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...     

Recent glitches detected in the Crab pulsar

From 2000 to 2010, monitoring of radio emission from the Crab pulsar at Xinjiang Observatory detected a total of nine glitches. The occurrence of glitches appears to be a random process as described by previous researches. A persistent change in pulse frequency and pulse frequency derivative after each glitch was found. There is no obvious correlation between glitch sizes and the time since last glitch. For these glitches Δν _p and D[(n)\dot]_p\Delta\dot{\nu}_{p} span two orders of magnitude. The pulsar suffered the largest frequency jump ever seen on MJD 53067.1. The size of the glitch is ∼6.8×10⁻⁶ Hz, ∼3.5 times that of the glitch occurred in 1989 glitch, with a very large permanent changes in frequency and pulse frequency derivative and followed by a decay with time constant ∼21 days. The braking index presents significant changes. We attribute this variation to a varying particle wind strength which may be caused by glitch activities. We discuss the properties of detected glitches in Crab pulsar and compare them with glitches in the Vela pulsar.     

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.     

Crab pulsar spectrum: A non-extensive approach

Non extensive statistical physics has been applied to various problems in physics including astrophysics. In this paper we explore the possibility of using non-extensive approach to explain the recently observed pulsed γ-ray from Crab pulsar above 100 GeV observed by VERITAS γ-ray telescope.     

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.     

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).     

A hard X-ray telescope and its observation of the Crab pulsar

The hard X-ray phoswich telescope, HAPI-1, is described. It was designed for making observations on board high-flying balloons. The telescope comprises a 145 cm² primary crystal of 5 cm thick Cs I(T1), effectively shielded over the lower 2π steradians by a 5 cm thick NaI(T1) crystal and has a field of view of approximately 4° HWHM determined by a graded shield and a collimator. The scintillation pulses originating in CsI and NaI crystals are distinguished by pulse shape discrimination. All sub-systems of the telescope are described. The Crab pulsar was obsserved by HAPI-1 in a balloon flight on 1984 May 23 in the energy range 20 to 200 keV and the observed result is presented.     

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.     

A momentum distribution of high energy particles around Crab pulsar

We determine the momentum distribution of the relativistic particles near the Crab pulsar from the observed X- and -ray spectra (10³10⁹ eV), provided that the curvature radiation is responsible for it. The power law spectrum for the relativistic electrons,f() ^–5, reproduces a close fit to the observed high-energy photon spectrum. The theoretically determined upper limit to the momentum (due to radiation damping), _M 8×10⁶, corresponds to the upper cut-off energy of the -ray spectrum, 10⁹ eV. The lower limit to the momentum, _m 1.8×10⁵, is chosen such that flattening of the X-ray spectrum below 10 keV is simulated. The number density of these electrons is found to be much higher than the Goldreich-Julian density. We also discuss pulse shape and polarization of high-energy photons. The extremely high density of particles and the steep momentum spectrum are difficult to understand. This may imply that another, more efficient, mechanism is in operation.     

The secular variation of pulsar magnetic dipole moments

The time dependences of the inertia tensor and of a dissipative torque caused by the nonleptonic weak interaction have been investigated for a certain class of pulsars with no solid core. Early in the life of the pulsar, the angular velocity vector is predicted to move with respect to fixed body axes in such a way that it becomes perpendicular to the magnetic dipole moment. During this motion, the solid outer shell suffers plastic deformation so that the dipole moment becomes approximately collinear with a principal axis. After 10⁴ or 10⁵ yr, the dissipative torque is negligibly small compared with the electromagnetic torque, the Euler equations are those for a simple rigid body, and alignment of spin and dipole moment occurs. If the dipole moment discussed by Lyneet al. (1975) is interpreted as being equal to the component perpendicular to the spin, its secular decay is a natural property of this model and is not a consequence of field decay through electrical resistivity.     

Mechanisms of optical,X-ray andγ-radiation from Crab pulsar

The synchrotron mechanism of radiation from the Crab pulsar has been investigated on the assumption that the mechanism acts in a source moving with relativistic velocity round a neutron star. A detailed matching has been made of the theoretical spectra of synchrotron radiation from relativistic electrons with the results of measurements of the radiation flux from the Crab pulsar in the infrared, optical and X-ray ranges. The parameters of the radiating region (intensity of the magnetic field, source dimensions, density and lifetime of radiating electrons) have been found. They are expressed through the ratio of the energy density of the magnetic field in the source to that of radiating electrons. The level of Compton-radiation in this region is estimated. Possible values of at which the level will correspond to the available results of measurements of the-radiation flux from the Crab pulsar are given. An estimate is presented for the surface magnetic field of the neutron star which does not contradict those obtained from considerations of the magnetic flux conservation when compressing the object up to the neutron star dimensions.     

Short time scale pulse stability of the Crab pulsar in the optical band

The fine structure and the variations of the optical pulse shape and phase of the Crab pulsar are studied on various time scales. The observations have been carried out on 4-m William Hershel and 6-m BTA telescopes with APD photon counter, photomultiplier based 4-channel photometer and PSD based panoramic spectrophotopolarimeter with 1 μs time resolution in 1994, 1999, 2003 and 2005–2006 years. The upper limit on the pulsar precession on Dec 2, 1999 is placed in the 10 s–2 hr time range. The evidence of a varying from set to set fine structure of the main pulse is found in the 1999 and 2003 years data. No such fine structure is detected in the integral pulse shape of 1994, 1999 and 2003 years. The drastic change of the pulse shape in the 2005–2006 years set is detected along with the pulse shape variability and quasi-periodic phase shifts. This work has been supported by the Russian Foundation for Basic Research (grant No 04-02-17555), Russian Academy of Sciences (program “Evolution of Stars and Galaxies”), by the Russian Science Support Foundation, and by INTAS (grant No 04-78-7366).     

The role of multipolar magnetic fields in pulsar magnetospheres

We explore the role of complex multipolar magnetic fields in determining physical processes near the surface of rotation powered pulsars. We model the actual magnetic field as the sum of global dipolar and star-centred multipolar fields. In configurations involving axisymmetric and uniform multipolar fields, 'neutral points' and 'neutral lines' exist close to the stellar surface. Also, the curvature radii of magnetic field lines near the stellar surface can never be smaller than the stellar radius, even for very high-order multipoles. Consequently, such configurations are unable to provide an efficient pair-creation process above pulsar polar caps, necessary for plasma mechanisms of generation of pulsar radiation. In configurations involving axisymmetric and non-uniform multipoles, the periphery of the pulsar polar cap becomes fragmented into symmetrically distributed narrow subregions where curvature radii of complex magnetic field lines are less than the radius of the star. The pair-production process is only possible just above these 'favourable' subregions. As a result, the pair plasma flow is confined within narrow filaments regularly distributed around the margin of the open magnetic flux tube. Such a magnetic topology allows us to model the system of 20 isolated subbeams observed in PSR B0943+10 by Deshpande & Rankin. We suggest a physical mechanism for the generation of pulsar radio emission in the ensemble of finite subbeams, based on specific instabilities. We propose an explanation for the subpulse drift phenomenon observed in some long-period pulsars.     

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.     

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.     

Photon capture in pulsar magnetic fields

We investigate the process of photon capture by strong magnetic fields, by transforming it into a positronium, and the subsequent decay of the positronium into two photons. We discuss the implications of this process for the polar gap models of pulsars. We find that the capture process is energy-dependent and photons above a certain energy (depending on the magnetic field) are not captured and can decay into electron-positron pairs. This leads to increased gap heights in the modle and leads to higher luminosities than found earlier. We also find that it may be possible for very high-energy positronia to escape the magnetosphere of the pulsar and be observed near the Earth as photons in agreement with the recent observations of 10¹² eV gamma-rays from some pulsars.