Radio-quiet pulsars with ultrastrong magnetic fields

The notable absence of radio pulsars having measured magnetic dipole surfac e field strengths above B-0 similar to x 10(13) G naturally raises the ques tion of whether this forms an upper limit to pulsar magnetization. Recently there has been increasing evidence that neutron stars possessing higher di pole spin-down fields do in fact exist, including a growing list of anomalo us X-ray pulsars (AXPs) with long periods and spinning down with high-perio d derivatives, which imply surface fields of 10(14)-10(15) G. Furthermore, the recently reported X-ray period and period derivative for the soft gamma -ray repeater (SGR) source SGR 1806-20 suggest a surface field around 10(15 ) G. None of these high-field pulsars have yet been detected as radio pulsa rs. We propose that high-field pulsars should be radio quiet because electr on-positron pair production in their magnetospheres, thought to be essentia l for radio emission, is efficiently suppressed in ultrastrong fields (B-0 greater than or similar to x 10(13) G) by the action of photon splitting, a quantum electrodynamical process in which a photon splits into two. Our co mputed radio quiescence boundary in the radio pulsar P-(P) over dot diagram , where photon splitting overtakes pair creation, is located just above the boundary of the known radio pulsar population, neatly dividing them from t he AXPs. We thus identify a physical mechanism that defines a new class of high-field radio-quiet neutron stars that should be detectable by their pul sed emission at X-ray and perhaps gamma-ray energies.