We present XMM-Newton and Chandra X-ray observations of the middle-aged radio pulsar PSR B0355+54. Our X-ray observations reveal emission not only from the pulsar itself, but also from a compact diffuse component extending ~50 in the opposite direction to the pulsars proper motion. There is also evidence for the presence of fainter diffuse emission extending ~5 from the point source. The compact diffuse feature is well-fitted with a power-law, the index of which is consistent with the values found for other pulsar wind nebulae. The morphology of the diffuse component is similar to the ram-pressure confined pulsar wind nebulae detected for other sources. The X-ray emission from the pulsar itself is described well by a thermal plus power-law fit, with the thermal emission most likely originating in a hot polar cap.
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