  Several supersonic runaway pulsar wind nebulae (sPWNe) with jet-like extended
structures have been recently discovered in X-rays. If these structures are the
product of electrons escaping the system and diffusing into the surrounding
interstellar medium, they can produce a radio halo extending for several arcmin
around the source. We model the expected radio emission in this scenario in the
Lighthouse Nebula sPWN. We assume a constant particle injection rate during the
source lifetime, and isotropic diffusion into the surrounding medium. Our
predictions strongly depend on the low- and high-energy cutoffs given in the
particle distribution. Our results indicate that extended radio emission can be
detected from the Lighthouse Nebula without the need to invoke extreme values
for the model parameters. We provide synthetic synchrotron maps that can be
used to constrain these results with observations by current highly sensitive
radio instruments.
