Mechanism of generation of the emission bands in the dynamic spectrum of the Crab pulsar

We show that the proportionately spaced emission bands in the dynamic spectrum of the Crab pulsar fit the oscillations of the square of a Bessel function whose argument exceeds its order. This function has already been encountered in the analysis of the emission from a polarization current with a superluminal distribution pattern: a current whose distribution pattern rotates (with an angular frequency ω) and oscillates (with a frequency  Ω > ω  differing from an integral multiple of ω) at the same time. Using the results of our earlier analysis, we find that the dependence on frequency of the spacing and width of the observed emission bands can be quantitatively accounted for by an appropriate choice of the value of the single free parameter  Ω/ω  . In addition, the value of this parameter, thus implied by Hankins & Eilek's data, places the last peak in the amplitude of the oscillating Bessel function in question at a frequency  (∼Ω³/ω²)  that agrees with the position of the observed ultraviolet peak in the spectrum of the Crab pulsar. We also show how the suppression of the emission bands by the interference of the contributions from differing polarizations can account for the differences in the time and frequency signatures of the interpulse and the main pulse in the Crab pulsar. Finally, we put the emission bands in the context of the observed continuum spectrum of the Crab pulsar by fitting this broad-band spectrum (over 16 orders of magnitude of frequency) with that generated by an electric current with a superluminally rotating distribution pattern.     

Formation of the radio profile components of the Crab pulsar

The induced Compton scattering of radio emission off the particles of the ultrarelativistic electron–positron plasma in the open field line tube of a pulsar is considered. We examine the scattering of a bright narrow radio beam into the background over a wide solid angle and specifically study the scattering in the transverse regime, which holds in a moderately strong magnetic field and gives rise to the scattered component nearly antiparallel to the streaming velocity of the scattering particles. Making use of the angular distribution of the scattered intensity and taking into account the effect of rotational aberration in the scattering region, we simulate the profiles of the backscattered components as applied to the Crab pulsar. It is suggested that the interpulse (IP), the high-frequency interpulse (IP') and the pair of so-called high-frequency components (HFC1 and HFC2) result from the backward scattering of the main pulse (MP), precursor (PR) and low-frequency component (LFC), respectively. The components of the high-frequency profiles, the IP' and HFCs, are interpreted for the first time. The HFC1 and HFC2 are argued to be a single component split by the rotational aberration close to the light cylinder. It is demonstrated that the observed spectral and polarization properties of the profile components of the Crab pulsar as well as the giant pulse phenomenon outside the MP can be explained in terms of our model.     

Very-high-energy gamma radiation associated with the unshocked wind of the Crab pulsar

We show that the relativistic wind of the Crab pulsar, which is commonly thought to be invisible in the region upstream of the termination shock at r r _S∼0.1 pc, in fact could be directly observed through its inverse Compton (IC) γ -ray emission. This radiation is caused by illumination of the wind by low-frequency photons emitted by the pulsar, and consists of two, pulsed and unpulsed , components associated with the non-thermal (pulsed) and thermal (unpulsed) low-energy radiation of the pulsar, respectively. These two components of γ -radiation have distinct spectral characteristics, which depend essentially on the site of formation of the kinetic-energy-dominated wind, as well as on the Lorentz factor and the geometry of propagation of the wind. Thus, the search for such specific radiation components in the spectrum of the Crab Nebula can provide unique information about the unshocked pulsar wind that is not accessible at other wavelengths. In particular, we show that the comparison of the calculated flux of the unpulsed IC emission with the measured γ -ray flux of the Crab Nebula excludes the possibility of formation of a kinetic-energy-dominated wind within 5 light-cylinder radii of the pulsar, R _w5 R _L. The analysis of the pulsed IC emission, calculated under reasonable assumptions concerning the production site and angular distribution of the optical pulsed radiation, yields even tighter restrictions, namely R _w30 R _L.     

国家授时中心40米射电望远镜Crab脉冲星周期跃变监测

脉冲星周期跃变是一种罕见的现象,是研究其内部结构的探针。针对2019年2月~12月国家授时中心昊平观测站40 m射电望远镜在脉冲星计时观测中监测Crab脉冲星的数据,采用脉冲星计时方法,用TEMPO2拟合程序进行分析。结果表明,Crab脉冲星在2019年7月23日(MJD 58687)附近发生了一次周期跃变现象,该跃变自转增量为Δv_g=5.33(4)×10^-7Hz,自转变化量为Δv_g/v=17.9(1)×10^-9,并伴随着恢复系数Q~0.88的指数恢复过程。此次Crab脉冲星周期跃变的监测及处理,证实了40 m射电望远镜对脉冲星的监测性能,同时为研究周期跃变的产生机理积累了样本。     

Optical polarization of the Crab pulsar: precision measurements and comparison to the radio emission

The linear polarization of the Crab pulsar and its close environment was derived from observations with the high-speed photopolarimeter Optical Pulsar TIMing Analyser at the 2.56-m Nordic Optical Telescope in the optical spectral range (400–750 nm). Time resolution as short as 11 μs, which corresponds to a phase interval of 1/3000 of the pulsar rotation, and high statistics allow the derivation of polarization details never achieved before. The degree of optical polarization and the position angle correlate in surprising details with the light curves at optical wavelengths and at radio frequencies of 610 and 1400 MHz. Our observations show that there exists a subtle connection between presumed non-coherent (optical) and coherent (radio) emissions. This finding supports previously detected correlations between the optical intensity of the Crab and the occurrence of giant radio pulses. Interpretation of our observations requires more elaborate theoretical models than those currently available in the literature.     

Insight-HXMT observations of the Crab pulsar

We report on X-ray emission properties of the Crab pulsar(PSR B0531+21) using observations by Insight-HXMT during its first year after launch. We obtained high signal-to-noise profiles in the X-ray energy band 11–250 keV. We have confirmed an increase in the flux ratio of the second peak over the main peak with increasing energy, consistent with other missions. The separation of the two peaks shows no significant trend with increasing energy. The phase-averaged spectrum, fitted by a logpar model, and the phase-resolved spectra of the Crab pulsar, fitted by a powerlaw in the different energy bands of HXMT, are consistent with RXTE and NuSTAR in that photon indices evolve as a function of phase as well as a function of energy, contributing to a broadband modeling.     

Pulse profile stability of the Crab pulsar

We present an X-ray timing analysis of the Crab pulsar, PSR B0531+21, using archival RXTE data. We have investigated the stability of the Crab pulse profile, in soft (2-20 keV) and hard (30-100 keV) X-ray energies, over the last decade of RXTE operation. The analysis includes measurement of the separation between the two pulse peaks and the intensity and widths of the two peaks. We did not find any significant time dependency in the pulse shape. The two peaks have been stable in phase, intensity and width f...     

Frequency dependence of the scattering pulse broadening for the Crab pulsar

We measured the frequency dependence of the pulsar pulse broadening by scattering over a wide frequency range, from 40 to 2228 MHz, based on direct measurements of this parameter using giant pulses from the pulsar PSR B0531+21 in the Crab Nebula. Our measurements were carried out at the following seven frequencies: 40, 60, and 111 MHz at the Pushchino Radio Astronomy Observatory (Astrospace Center, Lebedev Physical Institute, Russian Academy of Sciences), 406 MHz at the Medicina Observatory (Instituto di Radioastronomia, Italy), and 594, 1430, and 2228 MHz at the Kalyazin Radio Astronomy Observatory (Astrospace Center, Lebedev Physical Institute, Russian Academy of Sciences). The measured frequency dependence of the pulse broadening by scattering τ_SC (υ) ? υ^γ, where γ=?3.8±0.2, agrees with a model Gaussian distribution of interstellar inhomogeneities (γ=?4) but falls outside the error limits of correspondence to a Kolmogorov model spectrum of inhomogeneities (γ=?4.4).     

The possible role of r-modes in post-glitch relaxation of the Crab pulsar

The loss of angular momentum through gravitational radiation, driven by the excitation of r-modes, is considered for neutron stars that have rotation frequencies lower than the associated critical frequency. We find that for reasonable values of the initial amplitudes of such pulsation modes of the star, being excited at the event of a glitch in a pulsar, the total post-glitch losses correspond to a negligible fraction of the initial rise of the spin frequency in the case of Vela and older pulsars. However, for the Crab pulsar the same effect would result, within a few months, in a decrease in its spin frequency by an amount larger than its glitch-induced frequency increase. This could provide an explanation for the peculiar behaviour observed in the post-glitch relaxations of the Crab pulsar.     

Probing pulsar winds using inverse Compton scattering

We investigate the effects of inverse Compton scattering by electrons and positrons in the unshocked winds of rotationally-powered binary pulsars. This process can scatter low energy target photons to produce gamma rays with energies from MeV to TeV. The binary radio pulsars PSR B1259−63 and PSR J0045−73 are both in close eccentric orbits around bright main sequence stars which provide a huge density of low energy target photons. The inverse Compton scattering process transfers momentum from the pulsar wind to the scattered photons, and therefore provides a drag which tends to decelerate the pulsar wind. We present detailed calculations of the dynamics of a pulsar wind which is undergoing inverse Compton scattering, showing that the deceleration of the wind of PSR B1259−63 due to ‘inverse Compton drag' is small, but that this process may confine the wind of PSR J0045−73 before it attains pressure balance with the outflow of its companion star. We calculate the spectra and light curves of the resulting inverse Compton emission from PSR B1259−63 and show that if the size of the pulsar wind nebula is comparable to the binary separation, then the γ-ray emission from the unshocked wind may be detectable by atmospheric Cherenkov detectors or by the new generation of satellite-borne γ-ray detectors such as INTEGRAL and GLAST. This mechanism may therefore provide a direct probe of the freely-expanding regions of pulsar winds, previously thought to be invisible.     

Relationship between the nonstationary radio-luminosity variations of the Crab Nebula and the activity of its pulsar

Based on the half-century-long history of radio observations of the Crab Nebula, we investigate the evolution of its radio luminosity. We found a secular decrease in the radio luminosity; it has decreased by 9% since the discovery of the radio source in 1948. Apart from the secular decrease in the luminosity of the Crab Nebula, we identified two time intervals, 1981–1987 and 1992–1998, when radio bursts with energy release ～10⁴¹ erg took place. In these years, the spectral indices of the instantaneous spectra decreased significantly due to the increase in the flux densities at short (centimeter and millimeter) wavelengths. These events were preceded by sudden increases in the pulsar’s rotation rates, the largest of which, with an amplitude of ΔΩ/Ω = 3 × 10^?8, occurred in 1975 and 1989. We show that the magnetospheric instability mechanism that accompanies strong glitches can provide the energetics of the excess luminosity of the Nebula through the ejection of relativistic electrons with a total energy higher than 6 × 10⁴² erg from the pulsar’s magnetosphere.     

Very high energy gamma rays from the crab pulsar

The Ooty data on VHE (> 600 GeV) γ-rays from the Crab pulsar have been used to look at possible emission on three different timescales,viz. years, minutes and hours. When averaged over three years of observation, there is no significant time-averaged emission. But interesting aspects are revealed when the data are subdivided into miniruns of one-minute duration. Minutes with moderate γ-ray activity were isolated with a κ² analysis. The summed phasogram of such minutes shows two strong peaks coinciding with the radio main pulse and the interpulse respectively. The probability that these are due to chance is small. The phasogram has a bimodal distribution which indicates some emission from the middle region between the two phases. In general, there is no significant emission on the timescale of a few hours. However, the main pulse, as well as the bimodal distribution, were seen also in the total data of two nights of simultaneous observation at two sites during 1984–1985.     

The integrated optical spectrum of the Crab nebula and evidence for its fading synchrotron continuum

A flux-calibrated optical spectrum integrated over the entire Crab nebula was obtained by making drift scans with a long-slit spectrograph. Compared to observations obtained over the past 40 years, these new data confirm an earlier controversial result that the [O iii ]  λλ4959, 5007  equivalent width is increasing with time, although the rate of ∼0.9 per cent yr⁻¹ is somewhat slower than that measured previously. Additionally, the Hβ equivalent width is increasing at a comparable rate, but the measured fluxes of both Hβ and [O  iii ] have changed less than their respective equivalent widths. The different rates of change in the measured fluxes and equivalent widths of these lines suggest that the optical synchrotron continuum from the Crab nebula is indeed fading rapidly. The apparent decline is consistent with a rate around  −0.5 (±0.2)  per cent yr⁻¹ at wavelengths near 5000  Å inferred independently from measurements of the optical continuum flux during the same time period.     

A new look at pulsar statistics — Birthrate and evidence for injection

We make a statistical analysis of the periodsP and period-derivativesP of pulsars using a model independent theory of pulsar flow in theP-P diagram. Using the available sample ofP andP values, we estimate the current of pulsars flowing unidirectionally along theP-axis, which is related to the pulsar birthrate. Because of radio luminosity selection effects, the observed pulsar sample is biased towards lowP and highP. We allow for this by weighting each pulsar by a suitable scale factor. We obtain the number of pulsars in our galaxy to be 6.05_−2.80 ^+3.32 × 10⁵ and the birthrate to be 0.048_−0.011 ^+0.014 pulsars yr⁻¹ galaxy⁻¹. The quoted errors refer to 95 per cent confidence limits corresponding to fluctuations arising from sampling, but make no allowance for other systematic and random errors which could be substantial. The birthrate estimated here is consistent with the supernova rate. We further conclude that a large majority of pulsars make their first appearance at periods greater than 0.5 s. This ‘injection’, which runs counter to present thinking, is probably connected with the physics of pulsar radio emission. Using a variant of our theory, where we compute the current as a function of pulsar ‘age’ (1/2P/P), we find support for the dipole braking model of pulsar evolution upto 6 × 10⁶ yr of age. We estimate the mean pulsar braking index to be 3.7_−0.8 ^+0.8.     

空间硬X射线望远镜HAPI-1及其对蟹状星云脉冲星的观测

HAPI-1是我国第一个用于空间高能天文观测的硬X射线望远镜系统,由面积145cm~2厚0.5cm的CsI(T1)主探测晶体及其下部厚5cm的NaI(T1)反符合晶体构成复合晶体探测器,采用脉冲形状甄别技术区分两种晶体的输出信号,多种物质构成的夹层式屏蔽筒和准直器使望远镜具有约4°视场角(HWHM),电子学、姿态控制和数据获取系统使望远镜具有对20—200keV能区高能光子到达时刻和能量进行空间定向观测的能力。本文介绍HAPI-1的构成和主要性能,以及1984年5月利用该望远镜在我国高空科学气球上对蟹状星云脉冲星的观测结果。     

A short review of the pulsar magnetic inclination angles (II)

The pulsar magnetic inclination angle is a key parameter for pulsar physics. It influences the observable properties of pulsars, such as the pulse beam width, braking index, polarization, and emission geometry. In this study, we give a brief overview of the current state of knowledge and research on this parameter and its implications for the internal physics of pulsars. We use the observed pulsar data of magnetic inclination angle and braking index to constrain the star's number of precession cycles, $\xi$, which reflects the interaction between superfluid neutrons and other particles inside a neutron star (NS). We apply the method proposed by Cheng et al. (Cheng, Q., Zhang, S. N., Zheng, X. P., & Fan, X. L., 2019, Phys. Rev. D, 99, 083011) to analyze the data of PSR J2013 + 3845 and obtain the constraints for $\xi$ ranging from $2.393\times 10^5$ to $1.268\times 10^6$. And further analysis suggests that the internal magnetic field structure of PSR J2013 + 3845 is likely dominated by toroidal components. This study may help us understand the process of internal viscous dissipation and the related evolution of the inclination angles of pulsars, and may have important implications for the study of continuous gravitational wave emissions from NS.     

The major upgrade of the MAGIC telescopes,Part II: A performance study using observations of the Crab Nebula

MAGIC is a system of two Imaging Atmospheric Cherenkov Telescopes located in the Canary island of La Palma, Spain. During summer 2011 and 2012 it underwent a series of upgrades, involving the exchange of the MAGIC-I camera and its trigger system, as well as the upgrade of the readout system of both telescopes. We use observations of the Crab Nebula taken at low and medium zenith angles to assess the key performance parameters of the MAGIC stereo system. For low zenith angle observations, the standard trigger threshold of the MAGIC telescopes is ∼ 50  GeV. The integral sensitivity for point-like sources with Crab Nebula-like spectrum above 220 GeV is (0.66 ± 0.03)% of Crab Nebula flux in 50 h of observations. The angular resolution, defined as the σ of a 2-dimensional Gaussian distribution, at those energies is ≲ 0.07°, while the energy resolution is 16%. We also re-evaluate the effect of the systematic uncertainty on the data taken with the MAGIC telescopes after the upgrade. We estimate that the systematic uncertainties can be divided in the following components: < 15% in energy scale, 11%–18% in flux normalization and ± 0.15 for the energy spectrum power-law slope.