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When a planet is only observed to transit once, direct measurement of itsperiod is impossible. It is possible, however, to constrain the periods ofsingle transiters, and this is desirable as they are likely to represent thecold and far extremes of the planet population observed by any particularsurvey. Improving the accuracy with which the period of single transiters canbe constrained is therefore critical to enhance the long-period planet yield ofsurveys. Here, we combine Gaia parallaxes with stellar models and broad-bandphotometry to estimate the stellar densities of K2 planet host stars, then usethat stellar density information to model individual planet transits and inferthe posterior period distribution. We show that the densities we infer arereliable by comparing with densities derived through asteroseismology, andapply our method to 27 validation planets of known (directly measured) period,treating each transit as if it were the only one, as well as to 12 true singletransiters. When we treat eccentricity as a free parameter, we achieve afractional period uncertainty over the true single transits of$94^{+87}_{-58}\%$, and when we fix $e=0$, we achieve fractional perioduncertainty $15^{+30}_{-6}\%$, a roughly threefold improvement over typicalperiod uncertainties of previous studies.

Estimation of singly-transiting K2 planet periods with Gaia parallaxes