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In clustered environments, stellar encounters can liberate planets from theirhost stars via close encounters. Although the detection probability of planetssuggests that the planet population in open clusters resembles that in thefield, only a few dozen planet-hosting stars have been discovered in openclusters. We explore the survival rates of planets against stellar encountersin open clusters similar to the Pleiades, Hyades, and Praesepe and embeddedclusters. We performed a series of N-body simulations of high-density andlow-density open clusters, open clusters that grow via mergers of subclusters,and embedded clusters. We semi-analytically calculated the survival rate ofplanets in star clusters up to 1Gyr using relative velocities, masses, andimpact parameters of intruding stars. Less than 1.5% of close-in planets within1 AU and at most 7% of planets with 1-10 AU are ejected by stellar encountersin clustered environments after the dynamical evolution of star clusters. If aplanet population from 0.01-100 AU in an open cluster initially follows theprobability distribution function of exoplanets with semi-major axis ($a_p$)between 0.03-3 AU in the field discovered by RV surveys, the PDF of survivingplanets beyond ~10 AU in open clusters can be slightly modified to $\proptoa_p^{-0.76}$. The production rate of free-floating planets (FFPs) per star is0.0096-0.18, where we have assumed that all the stars initially have one giantplanet with a mass of 1--13 MJ in a circular orbit. The expected frequency ofFFPs is compatible with the upper limit on that of FFPs indicated by recentmicrolensing surveys. Our survival rates of planets in open clusters suggestthat planets within 10 AU around FGKM-type stars are rich in relatively-young(<~10-100 Myr for open clusters and ~1-10 Myr for embedded clusters), lessmassive open clusters, which are promising targets for planet searches.

Survival Rates of Planets in Open Clusters: the Pleiades, Hyades, and Praesepe clusters