Observations of PSR J1357-6429 at 2.1 GHz with the Australia Telescope Compact Array

PSR J1357$-$6429 is a young and energetic radio pulsar detected in X-rays and $\gamma$-rays. It powers a compact pulsar wind nebula with a jet visible in X-rays and a large scale plerion detected in X-ray and TeV ranges. Previous multiwavelength studies suggested that the pulsar has a significant proper motion of about 180 mas yr$^{-1}$ implying an extremely high transverse velocity of about 2000 km s$^{-1}$. In order to verify that, we performed radio-interferometric observations of PSR J1357$-$6429 with the the Australia Telescope Compact Array (ATCA) in the 2.1 GHz band. We detected the pulsar with a mean flux density of $212\pm5$ $\mu$Jy and obtained the most accurate pulsar position, RA = 13:57:02.525(14) and Dec = $-$64:29:29.89(15). Using the new and archival ATCA data, we did not find any proper motion and estimated its 90 per cent upper limit $\mu < 106$ mas yr$^{-1}$. The pulsar shows a highly polarised single pulse, as it was earlier observed at 1.4 GHz. Spectral analysis revealed a shallow spectral index $\alpha_{\nu}$ = $0.5 \pm 0.1$. Based on our new radio position of the pulsar, we disclaim its optical counterpart candidate reported before.