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.     

Anomalous frequency dependence of scattering of the radio emission from the Crab pulsar

The frequency dependence of scattering of the radio emission from the Crab pulsar at the low frequencies 111, 63, and 44 MHz has been measured and analyzed during sporadic enhancements of scattering and dispersion measure in October–December 2006 and December 2008. The frequency dependence of the scattering differs from the generally accepted dependence, τ _sc (ν) ∝ ν ^γ , where γ = −4.0 for Gaussian and γ = −4.4 for power-law Kolmogorov distributions of inhomogeneities of the scattering medium. In intervals of enhancement, the exponent of the frequency dependence γ decreased to −3.2(0.2) at the above frequencies. A model is proposed in which this is due to the presence of a dense plasma structure in the nebula in the line of sight toward the pulsar, in which scattering of the radio emission on turbulence differs from scattering in the interstellar medium. It is shown that the frequency dependence of scattering of the radio emission can be weaker in a dense plasma than in the rarefied interstellar medium.     

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.     

Monitoring of the radio emission of the Crab Nebula pulsar at low frequencies

Results of long-term (2002–2010) monitoring of giant radio pulses of the pulsar PSR B0531+21 in the Crab Nebula at ν = 44, 63, and 111 MHz are reported. The observations were conducted on the LPA and DKR-1000 radio telescopes of the Lebedev Physical Institute. The giant pulses were analyzed using specialized software for calculating the magnitude of the scattering τ _sc , signal-to-noise ratio, and other required parameters by modeling the propagation of a pulse in the scattering interstellar medium. Three pronounced sharp increases in the scattering were recorded in 2002–2010. Analysis of the dependence between the variations of the scattering and dispersion measure (data of Jodrell Bank Observatory) shows a strong correlation at all frequencies, ≈0.9. During periods of anomalous increase in scattering and the dispersion measure, the index γ in the frequency dependence of the scattering in the Crab Nebula, τ _sc (ν) ∝ ν ^−γ , was smaller than the generally accepted values γ = 4.0 for a Gaussian and γ = 4.4 for a Kolmogorov distribution. This difference in combination with the piece-wise power-law spectrum may be due to the presence of a dense plasma structure with developed Langmuir turbulence in the nebula, along the pulsar’s line of sight. The magnetic field in the Crab Nebula estimated from measurements of the rotation measure toward the pulsar is 100 μG.     

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.     

Distribution of interstellar plasma in the direction of PSR B0525+21 from data obtained on a ground–space interferometer

Observations on the RadioAstron ground–space interferometer with the participation of the Green Bank and Arecibo ground telescopes at 1668 MHz have enabled studies of the characteristics of the interstellar plasma in the direction of the pulsar PSR B0525+21. The maximum projected baseline for the ground–space interferometer was 233 600 km. The scintillations in these observations were strong, and the spectrum of inhomogeneties in the interstellar plasma was a power law with index n = 3.74, corresponding to a Kolmogorov spectrum. A new method for estimating the size of the scattering disk was applied to estimate the scattering angle (scattering disk radius) in the direction toward PSR B0525+21, θ _scat = 0.028 ± 0.002 milliarcsecond. The scattering in this direction occurs in a plasma layer located at a distance of 0.1Z from the pulsar, where Z is the distance from the pulsar to the observer. For the adopted distance Z = 1.6 kpc, the screen is located at a distance of 1.44 kpc from the observer.     

Deviation of the arrival-time delay of pulses for the Crab pulsar from a quadratic frequency region

Our measurements of the arrival-time delays of radio pulses from the Crab pulsar, PSR B0531+21, at low frequencies 111, 63, and 44 MHz revealed additional delays compared to the usual quadratic frequency relation, Δt(v) ∝ v ^?2. These additional delays are 65 ms between 63 MHz and 111 MHz—i.e., a factor of two longer than the pulsar’s period, i.e., a factor of five longer than the pulsar period—and cannot be explained by the “twisting” of the magnetic-field lines by the rotation of the pulsar. We suggest the model in which a previously unknown high-density plasma layer with a high electron concentration is present along the line of sight in the Crab nebula, causing an additional frequency-dependent delay of the observed radio pulses at low frequencies due to the contribution of the n _e ² v ^?4 term in the dispersion-delay formula. The parameters of this inferred layer have been derived: emission measure EM ? 4 × 10⁶ pc/cm⁶, electron density n _e ? 10⁶ cm^?3, depth along the line of sight d ? 4 × 10^?6 pc, and electron temperature T _e ≥ 2 × 10⁶ K.     

Refinement of the parameters of the binary pulsar B0655+64 based on 111 MHz observations

An analysis of monitoring observations for the pulsar PSR B0655+64, which is located in a binary system, at 111 MHz during 2002–2015 are presented. The Keplerian parameters of the pulsar have been refived: the longitude of periastron ω = 276_.^°5785 ± 0_.^°0005 and the orbital semi-major axis is a_p sin i = 4.124976± 0.000003 s. The parameters of the perturbed motion have been determined: the motion of periastron ω = 0_.^°315 ± 0_.^°005/ year, and the derivative of the period of the binary system ? = (-1.66 ± 0.11) × 10^-14 s/s = (-0.524 ± 0.038) µs/year. The estimated time scale for the decay of the PSR 0655+64 system is (1.7 ± 0.1) × 10¹¹ yrs.     

Distribution of the relative plasma turbulence level in the galaxy

The statistical dependence of τ/(DM)² (the ratio of the broadening of a pulsar pulse due to scattering in the interstellar medium to the square of the pulsar’s dispersion measure) on the pulsar’s dispersionmeasure, Galactic coordinates, age, and the angular distance to the nearest supernova remnant are studied. This parameter describes the relative level of electron density fluctuations in the turbulent interstellar plasma. It is shown that the interstellar plasma turbulence level is three orders of magnitude higher in the spiral arms of the Galaxy than outside the arms. The plasma turbulence level is approximately an order of magnitude higher in the Galactic arms, in regions within ?0.3° of supernova remnants, than outside these regions. We conclude that the source of energy for the turbulence in the Galactic arms is supernova explosions in the denser medium there.     

Instantaneous radio spectra of giant pulses from the crab pulsar from decimeter to decameter wavelengths

The results of simultaneous multifrequency observations of giant radio pulses from the Crab pulsar, PSR B0531+21, at 23, 111, and 600 MHz are presented and analyzed. Giant pulses were detected at a frequency as low as 23 MHz for the first time. Of the 45 giant pulses detected at 23 MHz, 12 were identified with counterparts observed simultaneously at 600 MHz. Of the 128 giant pulses detected at 111 MHz, 21 were identified with counterparts observed simultaneously at 600 MHz. The spectral indices for the power-law frequency dependence of the giant-pulse energies are from ?3.1 to ?1.6. The mean spectral index is ?2.7 ± 0.1 and is the same for both frequency combinations (600–111 MHz and 600–23 MHz). The large scatter in the spectral indices of the individual pulses and the large number of unidentified giant pulses suggest that the spectra of the individual giant pulses do not actually follow a simple power law. The observed shapes of the giant pulses at all three frequencies are determined by scattering on interstellar plasma inhomogeneities. The scatter-broadening of the pulses and its frequency dependence were determined as τ _sc = 20(ν/100)^?3.5±0.1 ms, where frequency ν is in MHz.     

Phase and intensity distributions of individual pulses of PSR B0950+08

The distribution of the intensities of individual pulses of PSR B0950+08 as a function of the longitudes at which they appear is analyzed. The flux density of the pulsar at 111 MHz varies strongly from day to day (by up to a factor of 13) due to the passage of the radiation through the interstellar plasma (interstellar scintillation). The intensities of individual pulses can exceed the amplitude of the mean pulse profile, obtained by accumulating 770 pulses, by more than an order of magnitude. The intensity distribution along the mean profile is very different for weak and strong pulses. The differential distribution function for the intensities is a power law with index n = ?1.1 ± 0.06 up to peak flux densities for individual pulses of the order of 160 Jy.     

Measurements of the scattering of pulsar radio emission

Measurements of the broadening of pulsar pulses by scattering in the interstellar medium are presented for a complete sample of 100 pulsars with Galactic longitudes from 6° to 311° and distances to three kiloparsec. The dependences of the scattering on the dispersion measure (τ _sc(DM) ∝ DM^α), frequency (τ _sc(v) ∝ v ^?γ ), Galactic longitude, and distance to the pulsar are analyzed. The dependence of the scattering on the dispersion measure in the near-solar neighbourhood can be represented by the power law τ _sc(DM) ∝ DM^2.2±0.1). Measurements at the low frequencies 111, 60, and 40 MHz and literature data are used to derive the frequency dependence of the scattering (τ _sc(v) ∝ V ^?γ ) over a wide frequency interval (covering a range of less than 10: 1) with no fewer than five frequencies. The index for the frequency dependence, γ = 4.1 ± 0.3, corresponds to a normal distribution for inhomogeneities in the turbulence in the scattering medium. Based on an analysis of the dependence of the scattering on the distance to the pulsar and on Galactic longitude, on average, the turbulence level C _n ² is the same in all directions and at all distances out to about three kpc, testifying to the statistical homogeneity of the turbulence of the scattering medium in the near-solar region of the Galaxy.     

Detection of radio emission from the AXP 4U 0142+61

The detection of pulsed radio emission from the X-ray pulsar AXP 4U 0142+61 with a period of P = 8.68832935(6) s and a period derivative of $ \dot P $ \dot P = 18.713(4) × 10⁻¹³ s/s is reported. The observations were carried out on two high-sensitivity radio telescopes of the Pushchino Radio Astronomy Observatory: the Large Phased Array at 111MHz and the DKR-1000 at 40MHz.Mean pulse profiles are presented; the measured flux density is S ₁₁₁ = 30 ± 20 mJy. The estimated distance derived from the dispersion measure, 27 pc/cm³, is 1.4 kpc, and the integrated radio luminosity is L _R = 1.5 × 10²⁷ erg/cm. Comparison with X-ray data shows an appreciable difference in the pulse duration (the radio pulse is about a factor of 20 more narrow) and strong variations in the flux density.     

Detection of radio recombination lines of hydrogen ionized by cosmic-ray protons in the cool interstellar medium

The emission of hydrogen radio recombination lines from a cloud of cool interstellar matter toward the radio source Cassiopeia A has been detected. The formation of the radio recombination lines is initiated by cosmic rays. The rate of ionization of the interstellar hydrogen by cosmic-ray protons measured from the radio recombination lines using the most direct method is ζ_H = (1 ± 0.25)×10⁻¹⁶ s⁻¹. This value of ζ_H is compared with measurements obtained using other methods.     

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 outer turbulence scale in the interstellar plasma

The structure function for phase fluctuations on spatial scales from 10⁶ to 10¹⁷ m is constructed using data on diffractive and refractive scintillation of pulsars, scattering angles, variations in pulse arrival times, and differences in dispersion measures observed for close pairs of pulsars in globular clusters. For distances R>1 kpc (a sample of pulsars with DM≥30 pc/cm³), the fluctuations in the interstellar electron density on scales from 10⁶ to 10¹⁴ m are well described by a Kolmogorov spectrum with index 11/3. Analysis of variations in the dispersion measures for close pairs of pulsars in globular clusters indicates an outer turbulence scale of L ₀=10¹⁵ m. The relative level of turbulent fluctuations is determined for the interstellar plasma, and the important role of turbulence in the energy balance is demonstrated.     

On the existence of planets around the pulsar PSR B0329+54

Results of timing measurements of the pulsar PSR B0329+54 obtained in 1968–2012 using the Big Scanning Antenna of the Pushchino Radio Astronomy Observatory (at 102 and 111 MHz), the DSS 13 and DSS 14 telescopes of the Jet Propulsion Laboratory (2388 MHz), and the 64 m telescope of the Kalyazin Radio Astronomy Observatory (610 MHz) are presented. The astrometric and rotational parameters of the pulsar are derived at a new epoch. Periodic variations in the barycentric timing residuals have been found, which can be explained by the presence of a planet orbiting the pulsar, with an orbital period P₁ = 27.8 yr, mass m _c sin i = 2M_?, and orbital semi-major axis a = 10.26 AU. The results of this study do not confirm existence of a proposed second planet with orbital period P₂ = 3 yr.     

Solubility of water in the α, β and γ phases of (Mg,Fe)2SiO4

 The solubility of hydroxyl in the α, β and γ phases of (Mg,Fe)₂SiO₄ was investigated by hydrothermally annealing single crystals of San Carlos olivine. Experiments were performed at a temperature of 1000° or 1100 °C under a confining pressure of 2.5 to 19.5 GPa in a multianvil apparatus with the oxygen fugacity buffered by the Ni:NiO solid-state reaction. Hydroxyl solubilities were determined from infrared spectra obtained of polished thin sections in crack-free regions ≤100 μm in diameter. In the α-stability field, hydroxyl solubility increases systematically with increasing confining pressure, reaching a value of ∼20,000 H/10⁶Si (1200 wt ppm H₂O) at the α-β phase boundary near 13 GPa and 1100 °C. In the β field, the hydroxyl content is ∼400,000 H/10⁶Si (24,000 wt ppm H₂O) at 14–15 GPa and 1100 °C. In the γ field, the solubility is ∼450,000 H/10⁶Si (27,000 wt ppm H₂O) at 19.5 GPa and 1100 °C. The observed dependence of hydroxyl solubility with increasing confining pressure in the α phase reflects an increase in water fugacity with increasing pressure moderated by a molar volume term associated with the incorporation of hydroxyl ions into the olivine structure. Combined with published results on the dependence of hydroxyl solubility on water fugacity, the present results for the α phase can be summarized by the relation C _OH = A(T)f nH₂Oexp(−PΔV/RT), where A(T) = 1.1 H/10⁶Si/MPa at 1100 °C, n = 1, and ΔV = 10.6×10^–6 m³/mol. These data demonstrate that the entire present-day water content of the upper mantle could be incorporated in the mineral olivine alone; therefore, a free hydrous fluid phase cannot be stable in those regions of the upper mantle with a normal concentration of hydrogen. Free hydrous fluids are restricted to special tectonic environments, such as the mantle wedge above a subduction zone. Received: 10 February 1995 / Accepted: 23 October 1995     

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.