On the potential of transit surveys in star clusters: impact of correlated noise and radial velocity follow-up

We present an extension of the formalism recently proposed by Pepper and Gaudi to evaluate the yield of transit surveys in homogeneous stellar systems, incorporating the impact of correlated noise on transit time-scales on the detectability of transits, and simultaneously incorporating the magnitude limits imposed by the need for radial velocity (RV) follow-up of transit candidates. New expressions are derived for the different contributions to the noise budget on transit time-scales and the least-squares detection statistic for box-shaped transits, and their behaviour as a function of stellar mass is re-examined. Correlated noise that is constant with apparent stellar magnitude implies a steep decrease in detection probability at the high-mass end which, when considered jointly with the RV requirements, can severely limit the potential of otherwise promising surveys in star clusters. However, we find that small-aperture, wide-field surveys may detect hot Neptunes whose RV signal can be measured with present-day instrumentation in very nearby (< 100 pc) clusters.