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

We show that the high-energy gamma-ray flux in the GeV domain from mature pulsar wind nebulae (PWNe) scales as the change in rotational kinetic energy I(Omega(2)(0) - Omega(2))/2 since birth, rather than the present-day spin-down power I Omega 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 spin-down power to relativistic electrons, and distance to the PWN, so that first-order analytic estimates of the birth period can be assessed from GLAST LAT observations of PWNe. The associated ("uncooled") photon spectral index in the GeV domain is expected to cluster around similar to 1.5, which is bounded at low energies by an intrinsic spectral break, and at higher energies by a second spectral break where the photon index steepens to similar to 2 due to radiation losses. However, if the spectral parameters deviate from the above-mentioned assumptions, we can combine GLAST LAT observations with multiwavelength data from radio to TeV gamma-ray observations to improve such birth period estimates. From the ATNF pulsar catalog we expect more than 50 Galactic PWNe to be detectable if the ratio of birth period to current period is < 0.5. However, many of them may remain unidentified during evolved stages characterized by low spin-down power and low synchrotron brightness, while only this relic GeV component is visible.