Pulsed optical emission by radio pulsars

The luminosity L of radio pulsars due to synchrotron radiation by the primary beam at the magnetosphere periphery is derived. There is a strong correlation between the observed optical luminosities of radio pulsars and the parameter $\dot P/P^4$ (where P is the pulsar period). This correlation predicts appreciable optical emission from several dozen pulsars, in particular, from all those with P<0.1 s. Agreement with optical observations can be achieved for Lorentz factors of the secondary plasma γ_p=2–13. Plasma with such energies can be produced only when the magnetic-field structure near the neutron-star surface deviates substantially from a dipolar field. The peak frequency of the synchrotron spectrum should shift toward higher values as the pulsar period P decreases; this is, in agreement with observational data for 27 radio pulsars for which emission has been detected outside the radio band.     

Radio emission from two anomalous X-ray pulsars

Observations of the anomalous X-ray pulsar (AXP) 1E 2259+586 and the AXP candidate 1RXS J1308.6+212708 at 111, 87, and 61 MHz are reported. The observations were carried out on two high-sensitivity radio telescopes of the Pushchino Radio Astronomy Observatory. Mean pulse profiles are presented, and the dispersion measures, distances, spectral indices, and integrated radio luminosities of both objects are estimated. Comparison with X-ray data shows large differences in the mean pulse widths and luminosities. The detection of radio emission from these two AXPs, together with other data, suggests the need to revise the radio-emission mechanisms in the magnetar model or the magnetar model itself.     

Peculiarities of radio pulsars with emission outside the radio range

Parameters of 100 radio pulsars detected outside the radio range (he pulsars) are compared with those of pulsars radiating only in the radio (n pulsars). The periods of he pulsars are, on average, appreciably shorter than those of n pulsars: 〈P〉 = 0.10 and 0.56 s, respectively. The distribution of the magnetic field at the light cylinder is shifted toward higher magnetic fields for the pulsars with high-energy radiation, compared to the distribution for pulsars radiating only in the radio. The magnetic fields at the light cylinder are 〈B _lc〉 = 9×10³ G for he radio pulsars, and 〈B_lc〉 = 56 G formost purely radio pulsars. This suggests the generation of high-energy nonthermal radiation in radio pulsars at the peripheries of their magnetospheres. The distribution of the spin-energy loss rate dE/dt is uniform for he pulsars, and is characterized by a higher average value \(\left( {\left\langle {\log \frac{{dE}} {{dt}}} \right\rangle = 35.53} \right) \) , compared to n pulsars, \(\left( {\left\langle {\log \frac{{dE}} {{dt}}} \right\rangle = 32.60} \right) \) . The spatial distribution of he pulsars is nonuniform: they form two well separated clouds.     

The space velocities of radio pulsars

Known models proposed to explain the high space velocities of pulsars based on asymmetry of the transport coefficients of different sorts of neutrinos or electromagnetic radiation can be efficient only in the presence of high magnetic fields (to 10¹⁶ G) or short rotation periods for the neutron stars (of the order of 1 ms). This current study shows that the observed velocities are not correlated with either the pulsar periods or their surface magnetic fields. The initial rotation periods are estimated in a model for the magnetedipolar deceleration of their spin, aßsuming that the pulsar ages are equal to their kinematic ages. The initial period distribution is bimodal, with peaks at 5 ms and 0.5 s, and similar to the current distribution of periods. It is shown that asymmetry of the pulsar electromagnetic radiation is insufficient to give rise to additional acceleration of pulsars during their evolution after the supernova explosion that gave birth to them. The observations testify to deceleration of the motion, most likely due to the influence of the interstellar medium and interactions with nearby objects. The time scale for the exponential decrease in the magnetic field τ_D and in the angle between the rotation axis and magnetic moment τ_ß are estimated, yielding τ_β = 1.4 million years. The derived dependence of the transverse velocity of a pulsar on the angle between the line of sight and the rotation axis of the neutron star corresponds to the expected dependence for acceleration mechanisms associated with asymmetry of the radiation emitted by the two poles of the star.     

The spectra of hard radiation from radio pulsars

The kinetic equation for the distribution function of relativistic electrons is solved taking into account quasi-linear interactions with waves and radiative processes. Mean values of the pitch angles ψ are calculated. If the particles of the primary beam with Lorentz factors γ_b～10⁶ are resonant, then the condition γ_bψ_b?1 is satisfied, the particle distribution is described by the function f _‖(γ) ∝ γ^?4, and the synchrotron radiation spectrum is characterized by the spectral index α=3/2. On the other hand, if a cyclotron resonance is associated with particles of the high-energy tail of the secondary plasma (γ_t～10⁵), then γ_tψ_t?1, and the distribution function has two parts—f _‖(γ) ∝ γ and f _‖(γ) ∝ γ^?2—which correspond to the spectral indices α₁=+1 and α₂=?0.5. This behavior is similar to that observed for the pulsar B0656+14. The predicted frequency of the maximum ν_m=7.5×10¹⁶ Hz coincides with the peak frequency for this pulsar. The model estimate for the total synchrotron luminosity of a typical radio pulsar with hard radiation L _s =3×10³³ erg/s is in agreement with observed values.     

Magnetic fields of radio pulsars

The mechanism of magnetodipole braking of radio pulsars is used to calculate new values of the surface magnetic fields of neutron stars. The angles β between the spin axes and magnetic moments of the neutron stars were estimated for 376 radio pulsars using three different methods. It is shown that small inclinations of magnetic axes dominate. The equatorial magnetic fields for the considered sample of pulsars are calculated using the β values obtained. As a rule, these magnetic fields are a factor of a few higher than the corresponding values in known catalogs.     

The distribution of space velocities of radio pulsars

The distribution of the directions of the space velocities of 67 radio pulsars is shown to be strongly anisotropic. This anisotropy cannot be explained by the structure of our Galaxy or by various types of solar motions. Pulsars with stronger surface magnetic fields B have higher velocities V. The mean value of V for B < 10¹⁰ G is 108 km/s, while 〈V〉 = 340 km/s for B > 10¹⁰ G. These results must be taken into account when identifying a mechanism to explain the observed pulsar velocities and their anisotropy.     

Integrated radio luminosities of pulsars

The integrated radio luminosities of 311 long-period (P > 0.1 s) and 27 short-period (P < 0.1 s) pulsars have been calculated using a new compilation of radio spectra. The luminosities are in the range 10²⁷ ? 10³⁰ erg/s for 88% of the long-period pulsars and 10²⁸ ? 10³¹ erg/s for 88% of the short-period pulsars. We find a high correlation between the luminosity L and the estimate L ₁ = S ₄₀₀ d ² from the catalog of Taylor et al. The factor η for the transformation of the rotational energy of the neutron star into radio emission increases-decreases with increasing period for long-period and short-period pulsars. The mean value of η is ?3.73 for the long-period and ?4.85 for short-period pulsars. No dependence was found between L and the pulsar’s kinematic age t _k = |z|/〈v _z〉, where |z| and 〈v _z〉 = 300 km/s are the pulsars’ height above the plane of the Galaxy and mean velocity. A dependence of L on the rate of rotational energy losses ? was found for both groups of pulsars. It is shown that L ∝ ? ^1/3 for the entire sample. The pulsar luminosity function is constructed, and the total number and birth rate of pulsars in the Galaxy are calculated.     

The magnetospheric structure of radio pulsars with interpulses

Pulsars with interpulses—pulse components located between the main pulses—are studied. About 50 such objects are currently known. Methods developed earlier to determine the angle β between the rotation axis and the magnetic moment of the neutron star are used to investigate the geometry of the magnetospheres in these objects. In a number of pulsars, β < 20°, so that not only interpulses, but also radiation between pulses and a correlation between the behaviors of the interpulses and main pulses, is expected. In other pulses, this angle is greater than 60°, and interpulses can appear if the radiation cone is sufficiently broad and there is a favorable orientation of the line of sight of the observer. Thus, the earlier prediction that there should be two types of pulsars with interpulses—aligned and orthogonal—is supported. Estimates of the ages of the pulsars in these two groups indicate that aligned rotators are appreciably older than orthogonal rotators.     

Period clustering of anomalous X-ray pulsars

The question of why the observed periods of anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) cluster in the range 2–12 s is discussed. The possibility that AXPs and SGRs are the descendants of high-mass X-ray binaries that have disintegrated in core-collapse supernova explosions is investigated. The spin periods of neutron stars in high-mass X-ray binaries evolve towards the equilibrium period, which is a few seconds, on average. After the explosion of its massive companion, the neutron star becomes embedded in a dense gaseous envelope, and accretion from this envelope leads to the formation of a residual magnetically levitating disk. It is shown that the expected mass of the disk in this case is 10^?7–10^?8 M_⊙, which is sufficient to support accretion at the rate 10¹⁴–10¹⁵ g/s over a few thousand years. During this period, the star manifests itself as an isolated X-ray pulsar with a number of parameters similar to those of AXPs and SGRs. The periods of such pulsars can cluster if the lifetime of the residual disk does not exceed the spin-down timescale of the neutron star.     

The formation of millisecond radio pulsars in close binary systems

An analysis of the basic parameters of a sample of radio and X-ray pulsars that are members of close binary systems is used to separate them into several families according to the nature of the pulsar companions and the previous evolution of the systems. To quantitatively describe the main parameters of close binaries containing neutron stars, we have performed numerical modeling of their evolution. The main driving forces of the evolution of these systems are the nuclear evolution of the donor, the magnetically coupled and radiation-induced stellar winds of the donor, and gravitational-wave radiation. We have considered donors that are low-mass stars in various stages of their evolution, nondegenerate helium stars, and degenerate stars. The systems studied are either the products of the normal evolution of close binaries with large initial component-mass ratios or result from inelastic collisions of old neutron stars with single and binary low-mass, main-sequence stars in the dense cores of globular clusters. The formation of single millisecond pulsars requires either the dynamical disruption of a low-mass (?0.1M_⊙) donor or its complete evaporation under the action of the X-ray radiation of the millisecond pulsar. The observed properties of binary radio pulsars with eccentric orbits combined with the bimodal spatial-velocity distribution of single radio pulsars suggest that it may be possible to explain the observed rotational and spatial motions of all radio pulsars as a result of their formation in close binaries. In this case, neutron stars formed from massive single stars or the components of massive wide binaries probably cannot acquire the high spatial velocities or rapid rotation rates that are required for the birth of a radio pulsar.     

A spindown mechanism for short-period radio pulsars

It is shown that a model with accretion in a “quasi-propeller” mode can explain the observed spindown of pulsars with periods P<0.1 s. The mean accretion rate for 39 selected objects is \(\dot M = 5.6 \times 10^{ - 11} M_ \odot /year\). If \(\dot M\) is constant during the pulsar’s lifetime, the neutron star will stop rotating after 10⁷ years. The mean magnetic field at the neutron-star surface calculated in this model, \(\bar H_0 = 6.8 \times 10^8 G\), is consistent to an order of magnitude with the values of H₀ for millisecond pulsars from known catalogs. However, the actual value of H₀ for particular objects can differ from the catalog values by appreciable factors, and these quantities must be recalculated using more adequate models. The accretion disk around the neutron star should not impede the escape of the pulsar’s radiation, since this radiation is generated near the light cylinder in pulsars with P<0.1 s. Pulsars such as PSR 0531+21 and PSR 0833-45 have probably spun down due to the effect of magnetic-dipole radiation. If the difference in the braking indices for these objects from n=3 is due to the effect of accretion, the accretion rate must be of the order of 10¹⁸ g/s.     

The origin of the rotational and spatial velocities of radio pulsars

We analyze possible origins of the observed high rotational and spatial velocities of radio pulsars. In particular, these can be understood if all radio pulsars originate in close binary systems with orbital periods of 0.1–100 days, with the neutron star being formed by a type Ib,c supernova. The high spatial velocities of pulsars (v _p up to 1000 km/s) reflect the high Keplerian velocities of the components of these binaries, while their short periods of rotation (P _p < 4 s) are due to the rapid rotation of the presupernova helium-star components with masses of 2.5–10 M_⊙, which is synchronous with their orbital rotation. Single massive stars or components in wide binaries are likely to produce only slowly rotating (P _p > 4 s) neutron stars or black holes, which cannot be radio pulsars. As a result, the rate of formation of radio pulsars should be a factor of a few lower than the rate of type II and type Ib,c supernovae estimated from observations. This scenario for the formation of radio pulsars is supported by (i) the bimodal spatial velocity distribution of radio pulsars; (ii) the coincidence of the observed spatial velocities of radio pulsars with the orbital velocities of the components of close binaries with nondegenerate helium presupernovae; (iii) the correlation between the orbital and rotational periods for 22 observed radio pulsars in binaries with elliptical orbits; and (iv) the similarity of the observed rate of formation of radio pulsars and the rate of type Ib,c supernovae.     

The electric fields of radio pulsars with asymmetric nondipolar magnetic fields

The effect of the curvature of open magnetic field lines on the generation of electric fields in radio pulsars is considered in the framework of a Goldreich-Julian model, for both a regime with a free outflow of electrons from the neutron-star surface and the case of a small thermoemission current. An expression for the electron thermoemission current in a strong magnetic field is derived. The electric field associated with the curvature of the magnetic flux tubes is comparable to the field generated by the relativistic dragging of the inertial frames.     

Classification of radio pulsars using the principle-components method

The principle-components method is used as a basis to analyze the distributions of known radio pulsars in spaces of eigenvectors of correlation matrices for various samples of pulsars and classification parameters (from 4 to 11 parameters characterizing the physical and kinematic properties of the objects). Pulsars with periods P < 0.1 s form a separate cluster, far from the cluster formed by “normal” pulsars with P ～ 1 s, in all the studied spaces. These two groups also differ appreciably in their other parameters (period derivatives, magnetic fields, pulse widths). In particular, the spatial velocities of short-period pulsars (106 km/s) are appreciably lower than those displayed by long-period pulsars (334 km/s). The distributions of the pulsars at southern (Z < 0) and northern (Z > 0) Galactic latitudes do not differ; i.e., there is no anisotropy in the motions in these two directions perpendicular to the Galactic plane, or in the corresponding distributions of the pulsar parameters.     

New observations of anomalous X-ray pulsars at low frequencies

We report the results of new observations of three anomalous X-ray pulsars: 1E 2259+586, 4U 0142+61, and XTE J1810-197. The observations were carried out on high-sensitivity radio telescopes of the Pushchino Radio Astronomy Observatory: the Large Phased Array at 111MHz and the DKR-1000 at 62 MHz. New, digital, multi-channel receivers designed for pulsar observations were used. Pulse profiles and dynamical spectra for the three pulsars are presented. The mean flux density for XTE J1810-197 is estimated to be ∼160 mJy at 62 MHz. An estimated spectral index for this pulsar is also presented.     

The death lines of radio pulsars for dipolar and asymmetric magnetic fields

The effect of curvature of open magnetic-field tubes on the death lines of radio pulsars is studied. The solution is obtained in the framework of a Goldreich-Julian model for both dipolar and asymmetric magnetic fields. The tube-axis curvature can shift the death line appreciably toward either longer or shorter periods. If the field is dipolar and gamma rays are generated by the inverse Compton effect, the formation of secondary plasma is more efficient near the death line. In the case of an asymmetric magnetic field, the generation of radio emission beyond the tube of open field lines is possible.     

Radio emission of RRAT pulsars at 111 MHz

Observations of the RRAT pulsars J0627+16, J0628+09, J1819?1458, J1826?1419, J1839?01, J1840?1419, J1846?0257, J1848?12, J1850+15, J1854+0306, J1919+06, J1913+1330, J1919+17, J1946+24, and J2033+00 observed earlier on the 64-m Parkes telescope (Australia) and the 300-m Arecibo radio telescope (Puerto Rico) at 1400 MHz were conducted at 111 MHz on the LSA radio telescope of the Pushchino Radio Astronomy observatory in 2010–2012. A characteristic feature of these pulsars is their sporadic radio emission during rare active epochs and the absence of radio emission during long time intervals. No appreciable flare activity of these pulsars was detected in the Pushchino observations. However, processing the observations using the Fast Folding Algorithm taking into account known information about the pulsar dispersion measures and periods shows that, even during quiescent intervals, the majority of the studied pulsars generate weak radio pulses with a period corresponding to that of the radio emission of the sporadic pulses observed at active epochs. The flux of this radio emission does not exceed 100 mJy at the pulse peak, even at the low frequency of 111 MHz. This considerably hinders detection of the radio emission of RRAT pulsars at high frequencies, since the radio fluxes of RRAT pulsars decreases with increasing frequency.     

Parameters of radio pulsars in binary systems and globular clusters

The parameters of radio pulsars in binary systems and globular clusters are investigated. It is shown that such pulsars tend to have short periods (of the order of several milliseconds). Themagnetic fields of most of the pulsars considered are weak (surface fields of the order of 10⁸?10⁹ G). This corresponds to the generally accepted view that short-period neutron stars are spun up by angular momentum associated with the stellar wind from a companion. However, the fields at the light cylinders in these objects are two to three orders of magnitude higher than for the main population of single neutron stars. The dependence of the pulse width on the period does not differ from the corresponding dependences for single pulsars, assuming the emission is generated inside the polar cap, at moderate distances from the surface or near the light cylinder. The radio luminosities of pulsars in binary systems do not show the correlation with the rate of loss of rotational energy that is characteristic for single pulsars, probably due to the influence of accreting matter from a companion. Moreover, accretion apparently decreases the power of the emergent radiation, and can explain the observed systematic excess of the radio luminosity of single pulsars compared to pulsars in binary systems. The distributions and dependences presented in the article support generally accepted concepts concerning the processes occurring in binary systems containing neutron stars.     

Average pulse profiles of radio pulsars at 102 and 111 MHz

Average profiles for 180, mostly faint, pulsars at 102 and 111 MHz are presented. Pulse shapes have been obtained for the first time for most of the faint pulsars (about 50% of the total sample). A comparison with high-frequency data (mostly at 234, 408, 610, 925, and 1408 MHz) demonstrates appreciable changes in the profile width and shape with frequency. For most pulsars, the number of components is preserved, but the intensities of individual components can change. As a rule, the profile width increases with decreasing frequency. The possible generation of emission at the cyclotron frequencies is considered.