The Crab pulsar is a quite young famous pulsar which radiates multi-wavelength pulsed photons. The latest detection of GeV and TeV pulsed emission with unprecedented signal-to-noise ratio, supplied by the powerful telescopes: Fermi, MAGIC and VERITAS, challenges the current popular pulsar models, which can be a valuable discriminator to justify the pulsar high-energy-emission models.Our work is divided into two steps. First of all, taking reasonable parameters (the magnetic inclination angle α = 45 • and the view angle ζ = 63 • ), we use the latest high-energy data to calculate radio, X-ray, γ-ray and TeV light curves from a geometric view to obtain some crucial information on emission locations. Secondly, we calculate the phase-averaged spectrum and phase-resolved spectra for the Crab pulsar and take a theoretical justification from a physical view for the emission properies as found in the first step. It is found that a Gaussian emissivity distribution with the peak emission near the null charge surface in the so-called annular gap region gives the best modeled light curves. The pulsed emission of radio, X-ray, γ-ray and TeV are mainly generated from the emission of primary particles or secondary particles with different emission mechanisms in the nearly similar region of the annular gap located in the only one magnetic pole, which leads to the nearly "phasealigned" multi-wavelength light curves. The emission of peak 1 (P1) and peak 2 (P2) is originated from the annular gap region near the null charge surface, while the emission of bridge is mainly originated from the core gap region.The charged particles cannot corotate with the pulsar and escape from the magnetosphere, which determines the original flowing primary particles. The acceleration electric field and potential in the annular gap and core gap are huge enough in the several tens of neutron star radii. Thus the primary particles are accelerated to ultrarelativistic energies, and produce numerous secondary particles (pairs) in the inner region of the annular gap and core gap. We emphasize that there are mainly two types of pairs, i.e., one is curvature-radiation induced (CR-induced), and the other is inverse-Compton-scattering induced (ICS-induced). The phase-averaged spectrum and phase-resolved spectra from soft X-ray to TeV band are produced by four components: synchrotron radiation from CR-induced and ICS-induced pairs dominates the X-ray band to soft γ-ray band (100 eV to 10 MeV); curvature radiation and synchrotron radiation from the primary particles mainly contribute to γ-ray band (10 MeV to ∼ 20 GeV); ICS from the pairs significantly contributes to the TeV γ-ray band (∼ 20 GeV to 400 GeV).The multi-wavelength pulsed emission from the Crab pulsar can be well modeled with the annular gap and core gap model. To distinguish our single magnetic pole model from two-pole models, the convincing values of the magnetic inclination angle and the viewing angle will play a key role.

The Vela pulsar represents a distinct group of γ-ray pulsars. Fermi γ-ray observations reveal that it has two sharp peaks (P1 and P2) in the light curve with a phase separation of 0.42 and a third peak (P3) in the bridge. The location and intensity of P3 are energy-dependent. We use the 3D magnetospheric model for the annular gap and core gap to simulate the γ-ray light curves, phase-averaged and phase-resolved spectra. We found that the acceleration electric field along a field line in the annular gap region decreases with heights. The emission at high energy GeV band is originated from the curvature radiation of accelerated primary particles, while the synchrotron radiation from secondary particles have some contributions to low energy γ-ray band (0.1 − 0.3 GeV). The γ-ray light curve peaks P1 and P2 are generated in the annular gap region near the altitude of null charge surface, whereas P3 and the bridge emission is generated in the core gap region. The intensity and location of P3 at different energy bands depend on the emission altitudes. The radio emission from the Vela pulsar should be generated in a high-altitude narrow regions of the annular gap, which leads to a radio phase lag of ∼ 0.13 prior to the first γ-ray peak.

Pulsed high‐energy radiation from pulsars is not yet completely understood. In this paper, we use the 3D self‐consistent annular gap model to study light curves for both young and millisecond pulsars (MSPs) observed by the Fermi Gamma‐ray Space Telescope. The annular gap can generate high‐energy emission for short‐period pulsars. The annular gap regions are so large that they have enough electric potential drop to accelerate charged particles to produce γ‐ray photons. For young pulsars, the emission region is from the neutron star surface to about half of the light cylinder radius, and the peak emissivity is in the vicinity of the null charge surface. The emission region for the millisecond pulsars is located much lower than that of the young pulsars. The higher energy γ‐ray emission comes from higher altitudes in the magnetosphere. We present the simulated light curves for three young pulsars (the Crab, the Vela and the Geminga) and three millisecond pulsars (PSR J0030+0451, PSR J0218+4232 and PSR J0437−3715) using the annular gap model. Our simulations can reproduce the main properties of the observed light curves.

Based on our previous work, we deduce a general formula for pressure of degenerate and relativistic electrons, Pe, which is suitable for superhigh magnetic fields, discuss the quantization of Landau levels of electrons, and consider the quantum electrodynamic (QED) effects on the equations of states (EOSs) for different matter systems. The main conclusions are as follows: Pe is related to the magnetic field B, matter density ρ, and electron fraction Ye; the stronger the magnetic field, the higher the electron pressure becomes; the high electron pressure could be caused by high Fermi energy of electrons in a superhigh magnetic field; compared with a common radio pulsar, a magnetar could be a more compact oblate spheroid-like deformed neutron star (NS) due to the anisotropic total pressure; and an increase in the maximum mass of a magnetar is expected because of the positive contribution of the magnetic field energy to the EOS of the star.

Due to the lack of long term pulsed emission in quiescence and the strong timing noise, it is impossible to directly measure the braking index n of a magnetar. Based on the estimated ages of their potentially associated supernova remnants (SNRs), we estimate the values of the mean braking indices of eight magnetars with SNRs, and find that they cluster in a range of 1 ∼42. Five magnetars have smaller mean braking indices of 1 < n < 3, and we interpret them within a combination of magneto-dipole radiation and wind aided braking, while the larger mean braking indices of n > 3 for other three magnetars are attributed to the decay of external braking torque, which might be caused by magnetic field decay. We estimate the possible wind luminosities for the magnetars with 1 < n < 3, and the dipolar magnetic field decay rates for the magnetars with n > 3 within the updated magneto-thermal evolution models. Although the constrained range of the magnetars' braking indices is tentative, due to the uncertainties in the SNR ages, which come from distance uncertainties and the unknown conditions of the expanding shells, our method provides an effective way to constrain the magnetars' braking indices if the measurements of the SNRs' ages are reliable, which can be improved by future observations.

We have observed a glitch in the Crab pulsar (PSR B0531+21) in the 0.5–10 keV X-ray band with the X-Ray Pulsar Navigation-I (XPNAV-1) satellite. This glitch occurred around 2017 November 8. Observations at radio frequency by the Jodrell Bank observatory and the Lovell telescope have confirmed it to be the largest ever observed. We report the results of X-ray observation of this glitch. The measured rotation frequency increase of the Crab is Δν 0 = (14.3 ± 2.0) × 10−6 Hz, corresponding to a fractional increase of Δν 0/ν 0 = (0.48 ± 0.09) × 10−6. Two transient components in the rotation frequency change are detected: one is the short transient term of Δν n1 = 6.6 × 10−6 Hz with a timescale of 38.6 days and the other is the very short one of Δν n2 = −1.35 × 10−6 Hz with a timescale of 2.4 days. The step change in the rotation frequency derivative is determined to be Hz s−1. We also examine the relationship between the persistent offset and Δν 0, giving . No significant X-ray flux changes are observed pre- and post-glitch.

Pulsars have been recognized to be normal neutron stars, but sometimes have been argued to be quark stars. Submillisecond pulsars, if detected, would play an essential and important role in distinguishing quark stars from neutron stars. We focus on the formation of such submillisecond pulsars in this paper. A new approach to the formation of a submillisecond pulsar (quark star) by means of the accretion‐induced collapse (AIC) of a white dwarf is investigated. Under this AIC process, we found that: (i) almost all newborn quark stars could have an initial spin period of ∼0.1 ms; (ii) nascent quark stars (even with a low mass) have a sufficiently high spin‐down luminosity and satisfy the conditions for pair production and sparking process and appear as submillisecond radio pulsars; (iii) in most cases, the times of newborn quark stars in the phase with spin period <1 (or <0.5) ms are long enough for the stars to be detected. As a comparison, an accretion spin‐up process (for both neutron and quark stars) is also investigated. It is found that quark stars formed through the AIC process can have shorter periods (≤0.5 ms), whereas the periods of neutron stars formed in accretion spin‐up processes must be longer than 0.5 ms. Thus, if a pulsar with a period shorter than 0.5 ms is identified in the future, it could be a quark star.

Integrated pulse profiles at 8.6 GHz obtained with the Shanghai Tian Ma Radio Telescope (TMRT) are presented for a sample of 26 pulsars. Mean flux densities and pulse width parameters of these pulsars are estimated. For eleven pulsars these are the first high-frequency observations and for a further four, our observations have a better signal-to-noise ratio than previous observations. For one (PSRs J0742−2822) the 8.6 GHz profiles differs from previously observed profiles. A comparison of 19 profiles with those at other frequencies shows that in nine cases the separation between the outmost leading and trailing components decreases with frequency, roughly in agreement with radius-to-frequency mapping, whereas in the other ten the separation is nearly constant. Different