The Radial Structure of Pulsar Radio Emission Regions

An important paramter in the study of the radial structure of the pulsar radio emission region is the altitude of the emission,but this cannot be derived directly from the observations.The altitude can be expressed as a function of frequency,rν∝ν^-ξ,and the method of K analysis can be used to calculate the power law index ξfrom observations at different frequencies,We have calculated the value of ξ for 18 pulsars observed at two frequencies,610MHz and 1408MHz and for three pulsars observed at three or more frequencies,The average value of ξis 0.27,which indicates that the emission altitude increases with decreasing frequency and that the radial structure is compact.     

Radio emission regions in pulsars

We study the concept of radius-to-frequency mapping using a geometrical method for the estimation of pulsar emission altitudes. The semi-empirical relationship proposed by Kijak &38; Gil is examined over three decades of radio frequency. It is argued that the emission region in a millisecond pulsar occupies the magnetosphere over a distance of up to about 30 per cent of the light-cylinder radius, and that in a normal pulsar occupies up to approximately 10 per cent of the light-cylinder radius.     

The population of pulsars with interpulses and the implications for beam evolution

The observed fraction of pulsars with interpulses, their period distribution and the observed pulse width versus pulse period correlation are shown to be inconsistent with a model in which the angle α between the magnetic axis and the rotation axis is random. This conclusion appears to be unavoidable, even when non-circular beams are considered. Allowing the magnetic axis to align from a random distribution at birth with a time-scale of  ∼7 × 10⁷ yr  can, however, explain those observations well. The time-scale derived is consistent with that obtained via independent methods. The probability that a pulsar beam intersects the line of sight is a function of the angle α and therefore beam evolution has important consequences for evolutionary models and for estimations of the total number of neutron stars. The validity of the standard formula for the spin-down rate, which is independent of α, appears to be questionable.     

A Two—Temperature Supernova Fallback Disk Model for Anomalous X—ray Pulsars

We present a case study of the relevance of the radially pulsational instability of a two-temperature accretion disk around a neutron star to anomalous X-ray pulsars (AXPs). Our estimates are based on the approximation that such a neutron star disk with mass in the range of 10^-6-10^-5M⊙ is formed by supernova fallback. We derive several peculiar properties of the accretion disk instability: a narrow interval of X-ray pulse periods; lower X-ray luminosities; a period derivative and an evolution time scale. All these results are in good agreement with the observations of the AXPs.     

A statistical study of 233 pulsar proper motions

We present and analyse a catalogue of 233 pulsars with proper motion measurements. The sample contains a wide variety of pulsars including recycled objects and those associated with globular clusters or supernova remnants. After taking the most precise proper motions for those pulsars for which multiple measurements are available, the majority of the proper motions (58 per cent) are derived from pulsar timing methods, 41 per cent using interferometers and the remaining 1 per cent using optical telescopes. Many of the one-dimensional (1D) and two-dimensional (2D) speeds (referring to speeds measured in one coordinate only and the magnitudes of the transverse velocities, respectively) derived from these measurements are somewhat lower than earlier estimates because of the use of the most recent electron density model in determining pulsar distances. The mean 1D speeds for the normal and recycled pulsars are 152(10) and 54(6) km s⁻¹, respectively. The corresponding mean 2D speeds are 246(22) and 87(13) km s⁻¹. PSRs B2011+38 and B2224+64 have the highest inferred 2D speeds of  ∼1600 km s⁻¹  . We study the mean speeds for different subsamples and find that, in general, they agree with previous results. Applying a novel deconvolution technique to the sample of 73 pulsars with characteristic ages less than 3 Myr, we find the mean three-dimensional (3D) pulsar birth velocity to be 400(40) km s⁻¹. The distribution of velocities is well described by a Maxwellian distribution with  1D rms σ= 265 km s⁻¹  . There is no evidence for a bimodal velocity distribution. The proper motions for PSRs B1830−08 and B2334+61 are consistent with their proposed associations with the supernova remnants W41 and G114.3+0.3, respectively.     

Millisecond pulsar velocities

We present improved timing parameters for 13 millisecond pulsars (MSPs), including nine new proper motion measurements. These new proper motions bring to 23 the number of MSPs with measured transverse velocities. In light of these new results we present and compare the kinematic properties of MSPs with those of ordinary pulsars. The mean transverse velocity of MSPs was found to be 85±13 km s⁻¹, a value consistent with most models for the origin and evolution of MSPs and approximately a factor of 4 lower than that of ordinary pulsars. We also find that, in contrast to young ordinary pulsars, the vast majority of which are moving away from the Galactic plane, almost half of the MSPs are moving towards the plane. This near-isotropy would be expected of a population that has reached dynamic equilibrium. Accurate measurements of MSP velocities have allowed us to correct their measured spin-down rates for Doppler acceleration effects, and thereby derive their intrinsic magnetic field strengths and characteristic ages. We find that close to half of our sample of MSPs have a characteristic age comparable to or greater than the age of the Galactic disc.     

Type I and two-gap superconductivity in neutron star magnetism

Neutron star inner cores with several charged baryonic components are likely to be analogues of the two-gap superconductor which is of current interest in condensed-matter physics. Consequently, type I superconductivity is less probable than type II but may nevertheless be present in some intervals of matter density. The intermediate-state structure formed at finite magnetic flux densities after the superconducting transitions is subject to buoyancy, frictional and neutron vortex interaction forces. These are estimated and it is shown that the most important frictional force is that produced by the stable stratification of neutron star matter, the irreversible process being diffusion in the normal, finite magnetic flux density, parts of the structure. The length-scale of the structure, in directions perpendicular to the local magnetic field is of crucial importance. For small scales, the flux comoves with the neutron vortices, as do the proton vortices of a type II superconductor. But for much larger length-scales, flux movement tends to that expected for normal charged Fermi systems.     

Fermion zero-mode influence on neutron-star magnetic field evolution

The quantum phenomenon of spectral flow which has been observed in laboratory superfluids, such as ³He-B, controls the drift velocity of proton type II superconductor vortices in the liquid core of a neutron star and so determines the rate at which magnetic flux can be expelled from the core to the crust. In the earliest and most active phases of the anomalous X-ray pulsars and soft-gamma repeaters, the rates are low and consistent with a large fraction of the active crustal flux not linking the core. If normal neutrons are present in an appreciable core matter-density interval, the spectral flow force limits flux expulsion in cases of rapid spin-down, such as in the Crab pulsar or in the propeller phase of binary systems.     

The possible role of r-modes in post-glitch relaxation of the Crab pulsar

The loss of angular momentum through gravitational radiation, driven by the excitation of r-modes, is considered for neutron stars that have rotation frequencies lower than the associated critical frequency. We find that for reasonable values of the initial amplitudes of such pulsation modes of the star, being excited at the event of a glitch in a pulsar, the total post-glitch losses correspond to a negligible fraction of the initial rise of the spin frequency in the case of Vela and older pulsars. However, for the Crab pulsar the same effect would result, within a few months, in a decrease in its spin frequency by an amount larger than its glitch-induced frequency increase. This could provide an explanation for the peculiar behaviour observed in the post-glitch relaxations of the Crab pulsar.     

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.     

The bottom magnetic field and magnetosphere evolution of neutron star in low-mass X-ray binary

The accretion-induced neutron star (NS) magnetic field evolution is studied through considering the accretion flow to drag the field lines aside and dilute the polar-field strength, and as a result the equatorial field strength increases, which is buried inside the crust on account of the accretion-induced global compression of star crust. The main conclusions of model are as follows: (i) the polar field decays with increase in the accreted mass; (ii) the bottom magnetic field strength of about 10⁸ G can occur when the NS magnetosphere radius approaches the star radius, and it depends on the accretion rate as     ; and (iii) the NS magnetosphere radius decreases with accretion until it reaches the star radius, and its evolution is little influenced by the initial field and the accretion rate after accreting  ∼0.01 M_⊙  , which implies that the magnetosphere radii of NSs in low-mass X-ray binaries would be homogeneous if they accreted the comparable masses. As an extension, the physical effects of the possible strong magnetic zone in the X-ray NSs and recycled pulsars are discussed. Moreover, the strong magnetic fields in the binary pulsars PSR 1831−00 and PSR 1718−19 after accreting about  0.5 M_⊙  in the binary-accretion phase,  8.7 × 10¹⁰  and  1.28 × 10¹² G  , respectively, can be explained through considering the incomplete frozen flow in the polar zone. As an expectation of the model, the existence of the low magnetic field  (∼3 × 10⁷ G)  NSs or millisecond pulsars is suggested.