The young PSR B0540-69.3 in the LMC is the only pulsar ( except the Crab pulsar ) for which a near-UV spectrum has been obtained .
However , the absolute flux and spectral index of the HST/FOS spectrum are significantly higher than suggested by previous broad-band time-resolved groundbased UBVRI photometry .
To investigate this difference , observations with ESO/VLT/FORS1 and analysis of HST/WFPC2 archival data were done .
We show that the HST and VLT spectral data for the pulsar have \phantom { \geq } \smash { \buildrel \over { \lower 2.675022 pt \hbox { $ \buildrel% \lower 2.140017 pt \hbox { $ \displaystyle > $ } \over { \sim } $ } } } 50 % nebular contamination and that this is the reason for the above mentioned difference .
The broadband HST spectrum for the range 3300–8000 Å is clearly nonthermal and has a negative spectral index , F _ { \nu } \propto \nu ^ { - \alpha } with \alpha _ { \nu } = 1.07 ^ { +0.20 } _ { -0.19 } .
This is different from the almost flat spectrum of the Crab pulsar , and also steeper than for the previously published broadband photometry of PSR B0540-69.3 .
We have also studied the spatial variations of the brightness and spectral index of the Pulsar Wind Nebula ( PWN ) around the pulsar , and find no significant spectral index variation over the PWN .
The HST data show a clear asymmetry of the surface brightness distribution along the major axis of the torus-like structure of the PWN with respect to the pulsar position , also seen in Chandra/HRC X-ray images .
This is different from the Crab PWN and likely linked to the asymmetry of the surrounding SN ejecta .
The HST/WFPC2 archival data have an epoch separation by 4 years , and this allows us to estimate the proper motion of the pulsar .
We find a motion of 4.9 \pm 2.3 mas yr ^ { -1 } ( corresponding to a transverse velocity of 1190 \pm 560 ~ { } km~ { } s ^ { -1 } ) along the southern jet of the PWN .
If this is confirmed at a higher significance level by future observations , this makes PSR B0540-69.3 the third pulsar with a proper motion aligned with the jet axis of its PWN , which poses constraints on pulsar kick models .
To establish the multiwavelength spectrum of the pulsar and its PWN , we have included recent Chandra X-ray data , and discuss the soft pulsar X-ray spectrum based on spectral fits including absorption by interstellar gas in the Milky Way , LMC as well as the supernova ejecta .
We have compared the multiwavelength spectra of PSR B0540-69.3 and the Crab pulsar , and find that both PSR B0540-69.3 and the Crab pulsar have a weaker flux in the optical than suggested by a low-energy power-law extension of the X-ray spectrum .
This optical depression is more severe for PSR B0540-69.3 than for the Crab pulsar .
The same trend is seen for the PWNe of the two pulsars , and continues for low energies also out in the radio band .
We discuss possible interpretations of this behavior .