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Constraining Orbital Periods from Nonconsecutive Observations: Period Estimates for Long-Period Planets in Six Systems Observed by K2 During Multiple Campaigns

Most planetary discoveries with the K2 and TESS missions are restricted to short periods because of the limited duration of observation. However, the re-observation of sky area allows for the detection of longer period planets. We describe new transits detected in six candidate planetary systems which were observed by multiple K2 mission campaigns. One of these systems is a multiplanet system with four candidate planets; we present new period constraints for two planets in this system. In the other five systems, only one transit is observed in each campaign, and we derive period constraints from this new data. The period distributions are highly multimodal resulting from missed potential transits in the gap between observations. Each peak in the distribution corresponds to transits at an integer harmonic of the two observed transits. We further detail a generalized procedure to constrain the period for planets with multiple observations with intervening gaps. Because long period photometrically discovered planets are rare, these systems are interesting targets for follow-up observations and confirmation. Specifically, all six systems are bright enough (V = 10.4-12.7) to be amenable to radial velocity follow-up. This work serves as a template for period constraints in a host of similar yet-to-be-discovered planets in long baseline, temporally gapped observations conducted by the TESS mission.