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X-ray/GeV emissions from Crab-like pulsars in LMC

We discuss X-ray and gamma-ray emissions from Crab-like pulsars, PSRs~J0537-6910 and~J0540-6919, in Large Magellanic Cloud. Fermi-LAT observations have resolved the gamma-ray emissions from these two pulsars and found the pulsed emissions from PSR~J0540-6919. The total pulsed radiation in the X-ray/gamma-ray energy bands of PSR~J0540-6919 is observed with the efficiency $η_{J0540}\sim 0.06$ (in 4$π$ sr), which is about a factor of ten larger than $η_{Crab}\sim 0.006$ of the Crab pulsar. Although PSR~J0537-6910 has the highest spin-down power among currently known pulsars, the efficiency of the observed X-ray emissions is about two orders of magnitude smaller than that of PSR~J0540-6919. This paper mainly discusses what causes the difference in the radiation efficiencies of these three energetic Crab-like pulsars. We discuss electron/positron acceleration and high-energy emission processes within the outer gap model. By solving the outer gap structure with the dipole magnetic field, we show that the radiation efficiency decreases as the inclination angle between the magnetic axis and the rotation axis increases. To explain the difference in the pulse profile and in the radiation efficiency, our model suggests that PSR~J0540-6919 has an inclination angle much smaller than the that of Crab pulsar (here we assume the inclination angles of both pulsars are $α<90^{\circ}$). On the other hand, we speculate that the difference in the radiation efficiencies between PSRs~J0537-6910 and J0549-6919 is mainly caused by the difference in the Earth viewing angle, and that we see PSR~J0537-6910 with an Earth viewing angle $ζ>>90^{\circ}$ (or $<<90^{\circ}$) measured from the spin axis, while we see PSR~J0540-6919 with $ζ\sim 90^{\circ}$.