Studying millisecond pulsars in X-rays

Millisecond pulsars represent an evolutionarily distinct group among rotation-powered pulsars. Outside the radio band, the soft X-ray range (～0.1–10 keV) is most suitable for studying radiative mechanisms operating in these fascinating objects. X-ray observations revealed diverse properties of emission from millisecond pulsars. For the most of them, the bulk of radiation is of a thermal origin, emitted from small spots (polar caps) on the neutron star surface heated by relativistic particles produced in pulsar acceleration zones. On the other hand, a few other very fast rotating pulsars exhibit almost pure nonthermal emission generated, most probably, in pulsar magnetospheres. There are also examples of nonthermal emission detected from X-ray nebulae powered by millisecond pulsars, as well as from pulsar winds shocked in binary systems with millisecond pulsars as companions. These and other most important results obtained from X-ray observations of millisecond pulsars are reviewed in this paper, as well as results from the search for millisecond pulsations in X-ray flux of the radio-quite neutron star RX J1856.5-3754.     

Evolution of neutron star magnetic fields

During the evolution of the neutron star its magnetic field first decays exponentially with the time and then may becomes quasi-stationary. The non-decaying magnetic field of the neutron star is generated by a degenerate electron gas which is in the Landau orbital ferromagnetism (LOFER) state. Possibly, due to the neutron star transition into the LOFER state, magnetic fields remained sufficiently strong in the case of such old magnetic neutron stars as powerful X-ray sources (e.g., Her X-1), millisecond pulsars and the binary pulsar PSR 0655+64.     

Thermal structure of the envelopes of rapidly rotating neutron stars

For a neutron star which rotates like the fastest millisecond pulsar we calculate the temperature profile within the envelope. We find a small decrease of the surface temperature and a considerable increase of the thickness of the liquid layer from the pole to the equator.     

The neutron stars of Soft X–ray Transients

Summary. Soft X–ray Transients (SXRTs) have long been suspected to contain old, weakly magnetic neutron stars that have been spun up by accretion torques. After reviewing their observational properties, we analyse the different regimes that likely characterise the neutron stars in these systems across the very large range of mass inflow rates, from the peak of the outbursts to the quiescent emission. While it is clear that close to the outburst maxima accretion onto the neutron star surface takes place, as the mass inflow rate decreases, accretion might stop at the magnetospheric boundary because of the centrifugal barrier provided by the neutron star. For low enough mass inflow rates (and sufficiently short rotation periods), the radio pulsar mechanism might turn on and sweep the inflowing matter away. The origin of the quiescent emission, observed in a number of SXRTs at a level of , plays a crucial role in constraining the neutron star magnetic field and spin period. Accretion onto the neutron star surface is an unlikely mechanism for the quiescent emission of SXRTs, as it requires very low magnetic fields and/or long spin periods. Thermal radiation from a cooling neutron star surface in between the outbursts can be ruled out as the only cause of the quiescent emission. We find that accretion onto the neutron star magnetosphere and shock emission powered by an enshrouded radio pulsar provide far more plausible models. In the latter case the range of allowed neutron star spin periods and magnetic fields is consistent with the values recently inferred from the properties of kHz quasi-periodic oscillation in low mass X–ray binaries. If quiescent SXRTs contain enshrouded radio pulsars, they provide a missing link between X–ray binaries and millisecond pulsars. Received 4 November 1997; Accepted 15 April 1998     

Millisecond pulsars

In 1982 we discovered a pulsar with the phenomenal rotation rate of 642 Hz, 20 times faster than the spin rate of the Crab pulsar. The absence of supernova debris in the vicinity of the pulsar at any wavelength indicates an age of the neutron star greater than 10⁵ yr. The miniscule spindown rate of 1.1 × 10^-19 confirms the old age and indicates a surface magnetic field of 10⁹ G. A second millisecond pulsar was discovered by Boriakoff, Buccheri & Fauci (1983) in a 120-day orbit. These fast pulsars may have been spun-up by mass transfer in a close binary evolutionary stage. Arrival-time observations of the 642-Hz pulsar display remarkably low residuals over the first 14 months. The stability implied by these observations, 3 × 10^-14, suggests that millisecond pulsars will provide the most accurate basis for terrestrial dynamical time. If so, the pulsar data will lead to improvements in the planetary ephemeris and to new searches for light-year scale gravitational waves. Many new searches for fast pulsars are under way since previous sky surveys excluded pulsars with spins above 60 Hz.     

Influence of electron-positron pair production on a pulsar magnetospheric structure

A self-consistent pulsar magnetospheric model with electron-positron pair production is considered. Unlike conventional models, the primary particles (electrons) are accelerated towards the neutron star and their curvature radiation towards a star generates electron-positron plasma near the neutron star. Inside an outflow channel, the generated plasma flows away from the pulsar magnetosphere. A part of the plasma electrons returns and, being accelerated towards the star, regenerate the plasma by their curvature radiation. It is shown that plasma production near the star causes an appearance of positron and electron equatorial belts. The plasma concentration and the flux of the returning electrons are estimated. The portion of the energy entering into the pulsar magnetosphere and its dependence on pulsar parameters are estimated.     

Accretion spin-up of low-magnetic neutron stars

The present paper is concerned with the spin-up of low-magnetic neutron stars by the accretion of matter onto the star. Calculations have been made for the evolution of the rotation of a neutron star and applied to different stellar models. It is shown that the existence of a millisecond pulsar imposes no restriction on any of the equations of state considered. However, constraints would arise with the possible discovery of third-octave pulsars (with frequencies in excess of 1000 Hz). Predictions are made as to the distribution of bursters over the orbital periods of neutron stars (about half of these having similar orbital periods). It is demonstrated that in the case of continued accretion onto a star, after it has acquired the critical angular frequency allowing no diviation from axial symmetry, specific accretion disks can be formed with a smooth transition into a star. The specific angular momentum is computed for a neutron star for the instant of the attainment of the Oppenheimer-Volkoff limit.     

Impact of neutron star oscillations on the accelerating electric field in the polar cap of pulsar

Pulsar “standard model”, that considers a pulsar as a rotating magnetized conducting sphere surrounded by plasma, is generalized to the case of oscillating star. We developed an algorithm for calculation of the Goldreich-Julian charge density for this case. We consider distortion of the accelerating zone in the polar cap of pulsar by neutron star oscillations. It is shown that for oscillation modes with high harmonic numbers (l,m) changes in the Goldreich-Julian charge density caused by pulsations of neutron star could lead to significant altering of an accelerating electric field in the polar cap of pulsar. In the moderately optimistic scenario, that assumes excitation of the neutron star oscillations by glitches, it could be possible to detect altering of the pulsar radioemission due to modulation of the accelerating field. This work was partially supported by RFBR grant 04-02-16720, and by the grants N.Sh.-5218.2006.2 and RNP-2.1.1.5940.     

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.     

Relaxation of the angular velocity of the vela pulsar within the framework of general relativity. Standard model of a neutron star

The dynamics of the rotation of a two-component system in the core of a neutron star is analyzed within the framework of the generai theory of relativity (GTR). A theory of the relaxation of the angular velocity of the Vela pulsar is developed with allowance for GTR corrections. From a comparison of the theory with observational data on the Vela pulsar, the relative moments and positions of the relaxation regions are found for one of the standard models of a neutron star. It is shown that the theory agrees with observations and supports this model neutron star as an acceptable pulsar model. Translated from Astrofizika, Vol. 43, No. 1, pp. 85-94, January–March, 2000.     

Spin evolution of neutron stars in binary systems

I review our understanding of the evolution of the spin periods of neutron stars in binary stellar systems, from their birth as fast, spin-powered pulsars, through their middle life as accretion-powered pulsars, upto their recycling or “rebirth” as spin-powered pulsars with relatively low magnetic fields and fast rotation. I discuss how the new-born neutron star is spun down by electromagnetic and “propeller” torques, until accretion of matter from the companion star begins, and the neutron star becomes an accretion-powered X-ray pulsar. Detailed observations of massive radio pulsar binaries like PSR 1259-63 will yield valuable information about this phase of initial spindown. I indicate how the spin of the neutron star then evolves under accretion torques during the subsequent phase as an accretion-powered pulsar. Finally, I describe how the neutron star is spun up to short periods again during the subsequent phase of recycling, with the accompanying reduction in the stellar magnetic field, the origins of which are still not completely understood.     

An Estimation of the Initial Period of Pulsars

The initial period of a pulsar is an important factor in our understanding of the formation of neutron stars and of the nature of the equation of state of neutron star matter.Up to now this quantity can only be obtained for a few pulsars for which accurate age and braking index are known.Based on the theory of the offcenter dipole emission,in which pulsars obtain theiry high velocities depending on the initial periods,we calculate the initial period using the proper motion data,Because the orbital velocity of the progenitor and asymmetric kick in the supernova explosion may also contribute to the observed velocity of the pusar,the derived values of initial periods are lower limits.For normal pulsars,the initial periods are in the range of 0.6～2.6ms.For the millisecond pulsars,the initial periods are comparable to their current periods,and the ratio between the initial period and the current period increases with the decrease of the current period.For PSR B1937 21 with the shortest period of 1.56ms,the ratio is 0.77.     

Flux-Vortex Pinning and Neutron Star Evolution

G. Srinivasan et al. (1990) proposed a simple and elegant explanation for the reduction of the neutron star magnetic dipole moment during binary evolution leading to low mass X-ray binaries and eventually to millisecond pulsars: Quantized vortex lines in the neutron star core superfluid will pin against the quantized flux lines of the proton superconductor. As the neutron star spins down in the wind accretion phase of binary evolution, outward motion of vortex lines will reduce the dipole magnetic moment in proportion to the rotation rate. The presence of a toroidal array of flux lines makes this mechanism inevitable and independent of the angle between the rotation and magnetic axes. The incompressibility of the flux-line array (Abrikosov lattice) determines the epoch when the mechanism will be effective throughout the neutron star. Flux vortex pinning will not be effective during the initial young radio pulsar phase. It will, however, be effective and reduce the dipole moment in proportion with the rotation rate during the epoch of spindown by wind accretion as proposed by Srinivasan et al. The mechanism operates also in the presence of vortex creep.     

Models for the formation of binary and millisecond radio pulsars

The peculiar combination of a relatively short pulse period and a relatively weak surface dipole magnetic field strength of binary radio pulsars finds a consistent explanation in terms of (i) decay of the surface dipole component of neutron-star magnetic fields on a timescale of (2–5) × 10⁶ yr, in combination with (ii) spin-up of the rotation of the neutron star during a subsequent mass-transfer phase. The four known binary radio pulsars appear to fall into two different categories. Two of them, PSR 0655 + 64 and PSR 1913 + 16, have short orbital periods (<25 h) and high mass functions, indicating companion masses 0.7M⊙ (∼1 (± 0.3) M⊙ and 1.4 M⊙, respectively). The other two, PSR 0820 + 02 and PSR 1953 + 29, have long orbital periods (117d), nearly circular orbits, and low, almost identical mass functions of about 3×10^-3 M⊙, suggesting companion masses of about 0.3M⊙. It is pointed out that these two classes of systems are expected to be formed by the later evolution of binaries consisting of a neutron star and a normal companion star, in which the companion was (considerably) more massive than the neutron star, or less massive than the neutron star, respectively. In the first case the companion of the neutron star in the final system will be a massive white dwarf, in a circular orbit, or a neutron star in an eccentric orbit. In the second case the final companion to the neutron star will be a low-mass (∼ 0.3 M⊙) helium white dwarf in a wide and nearly circular orbit. In systems of the second type the neutron star was most probably formed by the accretion-induced collapse of a white dwarf. This explains in a natural way why PSR 1953 + 29 has a millisecond rotation period and PSR 0820 + 02 has not. Among the binary models proposed for the formation of the 1.5-millisecond pulsar, the only ones that appear to be viable are those in which the companion disappeared by coalescence with the neutron star. In such models the companion may have been a red dwarf of mass 0.03M⊙, a neutron star, or a massive (>0.7M⊙) white dwarf. Only in the last-mentioned case is a position of the pulsar close to the galactic plane a natural consequence. In the first-mentioned case the progenitor system most probably was a cataclysmic-variable binary in which the white dwarf collapsed by accretion.     

The mass of the neutron star in the binary millisecond pulsar PSR J 1012 + 5307

We have measured the radial velocity variation of the white dwarf secondary in the binary system containing the millisecond pulsar PSR J 1012 + 5307. Combined with the orbital parameters of the radio pulsar, we infer a mass ratio q (≡ M ₁/ M ₂) = 10.5 ± 0.5. Our optical spectroscopy has also allowed us to determine the mass of the white dwarf companion by fitting the spectrum to a grid of DA model atmospheres: we estimate M ₂ = 0.16 ± 0.02 M⊙, and hence the mass of the neutron star is 1.64 ± 0.22 M⊙, where the error is dominated by that of M ₂. The orbital inclination is 52 ± 4°. For an initial neutron star mass of ∼ 1.4 M⊙, only a few tenths of a solar mass at most has been successfully accreted over the lifetime of the progenitor low-mass X-ray binary. If the initial mass of the secondary was ∼ 1 M⊙, our result suggests that the mass transfer may have been non-conservative.     

Comparison of Transient Network Brightenings and Explosive Events in the Solar Transition Region

I analyze the properties of the pulsed emission from the accreting millisecond pulsar SAX J1808.4-3658 in observations of its 1998 April outburst by the Rossi X-Ray Timing Explorer. Pulse phase spectroscopy shows that the emission evolves from a hard spectrum (power law with photon index of 2.39+/-0.06) to a soft spectrum (index of 3.39+/-0.24). This softening is also observable as a phase lag in the fundamental of low-energy photons with respect to high-energy photons. I show that this lag is roughly constant over 10 days of the outburst. I fit these data with a model in which the pulse emission is from a hot spot on the rotating neutron star and the flux as a function of phase is determined in a calculation which includes the effects of general relativity. The energy-dependent lags are very well described by this model. The harder spectra at earlier phases (i.e., as the spot approaches) are the result of larger Doppler-boosting factors that are important for this fast pulsar. Since this model is sensitive to the equatorial speed as an independent parameter and since the spin frequency is known, this offers us a new means of measuring the neutron star radius, which is notoriously difficult to determine.     

Relaxation of the Angular Velocity of the Vela Pulsar within the Framework of General Relativity. Quark Model of a Neutron Star

A previously developed theory of the relaxation of a pulsar's angular velocity within the framework of general relativity is compared with observational data for the Vela pulsar on the basis of a quark model of a neutron star. The relative moments of inertia and the positions of relaxation regions are found. It is shown that the model of a neutron star containing normal quark matter is inconsistent with observations of the relaxation of pulsar angular velocity.     

Evolution of Pulsars with Energy Release in the Superfluid Core of a Neutron Star

The effect of a neutron-proton vortex system on the rotation dynamics of neutron stars is examined. The dynamics of the motion of a two component superfluid system in the core of a neutron star yields an equation for the evolution of the pulsar's rotation period. The spin down of the star owing to energy release at the core boundary, which is associated with a contraction of the length of the neutron vortex as it moves radially and magnetic energy of the vortical cluster is released, is taken into account. Evolutionary curves are constructed for pulsars with different magnetic fields and stellar radii. For certain values of the coefficient of friction between the superfluid and normal components in the core of the neutron star, at the end of its evolution a radio pulsar may become an anomalous x-ray pulsar or a source of soft gamma radiation with a period on the order of 10 seconds.     

Internal heating and thermal emission from old neutron stars

The equilibrium composition of neutron star matter is achieved through weak interactions (direct and inverse beta decays), which proceed on relatively long time scales. If the density of a matter element is perturbed, it will relax to the new chemical equilibrium through non-equilibrium reactions, which produce entropy that is partly released through neutrino emission, while a similar fraction heats the matter and is eventually radiated as thermal photons. We examined two possible mechanisms causing such density perturbations: (1) the reduction in centrifugal force caused by spin-down (particularly in millisecond pulsars), leading to rotochemical heating, and (2) a hypothetical time-variation of the gravitational constant, as predicted by some theories of gravity and current cosmological models, leading to gravitochemical heating. If only slow weak interactions are allowed in the neutron star (modified Urca reactions, with or without Cooper pairing), rotochemical heating can account for the observed ultraviolet emission from the closest millisecond pulsar, PSR J0437-4715, which also provides a constraint on |dG/dt| of the same order as the best available in the literature. This work made use of NASA’s Astrophysics Data System Service, and received financial support from FONDECYT through regular grants 1020840 and 1060644.     

On the slow-down of the millisecond pulsar PSR 1937+214

There are indications that less than 10^–3 of the spin-down energy of the millisecond pulsar PSR 1937+214 emerges as electromagnetic radiation. The implications of this result are discussed. The surface magnetic field would then be 10⁷ G, making the pulsar optically undetectable, and casting aspersions on the accretion disc spin-up neutron star models for the pulsar. The pulsar should have an equatorial ellipticity 10^–9, which can be accounted for if the equatorial magnetic field departs from axisymmetry by one part in 10³.