Rotation of a two-component model neutron star in the GTR

Equations are obtained for the dynamics of the rotation of a two-component model neutron star within the framework of the generai theory of relativity. It is shown that for steady rotation of the star’s normal component, Ω_c = const, the angular velocity Ω_s of the superfluid component depends on the coordinates and is Ω_c + ω, where ω is the nondiagonal component of the metric tensor. Translated from Astrofizika, Vol. 40, No. 3, pp. 403–412, August, 1997.     

Nonradial oscillations of a neutron star in an inhomogeneous hydrodynamic model

An inhomogeneous model neutron star with a variable density profile of the type ₀(r)=_c[1–(2/3)r²/R²]exp(–r²/R²) is considered, where _c is the central density, R is the star's radius, and is the inhomogeneity parameter in the radial mass distribution. This parameterization adequately reproduces the results of numerical evolutionary calculations of the density profile and enables one to obtain in analytical form the parameters of hydrostatic equilibrium and the eigenmodes of nonradial oscillations of a nonrotating neutron star, modeled by a spherical mass of incompressible, inviscid liquid. It is shown that a characteristic manifestation of the star's inhomogeneity is the presence of a stable dipole f-mode, the lowest one in the spectrum of natural oscillations. The presence of this mode serves as a general and primary criterion that evidently distinguishes all inhomogeneous hydrodynamic models from the homogeneous Kelvin model, in which the quadrupole mode is the lowest stable mode. Estimates obtained for the periods of nonradial pulsations coincide with the periods of micropulses observed in the average pulse profiles of c-pulsars. This suggests that the detected variations in emission intensity in the range of micropulse duration (on the order of 10^–4 sec) are associated with nonradial stellar oscillations.Translated from Astrofizika, Vol. 39, No. 3, pp. 475–488, July–September, 1996.     

A two-density neutron star model with continuity of density

Tolman's V solution has found wide application to the redshift problems in astrophysics but it has a drawback that there is singularity at the centre. We have developed a two-density model with a parabolic density distribution in the core ande r ²ⁿ in the envelope. The most distinctive feature of the model is that there is a continuity of all four variables (E, P, , and ) at the boundary. In other analytic core-envelope models the continuity of only three varaibles is possible. This two-density structure has been used to model neutron stars and their mass, size, and red shifts have been obtained.     

Natural MHD oscillations of a neutron star

Natural, low-frequency, hydromagnetic oscillations of an isolated, nonrotating neutron star, which are localized in the peripheral crust, the structure of which is determined by the electron-nuclear plasma (the Ae phase), are studied. The plasma medium of the outer crust is treated as a homogeneous, infinitely conducting, incompressible continuum, the motions of which are determined by the equations of magnetohydrodynamics. In the approximation of a constant magnetic field inside the crust (the magnetic field outside the star is assumed to have a dipole structure), the spectrum of normal poloidal and toroidal hydromagnetic oscillations, due to presumed residual fluctuations of flow and their associated fluctuations in magnetic field strength, is calculated. Numerical estimates given for the periods of MHD oscillations fall in the range of periods of radio pulsar emission, indicating a close connection between the residual hydromagnetic oscillations and the electromagnetic activity of neutron stars. Translated from Astrofizika, Vol. 40, No. 1, pp. 77–86, January–March, 1997.     

The maximum mass of a neutron star

We consider the possibility that gravitational energy may play a local as well as global role in the behavior of matter in strong gravitational fields. A particular idealized equation, suggested as representing uniform energy density in general relativity, is examined, and its stability with respect to oscillatory and convective perturbations shown to be consistent with general relativistic hydrodynamics, subject to a new physical effect predicted for the behavior of fluids moving in strong fields. We calculate from this idealized equation the mass of a non-rotating neutron star, obtaining a maximum surface redshift ofz=2.48 and a maximum core mass of 9.79 ₁₄ ^–1/2 M. This compares withz=2.00 and 11.4 ₁₄ ^–1/2 M for a Schwarzschild star (=const.) and 6.8 ₁₄ ^–1/2 M for a causal star (dP/d1).     

Temperature profile within a magnetized neutron star

Erevan State University. Translated from Astrofizika, Vol. 32, No. 2, pp. 291–302, March–April, 1990.     

Isothermal neutron star cores

By considering the relativistic expression for isothermal NS cores,T·e ^/2 = constant, we have shown that some of the standard equations of state, when applied to NS cores, correspond to constancy of some adiabatic exponents. It has been shown that the equation of state,P=KE, corresponds to ₁ = to ₂ = ₃ 1 +K and the equation of state, dP/dE=K, corresponds to ₃ 1 +K. The conditions under which different equations of state represent isothermal cores have been obtained: For isothermal NS, the local temperatureT, can be expressed in terms of pressureP, energy densityE, and rest mass density . For example: (a)P =KE :T = constant × (E/); (b)P=KE :T = constant × (P/); (c) dP/dE =K :T ^K ; (d) = ₂ :T = constant × (P/E); and (e) = ₃ :T = constant × (P/)^1/2. Equation of state corresponding to = ₂ is obtained as:P=E/ln(K/E) and the equation corresponding to = ₃ comes out as:E=P ln(K/P). Core-envelope models can be developed for these two cases. When core equation corresponding to = ₂ or = ₃ is used in the core, we can ensure the continuity of dP/dE at the core-envelope boundary, along with the continuity ofP, E, , and . The parameters of isothermal NS cores corresponding to the cases = ₂ and = ₃, have been obtained. The maximum mass of these NS cores comes out to be 2.7 .     

Self-similar pressure oscillations in neutron star envelopes as probes of neutron star structure

We study eigenmodes of acoustic oscillations of high multipolarity l ∼ 100–1000 and high frequency (∼100 kHz), localized in neutron star envelopes. We show that the oscillation problem is self-similar. Once the oscillation spectrum is calculated for a given equation of state (EOS) in the envelope and given stellar mass M and radius R , it can be rescaled to a star with any M and R (but the same EOS in the envelope). For l ≳ 300, the modes can be subdivided into the outer and inner ones. The outer modes are mainly localized in the outer envelope. The inner modes are mostly localized near the neutron drip point, being associated with the softening of the EOS after the neutron drip. We calculate oscillation spectra for the EOSs of cold-catalyzed and accreted matter and show that the spectra of the inner modes are essentially different. A detection and identification of high-frequency pressure modes would allow one to infer M and R and determine also the EOS in the envelope (accreted or ground state) providing a new, potentially powerful method to explore the main parameters and internal structure of neutron stars.     

Unifying neutron star sub-populations in the supernova fallback accretion model

We employ the supernova fallback disk model to simulate the spin evolution of isolated young neutron stars(NSs). We consider the submergence of the NS magnetic fields during the supercritical accretion stage and its succeeding reemergence. It is shown that the evolution of the spin periods and the magnetic fields in this model is able to account for the relatively weak magnetic fields of central compact objects and the measured braking indices of young pulsars. For a range of initial parameters, evolutionary links can be established among various kinds of NS sub-populations including magnetars, central compact objects and young pulsars. Thus, the diversity of young NSs could be unified in the framework of the supernova fallback accretion model.     

Structure of neutron star cores

After reviewing the outer and central regions of a neutron star, we discuss the central region and the possibility that the core has a solid structure. We present the work of different groups on the solidification problem, suggesting that the neutron star-cores are indeed solid.     

Analysis of nonradial pulsations of a homogeneous neutron star

Nonradial pulsations of an isolated neutron star were studied in two continuum models — a self-gravitating spherical mass of an inviscid, incompressible fluid and an elastic Fermi continuum. A detailed analytical derivation of natural spheroidal and torsional oscillation frequencies of a neutron star of mass 1.4M based on notions about neutron matter as an elastic Fermi continuum is given. A comparison of numerical estimates of natural frequencies shows that both models predict the same order of pulsations 10⁴ Hz; however, the frequencies of spheroidal modes calculated in the elastic Fermi continuum model are about 2–2.5 times higher than the frequencies calculated in the framework of the Kelvin hydrodynamic theory.Translated from Astrofizika, Vol. 38, No. 1, pp. 121–139, January–March, 1995.     

Nucleosynthesis in neutron star atmospheres

The composition of neutron star atmospheres is calculated as a function of time including effects of diffusion, cooling and thermonuclear reactions. A seven-component nuclear reaction network with includes He⁴, C¹², O¹⁶, Ne²⁰, Mg²⁴, Si²⁸ and Fe⁵⁶ is utilized. Neutron star models with different initial nuclear abundances are compared as to subsequent nucleosynthesis. It is found that the final abundances are independent of original composition assuming He⁴ as the major initial constituent. The final composition of the atmosphere is predominantly Fe⁵⁶. Mass loss from an evolving neutron star is examined as a possible source of cosmic rays. It is found that a neutron star contributes only Fe⁵⁶ significantly to the cosmic-ray spectrum.     

Evidence for the free precession of a neutron star

Although the free precession of a neutron star has been put forward as the cause of long-period variations in some X-ray pulsar emissions, no corroborating evidence has been found. The recent observation of a pulsar in Cygnus X-3, a system with a well measured long-period variation, provides an opportunity to examine the possibility of free precession. The properties of the pulsar which have been observed so far are consistent with the neutron star having a small free precession amplitude.     

Precession as a probe of the neutron star interior

Strong evidence that some neutron stars precess (nutate) with long periods (∼1 yr) challenges our current understanding of the neutron star interior. I describe how neutron star precession can be used to constrain the state of the interior in a new way. I argue that the standard picture of the outer core, in which superfluid neutrons coexist with type II, superconducting protons, requires revision. One possible resolution is that the protons are not type II, but type I. Another possibility is that the neutrons are normal in the outer core. I conclude with a brief discussion of the implications for detectable gravitational wave emission from millisecond pulsars. Much of the work described here was supported by the National Science Foundation under Grant AST-00098728.     

Gravitational radiation of a differentially rotating superfluid neutron star

The gravitational radiation of a neutron star with a weakly coupled superfluid component is considered. It is assumed that regions can exist in the star's core which rotate at substantially higher angular velocities than the observed angular velocities of pulsars. A star of this sort has a quadrupole moment on the order of the maximum value for the neutron star configurations that have been discussed, so it could be a powerful source of gravitational radiation for the planned Advanced LIGO detector. Translated from Astrofizika, Vol. 51, No. 4, pp. 647–652 (November 2008).     

The energy loss of a rotating magnetized neutron star

The analysis of observations of pulsar B1931+24 shows that the mechanism of the spin-down of a rotating magnetized neutron star is due to the plasma generation in its magnetosphere and, consequently, the radio emission generation. The unique observation of the switch on and switch off of this pulsar allows us to distinguish between the energy loss in the absence of radio emission (the magnetodipole radiation) and the current loss due to the rotation energy expenditure to the relativistic plasma generation and acceleration in the pulsar magnetosphere. The inclination angle χ, the angle between the rotation axis and the magnetic dipole axis, can be stationary for this pulsar,  χ=χ_st  . From observations and theory it follows that  χ_st= 59°  .