Survey for Transiting Extrasolar Planets in Stellar Systems. Iii. a Limit on the Fraction of Stars with Planets in the Open Cluster Ngc 1245

We analyze a 19 night photometric search for transiting extrasolar planets in the open cluster NGC 1245. An automated transit search algorithm with quantitative selection criteria finds six transit candidates; none are bona fide planetary transits.We characterize the survey detection probability viaMonte Carlo injection and recovery of realistic limb-darkened transits. We use this to derive upper limits on the fraction of cluster members with close-in Jupiter radii, R J , companions. The survey sample contains 870 cluster members, and we calculate 95% confidence upper limits on the fraction of these stars with planets by assuming that the planets have an even logarithmic distribution in semimajor axis over the Hot Jupiter (HJ; 3:0 < P day 1 < 9:0) and Very Hot Jupiter (VHJ; 1:0 < P day 1 < 3:0) period ranges. For 1.5RJ companions we limit the fraction of cluster members with companions to<6.4% and<52% for VHJ and HJ companions, respectively. For 1.0RJ companions we find that<24% have VHJ companions. We do not reach the sensitivity to place any meaningful constraints on 1.0RJ HJ companions. From a careful analysis of the random and systematic errors of the calculation, we show that the derived upper limits contain aþ13%/ 7% relative error. For photometric noise and weather properties similar to those of this survey, observing NGC 1245 twice as long results in a tighter constraint onHJ companions than observing an additional cluster of richness similar to that of NGC 1245 for the same length of time as this survey. If 1% of stars have 1.5RJ HJ companions (as measured in radial velocity surveys), we expect to detect one planet for every 5000 dwarf stars observed for a month. To reach an 2% upper limit on the fraction of stars with 1.5RJ companions in the 3:0 < P day 1 < 9:0 range, we conclude that a total sample size of 7400 dwarf stars observed for at least a month will be needed. Results for 1.0RJ companions, without substantial improvement in the photometric precision, will require a small factor larger sample size.