Searching for Transiting Planets in Stellar Systems

We analyze the properties of searches devoted to finding planetary transits by observing simple stellar systems, such as globular clusters, open clusters, and the Galactic bulge. We develop the analytic tools necessary to predict the number of planets that a survey will detect as a function of the parameters of the system (age, extinction, distance, richness, mass function), the observational setup (nights observed, bandpass, exposure time, telescope diameter, detector characteristics), site properties (seeing, sky background), and the planet properties (frequency, period, and radius). We find that for typical parameters, the detection probability is maximized for I-band observations. At fixed planet period and radius, the signal-to-noise ratio of a planetary transit in the I band is weakly dependent on the mass of the primary for sources with flux above the sky background and falls very sharply for sources below sky. Therefore, for typical targets, the number of detectable planets is roughly proportional to the number of stars with transiting planets with fluxes above sky (and not necessarily the number of sources with photometric error less than a given threshold). Furthermore, for rising mass functions, the majority of the planets will be detected around sources with fluxes near sky. In order to maximize the number of detections, experiments should therefore be tailored such that sources near sky are above the required detection threshold. Once this requirement is met, the number of detected planets is relatively weakly dependent on the detection threshold, diameter of the telescope, exposure time, seeing, age of the system, and planet radius, for typical ranges of these parameters encountered in current transit searches in stellar systems. The number of detected planets is a strongly decreasing function of the distance to the system, implying that the nearest, richest clusters may prove to be optimal targets