cooling function

A cooling function is a function of temperature indicating the rate that a gas cools, more specifically, giving the rate it cools divided by the number density of gas particles squared.

R = n²Λ(T)

• R - the rate of cooling of the gas, e.g., energy/volume such as ergs/cm³/sec
• n - number density, e.g., number/cm³
• T - temperature.
• Λ(T) - cooling function.

Cooling generally depends upon the number density squared, so the cooling function, which captures the dependence on temperature yields power times volume, i.e., power times the reciprocal of number density, such as ergs cm³ s^-1.

Such functions are used in modeling the cooling of gas clouds into galaxies or protostars. The function depends upon the constitution of the gas, and takes into account the molecular structure, quantum mechanics, and states of ionization. The functions presume the gas's optical depth is much less than one (optically thin), i.e., a photon emitted will generally leave the cloud.

The function generally has multiple peaks and valleys due to the varied emission mechanisms that are most efficient at particular temperatures. The emission mechanisms are the same as those in radiative transfer, such as within stars, but cooling functions are for an optically-thin regime.