Modeling the Earth’s Nightglow Intensity of the Chamberlain and Herzberg I Bands and Comparing the Calculation Results with the Experimental Data

Abstract

The calculations of volume intensity profiles of the Earth’s nightglow of the Chamberlain and Herzberg I bands of molecular oxygen are given. The calculations of glow intensities of the Chamberlain and Herzberg I bands are compared with the experimental data obtained from the Discovery Space Shuttle (STS-53) and from the EbertFastie spectrograph (Kitt Peak National Observatory, USA, Arizona). It is shown that the best agreement between the calculation results and experimental data is observed when correcting the quantum yields of the vibrational levels A'³Δ_u and ${{{\text{A}}}^{3}}\Sigma _{{\text{u}}}^{ + }$ of the molecular oxygen states under triple collisions.

1 INTRODUCTION

Awareness of the possibility of upper atmosphere radiation at middle and low latitudes under quiet geomagnetic conditions did not arise until the task of estimating the planet’s surface illumination at nighttime was proposed. By the end of the second decade of the 20th century it became obvious that the Earth’s atmosphere is undergoing processes that are indicated by the intrinsic glow of the night atmosphere under quiet geomagnetic conditions (Shefov et al., 2006).

One of the sources of nightglow is electronically excited molecular oxygen O₂(A'³Δ_u, ${{{\text{A}}}^{3}}\Sigma _{{\text{u}}}^{ + }$), which is formed during triple collisions in the Earth’s atmosphere with the involvement of two O atoms and a third particle:

$${\text{O}} + {\text{O}} + {\text{M}} \to {{{\text{O}}}_{2}}({\text{A}}{{'}^{3}}{\kern 1pt} {{\Delta }_{{\text{u}}}},{{{\text{A}}}^{3}}\Sigma _{{\text{u}}}^{ + };\nu {\kern 1pt} ') + {\text{M}},$$

(1)

where ν ' is the vibrational level of the indicated state; M is the third particle in the collision. Oxygen atoms are effectively formed in the Earth’s atmosphere during the daytime during the photodissociation of O₂ molecules by the solar UV radiation: O₂ + hν → O + O. Triple collisions (1) with the formation of O₂(A'³Δ_u, ${{{\text{A}}}^{3}}\Sigma _{{\text{u}}}^{ + }$) are most effective in the Earth’s atmospheric layer with a thickness of ~10 km centered at the altitude of ~90 km (Shefov et al., 2006; Broadfoot and Bellaire, 1999). Further, the electronically excited oxygen molecule passes into the lower energy state, by emitting photons of light at the same time. Spontaneous transitions from the electronically excited A'³Δ_u to the electronically excited a¹Δ_g state of the oxygen molecule lead to the glow of Chamberlain (Ch) bands:

$${{{\text{O}}}_{2}}({\text{A}}{\kern 1pt} {{'}^{3}}{{\Delta }_{{\text{u}}}},\nu {\kern 1pt} ') \to {{{\text{O}}}_{2}}({{{\text{a}}}^{1}}{{\Delta }_{{\text{g}}}},\nu {\kern 1pt} {''}) + h{{{v}}_{{{\text{Ch}}}}},$$

(2)

while transitions from the electronically excited ${{{\text{A}}}^{3}}\Sigma _{{\text{u}}}^{ + }$ state to the ${{{\text{X}}}^{3}}\Sigma _{{\text{g}}}^{ - }$ ground state of the oxygen molecule leads to the glow of Herzberg I (HI) bands:

$${{{\text{O}}}_{2}}({{{\text{A}}}^{3}}\Sigma _{{\text{u}}}^{ + },\nu {\kern 1pt} ') \to {{{\text{O}}}_{2}}({{{\text{X}}}^{3}}\Sigma _{{\text{g}}}^{ - },\nu {\kern 1pt} {''}) + h{{\nu }_{{{\text{HI}}}}}.$$

(3)

This work uses experimental data on the characteristic concentrations [O] in the mentioned layer based on the characteristics of the fluorescence of atomic oxygen O for different months of the year under low (F10.7 = 75, 1976 and 1986) and high (F10.7 = 203, 1980 and 1981) solar activity at mid-latitudes (55.7° N; 36.8° E, Zvenigorod Observatory of the Obukhov Institute of Atmospheric Physics (IAP) of the Russian Academy of Sciences). Regular data on the fluorescence of atomic oxygen O were obtained from a semi-empirical model that integrates several types of different mid-latitude measurements, regression relations, and theoretical calculations over several decades by the IAP staff (Shefov et al., 2006). In accordance with the main seasonal patterns of variations in the intensity of the 557.7 nm emission, the atomic oxygen layer also significantly changes the position of its maximum, depending on both the month of observations and the solar activity (Shefov et al., 2006; Perminov et al., 1998). An increase in solar activity leads to a growth of the O concentration at the layer maximum and to a descent of its lower boundary (Semenov and Shefov, 1999).

The results obtained showed a significant change in the values of absolute concentrations of atomic oxygen at the layer maximum, the height of which also remained inconstant. The model calculation results for the 557.7 nm emission have revealed that there is a negative correlation between the height of the maximum of atomic oxygen and its concentration. Moreover, a negative correlation is clearly traced between an intensity of 557.7 nm emission and a height of the emitting layer maximum both for seasonal variations and for the dependence on solar activity (Semenov and Shefov, 1997; Shefov et al., 2000).

As a result of a change in profiles of the atomic oxygen concentration, the inevitable changes occur in profiles of the formation rate of the electronically-excited molecular oxygen ${\text{O}}_{2}^{*}$ in the Earth’s atmosphere due to process (1) and the glow intensity of various bands of molecular oxygen. Therefore, the glow intensities of the Chamberlain and Herzberg I bands depend both on the season and on the solar activity.

In this paper, the processes of excitation and quenching of electronically excited molecular oxygen in the Earth’s atmosphere at the nightglow heights are considered. It should be noted in this case that the Herzberg I bands have a wide spectrum in the Earth’s nightglow, in contrast to the Chamberlain bands, which are present in a smaller spectral range.

The purpose of this work was to compare the results of theoretical calculations of the glow intensities of the Chamberlain and Herzberg I bands with experimental data on the nightglow of molecular oxygen ${\text{O}}_{2}^{*}$ in the Earth’s atmosphere. Particular attention is paid to the peculiarities of the formation of different vibrational levels v' of the electronically excited states A'³Δ_u and ${{{\text{A}}}^{3}}{{\Sigma }}_{{\text{u}}}^{ + }$ of the oxygen molecule as a result of triple collisions (1).

2 THE EARTH’S NIGHTGLOW

Figure 1 shows several spontaneous radiative transitions from different vibrational levels of the A'³Δ_u state to different vibrational levels of the state a¹Δ_g, at which the emission of the brightest Chamberlain bands occurs. Several spontaneous radiative transitions from different vibrational levels of the ${{{\text{A}}}^{3}}{{\Sigma }}_{{\text{u}}}^{ + }$ state to various vibrational levels of the ${{{\text{X}}}^{3}}\Sigma _{{\text{g}}}^{ - }$ state are also given, at which the Herzberg I bands are emitted.

Fig. 1.

Electronic transitions inside the O₂ molecule.

All the mentioned states are below the O₂ molecule dissociation energy of ~41 300 cm^–1 (8065 cm^–1 = 1 eV). The wavelength λ of the Chamberlain and Herzberg I bands can be calculated using the formulas

$${{\lambda }_{{{\text{Ch}}}}} = {1 \mathord{\left/ {\vphantom {1 {({{E}_{{{\text{A}'(}\nu {{')}}}}} - {{E}_{{{\text{a}}(\nu '')}}}),}}} \right. \kern-0em} {({{E}_{{{\text{A'(}}\nu {{')}}}}} - {{E}_{{{\text{a}}(\nu '')}}}),}}$$

(4a)

where E_A'(ν') (cm^–1) is the energy of the vibrational level ν' of the A'³Δ_u state and E_a(ν'') (cm^–1) is the energy of the vibrational level ν" of the a¹Δ_g state,

$${{\lambda }_{{{\text{HI}}}}} = {1 \mathord{\left/ {\vphantom {1 {({{E}_{{{\text{A}}(\nu ')}}} - {{E}_{{{\text{X}}(\nu {''})}}}),}}} \right. \kern-0em} {({{E}_{{{\text{A}}(\nu ')}}} - {{E}_{{{\text{X}}(\nu {''})}}}),}}$$

(4b)

where ${{E}_{{{\text{A}}(\nu {\kern 1pt} ')}}}$ (cm^–1) is the energy of the vibrational level ν' of the ${{{\text{A}}}^{3}}{{\Sigma }}_{{\text{u}}}^{ + }$ state and ${{E}_{{{\text{X}}(\nu {\kern 1pt} {''})}}}$ (cm^–1) is the energy of the vibrational level ν" of the ${{{\text{X}}}^{3}}\Sigma _{{\text{g}}}^{ - }$ state.

Since the transitions between the considered states are dipole-forbidden the characteristic radiative times of the A'³Δ_u and ${{{\text{A}}}^{3}}{{\Sigma }}_{{\text{u}}}^{ + }$ states are on the order of 1 and 0.1 s, respectively (Bates, 1989). Therefore, when calculating the concentrations of electronically excited oxygen, it is necessary to take the quenching of О₂(A'³Δ_u) and О₂(${{{\text{A}}}^{3}}{{\Sigma }}_{{\text{u}}}^{ + }$) molecules into account not only during radiative transitions (2) and (3), but also during collisions with nitrogen N₂ and oxygen О₂ molecules (Kirillov, 2012):

$${{{\text{O}}}_{2}}({\text{A}}{\kern 1pt} {{'}^{3}}{{\Delta }_{{\text{u}}}},\nu {\kern 1pt} ') + {{{\text{N}}}_{2}} \to {{{\text{O}}}_{2}} + {{{\text{N}}}_{2}},$$

(5a)

$${{{\text{O}}}_{2}}({\text{A}}{\kern 1pt} {{'}^{3}}{{\Delta }_{{\text{u}}}},\nu {\kern 1pt} ') + {{{\text{O}}}_{2}} \to {{{\text{O}}}_{2}} + {{{\text{O}}}_{2}},$$

(5b)

$${{{\text{O}}}_{2}}({{{\text{A}}}^{3}}\Sigma _{{\text{u}}}^{ + },\nu {\kern 1pt} ') + {{{\text{N}}}_{2}} \to {{{\text{O}}}_{2}} + {{{\text{N}}}_{2}},$$

(5c)

$${{{\text{O}}}_{2}}({{{\text{A}}}^{3}}\Sigma _{{\text{u}}}^{ + },\nu {\kern 1pt} ') + {{{\text{O}}}_{2}} \to {{{\text{O}}}_{2}} + {{{\text{O}}}_{2}}.$$

(5d)

Since the N₂ concentrations at altitudes of 90–100 km exceed 10¹³ cm^–3, while the quenching constants of the A'³Δ_u and ${{{\text{A}}}^{3}}{{\Sigma }}_{{\text{u}}}^{ + }$ states exceed ~10^–12 cm³ s^–1 (Kirillov, 2010, 2014), the collisional lifetimes of the considered vibrational levels of these states are either comparable or much smaller than radiative ones of the Chamberlain and Herzberg I bands at nightglow altitudes. This means that the kinetics of Herzberg states within the considered range of atmospheric altitudes is largely determined by collisional processes.

The concentrations of excited oxygen О₂(A'³Δ_u) and О₂(${{{\text{A}}}^{3}}{{\Sigma }}_{{\text{u}}}^{ + }$) are calculated at the Earth’s upper atmosphere altitudes for vibrational levels ν' = 3–8 of both states for October 1976 and 1986, at the low solar activity, F10.7 = 75 (Antonenko and Kirillov, 2021). In calculations of concentrations of electronically excited oxygen О₂(A'³Δ_u) and О₂(${{{\text{A}}}^{3}}{{\Sigma }}_{{\text{u}}}^{ + }$), the following formulas will be used:

$$\begin{gathered} \text{[}{{{\text{O}}}_{2}}({\text{A}}{\kern 1pt} {{'}^{3}}{{\Delta }_{{\text{u}}}},\nu {\kern 1pt} ')] = q_{{\nu {\kern 1pt} {{'}}}}^{{{\text{A}}'}}{{\alpha }_{{{\text{A}}{\kern 1pt} '}}}~{{k}_{1}}{{[{\text{O}}]}^{2}} \\ \times \,\,{{([{{{\text{N}}}_{2}}] + [{{{\text{O}}}_{2}}])} \mathord{\left/ {\vphantom {{([{{{\text{N}}}_{2}}] + [{{{\text{O}}}_{2}}])} {({\text{A}}_{{\nu {\kern 1pt} '}}^{{{\text{A}}{\kern 1pt} '}} + {{k}_{{{\text{5a}}}}}[{{{\text{N}}}_{2}}] + {{k}_{{5{\text{b}}}}}[{{{\text{O}}}_{2}}])}}} \right. \kern-0em} {({\text{A}}_{{\nu {\kern 1pt} '}}^{{{\text{A}}{\kern 1pt} '}} + {{k}_{{{\text{5a}}}}}[{{{\text{N}}}_{2}}] + {{k}_{{5{\text{b}}}}}[{{{\text{O}}}_{2}}])}}, \\ \end{gathered} $$

(6a)

$$\begin{gathered} \text{[}{{{\text{O}}}_{2}}({{{\text{A}}}^{3}}\Sigma _{{\text{u}}}^{ + },{n}{\kern 1pt} ')] = q_{{\nu {\kern 1pt} '}}^{{\text{A}}}~{{\alpha }_{{\text{A}}}}~{{k}_{1}}{{[{\text{O}}]}^{2}} \\ \times \,\,{{([{{{\text{N}}}_{{\text{2}}}}] + [{{{\text{O}}}_{{\text{2}}}}])} \mathord{\left/ {\vphantom {{([{{{\text{N}}}_{{\text{2}}}}] + [{{{\text{O}}}_{{\text{2}}}}])} {({\text{A}}_{{\nu {\kern 1pt} '}}^{{\text{A}}} + {{k}_{{5{\text{c}}}}}[{{{\text{N}}}_{2}}] + {{k}_{{5{\text{d}}}}}[{{{\text{O}}}_{2}}])}}} \right. \kern-0em} {({\text{A}}_{{\nu {\kern 1pt} '}}^{{\text{A}}} + {{k}_{{5{\text{c}}}}}[{{{\text{N}}}_{2}}] + {{k}_{{5{\text{d}}}}}[{{{\text{O}}}_{2}}])}}, \\ \end{gathered} $$

(6b)

where ${{\alpha }_{{{\text{A}}{\kern 1pt} {\kern 1pt} '}}}$ and α_A are the quantum yields of the A'³Δ_u and ${{{\text{A}}}^{3}}{{\Sigma }}_{{\text{u}}}^{ + }$ states in triple collisions (1), while $q_{{\nu {\kern 1pt} {\kern 1pt} '}}^{{{\text{A}}{\kern 1pt} {\kern 1pt} '}}$ and $q_{{\nu {\kern 1pt} '}}^{{\text{A}}}$ are the quantum yields of the vibrational levels ν ' of these states, respectively; k₁ is the recombination rate constant in triple collisions (1), k_5a, k_5b, k_5c, and k_5d are the rate constants of reactions (5a)–(5d); and $A_{{\nu {\kern 1pt} '}}^{{{\text{A}}{\kern 1pt} '}}$ and $A_{{\nu {\kern 1pt} '}}^{{\text{A}}}$ are the sums of the Einstein coefficients for all spontaneous radiative transitions from the vibrational levels ν ' of the A'³Δ_u and ${{{\text{A}}}^{3}}{{\Sigma }}_{{\text{u}}}^{ + }$ states; moreover, for the A'³Δ_u state it is also necessary to take spontaneous transitions to the ground state ${{{\text{X}}}^{3}}\Sigma _{{\text{g}}}^{ - }$ at which the emission of Herzberg III bands occurs into account (Bates, 1989).

The recombination rate constant k₁ (cm⁶ s^–1) was used as a calculated value depending on the atmospheric temperature within the considered altitude interval according to Shefov et al. (2006); the constants of quenching of the electronically excited oxygen in double collisions of the molecular oxygen with particles of atmospheric components k_5a (cm³ s^–1), k_5b (cm³ s^–1), k_5c (cm³ s^–1), and k_5d (cm³ s^–1) were taken into account according to Kirillov (2010, 2014); the quantum yields ${{\alpha }_{{{\text{A}}{\kern 1pt} {{'}}}}}$ and α_A, according to Krasno-polsky (2011); the Einstein coefficients for all spontaneous transitions were taken according to Bates (1989).

The analytical formula for calculating quantum yields $q_{{\nu {\kern 1pt} '}}^{{{\text{A}}{\kern 1pt} '}}$ and $q_{{\nu {\kern 1pt} '}}^{{\text{A}}}$ was presented in (Kirillov, 2012):

$${{q}_{{\nu '}}} \sim {\text{exp}}[{{ - {{{({{E}_{{{\text{A}}',{\text{A}}({n}')}}} - {{E}_{0}})}}^{2}}} \mathord{\left/ {\vphantom {{ - {{{({{E}_{{{\text{A}}',{\text{A}}({n}')}}} - {{E}_{0}})}}^{2}}} {{{\beta }^{2}}}}} \right. \kern-0em} {{{\beta }^{2}}}}],$$

(7)

where E₀ = 40 000 cm^–1, β = 1500 cm^–1 are parameters determined using the least squares method by comparing the calculated vibrational populations of the A'³Δ_u and ${{{\text{A}}}^{3}}{{\Sigma }}_{{\text{u}}}^{ + }$ states with the results of ground-based observations. Equation (7) was used to calculate the values of $q_{{\nu {\kern 1pt} '}}^{{{\text{A}}{\kern 1pt} '}}$ and $q_{{\nu {\kern 1pt} '}}^{{\text{A}}}$; in this case the values of quantum yields were normalized in such a way so that a sum for each electronically excited state was equal to unity.

3 THE RESULTS OF MODELING THE GLOW INTENSITIES OF THE CHAMBERLAIN AND HERZBERG I BANDS

According to Eqs. (6a) and (6b), the profiles of altitude distribution of concentrations of the electronically excited molecular oxygen ${\text{O}}_{2}^{*}$ were calculated for the A'³Δ_u and ${{{\text{A}}}^{3}}{{\Sigma }}_{{\text{u}}}^{ + }$ states in the Earth’s upper atmosphere. When calculating the concentrations of electronically excited oxygen, the altitude temperature profiles were used which were compiled on the basis of long-term (1960–2000) measurements of temperature profiles at altitudes of 30–110 km (Semenov et al., 2004). The method that has been developed by these authors for calculating the altitude temperature profiles and the total atmospheric concentration makes it possible to determine the temperature and density of the atmosphere at middle latitudes for given heliogeophysical conditions (altitude, solar activity level, and year).

The values of the volume emission intensities of the bands corresponding to transitions (2) and (3) were calculated by the formula

$${{i}_{{\nu {\kern 1pt} '\nu {\kern 1pt} {''}}}}({\text{c}}{{{\text{m}}}^{{ - 3}}}\,{{{\text{s}}}^{{ - 1}}}) = [{\text{O}}_{2}^{*}]{{{\text{A}}}_{{\nu {\kern 1pt} '\nu {\kern 1pt} {''}}}},$$

(8)

where [${\text{O}}_{2}^{*}$] (cm^–3) is the calculated concentration of electronically excited oxygen ${\text{O}}_{2}^{*}$ depending on the altitude h (Antonenko and Kirillov, 2021) and ${{A}_{\nu }}_{{'\nu {\kern 1pt} {''}}}$ (s^–1) is the Einstein coefficient that corresponds to the spontaneous radiative transition from the vibrational level ν' of the upper state to the vibrational level ν" of the lower state in (2) and (3) (Bates, 1989).

Figure 2 shows the calculated altitude distributions of the volume emission intensities of the bands associated with spontaneous transitions A'³Δ_u (ν' = 6) → a¹Δ_g (v" = 3) (Figs. 2a, 2c) and ${{{\text{A}}}^{3}}{{\Sigma }}_{{\text{u}}}^{ + }$ (ν' = 6) → ${{{\text{X}}}^{3}}\Sigma _{{\text{g}}}^{ - }$ (ν" = 3) (Figs. 2b, 2d), for conditions of low (F10.7 = 75, 1976 and 1986) (Figs. 2a, 2b) and high (F10.7 = 203, 1980 and 1981) (Figs. 2c, 2d) solar activity at the middle latitudes of the Earth. The numerals stand for the months of the year: 1 for January, 2 for April, 3 for July, and 4 for October. The calculations used data on the atomic oxygen concentrations for the middle months of each season. Along horizontal axes, the values of the volume emossion intensity i (cm^–3 s^–1) are given; along the vertical axes, altitudes in km are laid.

Fig. 2.

The calculated altitude distributions of the volume emission rate i_ν'ν'' (cm^–3 s^–1) of the (a, c) Chamberlain bands and (b, d) Herzberg I bands at the middle latitudes of the Earth for different months of the year: January (1), April (2), July (3), October (4).

Figures 3a and 3b show fragments of the average nightglow spectrum in the ranges of 370–440 nm and 250–360 nm, respectively, measured by the spectrograph at the Discovery Space Shuttle (STS-53) in an interval from 115 to 900 nm over its 12-day mission in January 1995 (low solar activity conditions) (Broadfoot and Bellaire, 1999). The vertical axes show the intensities in Rayleigh/angstrom (R/Å) (1 R = 10⁶ photons/(cm² s)), while the horizontal axes show the wavelengths in angstroms (λ(Å)). The two numerals above the glow peaks denote vibrational levels (ν'–ν") at radiative transitions (2) and (3).

Fig. 3.

(a) A fragment of the averaged nightglow spectrum in the range of 370–440 nm, measured by a spectrograph from the Space Shuttle (Broadfoot and Bellaire, 1999): The ordinates are the intensities (R/Å), the abscissas are the wavelengths λ (Å), numerals above peaks indicate (ν'–ν") at radiative transitions (2). (b) A fragment of the averaged nightglow spectrum in the range of 250–360 nm, measured by a spectrograph from the Space Shuttle (Broadfoot and Bellaire, 1999): Ordinates present the intensities (R/Å), abscissas present the wavelengths λ (Å), numerals above the peaks indicate (ν'–ν") for radiative transitions (3). (c) Calculated values of the emission intensity for various Chamberlain bands taking into account the modified quantum yields $q_{{\nu {\kern 1pt} '}}^{{{\text{A}}{\kern 1pt} '}}$. (d) Calculated values of the emission intensity for various Herzberg I bands with allowance for the modified quantum yields $q_{{\nu {\kern 1pt} '}}^{{\text{A}}}$.

The calculated values of emission intensity I (cm^–2 s^–1) (histograms) for various Chamberlain and Herzberg I bands caused by radiative transitions (2), (3) and presented in Fig. 1 were obtained for October 1976 and 1986 (conditions of low solar activity F10.7 = 75) within the same wavelength range. The calculation results are shown in Figs. 3c and 3d; in this case, when recalculating the volume emission rate ${{i}_{{\nu {\kern 1pt} }}}_{{'\nu {\kern 1pt} {''}}}$ into the emission intensity ${{I}_{{\nu {\kern 1pt} }}}_{{'\nu {\kern 1pt} {''}}}$, the optically thin layer approximation is used, i.e., the absorption of photons inside the layer is neglected.

As the calculations have shown, a discrepancy between the calculated values of the emission intensity and the experimental values is observed for the third and fourth vibrational levels in the case of Chamberlain bands and for the third and fourth vibrational levels for the Herzberg bands. This discrepancy may be explained either by underestimated values of the quantum yields ${{q}_{{\nu {\kern 1pt} }}}_{'}$ for these vibrational levels, or by overestimated values of the constants of quenching processes (5a)–(5d) during a collision with N₂ and O₂ molecules.

In (Kirillov, 2010, 2014), the calculated constants for the processes of quenching the electronic excitation of Herzberg states showed good agreement with the results of laboratory measurements. For the quantum yields $q_{{\nu {\kern 1pt} '}}^{{{\text{A}}{\kern 1pt} '}}$ and $q_{{\nu {\kern 1pt} '}}^{{\text{A}}}$, in their evaluation in (Kirillov, 2012) the analytic formula (7) was initially used, which might give an error for vibrational levels for small values. Therefore, in these calculations, we vary the values of quantum yields (Table 1) by increasing their values by approximately one-third for the third and fourth vibrational levels of the ${{{\text{A}}}^{3}}{{\Sigma }}_{{\text{u}}}^{ + }$ state (Antonenko and Kirillov, 2021). For the A'³Δ_u state, the values of the normalizing coefficients of quantum yields for different vibrational levels are increased for the third level by 5 times and for the fourth level by 1.5 times. Accordingly, the values of the normalizing coefficients of quantum yields for other vibrational levels were reduced; this is also shown in Table 1. When using the modified quantum yields $q_{{\nu {\kern 1pt} '}}^{{\text{A}}}$, better agreement was achieved between the calculated intensities of the emission bands of the excited oxygen ${\text{O}}_{2}^{*}$ (${{{\text{A}}}^{3}}{{\Sigma }}_{{\text{u}}}^{ + }$, ν' = 3–8) and the spectra obtained from the Shuttle (Broadfoot and Bellaire, 1999), that is, the experimental data on the nightglow within a range of 250–360 nm, which is clearly seen in Fig. 3d.

Table 1.   The quantum yields ${{q}_{{\nu {\kern 1pt} }}}_{'}$ of the vibrational level ν' according to (Kirillov, 2012) and those modified in this paper

For the O₂(A'³Δ_u, ν' = 3–6) state, it is much more difficult to compare the theoretically calculated values of band intensities with the experimental data, since the Chamberlain band glow intensities are much lower and the experimental errors are higher. Figure 3c shows the results of calculations of the glow intensities of 10 Chamberlain bands. For the band emitted during the spontaneous transition (2) with ν'–ν" = 6–4, during the calculation with the Einstein coefficient according to Bates (1989), the obtained glow intensity values are significantly lower than in the spectrum received from an aircraft (Broadfoot and Bellaire, 1999). Therefore, in the present work, the Einstein coefficient for this transition was increased by a factor of five. After using the modified value of the Einstein coefficient, it became possible to obtain a glow peak in the region of 400 nm, as was observed in (Broadfoot and Bellaire, 1999).

The agreement of the theoretically calculated intensities of the Chamberlain and Herzberg I bands with the experimental data indicates that the experimentally obtained data on the glow of molecular bands can be used to estimate the rates of formation and quenching of various vibrational levels of electronically excited states in various collisional processes. In this case, the best agreement between the results of calculations and experimental data was obtained due to the correction of quantum yields $q_{{\nu {\kern 1pt} '}}^{{{\text{A}}{\kern 1pt} '}}$ and $q_{{\nu {\kern 1pt} '}}^{{\text{A}}}$, which were approximated in (Kirillov, 2012) by analytic formula (7).

Similarly, Fig. 4a shows the nightglow spectrum within the wavelength range of 370–440 nm, which was measured by the EbertFastie spectrograph (Kitt Peak National Observatory, Arizona, United States) at an altitude of 2080 m (Broadfoot and Kendall, 1968). At UV wavelengths (310–450 nm), a low brightness ultraviolet source was used (Broadfoot and Hunten, 1964). The observatory has been in operation since 1958, however, the authors Broadfoot and Kendall (1968) described observations referring to the measurements of 1961–1964 during a period of low solar activity. The theoretically calculated values of ten Chamberlain bands are presented in Fig. 4b. As can be seen from the comparison of panels a and b in Fig. 4, the calculated intensities of ten Chamberlain bands repeat the experimental data satisfactorily.

Fig. 4.

(a) A fragment of the averaged nightglow spectrum in the wavelength range of 370–440 nm, measured by the EbertFastie spectrograph (Kitt Peak Observatory) at an altitude of 2080 m (Broadfoot and Kendall, 1968). The intensities (R/Å) are on the ordinate axis. The wavelengths λ (Å) are on the abscissa. Numerals above the peaks are (ν'–ν") for radiative transitions (2). (b) Calculated values of the emission intensity for various Chamberlain bands taking into account the modified quantum yields $q_{{\nu {\kern 1pt} '}}^{{{\text{A}}{\kern 1pt} '}}$.

In this case, the satisfactory agreement between the results of calculations of the intensities of the molecular oxygen glow bands and the experimental data received from the Discovery Shuttle (STS-53) (Broadfoot and Bellaire, 1999) and at the Kitt Peak Observatory (Broadfoot and Kendall, 1968), was achieved due to the correction of quantum yields ${{q}_{{\nu {\kern 1pt} }}}_{'}$, which were approximated by the analytic formula (8) in (Kirillov, 2012). In most cases of spectral measurements (as in (Broadfoot and Bellaire, 1999; Broadfoot and Kendall, 1968)), the results are presented in the form of curves without rotation-structure resolution. Therefore, in this work, we compared the calculation results (histograms) with the maximum values of curves for each radiative transition.

The calculated values of $q_{{\nu {\kern 1pt} '}}^{{{\text{A}}{\kern 1pt} '}}$ and $q_{{\nu {\kern 1pt} '}}^{{\text{A}}}$ for triple collisions (1) according to Kirillov (2012) and the values modified in this work are presented in Table 1 and in Fig. 5. The modified values are highlighted in bold type in Table 1. The modified values $q_{{\nu {\kern 1pt} '}}^{{{\text{A}}{\kern 1pt} '}}$ and $q_{{\nu {\kern 1pt} '}}^{{\text{A}}}$ in Fig. 5 are represented by dashed lines.

Fig. 5.

(a) The values of the initial and modified quantum yields for the A'³Δ_u state. Along the vertical axis are the quantum yields $q_{{\nu {\kern 1pt} '}}^{{{\text{A}}{\kern 1pt} '}}$; along the horizontal axis are the vibrational levels ν'. (b) The values of the initial and modified quantum yields for the state ${{{\text{A}}}^{3}}{{\Sigma }}_{{\text{u}}}^{ + }$. Along the vertical axis are the quantum yields $q_{\nu }^{{\text{A}}};$ along the horizontal axis are the vibrational levels ν'.

Table 2 lists the emission intensities of the Chamberlain and Herzberg I bands ${{I}_{{\nu {\kern 1pt} {{'}}\nu {\kern 1pt} {{'' }}}}}$ (cm^–2 s^–1) for vibrational levels ν' = 3–8 of radiative transitions (2) and (3) for October 1976 and 1986 at low solar activity F10.7 = 75. It can be seen from Table 2 that the emission intensity of the considered Chamberlain bands is ~40% of the emission intensity of the Herzberg I bands, which was indicated by the authors of (Broadfoot and Bellaire, 1999; Slanger and Copeland, 2003).

Table 2.   The emission intensities of Chamberlain bands and Herzberg I bands (in Rayleighs, 1R = 10⁶ photon/(cm² s)) for vibrational levels ν' = 3–8

4 CONCLUSIONS

The intensities of the Chamberlain and Herzberg I band emissions due to radiative transitions from vibrational levels ν' = 3–6 of electronically excited oxygen О₂(A'³Δ_u) and from vibrational levels ν' = 3–8 of electronically excited oxygen О₂(${{{\text{A}}}^{3}}{{\Sigma }}_{{\text{u}}}^{ + }$) have been obtained for low (F10.7 = 75 in 1976 and 1986) solar activity in middle latitudes. The calculated values of the emission intensity of the Chamberlain bands under conditions of low solar activity have been compared with the experimental data obtained in the wavelength range of 370–440 nm by a spectrograph from the Space Shuttle (Broadfoot and Bellaire, 1999) and at the Kitt Peak Observatory (Broadfoot and Kendall, 1968) under the same conditions. In addition, for conditions of low solar activity, the calculated values of the emission intensity of the Herzberg I bands were compared with experimental data obtained within the wavelength range of 250–360 nm by a spectrograph from the Space Shuttle (Broadfoot and Bellaire, 1999). The comparison of the experimental data with the calculated values of intensities of the bands showed that the best agreement is observed after correcting the quantum yields of vibrational levels of the A'³Δ_u state $q_{{\nu {\kern 1pt} '}}^{{A{\kern 1pt} '}}$ and of vibrational levels of the ${{{\text{A}}}^{3}}{{\Sigma }}_{{\text{u}}}^{ + }$ state $q_{{\nu {\kern 1pt} '}}^{A}$ as a result of triple collisions (1), which were presented in (Kirillov, 2012).

It has been shown that the ratio of the calculated values of intensities of the Chamberlain and Herzberg I band emission from vibrational levels ν' = 3–8 of the A'³Δ_u and ${{{\text{A}}}^{3}}{{\Sigma }}_{{\text{u}}}^{ + }$ states corresponds to the ratio of the values in (Broadfoot and Bellaire, 1999; Slanger and Copeland, 2003), i.e., the glow intensity of the Chamberlain bands is ≈40% of the glow intensity of the Herzberg I bands.