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A starburst galaxy is a galaxy forming stars at a very high rate (undergoing a starburst) for its size (its stellar mass, i.e., the combined mass of all its stars), so high that all its gas would be gone if this had been going on for the life of the galaxy. For a Milky-Way-sized galaxy, this would raise its star formation rate from on the order of 25 solar masses per year (typical), to ten or more times that. The term quiescent, as in quiescent galaxy can refer to a galaxy that is not starburst, but is often used for a quenched galaxy, i.e., that isn't a star-forming galaxy (SFG), forming virtually no stars. (The actual Milky Way is estimated to produce on the order of one solar mass per year, substantially below typical but not quenched.)
Such extreme star formation can be detected in a distant galaxy by the strength of spectral features associated with hot, short-lived stars, which are necessarily recent. In many cases, such stars are hidden by the dust in the clouds that formed them, but are detected by infrared radiation reradiated from these clouds due to energy from the hot stars. It is thought that starbursts are triggered by close encounters and mergers between galaxies. There is evidence that starbursts can form so many stars so close together that a gas blowout results from the pressure created by the EMR and heated gas, changing it into in a quenched galaxy. A post-starburst galaxy (PSB galaxy) is one which is thought to have made this transition, which sometimes is a green valley galaxy (i.e., not totally quenched).