Abstract
Recent observations of a few young pulsar wind nebulae (PWNe) have revealed their morphologies in some detail. Given the availability of spatio-spectral-temporal data, we use our multi-zone (1D) leptonic emission code to model the PWNe associated with G29.7$-$0.3 (Kes 75) and G21.5$-$0.9 (G21.5), and obtain (by-eye) constraints on additional model parameters compared to spectral-only modelling. Kes 75 is a Galactic composite supernova remnant (SNR) with an embedded pulsar, PSR J1846$-$0258. X-ray studies reveal rapid expansion of Kes 75 over the past two decades. PWN G21.5 is also a composite SNR, powered by PSR J1833$-$1034. For Kes 75, we study a sudden plasma bulk speed increase that may be due to the magnetar-like outbursts of the central pulsar. An increase of a few per cent in this speed does not result in any significant change in the model outputs. For G21.5, we investigate different diffusion coefficients and pulsar spin-down braking indices. We can reproduce the broad-band spectra and X-ray surface brightness profiles for both PWNe, and the expansion rate, flux over different epochs, and X-ray photon index versus epoch and central radius for Kes 75 quite well. The latter three features are also investigated for G21.5. Despite obtaining reasonable fits overall, some discrepancies remain, pointing to further model revision. We find similar values to overlapping parameters between our 1D code and those of an independent 0D dynamical code (tide). Future work will incorporate spatial data from various energy wavebands to improve model constraints.