## 1 Introduction  
The solar-terrestrial space refers to the region of space that includes the outer solar atmosphere, solar-terrestrial interplanetary space, Earth's magnetic field, ionosphere, middle and upper atmosphere [1], which is subject to various solar activities such as sunspots and Coronal Mass Ejections (CMEs), as well as coupling among complex interactions between different parts of the solar-terrestrial space. These factors can disrupt the stability of the space environment, leading to disturbances such as geo-magnetic storms and auroras in the Earth's space environment [2, 3], and result in space weather disasters, for instance, the \"Carrington event\" in 1859 [4] and the collective fall of 40 SpaceX Starlink Satellites in 2022 just before reaching their designated orbit [5]. It is easy to see that the resulting space weather events can cause severe damage to space-based and ground-based systems, with profound effects on human activities [6]; therefore, there is a growing recognition of the importance of learning and warning against space weather disasters. The aurora is a space weather phenomenon commonly observed in mid-high latitudes but can also be seen in lower latitudes during periods of intense solar activities [7, 8]. The aurora originates from solar activity. During periods of increased solar activity, the solar wind, formed by the expansion of the corona, carries high-energy particles. These particles, under the influence of Earth's magnetic field, travel along magnetic field lines to the upper atmosphere above the polar regions [9]. The components of the upper atmosphere mainly include N\({}_{2}\), O\({}_{2}\), N and O. After the injection of auroral electrons, the neutral particles dissociate and ionize, while the auroral electrons are deposited gradually, ionizing them and generating large numbers of secondary electrons during the collision with atoms and molecules (mainly N\({}_{2}\), O\({}_{2}\), and N) [9], as shown by Equations (1)-(3):  
\[\mathrm{e_{p}+N_{2}\to e_{p}+N_{2}^{+}+e_{s}} \tag{1}\]  
\[\mathrm{e_{p}+O_{2}\to e_{p}+O_{2}^{+}+e_{s}} \tag{2}\]  
\[\mathrm{e_{p}+O\to e_{p}+O^{+}+e_{s}} \tag{3}\]  
where \(\mathrm{e_{p}}\) is the primary electrons and \(\mathrm{e_{s}}\) is the secondary electrons. The energy of secondary electrons is small, generally below 200 eV; this energy range can cause the excitation of the electronic states of numerous molecules and atoms, but only the first generation of secondary products can be further ionized [10], which can induce electronic excitations in molecules and atoms, generating a \"driving source\" for subsequent photochemical reactions. The photochemical reactions between the components are extremely complex, and the emission spectra range from extreme ultraviolet to the infrared spectral region, where the infrared band radiation accounts for more than 20% of the total emitted energy [10]. Due to their comparatively low photon energy, infrared photons usually cannot directly excite the electronic state of atoms or molecules, but rather rely on collisional excitation arising from photochemical reactions. The primary contributors to infrared radiation emissions are NO, NO\({}^{+}\), and CO\({}_{2}\). This paper focuses on the characteristics of 5.3 \(\upmu\)m radiance in the aurora, where NO infrared radiation at 5.3 \(\upmu\)m is the primary thermal equilibrium process in the atmosphere and is an important radiative cooling process in the altitude region of 110-300 km [11; 12; 13], which is known as the \"natural thermostat\" [14; 15]. The density variation of NO is predominantly determined by latitude, longitude, altitude, and seasonal changes [16; 17; 18]. Furthermore, it is impacted by X-rays and ultraviolet radiation at low latitudes [17; 19]. Specifically, under auroral conditions, the density of NO is also influenced by Joule heating and particle heating in the polar and mid-latitude regions, leading to an increase in kinetic temperature in the polar region [19; 20; 21].