A Model of the Spectral Evolution of Pulsar Wind Nebulae

S. J. Tanaka, F. Takahara

Published 2010-01-14Version 1

Recent observations suggest that many old pulsar wind nebulae (PWNe) are bright TeV gamma-ray sources without a strong X-ray counterpart. In this paper, we study the spectral evolution of PWNe taking into account the energy which was injected when they were young for old PWNe. We model the evolution of the magnetic field and solve for the particle distribution inside a uniformly expanding PWN. The model is calibrated by fitting the calculated spectrum to the observations of the Crab Nebula at an age of a thousand years. We find that only a small fraction of the injected energy from the Crab Pulsar goes to the magnetic field, consistent with previous studies. The spectral evolution model of the Crab Nebula shows that the flux ratio of TeV gamma-rays to X-rays increases with time, which implies that old PWNe are faint at X-rays, but not at TeV gamma-rays. The increase of this ratio is primarily because the magnetic field decreases with time and is not because the X-ray emitting particles are cooled more rapidly than the TeV gamma-ray emitting particles. Our spectral evolution model matches the observed rate of the radio flux decrease of the Crab Nebula.