Measurement of the inner turbulence scale of the interstellar plasma toward the pulsar PSR B2111+46

The pulsar PSR B2111+46 has been observed at 112 MHz, and a new approach to analyzing pulsar pulses scattered in turbulent interstellar plasma applied. This method is based on the dependence of the normalized energy in the trailing part of a pulse on the intrapulse time. Since the trailing edge of a pulse follow exponential law to high accuracy, the inner turbulence scale of the interstellar plasma exceeds the field coherence scale. The measured scattering parameter is τ _sc = 147 ± 1 ms. Analysis of the parameters of diffractive and refractive scintillations of the pulsar at 610 MHz together with the 112 MHz data shows that the spectrum of the interstellar plasma toward PSR B2111+46 is a piecewise power law: on scales of 10¹³–10¹⁴ cm, the exponent of the turbulence spectrum is n ≃ 4, whereas n = 3.5 on scales of 2 × 10⁸−10¹³ cm. The spectrum flattens with approach to the inner turbulence scale l: n = 3–3.2. The obtained inner turbulence scale is l = (3.5 ± 1.5) × 10⁷ cm. The distribution of the interstellar plasma toward the pulsar is close to statistically homogeneous. The local density (N _e = 0.4 cm⁻³) and filling factor (F = 0.04) of the interstellar plasma have been estimated. The similarity of N _e estimates obtained from the inner scale of the inhomogeneities and the ratio of the emission measure to the dispersion measure provides evidence that the inner turbulence scale corresponds to the ion inertial length.     

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.     

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.     

Giant pulses—The main component of the radio emission of the crab pulsar

The paper presents an analysis of dual-polarization observations of the Crab pulsar obtained on the 64-m Kalyazin radio telescope at 600 MHz with a time resolution of 250 ns. A lower limit for the intensities of giant pulses is estimated by assuming that the pulsar radio emission in the main pulse and interpulse consists entirely of giant radio pulses; this yields estimates of 100 and 35 Jy for the peak flux densities of giant pulses arising in the main pulse and interpulse, respectively. This assumes that the normal radio emission of the pulse occurs in the precursor pulse. In this case, the longitudes of the giant radio pulses relative to the profile of the normal radio emission turn out to be the same for the Crab pulsar and the millisecond pulsar B1937+21, namely, the giant pulses arise at the trailing edge of the profile of the normal radio emission. Analysis of the distribution of the degree of circular polarization for the giant pulses suggests that they can consist of a random mixture of nanopulses with 100% circular polarization of either sign, with, on average, hundreds of such nanopulses within a single giant pulse.     

Giant pulses of the Crab Nebula pulsar as an indicator of a strong electromagnetic wave

The spectra and visibility functions of giant pulses of the Crab Nebula pulsar derived from VLBI observations carried out through the “RadioAstron” project in 2015 are analyzed. Parameters of the scattering of the pulses in the interstellar medium are measured, namely, the scattering time and decorrelation bandwidth. A comparative analysis of the shapes of the spectra and visibility functions of giant pulses obtained in real observations and via modeling of their scattering is carried out. The results suggest the presence of short bursts (dt < 30 ns) in the structure of the giant pulses at 1668 MHz, whose brightness temperatures exceed 10³⁸ K. These pulses propagate in the pulsar magnetosphere in a strong electromagneticwave regime, leading to the generation of additional radiation perpendicular to the direction of propagation of the giant pulses. This radiation may be associated with anomalous components of the mean pulse profile observed at frequencies above 4 GHz.     

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.     

Giant pulses from the pulsar PSR B0950+08

Analysis of individual pulses of the pulsar B0950+08 at 112 MHz has shown that giant pulses with intensities exceeding the peak amplitude of the mean profile at these longitudes by two orders of magnitude are observed at the longitudes of all three components of the mean pulsar profile (the precursor and two-component main pulse). The maximum peak flux density of a recorded pulse is 15 240 Jy, and the energy of this pulse exceeds the mean pulse energy by a factor of 153. Strong but infrequent pulses at the longitude of the first component (precursor) can reach peak flux densities of 5750 Jy, exceeding the amplitude of the mean profile at this longitude by a factor of 490. It is shown that the emission at the precursor longitudes is virtually absent when giant pulses appear at the main-pulse longitudes, and vice versa: the presence of giant pulses at the precursor longitude results in the absence or considerable attenuation of the emission at other longitudes. The analysis shows that the cumulative probability function of the pulse peak flux densities has a piecewise power-law form. The power-law index for pulses with intensities exceeding 600 Jy appearing at the longitudes of the main pulse in the mean profile varies from n ₁ = ?1.25 ± 0.04 to n ₂ = ?1.84 ± 0.07. The obtained pulse energy distribution also has an inflection at E > 3000 Jy ms and a power-law form with the same index. The distribution of the pulse intensities at the precursor longitude was obtained, and forms a power law with index n = ?1.5 ± 0.1. The studied properties of the pulses at various longitudes of the mean profile are interpreted in the framework of induced scattering of the main-pulse emission by particles of ultrarelativistic, strongly magnetized plasma in the pulsar magnetosphere.     

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.     

The character of pulse delays during radio bursts in the pulsar B0943+10

Results of a new series of observations of the anomalous pulsar B0943+10 carried out on the Large Scanning Antenna and DKR-1000 radio telescope of the Pushchino Radio Astronomy Observatory at 112 and 62 MHz, respectively, are presented. Several hundred pulse-arrival times (PATs) obtained on various days in 2013–2016 that correspond to the burst (B) mode emission are analyzed. A method for establishing the many-hour pulse shift in the emission window from 3.5-minute fragments is proposed. The delay of the mean pulse relative to the pre-calculated value follows an exponential law with a relaxation time of about 47 minutes. The pulse delay grows by 6 ms during the five hours following the onset of a burst. The random scatter of the residual PAT deviations is comparable to the amplitude of the systematic variations in these times over the lifetime of the B mode. These observations show that the character of the pulse delay as a function of time is the same at 112 and 62 MHz.     

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.     

Results of three-frequency monitoring of giant pulses from the crab pulsar

We present the results of long-term, three-frequency monitoring of giant pulses from the Crab pulsar on the 64-m radio telescope in Kalyazin. The total monitoring time was 160 hours. The signal power was recorded simultaneously at 600, 1650, and 4850 MHz via direct sampling of the received signals in the total receiver bandwidth without any compensation for interstellar dispersion. In total, 1117 and 352 giant pulses were detected at 600 and 4850 MHz, respectively. The frequency band centered at 1650 MHz was contaminated by interference, and was used only to identify events found in other frequency bands. The cumulative energy distribution of the giant pulses follows a power law at 600 and 4850 MHz up to the highest energies. A deep modulation in the radio spectra of individual giant pulses was observed on both large (Δv/v ≈ 0.5) and small (Δv/v ≈ (2?4) × 10^?3) frequency scales. The simultaneous appearance of giant pulses at the interpulse longitudes at high (4850 MHz) and low (1650 and/or 600 MHz) frequencies testifies to their common origin, in spite of the observed differences in other parameters.     

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.     

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.     

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.     

A 12-Year Periodicity in the Pulse Arrival Times for the Pulsar PSR B0943+10

An analysis of observations obtained over 26 years beginning in 1992 have indicated the appearance of sinusoidal variations with a period of about 12 years in the residual deviations of the pulse arrival times (PATs) for the pulsar PSR B0943+10. This behavior in the PAT residuals could be due to the influence of a planet orbiting the pulsar. These observations were carried out on the Large Scanning Antenna of the Pushchino Radio Astronomy Observatory at 112 MHz.

     

New observations of anomalous X-ray pulsars at low frequencies

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

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.     

Probing cosmic plasma with giant pulses from the crab nebula pulsar

A review and comparative analysis of results from studies of the effects of scattering on the interstellar medium using giant pulses of the Crab Nebula pulsar (B0531+21) are presented. This analysis was based on eight epochs of Very Long Baseline Interferometry (VLBI) radio observations carried out as part of the scientific program of the Radio Astron mission during 2011–2015. The scintillation timescale t _scint and spectral index γ for the power-law energy distribution of the pulses were obtained for each observing epoch. The measured scintillation timescales are t _scint = 7.5?123 s at 1668 MHz and t _scint = 2.9 s at 327 MHz. The spectral indices are ?1.6...?2.5. The frequency and time characteristics of the scattering were measured using two independent methods: based on the decorrelation bandwidth Δν _d and the scattering timescale τ _SC. The angular size of the scattering disk θ _H of the pulsar was obtained, the phase structure functions constructed, and the distance to the effective scattering screen estimated. The derived diameter of the scattering disk θ _H at 1668 MHz ranges from 0.4 to 1.3 mas, while the scatteringdisk diameter at 327 MHz is 14.0 mas. The measured distance to the effective scattering screen ranges from 0.7 to 1.9 kpc, and varies from observation to observation in the same way as the scattering timescale and decorrelation bandwidth: τ _SC ≈ 0.9?5.8 μs and Δν _d ≈ 40.7?161 kHz at 1668 MHz. The scattering timescale and decorrelation bandwidth at 327 MHz are 2340 μs and 68 Hz.     

Distribution of inhomogeneities in the interstellar plasma in the directions of three distant pulsars from observations with the RadioAstron ground–space interferometer

The RadioAstron ground–space interferometer has been used to measure the angular sizes of the scattering disks of the three distant pulsars B1641–45, B1749–28, and B1933+16. The observations were carried out with the participation of the Westerbork Synthesis Radio Telescope; two 32-m telescopes at Torun, Poland and Svetloe, Russia (the latter being one antenna of the KVAZAR network); the Saint Croix VLBA antenna; the Arecibo radio telescope; the Parkes, Narrabri (ATCA), Mopra, Hobart, and Ceduna Australian radio telescopes; and the Hartebeesthoek radio telescope in South Africa. The full widths at half maximum of the scattering disks were 27 mas at 1668 MHz for B1641–45, 0.5 mas at 1668 MHz for B1749–28, and 12.3 at 316 MHz and 0.84 mas at 1668 MHz for B1933+16. The characteristic time scales for scatter-broadening of the pulses on inhomogeneities in the interstellar plasma τ_sc were also measured for these pulsars using various methods. Joint knowledge of the size of the scattering disk and the scatter-broadening time scale enables estimation of the distance to the effective scattering screen d. For B1641–45, d = 3.0 kpc for a distance to the pulsar D = 4.9 kpc, and for B1749–28, d = 0.95 kpc for D = 1.3 kpc. Observations of B1933+16 were carried out simultaneously at 316 and 1668 MHz. The positions of the screen derived using the measurements at the two frequencies agree: d ₁ = 2.6 and d ₂ = 2.7 kpc, for a distance to the pulsar of 3.7 kpc. Two screens were detected for this pulsar from an analysis of parabolic arcs in the secondary dynamic spectrum at 1668 MHz, at 1.3 and 3.1 kpc. The scattering screens for two of the pulsars are identified with real physical objects located along the lines of sight toward the pulsars: G339.1–04 (B1641–45) and G0.55–0.85 (B1749–28).     

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.