An emission line in a spectrum that is emitted only by a low-density gas, as in interstellar regions and nebulae. Such a line is said to be forbidden because it does not occur under normal conditions on Earth, where gases are denser. A forbidden line is produced when an electron jumps from an upper energy level, where it can remain for a long time, to a lower level; such a jump, or transition, is said to have a very low transition probability. In the Earth’s atmosphere, the excited atom would collide with other atoms or free electrons and lose energy in the collision (without producing a photon) long before it could radiate the energy away. However, in the low densities of interstellar space and the regions around hot stars, collisions are extremely rare and there is time for the spontaneous decay to occur. Forbidden lines are denoted by square brackets, such as the [O III] lines of doubly ionized oxygen. Forbidden lines disappear above a certain critical density (typically about 108 atoms/cm3), and so their existence is an indicator of density in interstellar gas. A semi-forbidden line, designated with a single square bracket, such as C III], occurs where the transition probability is about a thousand times higher than for a forbidden line.