Estimating the birth period of pulsars through GLAST/LAT observations of their wind nebulae

Understand

In this paper we show that the high energy $\gamma$-ray flux in the GeV domain from mature pulsar wind nebulae (PWN) scales as the change in rotational kinetic energy $I(\Omega_0^2-\Omega^2)/2$ since birth, rather than the present day spindown power $I\Omega\dot{\Omega}$.

• This finding holds as long as the lifetime of inverse Compton emitting electrons exceeds the age of the system.
• For a typical $\gamma^{-2}$ electron spectrum, the predicted flux depends mostly on the pulsar birth period, conversion efficiency of spindown power to relativistic electrons and distance to the PWN, so that first order estimates of the birth period can be assessed from {\it GLAST/LAT} observations of PWN.
• For this purpose we derive an analytical expression.