Magnetohydrodynamical simulations are presented of a magnetized pulsar windinteracting directly with the interstellar medium, or, in the case of asurrounding supernova remnant, with the associated freely expanding ejecta ofthe progenitor star. In both cases the simulations show that the pulsar windnebula will be elongated due to the dynamical influence of the toroidalmagnetic fields, which confirm predictions from a semi-analytical modelpresented by Begelman & Li. The simulations follow the expansion of the pulsarwind nebula when the latter is bounded by a strong shock and show that theexpansion can be modeled with a standard power-law expansion rate. Byperforming different simulations with different magnetization parameters, Ishow that the latter weakly correlates with the elongation of the pulsar windnebula. The results from the simulations are applied to determine the nature ofthe expansion rate of the pulsar wind nebula 3C58. It is shown that there isboth observational and theoretical evidence which supports the scenario inwhich the pulsar wind nebula 3C58 has caught up with the reverse shock of theassociated (but undetected) supernova remnant.
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