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Abstract

The predicted nature of the candidate redback pulsar 3FGL\,J2039.6$-$5618 was
recently confirmed by the discovery of $\gamma$-ray millisecond pulsations
(Clark et al. 2020, hereafter Paper\,I), which identify this $\gamma$-ray
source as \msp. We observed this object with the Parkes radio telescope in 2016
and 2019. We detect radio pulsations at 1.4\,GHz and 3.1\,GHz, at the 2.6ms
period discovered in $\gamma$-rays, and also at 0.7\,GHz in one 2015 archival
observation. In all bands, the radio pulse profile is characterised by a single
relatively broad peak which leads the main $\gamma$-ray peak. At 1.4\,GHz we
found clear evidence of eclipses of the radio signal for about half of the
orbit, a characteristic phenomenon in redback systems, which we associate with
the presence of intra-binary gas. From the dispersion measure of
$24.57\pm0.03$\,pc\,cm$^{-3}$ we derive a pulsar distance of $0.9\pm 0.2$\,kpc
or $1.7\pm0.7$\,kpc, depending on the assumed Galactic electron density model.
The modelling of the radio and $\gamma$-ray light curves leads to an
independent determination of the orbital inclination, and to a determination of
the pulsar mass, qualitatively consistent to the results in Paper\,I.