Despite the existence of co-orbital bodies in the solar system, and the prediction of the formation of co-orbital planets by planetary system formation models, no co-orbital exoplanets (also called trojans) have been detected thus far. Here we study the signature of co-orbital exoplanets in transit surveys when two planet candidates in the system orbit the star with similar periods. Such a pair of candidates could be discarded as false positives because they are not Hill-stable. However, horseshoe or long-libration-period tadpole co-orbital configurations can explain such period similarity. This degeneracy can be solved by considering the transit timing variations (TTVs) of each planet. We subsequently focus on the three-planet-candidate system TOI-178: the two outer candidates of that system have similar orbital periods and were found to have an angular separation close to π∕3 during the TESS observation of sector 2. Based on the announced orbits, the long-term stability of the system requires the two close-period planets to be co-orbital. Our independent detrending and transit search recover and slightly favour the three orbits close to a 3:2:2 resonant chain found by the TESS pipeline, although we cannot exclude an alias that would put the system close to a 4:3:2 configuration. We then analyse the co-orbital scenario in more detail, and show that despite the influence of an inner planet just outside the 2:3 MMR, this potential co-orbital system could be stable on a gigayear time-scale for a variety of planetary masses, either on a trojan or a horseshoe orbit. We predict that large TTVs should arise in such a configuration with a period of several hundred days. We then show how the mass of each planet can be retrieved from these TTVs.
Primordial migration of co-orbital satellites as a mechanism for the horseshoe orbit of Janus –Epimetheus
