A Spin-down Power Threshold for Pulsar Wind Nebula Generation?

A systematic X-ray survey of the most energetic rotation-powered pulsars known, based on spin-down energy loss rate, $\dot E$ = $I\omega\dot\omega$, shows that all energetic pulsars with $\dot E > \dot E_{c} \approx 3.4 \times\ 10^{36}$ erg s$^{-1}$ are X-ray bright, manifest a distinct pulsar wind nebula (PWN), and are associated with a supernova event, either historically or via a thermal remnant, with over half residing in shell-like supernova remnants. Below $\dot E_c$, the 2-10 keV PWN flux ratio $F_{PWN}/F_{PSR}$ decreases by an order-of-magnitude. This threshold is predicted by the lower limit on the spectral slope $\Gamma_{min} \approx 0.5$ observed for rotation-powered pulsars (Gotthelf 2003). The apparent lack of bright pulsar nebulae below a critical Edot suggests a change in the particle injection spectrum and serves as a constraint on emission models for rotation-powered pulsars. Neither a young age nor a high density environment is found to be a sufficient condition for generating a PWN, as often suggested, instead the spin-down energy loss rate is likely the key parameter in determining the evolution of a rotation-powered pulsar.