The young pulsar PSR B0540-69.3 and its synchrotron nebula in the optical and X-rays

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 $\ga$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 of 4 years, and this allows us to estimate the proper motion of the pulsar. We find a motion of $4.9\pm2.3$ mas yr-1 (corresponding to a transverse velocity of $1190\pm560 \rm ~km~s^{-1}$) 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