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We report the results of X-ray (Chandra X-ray Observatory (CXO)) and radio (ATCA) observations of the pulsar wind nebula (PWN) powered by the young pulsar PSR J1016â€"5857, which we dub “the Goose” PWN. In both bands, the images reveal a tail-like PWN morphology that can be attributed to the pulsar’s motion. By comparing archival and new CXO observations, we measure the pulsar’s proper motion ÎĽ = 28.8 ± 7.3 mas yrâˆ'1, yielding a projected pulsar velocity v ≈ 440 ± 110 km sâˆ'1 (at d = 3.2 kpc); its direction is consistent with the PWN shape. Radio emission from the PWN is polarized, with the magnetic field oriented along the pulsar tail. The radio tail connects to a larger radio structure (not seen in X-rays), which we interpret as a relic PWN (also known as a plerion). The spectral analysis of the CXO data shows that the PWN spectrum softens from Î" = 1.7 to Î" ≈ 2.3â€"2.5 with increasing distance from the pulsar. The softening can be attributed to the rapid synchrotron burn-off, which would explain the lack of X-ray emission from the older relic PWN. In addition to nonthermal PWN emission, we detected thermal emission from a hot plasma, which we attribute to the host supernova remnant. The radio PWN morphology and the proper motion of the pulsar suggest that the reverse shock passed through the pulsar’s vicinity and pushed the PWN to one side. [ABSTRACT FROM AUTHOR]