Polarization of the Crab Nebula with disordered magnetic components

In this paper, we present an expanding disc model to derive the polarization properties of the Crab nebula. The distribution function of the plasma and the energy density of the magnetic field are prescribed as functions of the distance from the pulsar using the model derived by Kennel and Coroniti with  σ= 0.003  , where σ is the ratio of the Poynting flux to the kinetic energy flux in the bulk motion just before the termination shock. Unlike the case for previous models, we introduce a disordered magnetic field, which is parametrized by the fractional energy density of the disordered component. The flow dynamics are not solved, and the mean field is toroidal.
The averaged degree of polarization over the disc is obtained as a function of the inclination angle and fractional energy density of the disordered magnetic field. It is found for the Crab Nebula that the disordered component contains about 60 per cent of the magnetic field energy. This value is supported by the facts that the disc appears not as 'lip-shaped' but as 'rings' in the observed intensity map, and that the highest degree of polarization of ∼40 per cent is reproduced for rings, which is consistent with the observations.
We suggest that, because the disordered field contributes to the pressure rather than to the tension, the pinch force may have been overestimated in previous relativistic magnetohydrodynamic simulations. The disruption of the oppositely directed magnetic fields, which is proposed by Lyuvarsky, may actually take place. The relativistic flow speed, which is indicated by the front–back contrast, can be detected in the asymmetry of distributions of the position angle and depolarization.     

On the structure of the inner Crab Nebula

Origin of the jet-like feature in the inner Crab Nebula is discussed. Because self-collimation processes in ultrarelativistic pulsar winds are extremely ineffective, it is suggested that the collimation occurs beyond the termination shock where the flow is already mildly (or non-) relativistic. It is argued that the shock shape is highly non-spherical because the energy flux in the pulsar wind decreases towards the axis. The shock near the axis should be much closer to the pulsar than at the equator and therefore the jet looks as if it originates directly from the pulsar.     

Crab脉冲星巨脉冲辐射等待时间分布的非稳态泊松模拟

利用中国科学院新疆天文台南山观测站26m射电望远镜, 在中心频率1556MHz, 对Crab脉冲星(PSR B0531+21)进行了长达12.6h的连续观测, 观测带宽为512MHz, 时间分辨率为32μs, 研究了巨脉冲辐射的等待时间分布特征. 观测共探测到2097个信噪比大于10的巨脉冲, 对应的流量密度大于100Jy. 巨脉冲的爆发率表现为高度的间歇性, 在较短的时间内具有较高的爆发率, 在相对长的宁静期内巨脉冲的爆发率较低, 尤其是中间脉冲相位内的巨脉冲爆发. 相邻两个巨脉冲的等待时间分布表现为幂律分布特征, 可以用一个非稳态的泊松过程进行模拟, 这表明巨脉冲的爆发是一种独立的随机事件. 此外, 主脉冲和中间脉冲相位上的巨脉冲具有不同的等待时间分布特征, 这意味着脉冲星不同磁极的巨脉冲辐射机制可能是不同的. 这些观测结果对于理解脉冲星的射电辐射机制具有重要意义.     

Observations of Giant Pulses of the Crab Pulsar

The Crab Pulsar was observed at 1540 MHz with the 25m radio telescope at Urumqi with a filterbank de-dispersion backend. A total of 2436 giant pulses with pulse energies larger than 4300 Jy μs were detected in two observing sets. All of these giant pulses are located in the main pulse (MP) and inter pulse (IP) windows of the average profile of the Crab Pulsar. The ratio of the numbers of giant pulses detected in the IP and MP windows is about 0.05. Our results show that, at 1540 MHz, the emission in the IP is contributed by giant and normal pulses, while that in the MP is almost dominated by giant pulses. The distribution of energy of the 2436 giant pulses at 1540 MHz can be described by a power-law with index α=3.13±0.09. The intrinsic threshold of giant pulse energy in the MP window is about 1400 Jy μs at 1540 MHz.     

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.     

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.     

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.     

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.     

A Large Glitch in the Crab Pulsar

1 INTRODUCTIONA pulsar glitch is a phenomenon in which the pulse frequency has a sudden increase, typicallywith a fractional ~litude an/u in the range of 10--8 -- 10--6. Glitches are Unpredictable butoccur at intervals of a few y6ars in many young pulsars. Coincident with the glitch, there is oftenan increajse in the magnitude of the frequency derivative followed by thlee types of recovery:almost no recoveryt partial recovery and total recovery on timescales from days to years. It isbelie…     

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...     

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.     

On the X-ray image of the Crab nebula: comparison with Chandra observations

An axisymmetric model for the Crab nebula is constructed to examine the flow dynamics in the nebula. The model is based on that of Kennel & Coroniti, although we assume that the kinetic-energy-dominant wind is confined to an equatorial region. The evolution of the distribution function of the electron–positron plasma flowing out in the nebula is calculated. Given viewing angles, we reproduce an image of the nebula and compare it with the Chandra observation.
The reproduced image is not ring-like, but is rather 'lip-shaped'. It is found that the assumption of a toroidal field does not reproduce the Chandra image. We must assume that there is a disordered magnetic field with an amplitude as large as the mean toroidal field. In addition, the brightness contrast between the front and back sides of the ring cannot be reproduced if we assume that the magnetization parameter σ is as small as ∼10⁻³. The brightness profile along the semimajor axis of the torus is also examined. The non-dissipative, ideal-magnetohydrodynamic approximation in the nebula appears to break down.
We speculate that if the magnetic energy is released by some process that produces a turbulent field in the nebula flow and causes heating and acceleration – for example, by magnetic reconnection – then the present difficulties may be resolved (i.e. we can reproduce a ring image and a higher brightness contrast). Thus, the magnetization parameter σ can be larger than previously expected.     

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.     

Wisps and knots in the central Crab nebula

The fast-spinning Crab pulsar (∼30 turn s⁻¹), which powers the massive expansion and synchrotron emission of the entire Crab nebula, is surrounded by quasi-stationary features such as fibrous arc-like wisps and bright polar knots in the radial range of 2×10¹⁶≲ r ≲2×10¹⁷ cm, as revealed by high-resolution (∼0.1 arcsec) images from the Wide Field and Planetary Camera 2 (WFPC2) on board the Hubble Space Telescope ( HST ). The spin-down energy flux (∼5×10³⁸ erg s⁻¹) from the pulsar to the luminous outer nebula, which occupies the radial range 0.1≲ r ≲2 pc, is generally believed to be transported by a magnetized relativistic outflow of an electron–positron e^± pair plasma. It is then puzzling that mysterious structures like wisps and knots, although intrinsically dynamic in synchrotron emission, remain quasi-stationary on time-scales of a few days to a week in the relativistic pulsar wind. Here we demonstrate that, as a result of slightly inhomogeneous wind streams emanating from the rotating pulsar, fast magnetohydrodynamic (MHD) shock waves are expected to appear in the pulsar wind at relevant radial distances in the forms of wisps and knots. While forward fast MHD shocks move outward with a speed close to the speed of light c , reverse fast MHD shocks may appear quasi-stationary in space under appropriate conditions. In addition, Alfvénic fluctuations in the shocked magnetized pulsar wind can effectively scatter synchrotron beams from gyrating relativistic electrons and positrons.     

Statistical studies of pulsar glitches

Shemar & Lyne have previously presented observations and an analysis of 32 glitches and their subsequent relaxations observed in a total of 15 pulsars. These data are brought together in this paper with those published by other authors. We show quantitatively how glitch activity decreases linearly with decreasing rate of slow-down. As indicated previously from studies of the Vela pulsar, the analysis suggests that 1.7 per cent of the moment of inertia of a typical neutron star is normally contained in pinned superfluid which releases its excess angular momentum at the time of a glitch. There is a broad range of glitch amplitude and there is a strong indication that pulsars with large magnetic fields suffer many small glitches while others show a smaller number of large glitches. Transient effects following glitches are very marked in young pulsars and decrease linearly with decreasing rate of slow-down, suggesting that the amount of loosely pinned superfluid decreases with age. We suggest that the low braking index of the Vela and Crab pulsars cannot be caused by a decreasing moment of inertia and should be attributed to step increases in the effective magnetic moment of the neutron star at the glitches.