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 \dot { E } 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 .