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.     

The turbulence spectrum of the interstellar plasma toward the pulsars PSR B0809+74 and B0950+08

The interstellar scintillation of the pulsars PSR B0809+74 and B0950+08 have been studied using observations at low radio frequencies (41, 62, 89, and 112 MHz), and the characteristic temporal and frequency scales for diffractive scintillations at these frequencies determined. A comprehensive analysis of the frequency and temporal structure functions reduced to a single frequency shows that the spectra of the inhomogeneities of the interstellar plasma toward both pulsars are described by a power law. The index of the interstellar plasma fluctuation spectrum toward PSR B0950+08 (n = 3.00 ± 0.05) differs appreciably from the Kolmogorov index. The spectrum toward PSR B0809+74 is a power law with index n = 3.7 ± 0.1. Strong angular refraction has been detected toward PSR B0950+08. Analysis of the distribution of inhomogeneities along the line of sight indicates that the scintillations of PSR B0950+08 take place in a turbulent layer with an enhanced electron density localized approximately 10 pc from the observer. The distribution of inhomogeneities for PSR B0809+74 is quasi-uniform. The mean square fluctuations of the electron density are estimated for inhomogeneities with characteristic scale ρ ₀ = 10⁷ m along the directions toward four pulsars. The local turbulence in the 10-pc layer is a factor of 20 higher on this scale than in the extended region responsible for the scintillations of PSR B0809+74.     

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°).     

Detection of regular variations in the intensity and pulse time of arrival of the anomalous pulsar PSR B0943+10

Timing of the anomalous pulsar PSR B0943+10 during 2007–2013 was carried out on the Large Phased Array radio telescope of the Pushchino Radio Astronomy Observatory at 112 MHz. The astrometric and rotational parameters for epoch MJD=56 500 have been determined. Considerable deviations of the pulse times of arrival from the precalculated values with a characteristic period of several years due to the presence of correlated low-frequency noise in the pulsar spin phase have been detected. These deviations can be explained in a planetary model by the presence of two companions of the pulsar, whose orbital parameters have been determined. A continuous increase in the longitude of the pulse maximum within the emission window, the pulse width, and the intensity have been detected after each switch to the burst mode. Together with the changes in pulse shape, degree of linear polarization of the pulse, and drift rate of individual pulses detected earlier, this indicates that all the main parameters of the radio emission in the B mode are unstable. This distinguishes PSR B0943+10 from all other modes-witching pulsars. The origin of the observed properties of this pulsar are probably associated with the interaction of its extended magnetosphere with the surrounding medium.     

Radio sounding of the circumsolar plasma using polarized pulsar pulses

We present the results of radio sounding observations probing the inner solar wind near the minimum of the solar-activity cycle, using polarized pulses from PSR B0525+21 and PSR B0531+21 received when the lines of sight toward these pulsars were close to the Sun. The observations were obtained in June 2005 and June 2007 on the Large Phased Array of the Lebedev Physical Institute at 111 MHz. An upper limit for the scattering of giant pulses from PSR B0531+21 due to their passage through the turbulent solar-wind plasma is determined. The arrival-time delays for pulses from PSR B0531+21 are used to derive the radial dependence of the mean density of the circumsolar plasma. The resulting density distribution indicates that the acceleration of fast, high-latitude solar-wind outflows continues to heliocentric distances of 5–10R _⊙, where R _⊙ is the solar radius. The mean plasma density at heliocentric distances of about 5R _⊙ is 1.4 × 10⁴ cm^?3, substantially lower than at the solar-activity maximum. This is associated with the presence of polar coronal holes. The Faraday rotation measure at heliocentric distances of 6–7R _⊙ is estimated. Deviations of the spatial distribution of the magnetic field from spherical symmetry are comparatively modest in the studied range of heliocentric distances.     

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.     

Two scales for the frequency dependence of the scattering of pulsar radio emission

We have measured the pulse broadening by scattering at 40, 60, and 111 MHz for the pulsars PSR B0809+74, B0950+08, B1919+21, and B2303+30. The frequency dependence of the scatter-broadening parameter is analyzed based on these measurements and data from the literature. The dependence obtained purely from the literature data is not consistent with the theory, and the scattering magnitudes differs considerably from the data of the catalog of 706 pulsars of Taylor et al. A two-component model for the frequency dependence of the scattering of the pulsar radio emission in the interstellar medium is proposed. Allowing for the presence of two scattering scales removes both inconsistencies between the observational data for these four pulsars and differences between the observed and theoretical frequency dependences for the scattering, as well as the need to invoke anomalous scattering magnitudes. The data of the catalog of Taylor et al. need to be corrected for the difference in the scattering magnitudes in the two branches of the frequency dependence.     

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.     

Observations of giant pulses from B1237+25 (J1239+2453) at 111 MHz. Detection and classification

An analysis of data from monitoring of individual pulses of the second-period pulsar PSR B1237+25 (J1239+2453) carried out on the Large Phased Array (LPA) of the Pushchino Radio Astronomy Observatory at 111 MHz during 2012–2015 is presented. The aim of this observing program is a search for anomalously strong and giant pulses. The regular generation of powerful individual pulses at the longitudes of three of five components in the main profile of PSR B1237+25 has been detected. The distribution of these strong pulses in flux density is bimodal, and has the power-law form characteristic for giant pulses, with power-law indices n = ?1.26 ± 0.05 and ?3.36 ± 0.34, which differentiates them from the regular pulses of pulsars, having a log–normal distribution. The characteristic pulse widths at the half-intensity level are 3–5 ms, which comprises 50–100% of the width of the corresponding component in the mean profile. The most powerful of the detected pulses had a peak flux density of 900 ± 160 Jy, and the strongest pulse exceeded the session-mean profile by a factor of 65.     

Distribution of regions of emission at different frequencies in pulsar magnetospheres

It is shown that the observed width of the emission profile W ₁₀ and the maximum derivative C of the polarization position angle for the mean profile of a pulsar can be used to calculate the ratio n of the emission-cone radius ?? to the minimum distance between the line of sight and the center of this cone fairly accurately. Estimates of n obtained earlier by eye based on the shape of the emission profiles are close to these more accurate values for pulsars from a catalog at a frequency near 1 GHz. Values of n are calculated for several dozen pulsars using data at 10 and 20 cm. In the standard model, the ratio of n at two frequencies is equal to the ratio of the squares of the distances from the center of the neutron star to the emission levels at the two frequencies. Statistical dependences of the profile width on the pulsar period for these wavelengths and a model assuming emission at the local plasma frequency are used to determine the absolute values of these distances. These estimates display good consistency and yield distances to the emission levels of the order of several tens of neutron-star radii. The calculations take into account possible variation of the dimensions of the polar cap associated with the inclination of the emission cone to the rotational axis of the pulsar; i.e., the influence of the angle ?? between the magnetic moment and rotational axis of the neutron star. Values of ?? calculated earlier for the pulsar sample considered are used for this analysis.     

Polarization of individual pulses of radio pulsars at the low frequencies 40, 60, and 103 MHz

Measurements of the linear polarization of individual pulses at 40, 60, and 103 MHz are presented for ten pulsars. The degree and position angle of a linear polarization were measured with a temporal resolution of 1–7 ms, and the longitudinal distributions of these parameters were constructed for each pulsar at one or more of these frequencies. These are the first such measurements for pulsars B0031-07, B0320 + 39, B0628-28, and B2217 + 47. Apart from B0628-28, all the pulsars are characterized by the simultaneous presence of orthogonal polarization modes in at least one component of the integral profile. The secondary polarization mode increases at frequencies ≤100 MHz for pulsars whose integrated pulses contain pairs of conal components (B0031-07, B0329 + 54, B0834 + 06, B1133 + 16, B2020 + 28). This is manifested both as an expansion of the longitudinal range where the secondary polarization mode is observed and an increase in its contribution to the emission at a given longitude. New data confirming the dependence of the linear polarization of individual pulses on the intensity and mode of the pulsar emission have been obtained.     

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.     

Characteristics of the pulsed emission of the peculiar pulsar B1822-09 at low radio frequencies

The pulse structure of the pulsar B1822-09 has been studied at 112, 62, and 42 MHz. The observations were conducted in 2010 on the Large Scanning Antenna and the DKR-1000 radio telescope of the Pushchino Radio Astronomy Observatory. The shape of the main pulse and interpulse undergo considerable changes at low radio frequencies. In the main pulse, the precursor disappears and is replaced by a new component that trails 50 ms behind the main component. At 62 MHz, the interpulse acquires a pronounced two-peaked shape. At 62 and 112 MHz, as well as at higher frequencies, the brighter second component of the interpulse follows the main pulse at 185° and has a relative amplitude of about 5%. The main pulse width changes with frequency according to the power law W _0.5 ∼ ν ^−0.15 in the frequency range 42–4750-MHz. The interpulse width follows this law only in the range 325–4750 MHz; at 112, 102, and 62 MHz, the interpulse is almost a factor of three broader than themain pulse. The parameters of the pulse’s scattering on interstellar plasma inhomogeneities and the initial pulse width before it enters the scattering medium have been measured at 62 and 42 MHz. The frequency dependence of the characteristic scale for scattering of the pulses of B1822-09 corresponds to a Kolmogorov spectrum for the electron-density fluctuations in the interstellar medium in the direction toward this pulsar.     

Optimal filtration and a pulsar time scale

An algorithm is proposed for constructing a group (ensemble) pulsar time based on the application of optimal Wiener filters. This algorithm makes it possible to separate the contributions of variations of the atomic time scale and of the pulsar rotation to barycentric residual deviations of the pulse arrival times. The method is applied to observations of the pulsars PSR B1855+09 and PSR B1937+21, and is used to obtain corrections to UTC relative to the group pulsar time PT_ens. Direct comparison of the terrestial time TT(BIPM06) and the group pulsar time PT_ens shows that they disagree by no more than 0.4 ± 0.17 μs. Based on the fractional instability of the time difference TT(BIPM06)-PT_ens, σ _z = (0.5 ± 2) × 10⁻¹⁵, a new limit for the energy density of the gravitational-wave background is established at the level Ω _g h ² ∼ 10⁻⁹.     

The geometry of radio pulsar magnetospheres

Data on the profiles and polarization of the 10- and 20-cm emission of radio pulsars are used to calculate the angle β between the rotational axis of the neutron star and its magnetic moment. It is shown that, for these calculations, it is sufficient to use catalog values of the pulse width at the 10% level W ₁₀, since the broadening of the observed pulses due to the transition to the full width W ₀ and narrowing of the pulses associated with the emission of radiation along tangents to the field lines approximately cancel each other out. The angles β ₁ are calculated for 283 pulsars at 20 cm and 132 pulsars at 10 cm, assuming that the line of sight passes through the center of the emission cone. The mean values of these angles are small and similar for the two wavelengths (〈β ₁〉 = 18° at λ = 10 cm and 〈β ₁〉 = 14° at λ = 20 cm). The angle β ₂ is estimated for several dozen pulsars for the case when the orientation of the angle to the line of sight is arbitrary. The mean value of β ₂ at 10 cm is found to be 〈β ₂〉 = 33.9° if the maximum derivative of the polarization position angle C is positive and 〈β ₂〉 = 52.1° ifC < 0. We find at 20 cm 〈β ₂〉 = 33.9° ifC > 0 and 〈β2〉 = 54.1° ifC < 0. The values at the two wavelengths are equal within the errors, and close to the β ₂ value obtained earlier at 30 cm (〈β ₂〉 = 36.4° if C >0 and 〈β2〉 = 49.1° if C < 0). The mean 〈β ₂〉 for the entire set of data can be taken to be 43.5°. The period dependence of the pulse width W(P) √ P ^−0.25 differs from the relation that is usually used in the polar-cap model, W(P) √ P ^−0.5. This difference could be associated with the rate of development of plasma instabilities near the surface of the neutron star (in the region where high-frequency radiation is generated). The role of the quadrupole component of the magnetic field is not important here. There is no dependence of the angle β on the pulsar age (z distance, luminosity L, or characteristic age τ = P/(2dP/dt)) for the studied sample.     

The radio emission of anomalous pulsars

Previously developed methods for estimating the angle β between the spin axis of a neutron star and its magnetic moment together with observational data for anomalous X-ray pulsars (AXPs) indicate that these objects are nearly aligned rotators, and that the drift model can be applied to them. The magnetospheres of aligned rotators are appreciably more extended than in pulsars with large values of β. With such extents for the magnetosphere, the conditions for the generation of transverse waves via the cyclotron instability are satisfied. The expected spectrum of the resulting radiation is very steep (its spectral index is α > 3), consistent with the observed radio spectra of known AXPs (α > 2). A large magnetosphere also favors the appearance of appreciable pitch angles for relativistic electrons, and therefore the generation of synchrotron emission. The maximum of this emission falls in the microwave range. This mechanism provides appreciable fluxes at frequencies of tens of gigahertz and can explain the observed enhanced AXP radiation in this range.     

Microstructure of pulsar radio pulses measured with a time resolution of 62.5 ns at 1650 MHz

We present an analysis of pulsar observations carried out on two frequency channels at 1634 MHz and 1650 MHz with a time resolution of 62.5 ns on the 70-m radio telescope of the NASA Deep Space Network in Tidbinbilla. The data were recorded using the S2 system, intended primarily for VLBI observations. Microstructure with characteristic timescales of 270, 80, and 150 µs was detected in pulsars B0833-45, B1749-28, and B1933 + 16, respectively. The distribution of microstructure timescales for the Vela pulsar (B0833-45) is characterized by a gradual growth with decreasing timescale to 200 µs; the distribution has a maximum at 20–200 µs and falls off sharply for timescales below 20 µs. The statistical relation between the microstructure modulation index m and the corresponding timescale τ_µ can be approximated by the power law dependence R∝τ _⊙ ^0.5 ; i.e., the intensity is higher for micropulses with longer durations. This contradicts the predictions of nonlinear models for the formation of micropulses by supercompact soliton wave packets. In all the pulsars studied, the time delays of the micropulses between the two frequency channels deviate from the expected dispersion laws for the interstellar plasma. In particular, the micropulses in the low-frequency channel arrive earlier than predicted by the dispersion measures derived previously from the mean pulse profiles. The deviation from the dispersion delay is determined most accurately for B0833-45, and is 4.9±0.2 µs. Such anomalous delays are probably associated with the effects of propagation of the radio emission within the pulsar magnetosphere.     

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.

     

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).     

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.