High-energy properties of pulsed emission from millisecond pulsars

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 gamma-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-X, pul(theo)) and the pulsar spin-down power (L-sd) satisfies (L-X, pul(theo)) proportional to L-sd(1.17 +/- 0.10) for the MSPs outside of 47 Tuc and Ltheo (L-X, pul(theo)) proportional to L-SD(0.58 +/- 0.06) for the MSPs in 47 Tuc, which is consistent with the relation between the observed pulsed component of X-ray luminosity (L-X, pul(obs)) and L-sd: L-X, pul(obs) proportional to L-sd(1.12 +/- 0.10) for the MSPs outside of 47 Tuc and L-X, pul(obs) proportional to L-sd(0.24 +/- 0.43) sd for the MSPs in 47 Tuc. We also applied our model to predict the averaged high-energy gamma-ray fluxes and to compare them with the sensitivity of AGILE and GLAST.