New generation mechanisms for X-ray quasi-periodic oscillations in accreting neutron stars

We propose three mechanisms for the generation of quasi-periodic oscillations (QPOs) in X-ray binaries. Two of them are based on an analogy with nonlinear oscillations of gaseous cavities in a fluid. The first mechanism, called magnetocavitation, implies that X-ray QPOs are produced by radial oscillations of the neutron-star magnetosphere interacting with accreted plasma. The photon-cavitation mechanism is considered when studying X-ray QPOs in neutron stars with critical (Eddington) luminosities. In this case, X-ray QPOs are generated by radial oscillations of photon cavities in the fully ionized hydrogen plasma that settles in the accretion column of a compact object. The mechanism according to which X-ray QPOs result from nonlinear oscillations of current sheets originating in accretion disks is suggested to explain QPOs in X-ray binaries with black holes and in cataclysmic variables. The calculated values of basic physical parameters of QPOs, such as the characteristic frequency, the dependences of QPO frequency and amplitude on X-ray flux, photon energy, and QPO lag time between photons at different energies are in good agreement with observational data.     

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.     

The two-dimensional structure of thin accretion disks

The two-dimensional structure of a thin accretion disk in the vicinity of a Schwarzschild black hole after passing a marginally stable orbit (r< 3r _g is discussed in terms of the Grad-Shafranov hydrodynamic equation. The accretion disk is shown to be sharply compressed as the sonic surface is approached, so the mass flow here is no longer radial. As a result, the dynamic forces ρ[(v ?)v] _θ , which are equal in magnitude to the pressure gradient ? _θ P on the sonic surface, become significant in vertical balance. Therefore, the disk thickness in the supersonic region (and, in particular, near the black-hole horizon) may be assumed to be determined not by the pressure gradient but by the shape of ballistic trajectories.     

Peculiarities of processing VLBI observations of pulsars

We determined the features of pulsars that were disregarded in standard amplitude-calibration procedures for VLBI observations. We suggest additional amplitude-calibration methods. These methods were used to process the VLBI observations of the pulsar PSR B0329+54 carried out with the HALCA ground—space interferometer. Data from the space radio telescope are corrected for a nonuniform reception band. We estimated the diameter of the scattering disk for this pulsar at a frequency of 1600 MHz: \( < 1\mathop .\limits^{''} 8 \times 10^{ - 3}\).     

Symmetry of the neutron and proton superfluidity effects in cooling neutron stars

We investigate the combined effect of neutron and proton superfluidities on the cooling of neutron stars whose cores consist of nucleons and electrons. We consider the singlet state paring of protons and the triplet pairing of neutrons in the cores of neutron stars. The critical superfluid temperatures T _c are assumed to depend on the matter density. We study two types of neutron pairing with different components of the total angular momentum of a Cooper pair along the quantization axis (|m _J |=0 or 2). Our calculations are compared with the observations of thermal emission from isolated neutron stars. We show that the observations can be interpreted by using two classes of superfluidity models: (1) strong proton superfluidity with a maximum critical temperature in the stellar core T _c ^max ?4×10⁹ K and weak neutron superfluidity of any type (T _c ^max ?2×10⁸ K); (2) strong neutron superfluidity (pairing with m _J =0) and weak proton superfluidity. The two types of models reflect an approximate symmetry with respect to an interchange of the critical neutron and proton pairing temperatures.     

Differential rotation of relativistic superfluid in neutron stars

It is shown how to set up a mathematically elegant and fully relativistic superfluid model that can provide a realistic approximation (neglecting small anisotropies due to crust solidity, magnetic fields, etc., but allowing for the regions with vortex pinning) of the global structure of a rotating neutron star, in terms of just two independently moving constituents. One of these represents the differentially rotating neutron superfluid, while the other part represents the combination of all the other ingredients, including the degenerate electrons, the superfluid protons in the core, and the ions in the crust, the electromagnetic interactions of which will tend to keep them locked together in a state of approximately rigid rotation. Order of magnitude estimates are provided for relevant parameters such as the resistive drag coefficient.     

The physics of strong magnetic fields in neutron stars

In this paper we present a new result, namely that the primal magnetic field of the collapsed core during a supernova explosion will, as a result of the conservation of magnetic flux, receive a massive boost to more than 90 times its original value by the Pauli paramagnetization of the highly degenerate relativistic electron gas just after the formation of the neutron star. Thus, the observed super-strong magnetic field of neutron stars may originate from the induced Pauli paramagnetization of the highly degenerate relativistic electron gas in the interior of the neutron star. We therefore have an apparently natural explanation for the surface magnetic field of a neutron star.     

Weakly radiating radio pulsars

We analyze the statistical distribution of weakly radiating pulsars, i.e., radio pulsars that have passed to the stage of an orthogonal rotator during the evolution of the inclination angle X. We discuss in detail the factors that lead to a significant reduction in the energy losses for this class of objects. We have determined the number of weakly radiating radio pulsars and their distribution in spin period P. The predictions of a theory based on the model of current losses are shown to be consistent with observational data.     

Evolution of the multipolar magnetic field in isolated neutron stars

The evolution of the multipolar structure of the magnetic field of isolated neutron stars is studied assuming the currents to be confined to the crust. We find that, except for multipoles of very high order ( l ≳25), the evolution is similar to that of a dipole. Therefore no significant evolution is expected in the pulse shape of isolated radio pulsars because of the evolution of the multipole structure of the magnetic field.     

The magnetosphere of oscillating neutron stars in general relativity

Just as a rotating magnetized neutron star has material pulled away from its surface to populate a magnetosphere, a similar process can occur as a result of neutron-star pulsations rather than rotation. This is of interest in connection with the overall study of neutron star oscillation modes but with a particular focus on the situation for magnetars. Following a previous Newtonian analysis of the production of a force-free magnetosphere in this way Timokhin et al., we present here a corresponding general-relativistic analysis. We give a derivation of the general relativistic Maxwell equations for small-amplitude arbitrary oscillations of a non-rotating neutron star with a generic magnetic field and show that these can be solved analytically under the assumption of low current density in the magnetosphere. We apply our formalism to toroidal oscillations of a neutron star with a dipole magnetic field and find that the low current density approximation is valid for at least half of the oscillation modes, similarly to the Newtonian case. Using an improved formula for the determination of the last closed field line, we calculate the energy losses resulting from toroidal stellar oscillations for all of the modes for which the size of the polar cap is small. We find that general relativistic effects lead to shrinking of the size of the polar cap and an increase in the energy density of the outflowing plasma. These effects act in opposite directions but the net result is that the energy loss from the neutron star is significantly smaller than suggested by the Newtonian treatment.     

Freely precessing neutron stars: model and observations

We present a model of a freely precessing neutron star, which is then compared against pulsar observations. The aim is to draw conclusions regarding the structure of the star, and to test theoretical ideas of crust–core coupling and superfluidity. We argue that, on theoretical grounds, it is likely that the core neutron superfluid does not participate in the free precession of the crust. We apply our model to the handful of proposed observations of free precession that have appeared in the literature. Assuming crust-only precession, we find that all but one of the observations are consistent with there being no pinned crustal superfluid at all; the maximum amount of pinned superfluid consistent with the observations is about 10⁻¹⁰ of the total stellar moment of inertia. However, the observations do not rule out the possibility that the crust and neutron superfluid core precess as a single unit. In this case the maximum amount of pinned superfluid consistent with the observations is about 10⁻⁸ of the total stellar moment of inertia. Both of these values are many orders of magnitude less than the 10⁻² value predicted by many theories of pulsar glitches. We conclude that superfluid pinning, at least as it affects free precession, needs to be reconsidered.     

On the mechanism of X-ray emission from radio pulsars

We discuss the correlations between the luminosities of radio pulsars in various frequency ranges and the magnetic fields on the light cylinder. These correlations suggest that the observed emission is generated in outer layers of the pulsar magnetospheres by the synchrotron mechanism. To calculate the distribution functions of the relativistic particles in the generation region, we use a model of quasilinear interactions between the waves excited by cyclotron instability and particles of the primary beam and the secondary electron—positron plasma. We derive a formula for calculating the X-ray luminosity L _x of radio pulsars. A strong correlation was found between L _x and the parameter \(\dot P_{ - 15} /P^{3.5}\), where P is the neutron-star rotation period, in close agreement with this formula. The latter makes it possible to predict the detection of X-ray emission from more than a hundred (114) known radio pulsars. We show that the Lorentz factors of the secondary particles are small (γ _p = 1.5–8.5), implying that the magnetic field near the neutron-star surface in these objects is multipolar. It follows from our model that almost all of the millisecond pulsars must emit X-ray synchrotron radiation. This conclusion differs from predictions of other models and can be used to test the theory under consideration. The list of potential X-ray radiators presented here can be used to search for X-ray sources with existing instruments.     

Magnetohydrodynamics in superconducting-superfluid neutron stars

Magnetohydrodynamic (MHD) equations are presented for the mixture of superfluid neutrons, superconducting protons and normal electrons believed to exist in the outer cores of neutron stars. The dissipative effects of electron viscosity and mutual friction resulting from electron-vortex scattering are also included. It is shown that Alfvén waves are replaced by cyclotron-vortex waves that have not been previously derived from MHD theory. The cyclotron-vortex waves are analogous to Alfvén waves with the tension arising from the magnetic energy density replaced by the vortex energy density. The equations are then put into a simplified form useful for studying the effect of the interior magnetic field on the dynamics. Of particular interest is the crust–core coupling time, which can be inferred from pulsar glitch observations. The hypothesis that cyclotron-vortex waves play a significant role in the core spin-up during a glitch is used to place limits on the interior magnetic field. The results are compared with those of other studies.     

A two-dimensional hydrostatically equilibrium atmosphere of a neutron star with given differential rotation

An analytic solution has been found in the Roche approximation for the axially symmetric structure of a hydrostatically equilibrium atmosphere of a neutron star produced by collapse. A hydrodynamic (quasione-dimensional) model for the collapse of a rotating iron core in a massive star gives rise to a heterogeneous rotating protoneutron star with an extended atmosphere composed of matter from the outer part of the iron core with differential rotation (Imshennik and Nadyozhin, 1992). The equation of state of a completely degenerate iron gas with an arbitrary degree of relativity is taken for the atmospheric matter. We construct a family of toroidal model atmospheres with total masses M≈ 0.1?2M _⊙ and total angular momenta J≈(1?5.5)×⁴⁹ erg s, which are acceptable for the outer part of the collapsed iron core, in accordance with the hydrodynamic model, as a function of constant parameters ω₀ and r ₀ of the specified differential rotation law Ω=ω₀exp[?(rsinθ)²/r ₀ ² ] in spherical coordinates. The assumed rotation law is also qualitatively consistent with the hydrodynamic model for the collapse of an iron core.     

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.     

Detection of giant pulses from the pulsar PSR B1112+50

We detected giant pulses from the pulsar PSR B1112+50. A pulse with an intensity that is a factor of 30 or more higher than the intensity of the average pulse is encountered approximately once in 150 observed pulses. The peak flux density of the strongest pulse is about 180 Jy. This value is a factor of 80 higher than the peak flux density of the average pulse. The giant pulses are narrower than the average profile by approximately a factor of 5 and they cluster about the center of the average profile.     

Mutual friction in superfluid neutron stars

We discuss vortex-mediated mutual friction in the two-fluid model for superfluid neutron star cores. Our discussion is based on the general formalism developed by Carter and collaborators, which makes due distinction between transport velocity and momentum for each fluid. This is essential for an implementation of the so-called entrainment effect, whereby the flow of one fluid imparts momentum in the other and vice versa. The mutual friction follows by balancing the Magnus effect that acts on the quantized neutron vortices with resistivity due to the scattering of electrons off of the magnetic field with which each vortex core is endowed. We derive the form of the macroscopic mutual friction force which is relevant for a model based on smooth-averaging over a collection of vortices. We discuss the coefficients that enter the expression for this force, and the time-scale on which the two interpenetrating fluids in a neutron star core are coupled. This discussion confirms that our new formulation accords well with previous work in this area.     

Interaction and ablation of fall-back discs in isolated neutron stars

An analysis of ablation processes is made for a fall-back disc with inner and outer radii external to the neutron-star light cylinder. The calculated ablation rate leads, with certain other assumptions, to a simple expression relating the inner radius and mean mass per unit area of any long-lived fall-back disc. Expressions for the torque components generated by interaction with the pulsar wind are obtained. It is not impossible that these could be responsible for small observable variations in pulse shape and spin-down rate but they are unlikely to be the source of the periodic changes seen in several pulsars.