Reverberation of pulsar wind nebulae (I): impact of the medium properties and other parameters upon the extent of the compression

The standard approach to the long-term evolution of pulsar wind nebulae (PWNe) is based on one-zone models treating the nebula as a uniform system. In particular for the late phase of evolved systems, many of the generally used prescriptions are based on educated guesses for which a proper assessment lacks. Using an advanced radiative code, we evaluate the systematic impact of various parameters, like the properties of the supernova ejecta, of the inner pulsar, as well of the ambient medium, upon the extent of the reverberation phase of PWNe. We investigate how different prescriptions shift the starting time of the reverberation phase, how this affects the amount of the compression, and how much of this can be ascribable to the radiation processes. Some critical aspects are the description of the reverse shock evolution, the efficiency by which at later times material from the ejecta accretes on to the swept-up shell around the PWN, and finally the density, velocity, and pressure profiles in the surrounding supernova remnant. We have explicitly treated the cases of the Crab Nebula, and of J1834.9-0846, taken to be representatives of the more and the less energetic pulsars, respectively. Especially for the latter object, the prediction of large compression factors is confirmed, even larger in the presence of radiative losses, also confirming our former prediction of periods of superefficiency during the reverberation phase of some PWNe.