DETECTABILITY OF FREE FLOATING PLANETS IN OPEN CLUSTERS WITH THE JAMES WEBB SPACE TELESCOPE

Recent observations have shown the presence of extra-solar planets in Galactic open stellar clusters, such as in Praesepe (M44). These systems provide a favorable environment for planetary formation due to the high heavy-element content exhibited by the majority of their population. The large stellar density, and corresponding high close-encounter event rate, may induce strong perturbations of planetary orbits with large semimajor axes. Here we present a set of N-body simulations implementing a novel scheme to treat the tidal effects of external stellar perturbers on planetary orbit eccentricity and inclination. By simulating five nearby open clusters, we determine the rate of occurrence of bodies extracted from their parent stellar system by quasi-impulsive tidal interactions. We find that the specific free-floating planet production rate (N) over dot(o) (total number of free-floating planets per unit of time, normalized by the total number of stars), is proportional to the stellar density rho(star) of the cluster: (N) over dot(o) = alpha rho(star), with alpha = (23 +/- 5) x 10(-6) pc(3) Myr(-1). For the Pleiades (M45), we predict that similar to 26% of stars should have lost their planets. This raises the exciting possibility of directly observing these wandering planets with the James Webb Space Telescope in the near-infrared band. Assuming a surface temperature for the planet of similar to 500 K, a free-floating planet of Jupiter size inside the Pleiades would have a specific flux of F-nu (4.4 mu m) approximate to 4 x 10(2) nJy, which would lead to a very clear detection (S/N similar to 100) in only one hour of integration.