2018MNRAS.475.2185C

Three gamma-ray millisecond pulsars (MSPs), PSR J1939+2134, PSR J1959+2048, and PSR J0034-0534, have been confirmed to have a common feature of phase-aligned in radio and gamma-ray bands. With a geometric (two-pole caustic) model and a physical outer gap model (revised 3D outer gap model) in a three dimensional (3D) retarded magnetic dipole with a perturbation magnetic field, the observed features of these MSPs are studied. In order to obtained the best-fitting model parameters, the Markov chain Monte Carlo technique is used and reasonable GeV band light curves for three MSPs are given. Our calculations indicate that MSPs emit high energy photons with smaller inclination angles (α ≃ 10°-50°), larger view angles (ζ ≃ 65°-100°), and smaller perturbation factor (ε ≃ -0.15-0.1). Note that the factor ε, describing the strength of the perturbed magnetic field, is all less than zero in these two models, so the magnetic field caused by current-induced play a leading role in the pulsed location of MSPs.