Abstract
We calculate the maximum luminosity of the synchrotron radiation in X-ray and optical bands, which is originated from the electromagnetic cascade in the magnetosphere of rotation-powered pulsars. We find that for pulsars with spin-down luminosity Lsd ≤ 1035 erg s−1, even if the full allowed energy range of the γ-ray photon emitted by the accelerated particles is taken into account, the observed non-thermal luminosities are higher than the maximum luminosity of synchrotron radiation from pairs created by two-photon collision. The synchrotron radiation from the inner region could explain the observed non-thermal luminosities, so that the γ-ray pulsars with Lsd ≤ 1035 erg s−1 would have multiple particle accelerators in the magnetosphere.
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