Energy release on the surface of a rapidly rotating neutron star during disk accretion: A thermodynamic approach

The total energy E of a star as a function of its angular momentum J and mass M in the Newtonian theory, E=E(J, M) [in general relativity, the gravitational mass of a star as a function of its angular momentum J and rest mass m, M=M(J, m)], is used to determine the remaining parameters (angular velocity, chemical potential, etc.) in the case of rigid rotation. Expressions are derived for the energy release during accretion onto a cool (with constant entropy), rapidly rotating neutron star (NS) in the Newtonian theory and in general relativity. A separate analysis is performed for the cases where the NS equatorial radius is larger and smaller than the radius of the marginally stable orbit in the disk plane. An approximate formula is proposed for the NS equatorial radius for an arbitrary equation of state, which matches the exact equation of state at J=0.     

Boundary layer on the surface of a neutron star

In an attempt to model the accretion on to a neutron star in low-mass X-ray binaries, we present 2D hydrodynamical models of the gas flow in close vicinity of the stellar surface. First, we consider a gas pressure-dominated case, assuming that the star is non-rotating. For the stellar mass we take   M _star= 1.4 × 10⁻² M_⊙  and for the gas temperature   T = 5 × 10⁶ K  . Our results are qualitatively different in the case of a realistic neutron star mass and a realistic gas temperature of T ≃ 10⁸ K, when the radiation pressure dominates. We show that to get the stationary solution in a latter case, the star most probably has to rotate with the considerable velocity.     

Dynamics of the flows accreting onto a magnetized neutron star

We investigate the unsteady column accretion of material at a rate \(10^{15} g s^{ - 1} \leqslant \dot M \leqslant 10^{16} g s^{ - 1}\) onto the surface of a magnetized neutron star using a modified first-order Godunov method with splitting. We study the dynamics of the formation and evolution of a shock in an accretion column near the surface of a star with a magnetic field 5×10¹¹≤B≤10¹³ G. An effective transformation of the accretion flow energy into cyclotron radiation is shown to be possible for unsteady accretion with a collisionless shock whose front executes damped oscillations. The collisionless deceleration of the accreting material admits the conservation of a fraction of the heavy nuclei that have not been destroyed in spallation reactions. The fraction of the CNO nuclei that reach the stellar atmosphere is shown to depend on the magnetic field strength of the star.     

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.     

Nodal and periastron precession of inclined orbits in the field of a rapidly rotating neutron star

We derive a formula for the nodal precession frequency and the Keplerian period of a particle at an arbitrary orbital inclination (with a minimum latitudinal angle reached at the orbit) in the post-Newtonian approximation in the external field of an oblate rotating neutron star (NS). We also derive formulas for the nodal precession and periastron rotation frequencies of slightly inclined low-eccentricity orbits in the field of a rapidly rotating NS in the form of asymptotic expansions whose first terms are given by the Okazaki-Kato formulas. The NS gravitational field is described by the exact solution of the Einstein equation that includes the NS quadrupole moment induced by rapid rotation. Convenient asymptotic formulas are given for the metric coefficients of the corresponding space-time in the form of Kerr metric perturbations in Boyer-Lindquist coordinates.     

A young cooling neutron star in the remnant of Supernova 1987A

We describe the cooling theory for isolated neutron stars that are several tens of years old. Their cooling differs greatly from the cooling of older stars that has been well studied in the literature. It is sensitive to the physics of the inner stellar crust and even to the thermal conductivity of the stellar core, which is never important at later cooling stages. The absence of observational evidence for the formation of a neutron star during the explosion of Supernova 1987A is consistent with the fact that the star was actually born there. It may still be hidden in the dense center of the supernova remnant. If, however, the star is not hidden, then it should have a low thermal luminosity (below ～10³⁴ erg s^?1) and a short internal thermal relaxation time (shorter than 13 yr). This requires that the star undergo intense neutrino cooling (e.g., via the direct Urca process) and have a thin crust with strong superfluidity of free neutrons and/or an anomalously high thermal conductivity.     

The radial disc structure around a magnetic neutron star: analytic and semi-analytic solutions

The radial structure of a thin accretion disc is calculated in the presence of a central dipole magnetic field aligned with the rotation axis. The problem is treated using a modified expression for the turbulent magnetic diffusion, which allows the angular momentum equation to be integrated analytically. The governing algebraic equations are solved iteratively between 1 and 10⁴ stellar radii. An analytic approximation is provided that is valid near the disruption radius at about 100 stellar radii. At that point, which is approximately 60 per cent of the Alfvén radius and typically about 30 per cent of the corotation radius, the disc becomes viscously unstable. This instability results from the fact that both radiation pressure and opacity caused by electron scattering become important. This in turn is a consequence of the magnetic field which leads to an enhanced temperature in the inner parts. This is because the magnetic field gives rise to a strongly enhanced vertically integrated viscosity, so that the viscous torque can balance the magnetic torque.     

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).     

Quasi-periodic oscillations in low-mass X-ray binaries and constraints on the equation of state of neutron star matter

Recently discovered quasi-periodic oscillations in the X-ray brightness of low-mass X-ray binaries are used to derive constraints on the mass of the neutron star component and the equation of state of neutron star matter. The observations are compared with models of rapidly rotating neutron stars which are calculated by means of an exact numerical method in full relativity. For the equations of state we select a broad collection of models representing different assumptions about the many-body structure and the complexity of the composition of superdense matter. The mass constraints differ from their values in the approximate treatment by ∼10 per cent. Under the assumption that the maximum frequency of the quasi-periodic oscillations originates from the innermost stable orbit, the mass of the neutron star is in the range M ∼1.92–2.25 M_⊙. The quasi-periodic oscillation in the Atoll-source 4U 1820−30 in particular is only consistent with equations of state that are rather stiff at high densities, which is explainable, so far, only with pure nucleonic/leptonic composition. This interpretation contradicts the hypothesis that the protoneutron star formed in SN 1987A collapsed to a black hole, since this would demand a maximum neutron star mass below 1.6 M_⊙. The recently suggested identification of quasi-periodic oscillations with frequencies of about 10 Hz with the Lense–Thirring precession of the accretion disc is found to be inconsistent with the models studied in this work, unless it is assumed that the first overtone of the precession is observed.     

Search for orbital motion of the pulsar 4U 1626–67: Candidate for a neutron star with a supernova fall-back accretion disk

We report here results from a new search for orbital motion of the accretion powered X-ray pulsar 4U 1626–67 using two different analysis techniques. X-ray light curve obtained with the Proportional Counter Array of the Rossi X-ray Timing Explorer during a long observation carried out in February 1996, was used in this work. The spin period and the local period derivative were first determined from the broad 2–60 keV energy band light curve and these were used for all subsequent timing analysis. In the first technique, the orbital phase dependent pulse arrival times were determined for different trial orbital periods in the range of 500 to 10,000 s. We have determined a 3σ upper limit of 13 lt-ms on the projected semimajor axis of the orbit of the neutron star for most of the orbital period range, while in some narrow orbital period ranges, covering about 10% of the total orbital period range, it is 20lt-ms. In the second method, we have measured the pulse arrival times at intervals of 100 s over the entire duration of the observation. The pulse arrival time data were used to put an upper limit on any periodic arrival time delay using the Lomb-Scargle periodogram. We have obtained a similar upper limit of 10 lt-ms using the second method over the orbital period range of 500–10,000 s. This puts very stringent upper limits for the mass of the compact object except for the unlikely case of a complete face-on orientation of the binary system with respect to our line-of-sight. In the light of this measurement and the earlier reports, we discuss the possibility of this system being a neutron star with a supernovae fall-back accretion disk.     

Linking jet emission and X-ray properties in the peculiar neutron star X-ray binary Circinus X-1

We present the results of simultaneous X-ray and radio observations of the peculiar Z-type neutron star X-ray binary Cir X-1, observed with the Rossi X-ray Timing Explorer satellite and the Australia Telescope Compact Array in 2000 October and 2002 December. We identify typical Z-source behaviour in the power density spectra as well as characteristic Z patterns drawn in an X-ray hardness–intensity diagram. Power spectra typical of bright atoll sources have also been identified at orbital phases after the periastron passage, while orbital phases before the periastron passage are characterized by power spectra that are typical neither of Z nor of atoll sources. We investigate the coupling between the X-ray and the radio properties, focusing on three orbital phases when an enhancement of the radio flux density has been detected, to test the link between the inflow (X-ray) and the outflow (radio jet) to/from the compact object. In two out of three cases, we associate the presence of the radio jet to a spectral transition in the X-rays, although the transition does not precede the radio flare, as detected in other Z sources. An analogous behaviour has recently been found in the black hole candidate GX 339-4. In the third case, the radio light curve shows a similar shape to the X-ray light curve. We discuss our results in the context of jet models, considering also black hole candidates.     

Comptonization and QPO origins in accreting neutron star systems

We develop a simple, time-dependent Comptonization model to probe the origins of spectral variability in accreting neutron star systems. In the model, soft 'seed photons' are injected into a corona of hot electrons, where they are Compton upscattered before escaping as hard X-rays. The model describes how the hard X-ray spectrum varies when the properties of either the soft photon source or the Comptonizing medium undergo small oscillations. Observations of the resulting spectral modulations can determine whether the variability is due to (i) oscillations in the injection of seed photons, (ii) oscillations in the coronal electron density, or (iii) oscillations in the coronal energy dissipation rate. Identifying the origin of spectral variability should help clarify how the corona operates and its relation to the accretion disc. It will also help in finding the mechanisms underlying the various quasi-periodic oscillations (QPOs) observed in the X-ray outputs of many accreting neutron star and black hole systems. As a sample application of our model, we analyse a kilohertz QPO observed in the atoll source 4U 1608–52. We find that the QPO is driven predominantly by an oscillation in the electron density of the Comptonizing gas.     

Resistive relaxation of a magnetically confined mountain on an accreting neutron star

Three-dimensional numerical magnetohydrodynamic (MHD) simulations are performed to investigate how a magnetically confined mountain on an accreting neutron star relaxes resistively. No evidence is found for non-ideal MHD instabilities on a short time-scale, such as the resistive ballooning mode or the tearing mode. Instead, the mountain relaxes gradually as matter is transported across magnetic surfaces on the diffusion time-scale, which evaluates to  τ_I∼ 10⁵–10⁸ yr  (depending on the conductivity of the neutron star crust) for an accreted mass of   M _a= 1.2 × 10⁻⁴ M_⊙  . The magnetic dipole moment simultaneously re-emerges as the screening currents dissipate over  τ_I  . For non-axisymmetric mountains, ohmic dissipation tends to restore axisymmetry by magnetic reconnection at a filamentary neutral sheet in the equatorial plane. Ideal-MHD oscillations on the Alfvén time-scale, which can be excited by external influences, such as variations in the accretion torque, compress the magnetic field and hence decrease  τ_I  by one order of magnitude relative to its standard value (as computed for the static configuration). The implications of long-lived mountains for gravitational wave emission from low-mass X-ray binaries are briefly explored.     

Evidence for a jet contribution to the optical/infrared light of neutron star X-ray binaries

Optical/near-infrared (optical/NIR, OIR) light from low-mass neutron star X-ray binaries (NSXBs) in outburst is traditionally thought to be thermal emission from the accretion disc. Here we present a comprehensive collection of quasi-simultaneous OIR and X-ray data from 19 low magnetic field NSXBs, including new observations of three sources: 4U 0614+09, LMC X−2 and GX 349+2. The average radio–OIR spectrum for NSXBs is  α≈+ 0.2  (where   L _ν∝ν^α  ) at least at high luminosities when the radio jet is detected. This is comparable to, but slightly more inverted than the  α≈ 0.0  found for black hole X-ray binaries. The OIR spectra and relations between OIR and X-ray fluxes are compared to those expected if the OIR emission is dominated by thermal emission from an X-ray or viscously heated disc, or synchrotron emission from the inner regions of the jets. We find that thermal emission due to X-ray reprocessing can explain all the data except at high luminosities for some NSXBs, namely, the atolls and millisecond X-ray pulsars. Optically thin synchrotron emission from the jets (with an observed OIR spectral index of  α_thin < 0  ) dominate the NIR light above     and the optical above     in these systems. For NSXB Z-sources, the OIR observations can be explained by X-ray reprocessing alone, although synchrotron emission may make a low-level contribution to the NIR, and could dominate the OIR in one or two cases.     

The estimations of neutron star mass and radius by the kHz QPOs

The kHz quasi‐periodic oscillations (QPOs) have been detected by the RXTE satellite in about thirty neutron stars (NSs) in low mass X‐ray binaries (LMXBs), which are usually interpreted to be related to the Keplerian motions in the orbit close to NS surface where the accreted matter is sucked onto the star. Based on the MHD Alfvén wave oscillation model and the relativistic precession model for the neutron star (NS) kHz QPOs, estimations of mass M and radius R of some NSs are given, which can give clues to evaluate the models. Furthermore, comparisons with theoretical M ‐R relations by stellar equations of state (EOSs) are presented (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Unipolar induction of a magnetized accretion disk around a black hole

The structure and magnitude of the electromagnetic field produced by a rotating accretion disk around a black hole were determined. The disk matter is assumed to be a magnetized plasma with a frozenin poloidal magnetic field. The vacuum approximation is used outside the disk.