Quantitative Estimates of Environmental Effects on the Star Formation Rate of Disk Galaxies in Clusters of Galaxies

A simple model is constructed to evaluate the change of star formation rate of a disk galaxy due to environmental effects in clusters of galaxies. Three effects, (1) tidal force from the potential well of the cluster, (2) increase of external pressure when the galaxy plows into the intracluster medium, (3) high-speed encounters between galaxies, are investigated. General analysis indicates that the star formation rate increases significantly when the pressure of molecular clouds rises above $\sim 3\times 10^5 cm^{-3} K$ in $\sim 10^8$ yr. The tidal force from the potential well of the cluster increases pressures of molecular clouds in a disk galaxy infalling towards the cluster center. Before the galaxy reaches the cluster center, the star formation rate reaches a maximum. The peak is three to four times larger than the initial value. If this is the main mechanism of the Butcher-Oemler effect, blue galaxies are expected to be located within $\sim 300$ kpc from the center of the cluster. However this prediction is inconsistent with the recent observations. The increase of external pressure when the galaxy plows into the intracluster medium does not change star formation rate of a disk galaxy significantly. The velocity perturbation induced by a single high-speed encounter between galaxies is too small to affect star formation rate of a disk galaxy, while successive high-speed encounters (galaxy harassment) trigger star formation activity because of the accumulation of gas in the galaxy center. Therefore, the galaxy harassment remains as the candidate for a mechanism of the Butcher-Oemler effect.