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.     

Rotational periods and other parameters of magnetars

The rotational periods P, period derivatives dP/dt, and magnetic fields B in the region where the emission of anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) is generated are calculated using a model that associates the emission of these objects with the existence of drift waves at the periphery of the magnetosphere of a neutron star. The values obtained for these parameters are P = 11?737 ms, dP/dt = 3.7 × 10^?16?5.5 × 10^?12, and log B (G) = 2.63?6.25. We find a dependence between the X-ray luminosity of AXPs and SGRs, L _x, and the rate at which they lose rotational energy, dE/dt, which is similar to the L _x(dE/dt) dependence for radio pulsars with detected X-ray emission. Within the errors, AXPs/SGRs and radio pulsars with short periods (P < 0.1 s) display the same slopes for their log(dP/dt)-log P relations and for the dependence of the efficiency of their transformation of rotational energy into radiation on their periods. A dipole model is used to calculate the surface magnetic fields of the neutron stars in AXPs and SGRs, which turn out to be, on average, comparable to the surface fields of normal radio pulsars (〈log B _s (G)〉 = 11.90).     

Angles between the rotational axis and magnetic moment in 80 pulsars from observations near 1 GHz

Data on the pulse structure and variations of the linear polarization angle at frequencies near 1 GHz have been used to estimate the angles β between the rotational axis and magnetic moment of the neutron stars assocaited with 80 pulsars. The calculations applied several methods. The minimum values of β were estimated from the observed pulse width W ₁₀ at the 10% level for the entire sample. Maximum estimates of β were obtained for six sources with small polarization position angle derivatives. Equations for the angle β were derived for various forms of the observed profile, and solutions obtained for 34 pulsars. The β values calculated using different methods are compared. For three pulsars with known interpulses, the obtained values of β demonstrate that two (PSR B1055-52 and PSR 1822-09) are aligned rotators, whereas the other (PSR B1702-19) is an orthogonal rotator. A search for interpulses and interpulse emission in PSRB1641-45, PSR1642-03, and PSR 1944+17 is necessary, and a search for an interpulse at 180° from the main pulse is required in PSR B2321-61.     

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.     

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.     

Properties of pulsars with short and long periods

A comparative analysis has been conducted for the timescale on which the observed radio emission of pulsars is switched off (nulling fraction), the polarization parameters, and the residual deviations in the pulse arrival times for pulsars with periods P >0.1 s and P <0.1 s. For the former group of pulsars, the greater the energy injected into the magnetosphere from internal layers of the neutron star, the smaller the nulling fraction; in the latter group, nullings are not observed at all. Mode switches are also observed only in pulsarswith long pulse-to-pulse intervals (P >1 s), and in many objects they are correlatedwith the presence of nullings. The degree of polarization grows with decreasing period, and is systematically higher in objects with P <0.1 s than in long-period pulsars. The relative deviations of the pulse arrival times are, on average, appreciably smaller for pulsars with P >0.1 s. The observed differences in the parameters of pulsars with short and long periods can be understood if the radiation of pulsars with P <0.1 s is generated near the light cylinder.

     

The drift model for AXPs and SGRs in the light of new observtional data

The latest observational data are analyzed to investigate their consistency with two known models for anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs): the magnetar and drift models. The results of spectral measurements disagree with the predictions of theories that assume the presence of super-strong magnetic fields on AXPs and SGRs and associated processes for the generation of electron-positron plasma in the upper layers of the neutron-star magnetosphere. We present arguments against the use of magnetic-dipole braking for these objects. The rotational periods P, period derivatives dP/dt, and magnetic fields B of known AXPs and SGRs are calculated for the drift model. The mean values of these parameters in the sample used are 〈P〉 = 108 ms and 〈log B _s [G]〉 = 12.08. Overall, the measured profiles, polarizations, and spectra can be brought into agreement with the drift model.     

A new model of a magnetar

A new model is put forward to explain the observed features of anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs). It is shown that drift waves can be excited in the magnetosphere of a neutron star with a rotational period of P～0.1 s, surface magnetic field B_s～10¹² G, and angle between the rotational axis and magnetic moment β<10°. These waves lead to the formation of radiation pulses with a period of P_dr～10 s. The rate of loss of rotational energy by such a star (～10³⁷ erg/s) is sufficient to produce the observed increase in the period \((\dot P \sim 10^{ - 10} )\), the X-ray luminosities of AXPs and SGRs (～10³⁴–10³⁶ erg/s), and an injection of relativistic particles into the surrounding supernova remnant. A modulation of the constant component of the radiation with a period of P～0.1 s is predicted. In order for SGRs to produce gamma-ray bursts, an additional source of energy must be invoked. Radio pulsars with periods of P_obs>5 s can be described by the proposed model; in this case, their rotational periods are considerably less than P_obs and the observed pulses are due to the drift waves.     

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.     

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 pulsar PSR B1931+24 as an orthogonal rotator

The angles of the magnetic moment μ and the line of sight L to the rotation axis Ω are estimated for the pulsar PSR B1921+24, which displays “on” and “off” periods in its radio emission. It is shown that this object is an orthogonal rotator, i.e., the angle β between μ and Ω is equal to 88°.2 and the angle between L and Ω is ζ = 98.7°, and that its rotation period should be twice the usually adopted value (P = 1.626 s). One possible reason for the peculiarities of this pulsar could be the precession of a relic disk in the equatorial region of the object. Further observations (in particular, in the infrared) are required to confirm the existence of such a disk. Polarization data for other pulsars whose radiation switches on and off (transients) are also required, to determine if they are likewise orthogonal rotators. Calculations for PSR B0656+14 show that β ∼ 20°, and the sharp increase of its pulse intensities is due to intrinsic reasons, and is not associated with a relic disk. Original Russian Text ? I.F. Malov, 2007, published in Astronomicheskiĭ Zhurnal, 2007, Vol. 84, No. 6, pp. 531–535.     

Contribution of thermal bremsstrahlung to microwave emission of solar flare loops

The contribution of thermal bremsstrahlung to the total microwave flux of a solar flare loop is considered. The total-flux data were obtained on the Nobeyama Radio Heliograph. The calculation of the thermal bremsstrahlung radio flux was based on determining the integrated temperature and number density of the hot flare-loop plasma from its soft X-ray flux, obtained using data from the GOES-10 and GOES-12 satellites. The effect of thermal bremsstrahlung on the total flux and the spectral index of the microwave radiation is insignificant at the burst maximum (F _th/F _tot < 3%, Δα < 0.2), while the contribution of bremsstrahlung can be substantial during the decay phase of the burst (up to 80%). This results in an appreciable decrease in the observed spectral index (to Δα ～ 1.5). Therefore, when diagnosing the parameters of the accelerated electrons based on the characteristics of their gyrosynchrotron radiation, the most accurate results can be obtained using the emission characteristics obtained near the burst maximum.     

Structure proof and significance of stereoisomeric 28,30-bisnorhopanes in petroleum and petroleum source rocks

Two C₂₈H₄₈-pentacyclic triterpanes were isolated from Monterey shale. X-ray crystallography of a crystal containing both compounds proved their structures as 17β,18α,21α(H)-28,30-bisnorhopane and 17β,18α,21β(H)-28,30-bisnorhopane. Several differences are found between 28,30-bisnorhopanes and the regular hopanes. Unlike the regular hopane epimers, for practical purposes the three epimeric 28,30-bisnorhopanes [17α,21β(H)-, 17β,21α(H)-, and 17β,21β(H)-]cannot be distinguished by their mass spectra. Special conditions are needed to separate them by gas chromatography. The diagenetically first-formed epimer is thought to be 17α,21β(H)- because it predominates in immature shales. The order of thermodynamic stability is 17β,2lα(H) < > 17α,21β(H) > 17β,21β(H), and all three epimers are present in petroleum. 25,28,30-Trisnorhopanes can be analyzed in similar fashion and are found to have similar thermodynamic characteristics. The percent of the ring D/E cis epimer of 28,30-bisnorhopane and/or 25,28,30-trisnorhopane is a useful maturation parameter similar to the 20S/20R sterane ratio. Evidence indicates 25-demethylation of 28,30-bisnorhopane to 25,28,30-trisnorhopane during advanced stages of biodegradation. Hence, percent ring $\text{D}\text{E}$cis 25,28,30-trisnorhopane has an application to maturation assessment in heavily biodegraded oils.     

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.     

Interpretation of K X-ray emission spectra and chemical bonding in oxides of Mg,Al and Si using quantitative molecular orbital theory

Quantitative molecular orbital calculations are reported for Mg, Al and Si in tetrahedral and octahedral coordination with oxygen. These calculations are employed to assign and interpret the ME_α, ME_β and OK_α X-ray emission spectra of the corresponding oxides. The interpretation of the MK_β spectrum reproduces the observed trends in main peak and satellite energies with variation of metal, ligand and geometry. The splitting of the main K_β peak, observed in many oxides, is found to be a result of interaction between adjacent metal atoms. The calculations also reproduce the observed trends in OK_α spectra. The electronic structures of the various oxides are discussed briefly.     

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.     

A correlation between the distributions of pulsars and emission measures in the galaxy

A correlation has been detected between the volume density of pulsars and the density of interstellar ionized gas on scales of more than 500 pc in Galactic longitude and 200 pc in Galactic latitude. On smaller scales, the correlation is present only for pulsars with ages less than 60000 years, which are located predominantly near supernova remnants and H II regions. This all indicates that pulsars are born in regions with high concentrations of interstellar gas. The minimum emission measures observed in the directions toward pulsars are inversely proportional to the pulsar ages. It is concluded that the ionized gas in the vicinities of a number of pulsars was formed during supernova explosions, and corresponds to Strömgren zones. The ionization of the gas in these zones requires a radiation energy on the order of 10⁵⁰–10⁵¹ erg.     

Synchrotron spectra of short-period pulsars

A model with synchrotron radiation near the light cylinder is proposed to explain the observed spectra of short-period pulsars (P≤0.1 s). These spectra can be described if a power-law energy distribution of the emitting electrons with exponent γ=2–8 is assumed. For most pulsars, the peak frequency ν_m is below 10 MHz. The ν_m(γ) dependence is derived, and shows that the peak frequencies for pulsars with spectral indices α<1.5 may fall in the observable range. In particular, ν_m may be ν_m ～ 100 MHz for PSR J0751 + 1807 and PSR J1640 + 2224. The observed radio spectrum of Geminga (PSR J0633 + 1746) can be described by a synchrotron model with a monoenergetic or Maxwellian distribution of relativistic electrons and a small angle β between the spin axis and magnetic moment (β ～ 10°).     

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.