Signatures of extended radio emission from escaping electrons in the Lighthouse Nebula

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 arcmins 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.