Radio-Quiet Pulsars with Ultrastrong Magnetic Fields

The notable absence of radio pulsars having measured magnetic dipole surface field strengths above B 0 ~3 × 10 13 G naturally raises the question of whether this forms an upper limit to pulsar magnetization. Recently there has been increasing evidence that neutron stars possessing higher dipole spin-down fields do in fact exist, including a growing list of anomalous X-ray pulsars (AXPs) with long periods and spinning down with high-period 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 pulsars. We propose that high-field pulsars should be radio quiet because electron-positron pair production in their magnetospheres, thought to be essential for radio emission, is efficiently suppressed in ultrastrong fields ( B 0 ≳4 × 10 13 G) by the action of photon splitting, a quantum electrodynamical process in which a photon splits into two. Our computed radio quiescence boundary in the radio pulsar P - diagram, where photon splitting overtakes pair creation, is located just above the boundary of the known radio pulsar population, neatly dividing them from the 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 pulsed emission at X-ray and perhaps gamma-ray energies.