Estimating Boltzmann vibrational temperature of N2 (B^3Pi_g) using ISUAL 630nm, N2 1P (623-754 nm) and 762 nm-filtered imager data
Authors: Kuo Cheng Ling ,   ISUAL Science Team
Published: March 2020

&lt;p&gt;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 N&lt;sub&gt;2&lt;/sub&gt; (B&lt;sup&gt;3&lt;/sup&gt;&amp;#928;&lt;sub&gt;g&lt;/sub&gt;) by analyzing the 630nm-filtered, N&lt;sub&gt;2&lt;/sub&gt; 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 N&lt;sub&gt;2&lt;/sub&gt; 1P-filtered emission (I&lt;sub&gt;1P, &lt;/sub&gt;&amp;#160;623 &amp;#8211; 754 nm) of TLEs indicates the intensity of N&lt;sub&gt;2&lt;/sub&gt; 1P &amp;#916;v=3 and partial with &amp;#916;v=2 where dominated emissions with upper state vibrational number v=4, 5 and 6, i.e., N&lt;sub&gt;2&lt;/sub&gt; 1P (4, 2), (4, 1), (5, 2) and (6, 3). The imager recorded 630 nm-filtered emissions (I&lt;sub&gt;630&lt;/sub&gt;) were contributed primarily from N&lt;sub&gt;2&lt;/sub&gt; 1P (10, 7) with v=10 while N&lt;sub&gt;2&lt;/sub&gt; 1P (3, 1) for 762 nm-filtered emissions (I&lt;sub&gt;762&lt;/sub&gt;) with v=3. Hence, we calculated the emission ratios of I&lt;sub&gt;630&lt;/sub&gt; to I&lt;sub&gt;1P&lt;/sub&gt;, I&lt;sub&gt;630&lt;/sub&gt; to I&lt;sub&gt;762&lt;/sub&gt; and I&lt;sub&gt;762&lt;/sub&gt; to I&lt;sub&gt;1P&lt;/sub&gt;. The emission ratios of I&lt;sub&gt;630&lt;/sub&gt; to I&lt;sub&gt;1P&lt;/sub&gt;, I&lt;sub&gt;630&lt;/sub&gt; to I&lt;sub&gt;762&lt;/sub&gt; and I&lt;sub&gt;762&lt;/sub&gt; to I&lt;sub&gt;1P &lt;/sub&gt;&amp;#160;also reflect the relative vibrational distributions of vibrational levels with LOW v=3 (I&lt;sub&gt;762&lt;/sub&gt;), MIDDLE v=4, 5, 6 (I&lt;sub&gt;1P, &lt;/sub&gt;&amp;#160;623 &amp;#8211; 754 nm), and HIGH v=10 (I&lt;sub&gt;630&lt;/sub&gt;). Therefore, we use the Boltzmann temperature for indicating the relative vibrational distributions of the specified group (LOW/MIDDLE/HIGH) of N&lt;sub&gt;2&lt;/sub&gt; (B&lt;sup&gt;3&lt;/sup&gt;&amp;#928;&lt;sub&gt;g&lt;/sub&gt;) vibrational levels. For ISUAL recorded sprites, the average brightness of N&lt;sub&gt;2&lt;/sub&gt; 1P (I&lt;sub&gt;1p&lt;/sub&gt;), 762 nm (I&lt;sub&gt;762&lt;/sub&gt;) and 630 nm (I&lt;sub&gt;630&lt;/sub&gt;) emission was 2.3, 0.6 and 0.02 MR. The N&lt;sub&gt;2&lt;/sub&gt; (B&lt;sup&gt;3&lt;/sup&gt;&amp;#928;&lt;sub&gt;g&lt;/sub&gt;) vibrational temperatures (T&lt;sub&gt;v&lt;/sub&gt;) were estimated to be 2800 K, 3200 K and 4300 K for multi-band emission ratios of I&lt;sub&gt;630&lt;/sub&gt;/ I&lt;sub&gt;1p&lt;/sub&gt;, I&lt;sub&gt;630&lt;/sub&gt;/ I&lt;sub&gt;762&lt;/sub&gt; and I&lt;sub&gt;762&lt;/sub&gt;/ I&lt;sub&gt;1p&lt;/sub&gt;. For observed elves, the average brightness I&lt;sub&gt;1p&lt;/sub&gt;, I&lt;sub&gt;762&lt;/sub&gt; and I&lt;sub&gt;630&lt;/sub&gt; were 170, 50 and 3 kR. The estimated T&lt;sub&gt;v&lt;/sub&gt; values were 3700 K, 3700 K and 3800 K for ratios I&lt;sub&gt;630&lt;/sub&gt;/ I&lt;sub&gt;1p&lt;/sub&gt;, I&lt;sub&gt;630&lt;/sub&gt;/ I&lt;sub&gt;762&lt;/sub&gt; and I&lt;sub&gt;762&lt;/sub&gt;/ I&lt;sub&gt;1p&lt;/sub&gt;. For observed gigantic jets, the derived T&lt;sub&gt;v&lt;/sub&gt; values were 3000 &amp;#8211; 5000 K for a ratio I&lt;sub&gt;762&lt;/sub&gt;/ I&lt;sub&gt;1p&lt;/sub&gt;. Through N&lt;sub&gt;2&lt;/sub&gt; (B&lt;sup&gt;3&lt;/sup&gt;&amp;#928;&lt;sub&gt;g&lt;/sub&gt;) T&lt;sub&gt;v&lt;/sub&gt; analyses from emission ratios of ISUAL multi-band observation, we derived the N&lt;sub&gt;2&lt;/sub&gt; (B&lt;sup&gt;3&lt;/sup&gt;&amp;#928;&lt;sub&gt;g&lt;/sub&gt;) vibrational temperature that ranges between 3000 and 5000 K or higher in TLEs. Accuracy and variations of derived N&lt;sub&gt;2&lt;/sub&gt; (B&lt;sup&gt;3&lt;/sup&gt;&amp;#928;&lt;sub&gt;g&lt;/sub&gt;) T&lt;sub&gt;v&lt;/sub&gt; 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).&lt;/p&gt;