Photon splitting and pair creation in highly magnetized pulsars

The absence of radio pulsars with long periods has lead to the popular noti on of a high-P "death line." In the standard picture, beyond this boundary, pulsars with low spin rates cannot accelerate particles above the stellar surface to high enough energies to initiate pair cascades, and the pair cre ation needed for radio emission is strongly suppressed. In this paper we ex plore the possibility of another pulsar "death line" in the context of pola r cap models, corresponding to high magnetic fields B in the upper portion of the period-period derivative diagram, a domain where few radio pulsars a re observed. The origin of this high-B boundary, which may occur when B bec omes comparable to or exceeds B-cr = 4.4 x 10(13) G, is also due to the sup pression of magnetic pair creation, but primarily because of ineffective co mpetition with magnetic photon splitting. Threshold pair creation also play s a prominent role in the suppression of cascades. We present Monte Carlo c alculations of the pair yields in photon splitting/ pair cascades that show that, in the absence of scattering effects, pair production is effectively suppressed, but only if all three modes of photon splitting allowed by QED are operating in high fields. This paper describes the probable shape and position of the new "death line," above which pulsars are expected to be ra dio-quiet, but perhaps still X-ray- and gamma-ray-bright. The hypothesized existence of radio-quiet sources finds dramatic support in the recent disco very of ultrastrong fields in soft gamma-ray repeaters and anomalous X-ray pulsars. Guidelines for moderate- to high-B pulsar searches at radio wavele ngths and also in the soft and hard gamma-ray bands are presented.