2007ApJ...666.1165Z

We make a modification of our previous outer gap model of high-energy emission from millisecond pulsars (MSPs) by taking the effects of the magnetic inclination angles and magnetic geometry into account. In the revised version of our outer gap model, a strong multipole magnetic field exists near the stellar surface, and the X-rays are produced by the backflow current of the outer gap and consist of one power-law and two thermal components. These X-rays collide with high-energy photons inside the outer gap to sustain the outer gap, and then high-energy γ-rays are produced in the outer gap. The fractional size of the outer gap is a function of the radial distance to the neutron star and the magnetic inclination angle for a given millisecond pulsar. We have applied this model to account for the pulsed X-ray emission from the MSPs outside of and in the globular cluster 47 Tuc, and our results indicate that the relation between the pulsed component of X-ray luminosity (L^theo_X,pul) and the pulsar spin-down power (L_sd) satisfies L^theo_X,pul∝L^1.17±0.10_sd for the MSPs outside of 47 Tuc and L^theo_X,pul∝L^0.58±0.06_sd for the MSPs in 47 Tuc, which is consistent with the relation between the observed pulsed component of X-ray luminosity (L^obs_X,pul) and L_sd: L^obs_X,pul∝L^1.12±0.10_sd for the MSPs outside of 47 Tuc and L^obs_X,pul∝L^0.24±0.43_sd for the MSPs in 47 Tuc. We also applied our model to predict the averaged high-energy γ-ray fluxes and to compare them with the sensitivity of AGILE and GLAST.