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.
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