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 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.     

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.     

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.     

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.     

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.     

Effect of the pulsar-tube radius on the gamma-ray curvature radiation from the polar regions of radio pulsars with non-dipolar magnetic fields

The effect of the radius of the tube of open magnetic-field lines on the gamma-ray curvature radiation from the polar regions of a radio pulsar with a non-dipolar magnetic field is analyzed. The pulsar is considered in a polar-cap model with free electron emission from the neutron-star surface. The effect of the non-dipolar magnetic field on the radius of curvature of the field lines and the field intensity is taken into account. In connection with the creation of electron-positron pairs, we take into account only the birth of pairs by curvature radiation in the magnetic field. The small non-dipolarity of the field enables the radio pulsar not to turn off, even after a considerable decrease in the pulsar-tube radius. For instance, with a 20% non-dipolarity (ν = 0.2), a pulsar with B = 10¹³ G and P = 0.5 s can still operate even for a fivefold decrease in the pulsar-tube radius. A maximum is observed in the dependence of the electrostatic potential in the diode on the non-dipolarity parameter ν at ν ～ 0.5–0.7. The pulse profile in non-thermal X-ray emission for ν ～ 0.5–0.7 may look virtually the same as for ν ～ 0.1–0.2. Decreases in the pulsar-tube radius could be due to a structure of currents in the magnetosphere that results in the pulsar diode on the neutron-star surface occupying only a small fraction of the pulsar tube, with the remainder of the tube containing an outer annular gap. The pulsar-tube size is also affected by the presence of a circum-pulsar disk. A change in the pulsar-tube radius could also be due to an external magnetic field, associated with either a magnetic white dwarf or a circum-pulsar disk.     

In situ study of the $$ R\overline{3} c \to R\overline{3} m $$ orientational disorder in calcite

The temperature dependences of the crystal structure and intensities of the (113) and (211) reflections in calcite, CaCO₃, were studied using Rietveld structure refinements based on synchrotron powder X-ray diffraction data. Calcite transforms from to at about T _c = 1,240 K. A CO₃ group occupies, statistically, two positions with equal frequency in the disordered phase, but with unequal frequency in the partially ordered phase. One position for the CO₃ group is rotated by 180° with respect to the other. The unequal occupancy of the two orientations in the partially ordered phase is obtained directly from the occupancy factor, x, for the O1 site and gives rise to the order parameter, S = 2x − 1. The a cell parameter shows a negative thermal expansion at low T, followed by a plateau region at higher T, then a steeper contraction towards T _c, where the CO₃ groups disorder in a rapid process. Using a modified Bragg–Williams model, fits were obtained for the order parameter S, and for the intensities of the (113) and (211) reflections. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

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.     

Differences in the parameters of radio pulsars with short and long periods

A comparative analysis of various parameters of pulsars with short (P < 0.1 s) and long (P > 0.1 s) periods is carried out. There is no correlation between the radio and gamma-ray luminosities of the pulsars and their surfacemagnetic fields, but there is a correlation between the X-ray luminosity and the surfacemagnetic field. A dependence of the X-ray and gamma-ray luminosities on the magnetic field at the light cylinder is also found. This result provides evidence for the formation of hard, non-thermal emission at the periphery of the magnetosphere. An appreciable positive correlation between the luminosity and the rate of rotational energy loss by the neutron star is observed, supporting the idea that all radio pulsars have the same basic source of energy. The efficiency of the transformation of rotational energy into radiation is significantly higher in long-period pulsars. The dependence of the pulse width on the pulsar period is steeper for pulsars with short periods than for those with long periods. The results obtained support earlier assertions that there are differences in the processes generating the emission in pulsars with P < 0.1 s and those with P > 0.1 s.     

A comparative analysis of the integrated radio luminosities of normal and millisecond pulsars

We present the results of a comparative statistical analysis of the integrated radio luminosities of millisecond and normal pulsars and their dependences on other parameters of the pulsars. The analysis is based on our own measurements of the flux densities, spectra, and integrated radio luminosities of the millisecond pulsars, as well as data from the literature used to determine the integrated radio luminosities for 545 pulsars, 50 of them millisecond pulsars. Despite large differences in their periods P, period derivatives $\dot P$ , magnetic fields B, and ages τ, the integrated radio luminosities of the millisecond and normal pulsars and their dependences on other parameters are approximately the same. The integrated radio luminosity depends on the parameter B/P ², which is proportional to the potential difference in the polar-cap gap; this may indicate that the radio energy of pulsars is determined by the energy of primary particles accelerated in the polar-cap gap. Secular decreases in the radio luminosities of both normal and millisecond pulsars were also detected.     

Optical observations of the gravitational lens SBS1 520+530 at the Ma $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} $$ danak Observatory

Observations of the gravitationally lensed quasar SBS 1520+530 obtained in 2000–2001 on the 1.5-m telescope of the Ma $\overset{\lower0.5em\hbox{$\overset{\lower0.5em\hbox{ danak Observatory (Uzbekistan) are presented. The photometric algorithms used to observe the components of SBS 1520+530 are discussed. The images have a resolution of 0.5″–0.6″, enabling us to detect the lensing galaxy in the R and I bands and to measure its luminosity and coordinates. The results of photometric observations of components A and B of SBS 1520+530 are presented; the light curves show variability on various time scales from a few weeks to a year. A gravitational-lens model for SBS 1520+530 is constructed utilizing all currently available data.     

Evolution of the angle between the magnetic moment and the rotation axis of radio pulsars

It is shown that, when angular-momentum losses of a radio pulsar are represented as a sum of magnetic-dipole and current losses, the angle between the magnetic moment and rotation axis of the radio pulsar tends to some equilibrium value (near 45°). This process takes place on a timescale of the order of the pulsar’s characteristic age. Taking into account the non-dipolarity of the pulsar’s magnetic field changes this equilibrium angle.     

Spontaneous strain below the I\bar 1 - P\bar 1 transition in anorthite at pressure

The phase transition between the and phases of anorthite has been studied at elevated pressure by single-crystal X-ray diffraction in a diamond-anvil cell. The phase transition is shown to be first-order in character for both end-member anorthite (CaAl₂Si₂O₈) and for an anorthite with a small amount of albite component (NaAlSi₃O₈) in solid solution. Reversals of the transition across the phase boundary at three other compositions show that the transition pressure (P _Tr) increases with increasing albite content. This behaviour is compared with that observed at elevated temperatures, and is analysed in terms of Landau theory.     

Microscopic dynamic and macroscopic thermodynamic character of the I\bar 1 - P\bar 1 phase transition in anorthite

The dynamic character of the phase transition in anorthite from Monte Somma has been studied by high-temperature hard mode infrared spectroscopy. The mean local order parameter, as revealed by the temperature evolution of the frequencies of absorption bands between 540 and 620 cm_-1, follows classical second-order Landau behaviour with a critical exponent β = 1.. There is no observable first-order step. Anomalous line broadening of the 582 cm_-1 band indicates that dynamic fluctuations with a relaxation time τ ≈ 10⁻¹⁰ s exist over a limited temperature interval of approximately 150 K about T_c, and decay rapidly as T becomes greater than T_c. Previous order-disorder models of the high-temperature phase are not supported by these results. The Ca-flip motions, which we link to the line broadening, stabilize the driving soft mode of the transition. These flip motion fluctuations do not give rise to departures from the classical Landau theory because of the essential co-elastic nature of the phase transition. In the light of these results the structural instability can be described as an essentially displacive transition.     

Near InfraRed Imaging Spectrograph (NIRIS) for ground-based mesospheric OH(6-2) and $$\hbox {O}_{2}$$(0-1) intensity and temperature measurements

This paper describes the development of a new Near InfraRed Imaging Spectrograph (NIRIS) which is capable of simultaneous measurements of OH(6-2) Meinel and \(\hbox {O}_{2}\)(0-1) atmospheric band nightglow emission intensities. In this spectrographic technique, rotational line ratios are obtained to derive temperatures corresponding to the emission altitudes of 87 and 94 km. NIRIS has been commissioned for continuous operation from optical aeronomy observatory, Gurushikhar, Mount Abu (\(24.6^{\circ }\hbox {N}\), \(72.8^{\circ }\hbox {E}\)) since January 2013. NIRIS uses a diffraction grating of 1200 lines \(\hbox {mm}^{-1}\) and 1024\(\times \)1024 pixels thermoelectrically cooled CCD camera and has a large field-of-view (FOV) of \(80^{\circ }\) along the slit orientation. The data analysis methodology adopted for the derivation of mesospheric temperatures is also described in detail. The observed NIRIS temperatures show good correspondence with satellite (SABER) derived temperatures and exhibit both tidal and gravity waves (GW) like features. From the time taken for phase propagation in the emission intensities between these two altitudes, vertical phase speed of gravity waves, \(c_{z}\), is calculated and along with the coherent GW time period ‘\(\tau \)’, the vertical wavelength, \(\lambda _{z}\), is obtained. Using large FOV observations from NIRIS, the meridional wavelengths, \(\lambda _{y}\), are also calculated. We have used one year of data to study the possible cause(s) for the occurrences of mesospheric temperature inversions (MTIs). From the statistics obtained for 234 nights, it appears that in situ chemical heating is mainly responsible for the observed MTIs than the vertical propagation of the waves. Thus, this paper describes a novel near infrared imaging spectrograph, its working principle, data analysis method for deriving OH and \(\hbox {O}_{2}\) emission intensities and the corresponding rotational temperatures at these altitudes, derivation of gravity wave parameters (\(\tau \), \(c_{z}\), \(\lambda _{z}\), and \(\lambda _{y})\), and results on the statistical study of MTIs that exist in the earth’s mesospheric altitudes.     

A dynamical model for the I\bar 1 - P\bar 1 phase transition in anorthite,CaAl2Si2O8

The non-ferroic triclinic to triclinic \(I\bar 1 - P\bar 1\) phase transition in anorthite is described in terms of the spontaneous onset of an order parameter η. A triclinic to triclinic phase transition can be driven by order parameters (representations) arising from the Γ, Z, X, U, V, R, Y, and T points of symmetry of the Brillouin zone. Each point leads to a set of two inequivalent representations and thus there is a total of sixteen inequivalent order parameters. However, only the R ₁ ⁺ representation is consistent with the change from the body-centered to primitive cell (increase of primitive cell size of two) and also with the origin of the two space groups (inversion center) being at the same position. The R ₁ ⁺ order parameter of the high symmetry triclinic phase \(P\bar 1_0\) (or equivalently \(I\bar 1\) ) causes a reciprocal lattice change and, in terms of the lower symmetry reciprocal lattice, the order parameter corresponds to the b^* point. This is consistent with experimentally observed x-ray diffuse scattering. Using induced representation theory, microscopic distortions compatible with the R ₁ ⁺ order parameter are obtained. Assuming a distortion in an arbitrary direction at the general 2(i) Wyckoff position (x₀,y₀,z₀) of \(P\bar 1_0\) (the higher symmetry phase) induced representation theory demands an opposite displacement at the position (x₀, y₀, z₀), an opposite displacement at (x₀+1,y₀+1,z₀+1), and the same displacement at ( \(\bar x\) ₀+1, \(\bar y\) ₀+1, \(\bar z\) ₀+1) of \(P\bar 1_0\) . This is also consistent with experiment. The presence of the weak c-type reflections above the transition is attributed to the fluctuating lower symmetry antiphase domains related by the translation (1/2, 1/2, 1/2).     

Thermodynamics of plagioclases I: Theory of the I\bar 1 - P\bar 1 phase transition in anorthite and Ca-rich plagioclases

Landau theory of the \(P\bar 1 - I\bar 1\) phase transition in Ca-rich plagioclases reveals the sensitivity of the phase transition behaviour to a) Al, Si disorder, b) structural replacement of Ca by Na, and c) inhomogeneities of lattice strains. The following effects are predicted:

1. A tricritical phase transition exists in fully ordered anorthite. Al, Si disorder and Na, Ca exchange lead to second order phase transitions.
2. The transition temperatures depend sensitively on the degree of Al, Si disorder and the chemical composition of the Ca-rich plagioclases. Increasing Na-content decreases the transition temperatures.
3. The thermal evolution of c and d reflections depends on the homogeneity of the crystal and do not necessarily reflect the temperature evolution of the macroscopic lattice strain. A simple quadratic dependence of the X-ray scattering intensity on the order parameter exists only for fully ordered, homogeneous anorthite.

The role of inhomogeneous Al, Si distributions and lattice relaxations are discussed including possible structural modulations.     

Computer simulation of the phase diagram for the MgO-SiO2 system at P - T parameters of the mantle transition zone

The paper reports an attempt to study the topologies of the phase diagram for the MgO-SiO₂ system at high pressure and temperature using computer simulation. Phase equilibria at MgSiO₃ stoichiometry is investigated, demonstrating that the invariant point Gr+Ilm+Pv is stable at 21.6 GPa and 2270 K. A thermodynamic data base for minerals in the MgO-SiO₂ system is established by supplementing the calorimetric data for low pressure phases and equations of state for low and high pressure phases with data calculated from high pressure synthesis experiments. A refined set of standard free energies of formation and phase transformations in the MgO-SiO₂ system is presented. The proposed phase diagram covers a wide range of pressure (up to 25 GPa) and temperature (up to 2500 K) and forms the basis for a geochemical interpretation of the nature of seismic discontinuites in the mantle.     

Thermodynamics of plagioclase III: Spontaneous strain at the I\overline 1 - P\overline 1 phase transition in Ca-rich plagioclase

The lattice parameters of anorthites An₉₈Ab₂ and An₁₀₀ have been measured from 22 to 1100 K. The spontaneous strain arising from the \(I\overline 1 - P\overline 1\) displacive transition in An₉₈ follows second order Landau behaviour. The spontaneous strain (? _s) couples quadratically to the order parameter (Q ⁰) with ? _s∝Q ⁰²∝(T _c ^* ?T) and T _c ^* =530 K in An₉₈. This is in contrast to the tricritical behaviour observed in pure anorthite. These observations are consistent with a Landau model for the free energy of Ca-rich plagioclases in which Al/Si order and Na content renormalize the fourth order coefficient.