2007ApJ...658.1177D

One of the most fundamental questions in pulsar physics is the generation of pair cascading to explain radio through γ-ray pulsed emission. In this paper we derive the pair production multiplicity κ for pulsars from the very high energy (VHE) γ-ray spectra of their pulsar wind nebulae (PWNs), as measured by H.E.S.S., since the IC-generated γ-ray spectra are free from assumptions of the associated nebular magnetic field strength. Most VHE PWNs have been resolved by H.E.S.S., and since the VHE size is already consistent with the maximal expected PWN size of the sources considered in this paper, the age of the VHE emitting electrons must at least be comparable to the age of the pulsar. This allows us to integrate the Goldreich-Julian current over the lifetime of the pulsar, resulting in time averages κ greater that 2000 and 500 for PSR B1509-58 and PSR B1823-13, respectively, whereas the H.E.S.S. data alone for Vela X indicate an anomalously low value, less than unity. The extreme brightness of Vela X in radio, however, indicates that most of the electrons from the pulsar have been reprocessed into the radio synchrotron domain, leading to an upper limit of κ<4x10⁵, if we assume the minimal field strength of 1.7 µG derived from a comparison of H.E.S.S. and ASCA/ROSAT data of Vela X. Similar (large) numbers are, however, derived for PSR B1823-13 and PSR B1509-58 if we extrapolate the H.E.S.S.-derived electron spectra into the uncooled domain toward the unseen radio nebular domain. Such divergent limits on κ can be resolved by adding forthcoming GLAST data to H.E.S.S. information.