In a Pulsar Wind Nebula (PWN), the lifetime of inverse Compton (IC) emitting e exceeds the lifetime of its progenitor pulsar (as well as its shell-type remnant), but it also exceeds the age of those that emit via synchrotron radiation. Therefore, during its evolution, the PWN can remain bright in IC so that its GeV-TeV gamma-ray flux remains high for timescales much larger (for 105-106 yrs) than the pulsar lifetime and the X-ray PWN lifetime. In this scenario, the magnetic field in the cavity induced by the wind of the progenitor star plays a crucial role. This scenario is in line with the discovery of several unidentified or "dark" sources in the TeV gamma-ray band without X-ray counterparts; and it is also finding confirmation in the recent discoveries at GeV gamma rays. Moreover, these consequences could be also important for reinterpreting the detection of starburst galaxies in the TeV gamma-ray band when considering a leptonic origin of the gamma-ray signal. Both theoretical aspects and their observational proofs will be discussed, as well as the first results of our new modeling code.

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