(F)our Auroral lines 5577 Å - The auroral green line The emission of the ``auroral green line'' at 5577 Å is in general the brightest emission, giving the aurora its characteristic green colour. It is emitted by atomic oxygen in its transition from the second lowest excited electronic state $O(^1S)$ to the lowest excited electronic state $O(^1D)$. The three main sources are energy transfer from $N_2(A^3\Sigma^+_u)$, dissociative recombination and direct electron excitation. Energy transfer via the reaction: $$N_2(A^3\Sigma^+_u) + O \rightarrow N_2 + O(^1S)$$ (2.1) has a yield of approximately 0.4 in aurora ( Strickland et al., 2000). According to Hill et al. (2000) the reaction rate depends on the neutral temperature and the vibrational level of the excited nitrogen molecule. The dissociative recombination of $O_2^+$ follows the reaction: $$O_2^+ + e_{a} \rightarrow 2O(^3P_2,^1D,^1S)$$ (2.2) where $e_a$ represents the ambient electrons. This reaction has a reaction rate ( Solomon et al., 1988) given by: $$\alpha = 1.9\cdot10^{-7}(T_e/300)^{-0.5} ^3/$$ (2.3) The yield of $O(^1S)$ from dissociative recombination is approximately 10 % and shows a weak dependency on electron temperature and the ratio between electron density and oxygen density ( Yee et al., 1989). The direct excitation of $O(^1S)$ by energetic electrons follows the reaction: $$O + e(E) \rightarrow O(^1S) + e(E-4.17 )$$ (2.4) With the cross section ( Itikawa and Ichimura, 1990) shown in green in Figure 2.1, this process is a source of the $O(^1S)$ state. The three sources have different altitude variation and change their relative contribution depending on ionospheric conditions (Sergienko private communication). Figure 2.1: Cross sections for electron excitation for the states that emit the lines measured by ALIS. (1) $e+O\rightarrow O(^1D) + e$ experimental values by Doering (1992) compared with theoretical values from Rees (1989). (2) $e+O\rightarrow O(^1S)+e$ experimental values by Doering and Gulcicek (1989) compared with theoretical values from Rees (1989). (3) $e+O\rightarrow O(3p\ ^3P_2)+e$ experimental and theoretical values from Itikawa and Ichimura (1990) and references therein. (4) Emission cross section for 8446 Å from Strickland et al. (1989). (5) Emission cross section for 4278 Å from Itikawa et al. (1986). 6300Å - The auroral red line The 6300 Å emission, the ``red line'', is sometimes seen in the upper border of auroral arcs. It is emitted by atomic oxygen in its transition from the lowest excited electronic state $O(^1D)$ to the atomic ground state $O(^3P_2)$. The metastable $O(^1D)$ state has a radiative lifetime of 107 s. The main sources of $O(^1D)$ are direct electron impact excitation of atomic oxygen: $$O(^3P_2) + e \rightarrow e + O(^1D)$$ (2.5) with the excitation cross section as shown in Figure 2.1 and dissociative recombination of $O_2^+$: $$O_2^+ + e \rightarrow O + O(^1D)$$ (2.6) with an $O(^1D)$ yield of 1.2 and a reaction rate according to equation (2.3). Due to the 107 s radiative lifetime of $O(^1D)$, the emission of the 6300 Å line competes with collisional de-excitation, quenching, as a cause of energy loss of $O(^1D)$, where the excitation energy is lost as kinetic, vibrational or rotational energy of the colliding particles without emission of photons. Here collisions with molecular oxygen and nitrogen follow: $$O(^1D) + N_2 @>q_1>> O(^3P_2) + N_2$$ (2.7) $$O(^1D) + O_2 @>q_2>> O(^3P_2) + O_2$$ (2.8) with the rate coefficients given by ( Mantas and Carlson, 1996): $$q_1 = 2.0\cdot10^{-11}\exp(107.8/T_n)\ {\text{cm\(^3\)s\(^{-1}\)}}$$ (2.9) $$q_2 = 2.9\cdot10^{-11}\exp(67.5/T_n)\ {\text{cm\(^3\)s\(^{-1}\)}}$$ (2.10) and with atomic oxygen: $$O(^1D) + O @>q_3>> O(^3P_2) + O$$ (2.11) with the rate coefficient ( Solomon et al., 1988) given by: $$q_3 = 2.0\cdot10^{-12}\ {\text{cm\(^3\)s\(^{-1}\)}}$$ (2.12) have to be taken into account. Further, $O(^1D)$ is quenched by thermal electrons: $$O(^1D) + e @>q_4>> O(^3P_2) + e$$ (2.13) with a quenching rate ( Rees, 1989): $$q_4 = 1.6\cdot10^{-12}T_e^{0.91}\ {\text{cm\(^3\)s\(^{-1}\)}}$$ (2.14) This implies that the emission of the 6300 Å mainly originates at high altitudes with peak volume emission rates typically between 200 and 400 km. At lower altitudes $O(^1D)$ loses its energy by quenching due to the increasing neutral number density. 8446 Å The 8446 Å emission, from atomic oxygen in the near infrared, results from the transition $O(3p^3P)\rightarrow O(3s^3S)$. These states have a slightly higher excitation energy than the upper states of the auroral green and red lines: $O(3p^3P)$ has an excitation energy of 10.99 eV. The upper state $O(3p^3P)$ is excited mainly by direct electron impact on $O$: $$O(^3P_2) + e \rightarrow e + O(3p^3P)$$ (2.15) but a minor source is dissociative electron excitation: $$O_2 + e\rightarrow O + O(3p^3P)$$ (2.16) The $O(3p^3P)$ state is also populated by cascading from optically thick emissions from higher lying states, that are excited by electron impact. Cross sections for electron excitation are reported by Itikawa and Ichimura (1990), and emission cross sections are cited in Strickland et al. (1989) where an estimate for the optically thick cascade contribution from higher-lying oxygen states is accounted for. 4278 Å -- a $\mathbf{N}_{\mathbf{2}}^{\boldsymbol{+}}$ 1NG line The $N_2^+$ emission 4278 Å in the blue region of the visible spectum is emitted by the transition from the $N_2^+(B^2\Sigma_u^+)$ state to the first vibrational level of electronic ground state of the molecular nitrogen ion $N_2^+(X^2\Sigma_u^+)$. According to Borst and Zipf (1970), 11 % of the $N_2$ ionization is to the $B^2\Sigma_u^+$ state of which 19 % emits 4278 Å photons. As a consequence a total of 2.13 % of the $N_2$ ionization results in emission of 4278 Å ( Vallance Jones, 1974). Later emission cross sections have been reported ( Itikawa et al., 1986) and are shown in Figure 2.1.