This figure illustrates the rotatitional energies of a simple diatomic molecule. Collisions with other molecules in the gas, which in the interstellar medium are predominantly molecules of molecular hydrogen and atoms of helium, cause a molecule to change quantum state. A collision can either speed up the rotation (increase the rotational energy) or slow it down. The amount by which the rotational energy can be changed depends on the speed of the colliding partner. A slow collider might only have enough kinetic energy to change the molecular rotation to that of an adjacent state, whereas a fast collider might result in a large change of rotational energy.
the radiation for a given transition appears at a well-defined frequency. In a plot of radiation intensity versus frequency, the emission appears as a series of narrow spectral lines. Spectral line radiation is measured with spectrometers.
The simplest spectrometer to imagine is one consisting of a series of narrow filters, each tuned to s slightly different frequency. Each passes a narrow band of frequencies, whose intensity is recorded. A plot of intensity versus frequency is called a spectrum.
As a molecule sits undisturbed in a given rotational state, it becomes more and more probable that it will spontaneously decayto the next lower state, with the excess energy being carried off as a photon. Each energy state has its own characteristic half life, that is, the time during which on the average, half the molecules would decay. (The process is statistical. We can never predict exactly when a molecule will decay.) If the time between collisions, which can knock molecules into the state is long compared to the half life, then the state will generally tend to be empty. In a low density gas (in which collisions would be rare) most molecules would occupy only the lowest few energy states. Then, only the spectral lines connecting these lowest energy levels would have any detectable intensity. On the other hand, in a sufficiently dense gas, collisions would happen more frequently than spontaneous decays, and more spectral lines would be observed.
Temperature is a measure of the speed of theransom motions of molecules in a gas. In a hot gas, the speed is high. In a cold gas, the molecules move slowly. When a molecule it hit by a fast helium atom or hydrogen molecule hits our molecule, it can impart a lot of energy and knock it into a high rotational level. Thus, in a hot gas, higher energy states will be populated than in a cold gas. The relative intensities of spectral lines can thus be used to measure the gas temperature.
The alert reader will have noticed that a low population of high energy states can mean either low temperature or low density. Indeed, spectroscopists speak of an excitation temperature, which is the apparent temperature derived from the ratios of populations of two levels. The excitation temperature can be low because the kinetic (collision) temperature is low, or because the density is low. However, in low density situations, the excitation temperature is usually different for different transitions. By seeing how the excitation temperature varies from transition to transition, the effects of kinetic temperature and gas density can be separated.
When the emitting object is approaching, the frequency is shifted higher, while the shift is to lower frequency for a receding object. The actual frequency at which a spectral line is observed, compared to the frequency measured in the laboratory, tells us how fast a molecular cloud is moving towards or away from us. The random motions of molecules in a gas, the same motions which give rise to temperature, cause a spectral line to be broadened, because on the average, some molecules are moving away from us and others are approaching. Furthermore, turbulent motions in the gas will cause line broadening. By comparing the actual width of a spectral line with the one expected for the temperature of the gas, the amount of turbulence can be obtained. Large scale motions in the gas, such as rotation, expansion, collapse, etc. also leave characteristic signatures in the shape of the spectral line.