Statistical model for the abundance of deuterated ammonia in interstellar space

The elemental abundance of deuterium to normal hydrogen in the universe is on the order of 10⁻⁵. A random distribution would therefore give a ratio of triply deuterated ammonia, ND₃, to NH₃ of ${10}^{-15}$. Observations indicate an ND₃ to NH₃ ratio of roughly ${10}^{-3}$, implying enrichment of triply deuterated ammonia by about twelve orders of magnitude. A simple model, based on the elemental abundances of N, D and H, is developed and solved analytically. At zero temperature the expressions are particularly simple. Effects of finite temperature are included through the partition functions of the isotopologues. It is found that the effect of finite temperature is modest in the temperature range 10–100 K. The results of the model are in good agreement with the observed abundances so local thermal equilibrium may therefore be a reasonable approximation and thus also be an explanation for the apparent enrichment of deuterated isotopologues.