Definition of Symbols

Symbol	Parameter	Unit
\(I(\lambda, T)\)	Spectral radiance	\(Wm^{-2} sr^{-1} \mu m^{-2}\)
\(Q(T)\)	Partition function	–
\(R\)	Spectral resolution	–
\(T\)	Temperature	\(K\)
\(N\)	Column integrated \(\text{H}_3^+\) density	\(m^{-2}\)
\(b(\lambda)\)	Background level	\(Wm^{-2} sr^{-1} \mu m^{-2}\)
\(\lambda\)	Wavelength	\(\mu m\)
\(\sigma(\lambda)\)	Wavelength dependent line width	\(\mu m\)
\(s(\lambda)\)	Wavelength dependent line shift	\(\mu m\)
\(g_{ns}\)	Spin weighting	–
\(J\)	Angular momentum quantum nbr	–
\(w_{if}\)	Emission frequency	\(cm^{-1}\)
\(w_{upper}\)	Upper energy level	\(cm^{-1}\)
\(A_{if}\)	Einstein A coefficient	–
\(h\)	Planck’s constant	\(m^{-2} kg s^{-1}\)
\(c\)	Speed of light	\(m s^{-1}\)
\(k\)	Boltzmann’s constant	\(m^2 kg s^{-2} K^{-1}\)