The effects of magnetic field, age and intrinsic luminosity on Crab-like pulsar wind nebulae

Abstract

We investigate the time-dependent behaviour of Crab-like pulsar wind nebulae (PWNe) generating a set of models using four different initial spin-down luminosities (L0 = {1, 0.1, 0.01, 0.001} × L0,Crab), eight values of magnetic fraction (η = 0.001, 0.01, 0.03, 0.1, 0.5, 0.9, 0.99 and 0.999, i.e. from fully particle dominated to fully magnetically dominated nebulae) and three distinctive ages: 940, 3000 and 9000 years. We find that the self-synchrotron Compton (SSC) contribution is irrelevant for LSD = 0.1, 1 and 10 per cent of the Crab power, disregarding the age and the magnetic fraction. SSC only becomes relevant for highly energetic (∼70 per cent of the Crab), particle dominated nebulae at low ages (of less than a few kyr), located in a far-infrared (FIR) background with relatively low energy density. Since no pulsar other than Crab is known to have these features, these results clarify why the Crab nebula, and only it, is SSC dominated. No young PWN would be detectable at TeV energies if the pulsar´s spin-down power is 0.1 per cent Crab or lower. For 1 per cent of the Crab spin-down, only particle-dominated nebulae can be detected by HESS-like telescopes when young enough (with details depending on the precise injection and environmental parameters). Above 10 per cent of the Crab´s power, all PWNe are detectable by HESS-like telescopes if they are particle dominated, no matter the age. The impact of the magnetic fraction on the final spectral energy distribution is varied and important, generating order of magnitude variations in the luminosity output for systems that are otherwise the same (equal P, P˙, injection and environment).