We reexamine the outer-gap size by taking the geometry of the dipole magnetic field into account. Furthermore, we also consider that instead of taking the gap size at half of the light cylinder radius to represent the entire outer gap, it is more appropriate to average the entire outer-gap size over the distance. When these two factors are considered, the derived outer-gap size ƒ （P, B,〈r〉（α）） is a function not only of the period P and magnetic field B of the neutron star but also of the average radial distance to the neutron star, 〈r〉, which depends on the magnetic inclination angle α We use this new outer-gap model to study the γ-ray luminosity of pulsars, which is given by Lγ= ƒ3(P, B, 〈r〉(α))Lsd, where Lsd is the pulsar spin-down power, and to study the death lines of γ-ray emission of the pulsars. Our model can predict the γ-ray luminosity of an individual pulsar if its P, B, and α are known. Since different pulsars have different α, this explains why some γ-ray pulsars We have very similar P and B but very different γ-ray luminosities. In determining the death line of γ-ray pulsars, we have used a new criterion based on a concrete physical property, i.e., that the fractional size of the outer gap at the null-charge surface for a given pulsar cannot be larger than unity. In an estimate of the fractional size of the outer gap, two possible X-ray fields are considered: (1) X-rays produced by neutron star cooling and polar-cap heating, and (2) X-rays produced by the bombardment of relativistic particles from the outer gap onto the stellar surface (the outer gap is called a "self-sustained outer gap"). Since it is very difficult to measure α in general, we use a Monte Carlo method to simulate the properties of γ-ray pulsars in our Galaxy. We find that this new outer-gap model predicts many more weak γ-ray pulsars, which have a typical age between 0.3 and 3 Myr, than does the old model. For all simulated γ-ray pulsars with self-sustained outer gaps, the γ-ray luminosity Lγ satisfies Lγ ∝ Lδsd, where the value of δ depends on the sensitivity of the γ-ray detector. For EGRET, δ～0.38, whereas δ～0.46 for GLAST. For γ-ray pulsars with Lsd≤Lcrit sd, δ～1, and, Lcrit sd=1.5×10 34P1/3 ergs s-1 is determined by ƒ (〈r〉～rL)=1. These results are roughly consistent with the observed luminosity of γ-ray pulsars. These predictions are very different from those of the previous outer-gap model, which predicts a very flat relation between Lγ and Lsd.

We present a self-consistent model to describe X-ray and γ-ray emission from millisecond pulsars (MSPs). The X-rays of MSPs are produced by the backflow of primary charged particles from the outer gap and most likely consist of three components, two thermal components and one power law component if there is a strong multipole magnetic field on the stellar surface. The backflow of ultra-relativistic particles emits photons with energies about several tens of GeV via curvature radiation. These photons cause an electromagnetic cascade about 2-3 stellar radii above the polar cap. The synchrotron radiation of these cascade e± pairs produces hard X-rays with a power law index～1.5. Near 10 5cm above the stellar surface, the primary charged particles encounter the strong surface magnetic field, which alters the local radius of curvature greatly, and they quickly loose more than half of their remaining energies to curvature radiation. These curvature photons heat up the polar cap area with a radius～10 5cm, which produce the softer thermal X-ray component. Finally, the primary charged particles deposit their remaining energies in a much smaller polar cap area, which corresponds to the footprints of outer gap and produce the medium hard X-ray component. γ-rays are produced in the outer gap through synchro-curvature radiation. We have applied this model to the MSPs which emit pulsed X-rays and likely γ-rays such as PSR J0437-4715, PSR J2124-3358, PSR J0218+4232 and PSR B1821-24. Our results give an agreement between predicted spectrum and the observed spectrum of MSP emission.

We present a model for the high-energy γ-ray emission from the outer gap of soft gamma-ray repeaters (SGRs) during their quiescent states. In this model, X-rays come from the stellar surface, but the emerging X-ray spectrum will have a power-law tail because of the multiple scattering at the cyclotron resonance in the magnetosphere, as pointed out by Thompson, Lyukitov, & Kulkarni. The outer gap is sustained by the collision between these X-rays with the high-energy photons produced in the outer gap through the photonphoton pair production.We have taken a magnetic dipole geometry into account in estimating the fractional size of the outer gap. The fractional size of the outer gap depends on the period, surface magnetic field, average X-ray energy, and the magnetic inclination angle of the neutron star. After the average fractional size outer gap is determined, the spectrum and luminosity of high-energy photons from the outer gap can be calculated.We apply this model to some SGRs, such as SGR 1806-20 and SGR 1900+14, and compare the expected integral fluxes with the sensitivities of EGRET, GLAST, MAGIC, and VERITAS.We predict that the integral flux of SGR 1900+14 may be greater than the sensitivity of GLAST, and especially that the integral flux for a large magnetic inclination angle (say 80°) may be greater than the sensitivities of GLAST and MAGIC. However, we predict that SGR 1806-20 would not be detected by GLAST because its distance is about 3 times of that of SGR 1900+14.

We present a theoretical study of phase-dependent X-ray emission from the Crab pulsar. In the threedimensional outer gap model for the Crab pulsar, X-ray emission is produced by synchrotron radiation of the secondary e

We present a calculation of a three-dimensional pulsar magnetosphere model to explain high-energy emission from the Geminga pulsar with a thick outer gap. High-energy γ-rays are produced by primary accelerated particles with a power-law energy distribution through curvature radiation inside the outer gap. We also calculate the emission pattern, pulse profile and phase-resolved spectra of high-energy γ-rays of the Geminga pulsar, and find that its pulse profile is consistent with the observed one if the magnetic inclination and viewing angle are～50° and～86° respectively. We describe the relative phases among soft (thermal) X-rays, hard (non-thermal) X-rays, and γ-rays. Our results indicate that X-ray and γ-ray emission from the Geminga pulsar may be explained by the single thick outer gap model Finally, we discuss the implications of the radio and optical emission of the Geminga pulsar.

We consider a possible contribution of mature γ-ray pulsars (with ages of ≥10 5 yrs) to cosmic ray positrons. Within the framework of the γ-ray pulsar outer gap model, e±pairs in the pulsar magnetosphere are produced by the cascade of e±pairs through synchrotron radiation of the return current from the outer gap. A good fraction of these cascade e±pairs are reflected by the hard X-rays from the polar cap via resonant scattering and escape from the pulsar through the light cylinder. The escaped pairs are accelerated to relativistic energies in the pulsar wind driven by low-frequency electromagnetic waves. Using Monte Carlo simulations, we generate a sample of the mature γ-ray pulsars in our Galaxy and calculate the positron production rate from these pulsars. In a simple "leaky box" model, we calculate the ratio of cosmic-ray positrons to total electrons. Our result indicates that the pulsar contribution to the cosmic ray positrons peaks at about 60GeV and the observed e+/(e−+ e+) ratio can be explained in this model.

We present a statistical study on possible association between the unidentified γ-ray point sources at the Galactic (|b|≤5°) and the Galactic young pulsars with ages of less than 10 6 yr. Based on the possible positional coincidence of the unidentified EGRET sources in the third catalog with the Galactic objects given by Romero et al. (1999) as well as the outer gap model of γ-ray pulsars proposed by Zhang & Cheng (1997), we have made a statistical analysis on whether most unidentified EGRET point sources in the Galactic plane have pulsar origin. In our analysis, we use an evolving γ-ray solid angle which is the function of pulsar's parameters such as period, magnetic field and magnetic inclination angle. The simulated distributions of the distance and γ-ray energy flux are compared to observed data using Kolmogorov-Smirnov (KS) test. Our results suggest that young pulsars may account for the majority of unidentified EGRET sources that are positionally associated with supernova remnants and OB star associations, in such a way that two thirds are young radio quiet pulsars and one third are young radio pulsars.We have studied the variability of these unidentified γ-ray sources and found that most of them may be non-variable. Furthermore, we expect that GLAST may detect～80 100 radio pulsars and～1100 100 unidentified γ-ray point sources in the Galactic plane with |b|≤5°, where 100 is the birth rate of neutron stars in units of 100 years. This model predicts that γ-ray point sources located at small distances are more than those predicted by aγ-ray pulsar model with a constant beaming solid angle.

We study statistical properties of the Galactic population of X-ray pulsars with ages of less than 10 6 yr using the Monte Carlo method. Combining the initial magnetic

We use a new self-consistent model to derive the conversion efficiency from rotation power to γ-ray power for pulsars (ηth). Our result indicates that ηth; ∝τ6/7P2, where τ and P are the characteristic age and period of the pulsar, which shows that although the efficiency increases with the characteristic age of the pulsar, it also depends on the pulsar period. We test our model results with the survey of high-energy γ-rays from pulsars by EGRET. Our model not only successfully explains the efficiency of the confirmed γ-ray pulsars but also explains why the γ-ray efficiency of millisecond pulsars is so low.

We propose a self-consistent mechanism to estimate the size of the acceleration region in the outer magnetosphere of pulsars (outer gap) and calculate the high-energy radiation produced by the synchrocurvature mechanism from the outer gap. We Dnd that a power-law energy distribution of the accelerated particles can be obtained if the outer gap is thick enough that E•B inside the gap can be approximately proportional to (Ωr/c)1/2B(r). We apply our model to explain X-rays and γ-rays from Geminga and PSR B1055-52, whose outer gaps may occupy～70% of the outer magnetosphere region. If the radius of curvature near the light cylinder of the medium outer gap is larger than the dipolar structure, then perhaps this model may also apply to PSR B1951+32, PSR B1706-44, and others.