnetic processes in a plasma surrounding a neutron star are obtained by using the general relativistic form of Maxwell equations in a geometry of slow rotating gravitational object. In addition to the general-relativistic effect first discussed by Khanna and Camenzind (Astron. Astrophys. 307:665, 1996) we predict a mechanism of the generation of azimuthal current under the general relativistic effect of dragging of inertial frames on radial current in a plasma around neutron star. The azimuthal current being proportional to the angular velocity ω of the dragging of inertial frames can give valuable contribution on the evolution of the stellar magnetic field if ω exceeds 2.7×10¹⁷(n/σ) s⁻¹ (n is the number density of the charged particles, σ is the conductivity of plasma). Thus in general relativity a rotating neutron star, embedded in plasma, can in principle generate axial-symmetric magnetic fields even in axisymmetry. However, classical Cowling’s antidynamo theorem, according to which a stationary axial-symmetric magnetic field can not be sustained against ohmic diffusion, has to be hold in the general-relativistic case for the typical plasma being responsible for the rotating neutron star.     

On steady-state nuclear burning in accreting neutron stars

The properties of the hydrogen burning shell in the envelope of an accreting neutron star have been studied for a range of mass accretion rates, neutron star radii, and metal abundances of the accreted matter. It is found that the hydrogen burning shells lie at densities ranging from 10⁵–6×10⁶ gm cm^–3. For mass accretion rates in excess ofM _c2 hydrogen and helium burn together. ForM _c1MM _c2, the hydrogen burning shell is stabilized by the limited CNO cycle. Implications of these results to the X-ray burst phenomena are briefly discussed.     

The Crust Properties and Cooling of Strange Stars

We investigate the influence of the following parameters on the crust properties of strange stars: the strange quark mass (m _s), the strong coupling constant (α_c) and the vacuum energy density (B). It is found that the mass density at the crust base of strange stars cannot reach the neutron drip density. For a conventional parameter set of m _s=200 MeV, B ^1/4 = 145 MeV and α_c = 0.3, the maximum density at the crust base of a typical strange star is only 5.5 × 10¹⁰ gcm^-3, and correspondingly the maximum crust mass is 1.4 ×10^-6 M_⊙. Subsequently, we present the thermal structure and the cooling behavior of strange stars with crusts of different thickness, and under different diquark pairing gaps. Our work might provide important clues for distinguishing strange stars from neutron stars.     

Isotopic r-process abundances produced by supernova explosions

The rapid neutron capture process (r-process) is one of the major nucleosynthesis processes responsible for the synthesis of heavy nuclei beyond iron. Isotopes beyond Fe are most exclusively formed in neutron capture processes and more heavier ones are produced by the r-process. Approximately half of the heavy elements with mass number A>70 and all of the actinides in the solar system are believed to have been produced in the r-process. We have studied the r-process in supernovae for production of heavy elements beyond A=40 with the newest mass values available. The supernovae envelopes at a temperature >10⁹ K and neutron density of 10²⁴ cm⁻³ are considered to be one of the most potential sites for the r-process. We investigate the r-process in a site-independent, classical approach which assumes a chemical equilibrium between neutron captures and photodisintegrations followed by a β-flow equilibrium. We have studied the r-process path corresponding to temperatures ranging from 1.0×10⁹ K to 3.0×10⁹ K and neutron density ranging from 10²⁰ cm⁻³ to 10³⁰ cm⁻³. The primary goal of the r-process calculations is to fit the global abundance curve for solar system r-process isotopes by varying time dependent parameters such as temperature and neutron density. This method aims at comparing the calculated abundances of the stable isotopes with observation. The abundances obtained are compared with supernova explosion condition and found in good agreement. The elements obtained along the r-process path are compared with the observed data at all the above temperature and density range.     

Hydrogen molecular ion in the magnetic field of a neutron star

The paper discusses the structure and energies of rotational-vibrational levels of a molecular ion H ₂ ⁺ in a strong magnetic field typical of neutron stars,B=10¹²–10¹³ G. The study is based on the calculations of the potential energy surface of this molecular ion presented in the paper by Khersonskii (1984a). The energies of the rovibrational levels are calculated with the aid of the perturbation theory. The number of levels in a H ₂ ⁺ potential hole is determined at different magnetic intensities. In particular, it is ascertained that the number of levels decreases as the strength of the magnetic field increases. The effect of nuclear spins on the structure of the rotational levels is considered.     

UBV photometry of X-ray system with M2 III type red giant V934 her (4U 1700+24)

V934 Her is a detached system, consisting of a cool giant and a neutron star. The neutron star accretes matter fromthe stellarwind of the giant.Multicolor photoelectric observationsmade in 1997–2011 revealed a 415-day period, close to that, discovered spectroscopically from radial velocities. This period is considered to be the orbital period of orbital motion of the neutron star around the red giant. The wave with this period in the U-band has the largest amplitude 0^m.12. We also detected multiperiodic pulsations of the red giant. The light curve in the V -band is dominated by a pulsation wave with the period of 28.82 days and the amplitude of 0^m.10.     

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.     

Types I and II supernovae and the neutrino mechanism of thermonuclear explosion of degenerate carbon-oxygen stellar cores

The present work studies the hydrodynamic process of thermonuclear explosion of hydrostatic equilibrium, degenerate carbon-oxygen cores withM _C=1.40M _⊙ with different values of central densityϱ _c within the interval 2 × 10⁹ <ϱ _c < 3 × 10¹⁰ g cm⁻³. The initial temperature distribution has been determined by the preceding thermal stage of explosion. The calculations successively include the kinetics of thermonuclear burning, the kinetics of β-processes, and neutrino energy losses. By considering the neutrino mechanism of heating and carbon ignition we obtained in our numerical hydrodynamic calculations two characteristic versions of the development of an explosion: (a) at 2 × 10⁹ <ϱ _c < 9 × 10⁹ g cm⁻³ there is disruption of the whole star with either complete or partial burning of the carbon and a 10⁵⁰–10⁵¹ erg kinetic energy; and (b) at 9 × 10⁹ <ϱ _c < 3 × 10¹⁰ g cm⁻³ the stellar core collapses into a neutron star with partial outburst of the outer envelope with a smaller kinetic energy of 10⁴⁹–10⁵⁰ erg. The paper proposes and details a hypothesis (the scenario of supernovae and the formation of neutron stars) on the first version of explosion, corresponding to SNII, and on the second, supplemented by some mechanism of slow energy release into the envelope expelled from the newly formed neutron star, corresponding to SNI. On the basis of the proposed hypothesis a satisfactory agreement with the observed masses and energies of the supernovae envelope, their light curves and spectra, as well as with the data on their chemical composition has been obtained. For this agreement we must assume that type I pre-supernovae are almost bare compact carbon-oxygen stellar cores, and that type II presupernovae are red supergiants. It is most probable that the evolution of type I pre-supernovae occurs in close binaries while the evolution of type II pre-supernovae seems to be very similar to the evolution of a single star.     

Constraining the gravitational redshift of a neutron star from the Σ-meson well depth

The effect of the Σ-meson well depth on the gravitational redshift is examined within the framework of relativistic mean field theory for the baryon octet system. It is found that, for a stable neutron star, the gravitational redshift increases with the central energy density increase or with the mass increase but decreases as the radius increases. Considering a change of U_S^(N)U_{\Sigma}^{(N)} from −30 MeV to 30 MeV, for a stable neutron star the gravitational redshift near to the maximum mass increases. In addition, it is also found that the growth of the U_S^(N)U_{\Sigma}^{(N)} makes the gravitational redshift as a function of M _max/R increase, the higher the U_S^(N)U_{\Sigma}^{(N)} the less the change in the gravitational redshift.     

Vortex structure of neutron stars with triplet neutron superfluidity

The vortex structure of the “npe” phase of neutron stars with a ³P₂ superfluid neutron condensate of Cooper pairs is discussed. It is shown that, as the star rotates, superfluid neutron vortex filaments described by a unitary ordering parameter develop in the “npe” phase. The entrainment of superconducting protons by the rotating superfluid neutrons is examined. The entrainment effect leads to the appearance of clusters of proton vortices around each neutron vortex and generates a magnetic field on the order of 10¹² G. ³P₂ neutron vortex filaments combine with quark semi-superfluid vortex filaments at the boundary of the “npe” and “CFL” phases. At the boundary of the “Aen” and “npe” phases, they combine with ¹S₀ neutron vortex filaments. In this way, a unified vortex structure is formed. The existence of this structure and its collective elastic oscillations explain the observed oscillations in the angular rotation velocity of pulsars.     

Solar Proton Rigidity Spectra From 1 to 10 gv of Selected Flare Events Since 1960

We have deduced the power-law rigidity spectra, J(P)=AP ^–, and the spectral evolution of the solar flare events that occurred in the present solar activity cycle on 6 November 1997, 14 July 2000, and 15 and 18 April 2001. The implications of these results for the acceleration of high-energy protons are discussed. The analysis is based on the ratios of the Mt. Washington to the Durham neutron monitor count-rate increases during the solar flare events. These two neutron monitors are located at different elevations (828 and 1030 g cm^–2, respectively) but at approximately the same geographical latitude and longitude. The proton spectra from 1 to 10 GV determined from the ratios of the count rate increases of the two neutron monitors are found to agree with those deduced from the global neutron monitor network or selected neutron monitors in 10 solar flare events from 1960 to 1990 for which comparative results are available. Thus the ratio method is quick, easy and reliable for deducing the spectral shape of solar flare protons at neutron monitor rigidities and for obtaining the spectral evolution as a function of time.     

One-photon and two-photon annihilation of positronium in strong magnetic fields

In the presence of a strong magnetic field (such as those believed to be characteristic of neutron stars:B-10¹² Gauss) positronium may annihilate through the emission of a single photon, the magnetic field providing the photon momentum. We report on calculations of the one-photon and two-photon annihilation rates for the ground state of positronium, for magnetic fields in the range (1–44)×10¹² Gauss, and give, in the two-photon case, the minimum energy half-width of the emission line due to the momentum contributions from the magnetic field. We find that unless neutron stars have magnetic fields in excess of 10¹³ Gauss, it is unlikely that the one-photon process will be observable.Research supported in part by the National Research Council of Canada.     

Nucleon superfluidity versus thermal states of isolated and transiently accreting neutron stars

The properties of superdense matter in neutron star (NS) cores control NS thermal states by affecting the efficiency of neutrino emission from NS interiors. To probe these properties we confront the theory of thermal evolution of NSs with observations of their thermal radiation. Our observational basis includes cooling isolated NSs (INSs) and NSs in quiescent states of soft X-ray transients (SXTs). We find that the data on SXTs support the conclusions obtained from the analysis of INSs: strong proton superfluidity with T _cp ^max≳10⁹ K should be present, while mild neutron superfluidity with T _cn ^max≈2×(10⁸−−10⁹) K is ruled out in the outer NS core. Here T _cn ^max and T _cp ^max are the maximum values of the density dependent critical temperatures of neutrons and protons. The data on SXTs suggest also that: (i) cooling of massive NSs is enhanced by neutrino emission more powerful than the emission due to Cooper pairing of neutrons; (ii) mild neutron superfluidity, if available, might be present only in inner cores of massive NSs. In the latter case SXTs would exhibit dichotomy, i.e. very similar SXTs may evolve to very different thermal states.