Ancient Pulsar Wind Nebulae in light of recent GeV and TeV observations

In a Pulsar Wind Nebula (PWN), the lifetime of inverse Compton emitting electrons exceeds the lifetime of its progenitor pulsar, but it exceeds also the age of the electrons that emit via synchrotron radiation; i.e. during the evolution of the PWN, it can remain bright in IC, whereas its GeV-TeV gamma-ray (for 10$^5-10^6$ years) flux remains high for timescales much larger than the Pulsar lifetime and the PWN visible in X-rays. The shell-type remnant of the supernova explosion in which the pulsar was formed also has a much shorter lifetime. In this scenario, the magnetic field in the cavity induced by the wind of the progenitor star plays a crucial role. This is in line with the discovery of several unidentified sources in the TeV gamma-ray band without X-ray counterparts. Moreover, the consequences are important also in order to reinterprete the detection of starburst galaxies in the TeV gamma-ray band considering a leptonic origin of the gamma-ray signal.