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We study the spectral evolution of PWNe taking into account the energy injected when they are young. We model the evolution of the magnetic field inside a uniformly expanding PWN. Considering time dependent injection from the pulsar and coolings by radiative and adiabatic losses, we solve the evolution of the particle distribution function. The model is calibrated by fitting the calculated spectrum to the observations of the Crab Nebula at an age of a thousand years.The spectral evolution of the Crab Nebula in our model shows that the flux ratio of TeV γ-rays to X-rays increases with time, which implies that old PWNe are faint in X-rays, but not in TeV γ-rays. The increase of this ratio is because the magnetic field decreases with time and is not because the X-ray emitting particles are cooled more rapidly than the TeV γ-ray emitting particles. Our spectral evolution model matches the observed rate of the radio flux decrease of the Crab Nebula. This result implies that our magnetic field evolution model is close to the reality. Finally, from the viewpoint of the spectral evolution, only a small fraction of the injected energy from the Crab Pulsar needs to go to the magnetic field, which is consistent with previous studies.

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We have studied the rapid X-ray variability of three extragalactic TeV c-ray sources : Mrk 421, Mrk 501, and PKS 2155[304. Analyzing the X-ray light curves obtained from ASCA and/or Rossi X-Ray T iming Explorer observations between 1993 and 1998, we have investigated the variability in the time domain from 103 to 108 s. For all three sources, both the power spectrum density (PSD) and the structure function (SF) show a rollover with a timescale of the order of 1 day or longer, which may be interpreted as the typical timescale of successive Ñare events. Although the exact shape of turnover is not well constrained and the low-frequency (long timescale) behavior is still unclear, the high-frequency (short timescale) behavior is clearly resolved. We found that, on timescales shorter than 1 day, there is only small power in the variability, as indicated by a steep power spectrum density of f~2F~3. This is very di †erent from other types of mass-accreting black hole systems, for which the short-timescale variability is well characterized by a fractal, Ñickering-noise PSD ( f~1F~2). The steep PSD index and the characteristic timescale of Ñares imply that the X-rayÈemitting site in the jet is of limited spatial extent : D º 1017 cm distant from the base of the jet, which corresponds to º102 Schwarzschild radii for 107h10 black hole systems. M _