Search for an alien communication from the Solar System to a neighbor star

Under the hypothesis that our Galaxy has been fully explored by self-reproducing probes forming an efficient communication network at the galactic scale by direct links between neighboring systems, using the systems' host stars as Gravitational Lenses (GL), we identify Wolf 359, the third nearest stellar system, as the best target for a search for interstellar communication from the hypothesized alien probes. Indeed, the Earth is a transiting planet as seen from Wolf 359, meaning that our planet could pass in the communication beam of the probe once per orbit. We present a first attempt to detect optical messages emitted from the Solar System to this star, based on observations gathered by the TRAPPIST-South and SPECULOOS-South robotic telescopes. While sensitive enough to detect constant emission with emitting power as small as 1W, this search led to a null result. We note that the GL-based interstellar communication method does not necessarily require to emit from the so-called "Solar Gravitational Line" (SGL), starting at ~550 au from the Sun, and that the probe(s) could be located closer to the Sun and off-center relative to the SGL. Basing on this consideration, we searched in our data for a moving object whose motion would be consistent with the one of the hypothesized alien transmitter, assuming it to use a solar sail to maintain its distance to the Sun. We could not reliably identify any such object up to magnitude ~23.5, which corresponds to an explored zone extending as far as Uranus orbit.