Ensemble analysis of open cluster transit surveys: upper limits on the frequency of short-period planets consistent with the field

Several photometric surveys for short-period transiting giant planets have targeted a number of open clusters, but no convincing detections have been made. Although each individual survey typically targeted an insufficient number of stars to expect a detection assuming the frequency of short-period giant planets found in surveys of field stars, we ask whether the lack of detections from the ensemble of open cluster surveys is inconsistent with expectations from the field planet population. We select a subset of existing transit surveys with well-defined selection criteria and quantified detection efficiencies, and statistically combine their null results to show that the upper limit on the planet fraction is 5.5% and 1.4% for 1.0 $R_{J}$ and 1.5 $R_{J}$ planets, respectively in the $3<P<5$ day period range. For the period range of $1<P<3$ days we find upper limits of 1.4% and 0.31% for 1.0 $R_{J}$ and 1.5 $R_{J}$, respectively. Comparing these results to the frequency of short-period giant planets around field stars in both radial velocity and transit surveys, we conclude that there is no evidence to suggest that open clusters support a fundamentally different planet population than field stars given the available data.

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