Theory of Radiative Transfer for 3.3-micron $CH_4$ emissions from the Auroral Regions of Jupiter

Radiative transfer programs to simulate the 3-micron auroral $CH_4$ emissions of Jupiter have been developed. The formalism of the radiative transfer calculations including the thermal, fluorescent, and auroral emissions of the $CH_4$ bands for an atmospheric layer having an optical depth of ${\tau}_v$ is given by: ${\mu}dI_v/d{\tau}_v=I_v-{\varpi}_v{^*}J_v(1-{\varpi}_v{^*})B_v-{\varpi}{^*}F_{ov}{e}{x}{p}(-{\tau}_v/{\mu}_o)4{\pi}-hv{\varpi}{^*}V/4{\pi}$ where ${\varpi}_v{^*}$ is the single scattering albedo of $CH_4$ consisting of Einstein A coefficient and collisional deexcitation rate. Other terms are usual radiative transfer parameters appearing in textbooks including the terms for scattered ${\varpi}_v{^*}J_v$, thermal $(1-{\varpi}_v{^*})B_v$, and attenuated solar radiations $F_{ov}$ at the certain atmospheric layer. For auroral excitations, we include V, which is the number of excited states per $cm^3$ persec by auroral particle bombardments. We apply this formalism to the high-resolution spectra of the auroral regions observed with GNIRS/Gemini North, and will present preliminary results for the 3 micron auroral processes of Jupiter.