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During the evolution of proto-planetary disc, photo-evaporations of bothcentral and external stars play important roles. Considering the complicatedradiation surroundings in the clusters, where the star formed, theproto-planetary discs survive in different lifetimes due to flyby events. Inthis paper, we mainly focus on the disc around a T Tauri star, which encounterswith another main-sequence star with different temperatures in hyperbolicorbits with different peri-center distances, eccentricities and inclinations.We find the criterion for gap-opening due to photo-evaporation of central starafter the flyby event. A gap is opened in the late stage of gas disc, andinduce that the gap only influence the planet formation and migrationlimitedly. If the flyby orbit has a moderate value of peri-center distance,which weakly depends on the eccentricity and inclination, the externalphoto-evaporation lead to a maximum mass loss during the flyby event. Flybystars in orbits with smaller eccentricities or larger inclinations inducelarger mass loss. Adopting a simple multiple flyby models, we conclude that inopen clusters, gas discs usually survive in typical lifetimes between 1 and 10Myr, except there are many massive stars in dense open clusters. In globularclusters, discs disperse very quickly and hardly produce the gas giant planets.The fast-depleted discs are probably responsible for the null detection ofgiant planets in globular clusters.

Photo-evaporation of proto-planetary gas discs due to flybys of external single stars in different orbits