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