The study of the younger, and brighter, pulsars is important to understand the optical emission properties of isolated neutron stars. PSRB0540-69, the second brightest (V~22) optical pulsar, is obviously a very interesting target for these investigations. The aim of this work is threefold: constraining the pulsar proper motion and its velocity on the plane of the sky through optical astrometry, obtaining a more precise characterisation of the pulsar optical spectral energy distribution (SED) through a consistent set of multi-band, high-resolution, imaging photometry observations, measuring the pulsar optical phase-averaged linear polarisation, for which only a preliminary and uncertain measurement was obtained so far from ground-based observations. We performed high-resolution observations of PSRB0540-69 with the WFPC2 aboard the HST, in both direct imaging and polarimetry modes. From multi-epoch astrometry we set a 3sigma upper limit of 1 mas/yr on the pulsar proper motion, implying a transverse velocity <250 km/s at the 50 kpc LMC distance. Moreover, we determined the pulsar absolute position with an unprecedented accuracy of 70 mas. From multi-band photometry we characterised the pulsar power-law spectrum and we derived the most accurate measurement of the spectral index (0.70+/-0.07) which indicates a spectral turnover between the optical and X-ray bands. Finally, from polarimetry we obtained a new measurement of the pulsar phase-averaged polarisation degree (16+/-4%),consistent with magnetosphere models depending on the actual intrinsic polarisation degree and depolarisation factor, and we found that the polarisation vector (22+/-12deg position angle) is possibly aligned with the semi-major axis of the pulsar-wind nebula and with the apparent proper motion direction of its bright emission knot.
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