A MODEL OF THE SPECTRAL EVOLUTION OF PULSAR WIND NEBULAE

Abstract

We study the spectral evolution of PWNe taking into account the energy\ninjected when they are young. We model the evolution of the magnetic field\ninside a uniformly expanding PWN. Considering time dependent injection from the\npulsar and coolings by radiative and adiabatic losses, we solve the evolution\nof the particle distribution function. The model is calibrated by fitting the\ncalculated spectrum to the observations of the Crab Nebula at an age of a\nthousand years. The spectral evolution of the Crab Nebula in our model shows\nthat the flux ratio of TeV gamma-rays to X-rays increases with time, which\nimplies that old PWNe are faint in X-rays, but not in TeV gamma-rays. The\nincrease of this ratio is because the magnetic field decreases with time and is\nnot because the X-ray emitting particles are cooled more rapidly than the TeV\ngamma-ray emitting particles. Our spectral evolution model matches the observed\nrate of the radio flux decrease of the Crab Nebula. This result implies that\nour magnetic field evolution model is close to the reality. Finally, from the\nviewpoint of the spectral evolution, only a small fraction of the injected\nenergy from the Crab Pulsar needs to go to the magnetic field, which is\nconsistent with previous studies.\n