Time-dependent Modeling of Pulsar Wind Nebulae

A spatially independent model that calculates the time evolution of the electron spectrum in a spherically expanding pulsar wind nebula (PWN) is presented, allowing one to make broadband predictions for the PWN's non-thermal radiation. The source spectrum of electrons injected at the termination shock of the PWN is chosen to be a broken power law. In contrast to previous PWN models of a similar nature, the source spectrum has a discontinuity in intensity at the transition between the low and high-energy components. To test the model, it is applied to the young PWN G21.5--0.9, where it is found that a discontinuous source spectrum can model the emission at all wavelengths better than a continuous one. The model is also applied to the unidentified sources HESS J1427--608 and HESS J1507--622. Parameters are derived for these two candidate nebulae that are consistent with the values predicted for other PWNe. For HESS J1427--608 a present-day magnetic field of $B\s{age}=0.4\,\mu\text{G}$ is derived. As a result of the small present-day magnetic field, this source has a low synchrotron luminosity, while remaining bright at GeV/TeV energies. It is therefore possible to interpret HESS J1427--608 within the ancient PWN scenario. For the second candidate PWN HESS J1507--622, a present-day magnetic field of $B\s{age}=1.7\,\mu\text{G}$ is derived. Furthermore, for this candidate PWN a scenario is favoured in the present paper in which HESS J1507--622 has been compressed by the reverse shock of the supernova remnant.