Estimating Boltzmann vibrational temperature of N2 (B^3Pi_g) using ISUAL 630nm, N2 1P (623-754 nm) and 762 nm-filtered imager data

Multi-band observation of transient luminous events (TLEs) is one of the useful methodologies to be employed in sprite campaigns. Here, we show a method to estimate the Boltzmann vibrational temperature of N₂ (B³Π_g) by analyzing the 630nm-filtered, N₂ 1P-filtered and 762 nm-filtered images of TLEs. Our advanced method is validated in compassion with derived relative vibrational distributions by sprite spectrum (Kanmae et al., 2007). The imager recorded N₂ 1P-filtered emission (I_1P,  623 – 754 nm) of TLEs indicates the intensity of N₂ 1P Δv=3 and partial with Δv=2 where dominated emissions with upper state vibrational number v=4, 5 and 6, i.e., N₂ 1P (4, 2), (4, 1), (5, 2) and (6, 3). The imager recorded 630 nm-filtered emissions (I₆₃₀) were contributed primarily from N₂ 1P (10, 7) with v=10 while N₂ 1P (3, 1) for 762 nm-filtered emissions (I₇₆₂) with v=3. Hence, we calculated the emission ratios of I₆₃₀ to I_1P, I₆₃₀ to I₇₆₂ and I₇₆₂ to I_1P. The emission ratios of I₆₃₀ to I_1P, I₆₃₀ to I₇₆₂ and I₇₆₂ to I_1P  also reflect the relative vibrational distributions of vibrational levels with LOW v=3 (I₇₆₂), MIDDLE v=4, 5, 6 (I_1P,  623 – 754 nm), and HIGH v=10 (I₆₃₀). Therefore, we use the Boltzmann temperature for indicating the relative vibrational distributions of the specified group (LOW/MIDDLE/HIGH) of N₂ (B³Π_g) vibrational levels. For ISUAL recorded sprites, the average brightness of N₂ 1P (I_1p), 762 nm (I₇₆₂) and 630 nm (I₆₃₀) emission was 2.3, 0.6 and 0.02 MR. The N₂ (B³Π_g) vibrational temperatures (T_v) were estimated to be 2800 K, 3200 K and 4300 K for multi-band emission ratios of I₆₃₀/ I_1p, I₆₃₀/ I₇₆₂ and I₇₆₂/ I_1p. For observed elves, the average brightness I_1p, I₇₆₂ and I₆₃₀ were 170, 50 and 3 kR. The estimated T_v values were 3700 K, 3700 K and 3800 K for ratios I₆₃₀/ I_1p, I₆₃₀/ I₇₆₂ and I₇₆₂/ I_1p. For observed gigantic jets, the derived T_v values were 3000 – 5000 K for a ratio I₇₆₂/ I_1p. Through N₂ (B³Π_g) T_v analyses from emission ratios of ISUAL multi-band observation, we derived the N₂ (B³Π_g) vibrational temperature that ranges between 3000 and 5000 K or higher in TLEs. Accuracy and variations of derived N₂ (B³Π_g) T_v are also discussed while the relative population of vibrational levels in the Boltzmann equilibrium are also compared with past spectra observation. The details are shown in the publication (https://doi.org/10.1029/2019JA027311).