The mesopause region is essential to understanding the chemical and physical processes in the upper atmosphere because this is the region of coldest temperature (during summer at high latitudes) and highest turbulence in the atmosphere (e.g., Lübken, 1997), the region of formation of such phenomena as noctilucent clouds (NLCs) and polar mesospheric summer echoes (PMSEs) (e.g., Rapp and Lübken, 2004), the region of gravity wave (GW) breaking and the formation of secondary GWs (Becker and Vadas, 2018), and the region of coupling between the mesosphere and thermosphere. This region is characterized by different airglow emissions and, particularly, by the emissions of the atmospheric band, which is produced by the excited state of molecular oxygen O2b1Σg+. Airglow observation in the atmospheric band is a useful method to study dynamical processes in the mesopause region. There have been a number of reports of GW detection in this band (Noxon, 1978; Viereck and Deehr, 1989; Zhang et al., 1993). Planetary wave climatology has been investigated by the Spectral Airglow Temperature Imager (SATI) instrument (López-González et al., 2009). In addition, the parameters of tides have been reported from SATI (López-González et al., 2005) and high-resolution Doppler imager (HRDI) observations (Marsh et al., 1999). In number of works Sheese et al. (2010, 2011) inferred temperature from atmospheric band observation. Furthermore, the response of mesopause temperature and atomic oxygen during major sudden stratospheric warming was studied utilizing atmospheric band emission by Shepherd et al. (2010). Various works have focused on atmospheric band emission modeling with respect to gravity waves and tides (e.g., Hickey et al., 1993; Leko et al., 2002; Liu and Swenson, 2003). The specific theory of the gravity wave effects on O2b1Σg+ emission was derived in Tarasick and Shepherd (1992). Moreover, atmospheric band observations have been widely utilized to infer atomic oxygen, which is an essential chemical constituent for energetic balance in the extended mesopause region (e.g., Hedin et al., 2009, and references there in), and ozone concentration (Mlynczak et al., 2001). Although there is a large field of application of atmospheric band emissions, there is a lack of knowledge on the processes of the O2b1Σg+ population. Two main mechanisms of nighttime population (note that the daytime mechanisms are quite different; see, e.g., Zarboo et al., 2018) were proposed: the first is the direct population from a three-body recombination of atomic oxygen (e. g. Deans et al., 1976); the second is the so-called two-step mechanism, which assumes an intermediate excited precursor O2* (e. g. Witt et al., 1984; Greer et al., 1981). It has been shown by laboratory experiments that the first mechanism alone has not explained observed emissions (Young and Sharpless, 1963; Clyne at al., 1965; Young and Black, 1966; Bates, 1988). The second mechanism entails a discussion about the precursor excited state and additional ambiguities in their parameters (e.g., Greer et al., 1981; Ogryzlo et al., 1984). Thus, Witt et al. (1984) proposed the hypothesis that the O2c1Σu- state is, possibly, the precursor; López-González et al. (1992a) suppose that the precursor could be O2(5Πg); and Wildt et al. (1991) found through laboratory measurements that it could be O2A3Σu+. Hence, the problem of identification is still not solved. The essential step in this direction has been made after the ETON 2 (Energy Transfer in the Oxygen Nightglow) rocket experiment. The ETON 2 mission yielded empirical fitting parameters that allow us to either quantify the O2b1Σg+ (and consequently volume emission) by known O or atomic oxygen by known volume emission values (McDade et al., 1986). Despite the significance of this work, the temperature and density of air (necessary for derivation) were taken from the CIRA-72 and MSIS-83 (Hedin, 1983) models. This leads to some degree of uncertainty (e.g., Murtagh et al., 1990). Thus, more solid knowledge on these fitting coefficients based on consistent measurements of atomic oxygen, the volume emission of the atmospheric band, and temperature and density of the background atmosphere is desirable. In this paper we present common volume measurements of these parameters performed in the course of the WADIS-2 sounding rocket mission. In the next section, we describe the rocket experiment and obtained data relevant for our study. In Sect. 3, to make the paper easier to understand, we repeat some theoretical approximations from McDade et al. (1986). The obtained results of our calculations are discussed in Sect. 4. Concluding remarks and a summary are given in the last section.

The WADIS (Wave propagation and dissipation in the middle atmosphere: Energy budget and distribution of trace constituents) sounding rocket mission aimed to simultaneously study the propagation and dissipation of GWs and measure the concentration of atomic oxygen. It comprised two field campaigns conducted at the Andøya Space Center (ASC) in northern Norway (69∘ N, 16∘ E). The WADIS-2 sounding rocket was launched during the second campaign on 5 March 2015 at 01:44:00 UTC under nighttime conditions. For a more detailed mission description, the reader is referred to Strelnikov et al. (2017) and the accompanying paper by Strelnikov et al. (2018).

The WADIS-2 sounding rocket was equipped with the CONE instrument to measure absolute neutral air density and temperature with high spatial resolution, an instrument for atomic oxygen density measurements (FIPEX; Flux Probe Experiment), and an airglow photometer for atmospheric band (762 nm) volume emission observation.

CONE (COmbined measurement of Neutrals and Electrons), operated by IAP (Leibniz Institute of Atmospheric Physics at Rostock University), is a classical triode-type ionization gauge optimized for a pressure range between 10-5 and 1 mbar. The triode system is surrounded by two electrodes: whilst the outermost grid is biased to +3 to +6 V to measure electron densities at a high spatial resolution, the next inner grid (-15 V) is meant to shield the ionization gauge from ionospheric plasma. CONE is suitable for measuring absolute neutral air number densities at an altitude range between 70 and 120 km. To obtain absolute densities, the gauges are calibrated in the laboratory using a high-quality pressure sensor, like a Baratron. The measured density profile can be further converted to a temperature profile assuming hydrostatic equilibrium. For a detailed description of the CONE instrument, see Giebeler et al. (1993) and Strelnikov et al. (2013). Molecular oxygen and molecular nitrogen are derived from CONE atmospheric number density measurements and partitioning according to the NRLMSISE-00 reference atmosphere (Picone et al., 2002).

The airglow photometer operated by MISU (Stockholm University, Department of Meteorology) measures the emission of the molecular oxygen atmospheric band around 762 nm from the overhead column, from which the volume emission rate is inferred by differentiation. For airglow measurements in general, a filter photometer is positioned under the nose cone viewing along the rocket axis with a defined field of view (FOV). For WADIS-2, however, the FOV of ±3∘ was tilted from the rocket axis by 3∘ to avoid having other parts of the payload within the FOV and at the same time roughly view the same volume as the other instruments. The optical design is a standard radiometer-type system with an objective lens, a field lens, aperture, and stops, which provide an even illumination over a large portion of the detector surface (photomultiplier tube) and a defined FOV. At the entrance of the photometer there is an interference filter with a passband of 6 nm centered at 762 nm. During ascent, after the nose cone ejection, the photometer then counts the incoming photons from the overhead column (or actually the overhead cone). When the rocket passes through the layer the measured photon flux drops and above the emission layer only weak background emissions are present (e.g., the zodiacal and galactic light). After the profile has been corrected for background emissions and attitude (van Rhijn effect) it is converted from counts to radiance using preflight laboratory calibrations. The calibration considers the spectral shape of the 0–0 band of the O2b1Σg+-X3Σg-0,0 atmospheric band system and the overlap of the interference filter passband. The profile is then smoothed and numerically differentiated with respect to altitude to yield the volume emission rate of the emitting layer. The data were sampled with 1085 Hz, which results in an altitude resolution of about 0.75 m during the passage of the airglow layer (the velocity was ∼800 m s-1 at 95 km). However, because of the high noise level, the profile needed to be averaged to a vertical resolution of at least 3 km in order to get satisfactory results after the differentiation. A more detailed description and review of this measurement technique is given by Hedin et al. (2009).

The aim of the FIPEX developed by the IRS (Institute of Space Systems, University of Stuttgart) is to measure the atomic oxygen density along the rocket trajectory with high spatial resolution. It employs a solid electrolyte sensor, which has a selective sensitivity to atomic oxygen. A low voltage is applied between anode and cathode pumping oxygen ions through the electrolyte ceramic (yttria-stabilized zirconia). The current measured is proportional to the oxygen density. Sampling is realized with a frequency of 100 Hz and enables a spatial resolution of ∼10 m. Laboratory calibrations were done for molecular and atomic oxygen. For a detailed description of the FIPEX instruments and their calibration techniques, see Eberhart et al. (2015, 2018).

Here, we are repeating the theory of O2b1Σg+-X3Σg-0,0 nighttime emissions following McDade et al. (1986) to make our paper more readable, using all nomenclature as in the original paper. All utilized reactions are listed in Table 1, together with corresponding reaction rates, branching ratios, quenching rates, and spontaneous emission coefficients. Some components have been updated according to modern knowledge, thus deviating from the work of McDade et al. (1986).

Assuming a direct one-step mechanism as the main one for the population and that O2b1Σg+ is in photochemical equilibrium, we can write its concentration as a ratio of production to the loss term: O2b1Σg+=εk1O2MA2+k2O2O2+k2N2N2+k2OO, where k1 is the reaction rate for the three-body recombination of atomic oxygen, ε is the corresponding quantum yield of O2b1Σg+ formation, A2 represents the spontaneous emission coefficient, and k2O2, k2N2, k2O are the quenching coefficients for reactions with O2, N2, and O, respectively. Then the volume emission, Vat, is obtained by multiplying the O2b1Σg+ concentration by the spontaneous emission coefficient, A1, of Reaction (R5) (hereafter, nomenclature RX means the reaction X for Table 1).

In the case of known temperature, volume emission, and concentrations of O, O2, N2, and M, the quantum yield of O2b1Σg+ formation can be calculated as follows: ε=VatA2+k2O2O2+k2N2N2+k2OOA1k1O2M.

In the case of the two-step mechanism, the unknown excited-state O2* is populated at the first step from Reaction (R7). Then, it can be deactivated by quenching (Reaction R9), spontaneous emission (Reaction R10), or producing O2b1Σg+ by Reaction (R8). Note that Reaction (R8) is one pathway of the overall quenching Reaction (R9).

In the second step, O2* is transformed into O2b1Σg+, which can be deactivated by quenching (Reactions R2–R4) and by spontaneous emission (Reaction R6). Assuming photochemical equilibrium for O2* and, as before, for O2b1Σg+, the volume emission in the case of O2b1Σg+-X3Σg-0,0 is Vat=A1αk1O2Mγk3O2O2A2+k2O2O2+k2N2N2+k2OOA3+k3O2O2+k3N2N2+k3OO, where the quantum yield of O2* formation is α, the quantum yield of O2b1Σg+ formation is γ, the spontaneous emission coefficient is A3, and k3O2, k3N2, k3O are unknown quenching rates of O2*. Note that the assumption about photochemical equilibrium for O2* and O2b1Σg+ is valid because the O2b1Σg+ radiative lifetime is less than 12 s and all potential candidates for O2* have lifetimes less than several seconds (e.g., López-González et al., 1992a, b, c; Yankovsky et al., 2016, and references therein).

Collecting all known values on the right-hand side (RHS), all unknown summands on the left-hand side (LHS), and omitting emissive summand A3 as noneffective loss (McDade et al., 1986), Eq. (3) can be rearranged as follows: CO2O2+COO=A1k1O2MO2VatA2+k2O2O2+k2N2N2+k2OO, where CO2=1+k3N2N2k3O2O2αγ and CO=k3Oαγk3O2 are the fitting coefficients that can be calculated by the least-squares fit (LSF) procedure. Such derivation assumes that the coefficients are temperature independent (or temperature dependence is weak). This means that the reaction rates k3 are assumed to be temperature independent (dependence is weak) or have the same temperature dependency for all quenching partners (N2, O2, O). Currently, this statement on the basis of available information about potential precursors is assumed true, but solid evidence is absent. We calculated them based on our measurements and will discuss the results in the following section.

In a more general case the population of O2b1Σg+ occurs via both channels: one-step and two-step. We discuss such processes in Sect. 4.3 and derive an expression for the corresponding fit function in Appendix A.

Figure 1 shows input data for our calculations: temperature from the CONE instrument (Fig. 1a), number density of air (Fig. 1b), atomic oxygen concentration measured by FIPEX (Fig. 1c), and volume emission at 762 nm from the photometric instrument (Fig. 1d). A temperature minimum of ∼158 K was observed at 104.2 km. A local temperature peak was measured at 98.9 km with values of 204.5 K. The secondary temperature minimum was visible at 95.4 km and amounted to ∼173 K. The atomic oxygen concentration (Fig. 1c) had a peak of ∼4.7×1011 [cm-3] at 97.2 km and approximately coincided with the secondary temperature peak. The peak of volume emission was detected between 95 and 97 km with values of more than 1700 [phot. cm-3 s-1]; this is slightly beneath the atomic oxygen corresponding maximum and slightly above the secondary temperature minimum. Note that this points to the competition of temperature and the atomic oxygen concentration in processes of atomic oxygen excited-state O2b1Σg+ formation. Independently of the mechanism of atmospheric band emission (Eq. 1 or Eq. 3), the numerator is directly proportional to the square of the atomic oxygen concentration and inversely proportional to the third power of the temperature (via reaction rate k1 and M, considering the ideal gas low). Our rocket experiment shows an essential difference of emissions between ascending and descending flights (see Strelnikov et al., 2018). It also demonstrates significant variability in other measured parameters, including neutral temperature and density as well as atomic oxygen density (Strelnikov et al., 2017, 2018). This suggests that, in the case of the ETON 2 experiments, the temporal extrapolation of atomic oxygen for the time of the emission measurement flight (which was approximately 20 min earlier) may lead to serious biases in estimations because, as one can see from Eqs. (1) and (3), volume emission depends on the atomic oxygen concentration quadratically. Since the best-quality data were obtained during the descent of the WADIS-2 rocket flight, we chose this data set for our analysis (Strelnikov et al., 2018). The region above 104 km is subject to auroral contamination. In the region below 92 km, negative values may occur in the volume emission profile as a result of self-absorption in the denser atmosphere below the emission layer. Hence, we considered the region near the emission peak between 92 and 104 km as most appropriate for our study. The comparisons of our measurements with other observations, as well as with the results of modeling, are presented in several papers (e.g., Eberhart et al., 2018; Strelnikov et al., 2018).

Based on the rocket-borne common volume simultaneous observations of atomic oxygen, atmospheric band emission (762 nm), and density and temperature of the background atmosphere, the mechanisms of O2b1Σg+ formation were analyzed. Our calculations show that one-step direct excitation alone is less probable for the reasons discussed above (Sect. 4.1).

For the case of the two-step mechanism, we found new coefficients for the fit function in accordance with McDade et al. (1986) based on self-consistent temperature, atomic oxygen, and volume emission observation. These coefficients amounted to CO2=9.8+6.5-5.3 and CO=2.1-0.6+0.3. The CO2 coefficient is partially, within the error range, in agreement with CO2 coefficients given in McDade et al. (1986), and the CO coefficient is approximately 1 order lower. The general implication of these results is the parameterization of volume emission in terms of known atomic oxygen. This can be utilized either for atmospheric band volume emission modeling or for the estimation of atomic oxygen by known volume emission. We identified two candidates for the intermediate state of O2*. Our results show that O2A′3Δu or O2(5Πg) may serve as a precursor.

Taking into account both channels of O2b1Σg+ formation, we proposed a combined mechanism. In this case, atomic oxygen via volume emission or volume emission based on known atomic oxygen can be calculated by Eq. (5). The recommended fitting coefficients amounted to D1=0.231-0.142+0.358 and D2=0.08-0.04+0.12, with the efficiency of the direct channel as ε̃=0.022. These coefficients have a mean total efficiency (α̃γ̃=0.08-0.04+0.12) and a ratio of quenching coefficients (k̃3O/k̃3O2=0.231-0.142+0.358) for the two-step channel. The analysis of their values indicates that O2A′3Δu and O2(5Πg) may serve as possible precursors for the two-step channel in the combined mechanism. In the context of our rocket experiment, we do not have the possibility to figure out which mechanism is true. Nevertheless, we consider the combined mechanism as more relevant to nature because it has a higher generality. This conclusion does not contradict the current point of view that the two-step mechanism is dominant because ε̃ is assumed to be 1.5 %–3 %. Moreover, it is possible that in reality the mechanism is much more complex and it has a multichannel or more than two-step nature. Undoubtedly, more common volume simultaneous observations of the atmospheric band and atomic oxygen concentrations would be desirable to confirm and improve these results.