We have used the ESO NTT/EMMI and VLT/FORS1 instruments to examine the LMC supernova remnant 0540-69.3 as well as its pulsar (PSR B0540-69) and pulsar-powered nebula in the optical range.Spectroscopic observations of the remnant covering the range of 3600-7350 A centered on the pulsar produced results consistent with those of Kirshner et al. (1989), but also revealed many new emission lines. The most important are [Ne III] 3869, 3967 and Balmer lines of hydrogen. In both the central part of the remnant, as well as in nearby H II regions, the [O III] temperature is higher than about 20 000 K, but lower than previously estimated. For PSR B0540-69, previous optical data are mutually inconsistent: HST/FOS spectra indicate a significantly higher absolute flux and steeper spectral index than suggested by early time-resolved groundbased UBVRI photometry. We show that the HST and VLT spectroscopic data for the pulsar have more then about 50% nebular contamination, and that this is the reason for the previous difference. Using HST/WFPC2 archival images obtained in various bands from the red part of the optical to the NUV range we have performed an accurate photometric study of the pulsar, and find that the spectral energy distribution of the pulsar emission has a negative slope with 1.07 +/- 0.2. This is steeper than derived from previous UBVRI photometry, and also different from the almost flat spectrum of the Crab pulsar. We also estimate that the proper motion of the pulsar is 4.9 +/- 2.3 mas/yr, corresponding to a transverse velocity of 1190 +/- 560 km/s, projected along the southern jet of the pulsar nebula.
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