Technical Note: on the Possibly Missing Mechanism of 15 Μm Emission in the Mesosphere–lower Thermosphere (mlt)

Accurate knowledge of the rate as well as the mechanism of excitation of the bending mode of CO 2 is necessary for reliable modeling of the mesosphere–lower thermosphere (MLT) region of the atmosphere. Assuming the excitation mechanism to be thermal collisions with atomic oxygen, the rate coefficient derived from the observed 15 µm emission by space-based experiments (k ATM = 6.0 × 10 −12 cm 3 s −1) differs from the laboratory measurements (k LAB = (1.5−2.5)×10 −12 cm 3 s −1) by a factor of 2– 4. The general circulation models (GCMs) of Earth, Venus, and Mars have chosen to use a median value of k GCM = 3.0 × 10 −12 cm 3 s −1 for this rate coefficient. As a first step to resolve the discrepancies between the three rate coefficients, we attempt to find the source of disagreement between the first two. It is pointed out that a large magnitude of the difference between these two rate coefficients (k x ≡ k ATM − k LAB) requires that the unknown mechanism involve one or both major species: N 2 , O. Because of the rapidly decreasing volume mixing ratio (VMR) of CO 2 with altitude, the exciting partner must be long lived and transfer energy efficiently. It is shown that thermal collisions with N 2 , mediated by a near-resonant rotation-to-vibration (RV) energy transfer process , while giving a reasonable rate coefficient k VR for de-excitation of the bending mode of CO 2 , lead to vibration-to-translation k VT rate coefficients in the terrestrial atmosphere that are 1–2 orders of magnitude larger than those observed in the laboratory. It is pointed out that the efficient near-resonant rotation-to-vibration (RV) energy transfer process has a chance of being the unknown mechanism if very high rotational levels of N 2 , produced by the reaction of N and NO and other collisional processes, have a super-thermal population and are long lived. Since atomic oxygen plays a critical role in the mechanisms discussed here, it suggested that its density be determined experimentally by ground-and space-based Raman lidars proposed earlier.


Introduction
The 15 µm emission from CO 2 is the dominant cooling mechanism in the MLT region (Gordiets et al., 1982;Dickinson, 1984;Sharma and Wintersteiner, 1990;Wintersteiner et al., 1992;López-Puertas et al., 1992;Sharma and Roble, 2002).The magnitude of this cooling impacts both the temperature and height of the terrestrial mesopause (Bougher et al., 1994).This process is also important in the Martian and Venusian atmospheres (Bougher et al., 1999), especially the latter, where it acts as a thermostat during the long day (243 times the length of terrestrial day).The 15 µm emission from CO 2 has been used by a number of satellites (Offermann et al., 1999;Russell et al., 1999;Fischer et al., 2008) to retrieve atmospheric temperature as a function of altitude.Finding the mechanism leading to this emission is therefore very important.
To resolve the discrepancy between k ATM and k LAB , Feofilov et al. ( 2012) postulate that nonthermal, or "hot", oxygen atoms, produced in the MLT region by photolysis of O 2 and dissociative recombination of O + 2 , etc., may serve as an additional source of CO 2 (v 2 ) level excitation.These authors have derived CO 2 volume mixing ratio (VMR) parts per million by volume (ppmv) in the MLT region for the time of their experiment from atmospheric models as well as space-based observations.The average VMR, according to the MLW atmosphere, is about 268 ppmv at 90 km altitude and about 105 ppmv at 105 km altitude, in general agreement with the values given by Rinsland et al. (1992).This means that for every collision a "hot" oxygen atom undergoes with CO 2 , it must undergo (10 6 /268 =)3731 collisions at 90 km altitude and (10 6 /105 =)9524 collisions at 105 km altitude with other atmospheric constituents, mostly with N 2 , O 2 and O. Solution of the time-dependent Boltzmann equation with realistic potential functions (Dothe et al., 1997) has shown that a 1 eV "hot" atom loses most of its energy in a few collisions.The chance of a "hot" atom colliding with CO 2 is therefore virtually nil.However, since CO 2 is the dominant constituent in the Martian and Venusion atmospheres, "hot" O atoms may play a significant role in exciting its vibrations on these planets.In the terrestrial atmosphere, another reservoir of energy that either takes energy from various nonthermal energy sources, e.g., "hot" O atoms, and that may or may not be in local thermodynamic equilibrium, but one that readily transfers energy preferentially to the bending mode of CO 2 must be found to explain large k x .The situation is similar to that of elevated 4.3 µm (v 3 mode) CO 2 emissions from the hydroxyl layer in the nocturnal mesosphere (Kumer et al., 1978;López-Puertas et al., 2004).Highly vibrationally excited OH, produced by the reaction of H + O 3 , because of its short lifetime can only transfer a very small amount of energy directly to trace species CO 2 , even though transfer of vibrational energy from higher levels (v = 8 and 9) of OH to the v 3 mode of CO 2 is a fast near-resonant process (Burtt and Sharma, 2008b).The vibrational energy from higher levels (v = 8 and 9) of OH is instead transferred to N 2 by a fast near-resonant process (Burtt and Sharma, 2008a).The longer-lived and super-thermal vibrationally excited N 2 transfers its energy, again by a fast near-resonant process (Sharma andBrau, 1967, 1969), to the v 3 mode of CO 2 , the latter radiating around 4.3 µm.The longer-lived N 2 (v = 1) molecule acts as a reservoir that takes energy from OH and stores it until it is preferentially released to CO 2 .

Hypothesis
We advance the hypothesis that rotational degrees of freedom of N 2 and O 2 are the reservoirs that transfer their energy efficiently to the v 2 mode of CO 2 .High rotational levels of these reservoirs by a near-resonant rotation-to-vibration energy transfer process are responsible for efficiently exciting the bending (v 2 ) mode of CO 2 leading to 15 µm emission.These rotational levels may be thermal or long-lived nonthermal.

Thermal rotational levels
Since the N 2 density at the altitudes under consideration is much greater than the O 2 density, we provide a justification for the deactivation of CO 2 (01 1 0) by N 2 .The reaction is exothermic by 46 and 14 cm −1 for J = 15 and 16 and endothermic by 17 and 49 cm −1 for J = 17 and 18.The CO 2 molecule, in the dipole-hexadecapole moment and quadrupole-hexadecapole moment interactions involved undergoes J = ± 3, ± 2, ± 1, 0 in the process.Since CO 2 has a much smaller rotational constant (≈ 0.39 cm −1 ) than N 2 (≈ 1.99 cm −1 ), we, for the rough estimate, ignore the contributions of its rotational transitions to the energy transfer process.The near-resonant processes, mediated by longrange multipole and dispersion interactions, transfer a small amount of energy from internal degrees of freedom (vibration and rotation) to translation, and can therefore have a much larger cross section.On the other hand, processes that require transfer of a large amount of energy from internal (vibration and rotation) degrees of freedom to translation and can be mediated only by short-range repulsive forces tend to have a smaller cross section.This is the rationale for selecting J = 8 transitions, since they are both near-resonant and can be mediated by long-range forces.At 183 K, a temperature relevant to the MLS atmosphere (Table 1b), at about 90 km altitude, about 2.4 % of the N 2 molecules reside in one of these four rotational levels.The density of N 2 in these four thermalized rotational levels is (0.0241/0.018 =)1.34 times that of atomic oxygen.The unexplained rate coefficient k x (v 2 ) at 90 km altitude for pumping of the v 2 mode of CO 2 is (3.1 ± 1.5) × 10 −12 cm 3 s −1 .The sum of the rate coefficients of Reaction (R2) at 168 K for all four rotational levels k VR (N 2 ) has to be nearly equal to or greater than (3.1 ± 1.5) × 10 −12 /1.34 = (2.32 ± 1.1) × 10 −12 cm 3 s −1 to make Reaction (R2) the dominant mechanism for pumping of the v 2 mode of CO 2 .Since only 2.4 % of the N 2 molecules participate in the RV energy transfer process, the rate coefficient for deactivation of CO 2 (v 2 ) by N 2 would be k VT (N 2 ) = ((2.32± 1.1) × 0.024) × 10 −12 = (5.6 ± 2.6) × 10 −14 .A larger calculated rate coefficient k N 2 would not be a problem, since the v 2 mode of CO 2 at least up to 90 km altitude is in local thermodynamic equilibrium (LTE); i.e., its vibrational temperature is nearly the same as the translational temperature (Feofilov et al., 2012;López-Puertas et al., 1992;Stair et al., 1985).Tables 1a-d, using the atmospheres, provided by Feofilov and López-Puertas, give the rate coefficients k VT (N 2 ), the fifth column, and k VR (N 2 ), the last column, required by k x given by these atmospheres.The rate coefficient k VT (N 2 ) for the deactivation of the bending mode of CO 2 by N 2 at low temperatures has been measured at room temperature by Merrill and Amme (1969) using ultrasonic velocity dispersion measurements and by Cannemeyer and De Vries (1974) using an optic-acoustic effect.Taine et al. (1978Taine et al. ( , 1979)), by the photoacoustic method, and Allen et al. (1980), by the laser fluorescence technique, have measured k VT (N 2 ) at low temperatures.These studies are in general agreement with that of Allen et al. (1980) giving k VT (N 2 ) equal to 1.4×10 −15 cm 3 s −1 at 170 K and 3.7×10 −15 cm 3 s −1 295 K about 1 order of magnitude smaller at lower temperature and 2 orders magnitude smaller at higher temperature than the values given in Tables 1a-d.Clearly, another mechanism is needed to explain the large observed values of k x ≡ k ATM − k LAB .It has already been noted that, since k x is almost equal to (Tables 1c and d) or greater (Tables 1a and b) than k LAB , it must involve a major species with a large rate coefficient.Sharma (1971) has calculated the probability per collision of the reaction

Nonthermal rotational levels
a much studied process because of its importance in CO 2 lasers, assuming a vibration-to-rotation (VR) energy transfer (ET) mechanism mediated by long-range multipolar interactions.In spite of a large scatter in the experimental data, a situation typical of low-temperature experiments involving water vapor, the agreement is quite good.The calculated probability per collision is 0.06 at 200 K and 0.08 at 300 K.The rate coefficients (σ v), assuming a gas kinetic rate of 2×10 −10 cm 3 s −1 at 200 K and 2.5×10 −10 cm 3 s −1 at 300 K, are 1.2 × 10 −11 and 2.0 × 10 −11 cm 3 s −1 at 200 and 300 K, respectively.Allen et al. (1980) have measured rate coefficients for the deactivation of the bend-stretch mode of CO 2 by H 2 in the 170-295 K temperature range, obtaining values of 7.5 × 10 −12 and 5.0 × 10 −12 cm 3 s −1 at 170 and 295 K, respectively, the probability of energy transfer per collision P at the two temperatures being 1.4 × 10 −2 and 7.4 × 10 −3 .The inverse temperature dependence of this rate coefficient www.atmos-chem-phys.net/15/1661/2015/Rate coefficients are in units of cm 3 s −1 × 10 12 .k x = k ATMk LAB .k ATM provided by A. G. Feofilov (3 November 2014).k LAB is taken as equal to 2.5 × 10 12 cm 3 s −1 throughout, based on the work of Castle et al. (2012).Feofilov (3 November 2014).k LAB is taken as equal to 2.5 × 10 12 cm 3 s −1 throughout, based on Castle et al. (2012).k ATM = 4.5 × 10 −12 cm 3 s −1 is the average of (3 − 6) × 10 −12 cm 3 s −1 given by López-Puertas et al. (1992).
is at odds with the Landau-Teller TV energy transfer mechanism and very much in accord with the near-resonant energy transfer mechanism (Sharma andBrau, 1967, 1969).Sharma (1969) has calculated the deactivation of CO 2 (v 2 ) by H 2 assuming a near-resonant VR energy transfer mechanism mediated by dipole-quadrupole interaction, CO 2 (01 1 0) + H 2 (v = 0, J = 1) → CO 2 (00 0 0) (R4) obtaining inverse temperature dependence with P (300 K) ≈ 4 × 10 −3 and good agreement with the then available data, but smaller than the value measured by Allen et al. (1980) by a factor of about 2. The VR energy transfer processes are seen to be capable of giving rate coefficients of a desired magnitude.The only molecule with large and nearly constant VMR with an altitude capable of collisionally converting the vibrational energy of CO 2 (01 1 0) into its rotational energy is N 2 .
Rotationally super-thermal N 2 may be produced by collisions of fast O atoms with N 2 .Sharma and Sindoni (1993) have calculated the differential cross section of Ar-CsF colliding with 1.0 initial relative translational energy as a function of the laboratory recoil velocity of CsF, obtaining excellent agreement for all eight laboratory scattering angles for which the data were available.The calculation exhibits a rich rotational structure showing primary and supernumerary rainbows, with rotational levels of CsF as high as J = 194 populated.There is no reason why correspondingly high rotational levels of N 2 may not be populated in collisions with fast O atoms.Duff andSharma (1996, 1997) have calculated the rate coefficient of the reaction of N with NO, ) in the 100-1000 K temperature, obtaining excellent agreement with the available experimental data and conforming to JPL recommendations (Sander et al., 2011).The calculation (Duff and Sharma, 1997) shows that the product N 2 is produced in excited vibrational and rotational states; vibrational levels 2-7 are each populated with a probability of about 0.1, with rotational levels of vibrational states 1-4 peaking around J = 45, while those of vibrational states 5-8 peaked around J = 40.The VR energy transfer process is near-resonant, with | E| ≤ 50 cm −1 for seven rotational levels 36-42.This process has the potential to be the soughtafter mechanism, provided rotational levels relax in small steps ( J = −2, E ≈ 230 cm −1 ) with a small rate coefficient.The calculation would proceed in the manner of Sharma and Kern (1971), who showed that the greater rate of deactivation of vibrationally excited CO by para-hydrogen over ortho-hydrogen is due to the near-resonant VR process mediated by multipolar interactions

Conclusions
A large value of k x requires the rate coefficient of the unknown mechanism to be equal to k x × (M VMR)/(O VMR), where M is the species participating in the unknown mechanism.While k x may stay constant or increase by a factor of less than 2, the O atom VMR increases by about 1 order of magnitude, going from 90 to 105 km in altitude.The only species that stands a chance of meeting these stringent requirements is N 2 ; its VMR, while not increasing, stays nearly constant at about 0.78.It is shown that the CO 2 (v 2 )-N 2 nearresonant VR rate coefficients could be large enough to meet the requirements.In the thermal atmosphere, the VR processes lead to VT rate coefficients that are 1-2 orders of magnitude too large.Rotationally super-thermal N 2 , produced by collisions of fast O atoms with N 2 or by the N + NO reaction or any other mechanism, hold out hope if these rotational levels relax in small steps ( J = −2, E ≈ 230 cm −1 ) with a small rate coefficient.The 15 µm (bending mode v 2 ) emission from CO 2 is also an important cooling mechanism in the atmospheres of Venus and Mars (Bougher et al., 1999), especially the former, where it acts as a thermostat during the long day (243 times the length of the terrestrial day).The atmospheres of Venus and Mars are similar (∼ 95 % CO 2 , a few percent of N 2 ) and, in these atmospheres, direct excitation of CO 2 vibrations by fast O atoms may be an important cooling mechanism.
The density of atomic oxygen plays very important role in cooling planetary atmospheres.Recently published values of atomic oxygen density (Kaufmann et al., 2014) derived from nighttime limb measurements of atomic oxygen green line intensity in the mesopause region, by the SCIA-MACHY instrument on the European Environmental Satellite, are "at least 30 % lower than atomic oxygen abundances obtained from SABER" instrument on the TIMED satellite.Perhaps it is time that atomic oxygen density is measured using the ground-based (Sharma and Dao, 2006) and spacebased (Sharma and Dao, 2005) Raman lidars proposed earlier.