Introduction
The 15 µm emission from CO2 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 CO2 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.
Translational energy (heat) is collisionally converted into vibrational
energy of the bending mode of CO2. A fraction of the resulting
vibrational energy is radiated away to space, cooling the atmosphere. The
dominant mechanism for this conversion is believed to be the collisions
between CO2 and O,
CO2(0000)+O(3P)→CO2(0110)+O(3P)
and
CO2(0110)→CO2(0000)+hv(667cm-1).
This process is endothermic by the energy of the emitted photon,
667 cm-1 (∼ 15 µm). In the chemical literature, the
rate coefficients of the reactions are given in the exothermic direction
(reverse of Reaction 1a),
and we will follow that convention. The room temperature value of the rate
coefficient kATM for the exothermic process derived by modeling
the 15 µm emission, observed by the Spectral Infrared Rocket
Experiment (SPIRE) (Stair et al., 1985) from the MLT region of the
atmosphere, is 5×10-13 cm3 s-1 (Sharma and Nadile,
1981), 5.2×10-12 cm3 s-1 (Stair et al., 1985),
3.5×10-12 cm3 s-1 (Sharma, 1987), and (3-9)×10-12 cm3 s-1 (Sharma and Wintersteiner, 1990). These studies
gave values of kATM that are 1–2 orders of magnitude greater
than values recommend earlier (Crutzen, 1970; Taylor, 1974). Later analyses
of space-based observations have given values around 6×10-12
(cm3 s-1) (Wintersteiner et al., 1992; López-Puertas et al.,
1992; Ratkowski et al., 1994; Gusev et al., 2006; Feofilov et al., 2012, and
references therein), except for the Vollmann and Grossmann (1997) study
giving a value of 1.5×10-12 (cm3 s-1). The study of
Feofilov et al. (2012) determined the rate coefficient by coincidental
SABER/TIMED and Fort Collins sodium lidar observations in the MLT region and
arrived at values of (5.5± 1.1)×10-12 cm3s-1 at
90 km altitude and (7.9± 1.2)×10-12 cm3 s-1 at
105 km, with an average value of (kATM=6.5± 1.5)×10-12 cm3 s-1. The study of López-Puertas et al. (1992)
“suggests a value of between 3 and 6×10-12 cm3 s-1
at 300 K” and temperature “independent or negative temperature
dependence”. This study derives the values for all input parameters from
ATMOS/Spacelab 3 observations (Farmer et al., 1987; Rinsland et al., 1992),
except the VMR of atomic oxygen, which is taken from atmospheric models.
The laboratory measurements (Shved et al., 1991; Pollock et al., 1993;
Khvorostovskaya et al., 2002; Castle et al., 2006, 2012) and theoretical
calculations (de Lara-Castells et al., 2006, 2007) give room temperature
values of kLAB≈(1.5-2.5)×10-12 (cm3
s-1). The values of kVT determined by modeling
15 µm emission from the MLT region, termed kATM, are
thus larger than the calculated and measured values by a factor of about 4.
Castle et al. (2012) have measured the deactivation of CO2(v2) by
O(3P) in the 142–490 K temperature range, obtaining values of the rate
coefficient kLAB=(2.5± 0.4)×10-12 cm3s-1 at 183 K and (2.4± 0.4)×10-12 cm3s-1 at 206 K. The unexplained rate coefficient
kx(v2) is (5.6± 1.1-2.5± 0.4)×10-12=(3.1± 1.5)×10-12 cm3s-1 at 90 km altitude (T≈183 K) and is (7.9± 1.2-2.4± 0.4)×10-12=(5.5± 1.6)×10-12 cm3s-1 at 105 km altitude
(Table 1b). kx(v2) increases by a factor of 1.8 in going from
90 km altitude to 105 km altitude (≈206 K), showing a steep
variation with altitude. Using the average of the value of kATM 3
and 6×10-12 cm3 s-1, 4.5×10-12 cm3 s-1, suggested by López-Puertas et al. (1992),
and kLAB=2.5×10-12 cm3 s-1, we get
kx=2.0×10-12 cm3 s-1, a smaller value
independent of temperature (altitude). It should be noted that the
contribution to the rate coefficient kATM by unknown mechanism
kx nearly equals (López-Puertas et al., 1992) or is greater
(Feofilov et al., 2012) than kLAB, the contribution by the major
constituent atomic oxygen. As pointed out by Feofilov (2014), the
GCM (general circulation models) use of a
value of kGCM=3.0×10-12 cm3s-1 for this
rate coefficient (Bougher et al., 1999) further complicates the problem. To
resolve this difficult problem, we break it into pieces and attempt to find
the cause of discrepancy between kATM and kLAB.
To resolve the discrepancy between kATM and kLAB,
Feofilov et al. (2012) postulate that nonthermal, or “hot”, oxygen atoms,
produced in the MLT region by photolysis of O2 and dissociative
recombination of O2+, etc., may serve as an additional source of
CO2(v2) level excitation. These authors have derived CO2 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 CO2, it
must undergo (106/268=)3731 collisions at 90 km altitude and
(106/105=)9524 collisions at 105 km altitude with other atmospheric
constituents, mostly with N2, O2 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 CO2 is
therefore virtually nil. However, since CO2 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 non-thermal 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 CO2 must be found
to explain large kx. The situation is similar to that of elevated
4.3 µm (v3 mode) CO2 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 + O3, because of its short lifetime can only transfer a very small
amount of energy directly to trace species CO2, even though transfer of
vibrational energy from higher levels (v=8 and 9) of OH to the v3
mode of CO2 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 N2 by a fast near-resonant process (Burtt and Sharma,
2008a). The longer-lived and super-thermal vibrationally excited N2
transfers its energy, again by a fast near-resonant process (Sharma and Brau,
1967, 1969), to the v3 mode of CO2, the latter radiating around
4.3 µm. The longer-lived N2(v=1) molecule acts as a
reservoir that takes energy from OH and stores it until it is preferentially
released to CO2.
Test of the hypothesis
Thermal rotational levels
Since the N2 density at the altitudes under consideration is much
greater than the O2 density, we provide a justification for the
deactivation of CO2(0110) by N2. The reaction
CO2(0110)+N2(J)→CO2(0000)+N2(J+8)+ΔE
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 CO2 molecule, in the
dipole-hexadecapole moment and quadrupole–hexadecapole moment interactions
involved undergoes ΔJ=± 3,± 2,± 1,0 in the
process. Since CO2 has a much smaller rotational constant (≈0.39 cm-1) than N2 (≈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 long-range
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 ΔJ=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 N2 molecules reside in one of these
four rotational levels. The density of N2 in these four thermalized
rotational levels is (0.0241/0.018=)1.34 times that of atomic oxygen. The
unexplained rate coefficient kx(v2) at 90 km altitude for
pumping of the v2 mode of CO2 is (3.1± 1.5)×10-12 cm3s-1. The sum of the rate coefficients of
Reaction (R2) at 168 K for all four rotational levels
kVR(N2) has to be nearly equal to or greater than
(3.1± 1.5)×10-12/1.34=(2.32± 1.1)×10-12 cm3s-1 to make Reaction (R2) the dominant mechanism for
pumping of the v2 mode of CO2. Since only 2.4 % of the N2
molecules participate in the RV energy transfer process, the rate coefficient
for deactivation of CO2(v2) by N2 would be
kVT(N2)=((2.32± 1.1)×0.024)×10-12=(5.6± 2.6)×10-14. A larger calculated rate coefficient
kN2 would not be a problem, since the v2 mode of
CO2 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
kVT(N2), the fifth column, and kVR(N2), the
last column, required by kx given by these atmospheres. The rate
coefficient kVT(N2) for the deactivation of the bending mode
of CO2 by N2 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. (1978, 1979), by the photoacoustic method, and Allen et
al. (1980), by the laser fluorescence technique, have measured
kVT(N2) at low temperatures. These studies are in general
agreement with that of Allen et al. (1980) giving kVT(N2)
equal to 1.4×10-15 cm3s-1 at 170 K and 3.7×10-15 cm3s-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 kx≡kATM-kLAB. It has already been noted that, since kx is
almost equal to (Tables 1c and d) or greater (Tables 1a and b) than
kLAB, it must involve a major species with a large rate
coefficient.
Nonthermal rotational levels
Sharma (1971) has calculated the probability per collision of the reaction
CO2(0110)+H2O→CO2(0000)+H2O,
a much studied process because of its importance in CO2 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 (σv), assuming a gas kinetic rate of 2×10-10 cm3 s-1 at 200 K and 2.5×10-10 cm3 s-1 at 300 K, are 1.2×10-11 and
2.0×10-11 cm3 s-1 at 200 and 300 K, respectively.
Rate coefficient for deactivation of CO2(v2) by thermal N2, kVT(N2), required if collisions with thermal
N are the missing source of 15 µm emission as function of altitude for different model atmospheres. (a) MLW atmosphere (A. G. Feofilov, 19
October 2014),
(b) MLS atmosphere (A. G. Feofilov, 19 October
2014), (c) polar summer SABER model atmosphere (López-Puertas, 11 November
2014), and (d) polar winter SABER model atmosphere (López-Puertas, 11
November 2014).
Altitude (km)
Temperature (K)
kx
(O VMR)/
kVT(N2)
N2P4(J)
kVT(N2)
(N2 VMR)
(a)
91
169
3.4
0.023
0.0782
0.0183
4.27
93
174
4.1
0.029
0.1189
0.0206
5.77
96
185
4.7
0.043
0.2021
0.0249
8.12
99
199
5.0
0.056
0.280
0.0314
8.92
102
213
5.2
0.089
0.463
0.0381
12.1
105
227
5.4
0.129
0.697
0.0451
15.4
(b)
90
183
3.1
0.018
0.0558
0.0241
2.32
93
179
4.1
0.028
0.1148
0.0223
5.15
96
178
4.7
0.05
0.235
0.0218
10.8
99
182
5.1
0.079
0.4029
0.0237
17.0
102
191
5.2
0.156
0.8112
0.0277
29.3
105
206
5.4
0.219
1.1826
0.0372
31.8
(c)
95
179.7
2.0
0.0198
0.0396
0.02264
1.75
98
183.7
2.0
0.0358
0.0716
0.02438
2.97
101
194.5
2.0
0.0591
0.1182
0.02927
4.04
104
214.6
2.0
0.0920
0.184
0.03897
4.72
107
254.8
2.0
0.130
0.260
0.05928
4.39
110
304.4
2.0
0.163
0.326
0.08339
3.91
(d)
95
179.6
2.0
0.0125
0.025
0.02264
1.10
98
239.7
2.0
0.021
0.042
0.05162
0.814
101
296.0
2.0
0.031
0.062
0.07949
0.780
104
346.8
2.0
0.041
0.082
0.1016
0.807
107
380.3
2.0
0.047
0.094
0.1142
0.823
110
395.2
2.0
0.054
0.108
0.1192
0.906
Rate coefficients are in units of cm3s-1×1012.kx=kATM – kLAB. kATM
provided by A. G. Feofilov (3 November
2014). kLAB is taken as equal to 2.5×1012 cm3 s-1 throughout, based on the work of Castle et
al. (2012).kVT(N2) is the N2 – CO2(v2)
VT rate coefficient
needed to explain kx.N2P4(J) is the fraction of N2 molecules in the four rotational
levels 15–18.kVR(N2) is the N2 – CO2(v2) VR rate
coefficient
needed to explain kx.kx=kATM-kLAB;kATM provided by
A. G. Feofilov (3 November 2014). kLAB is
taken as equal to 2.5×1012 cm3 s-1 throughout, based
on Castle et
al. (2012).kATM=4.5×10-12 cm3 s-1 is the average of
(3-6)×10-12 cm3 s-1 given by López-Puertas et
al. (1992).
Allen et al. (1980) have measured rate coefficients for the deactivation of
the bend-stretch mode of CO2 by H2 in the 170–295 K temperature
range, obtaining values of 7.5×10-12 and 5.0×10-12 cm3 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 is at odds with the Landau–Teller TV
energy transfer mechanism and very much in accord with the near-resonant
energy transfer mechanism (Sharma and Brau, 1967, 1969). Sharma (1969) has
calculated the deactivation of CO2(v2) by H2 assuming a
near-resonant VR energy transfer mechanism mediated by dipole–quadrupole
interaction,
CO2(0110)+H2(v=0,J=1)→CO2(0000)
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 CO2(0110) into its rotational energy is
N2.
Rotationally super-thermal N2 may be produced by collisions of fast O
atoms with N2. 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 N2 may not be populated in collisions with
fast O atoms.
Duff and Sharma (1996, 1997) have calculated the rate coefficient of the
reaction of N with NO,
N+NO→N2+O+3.25eV,
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 N2 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
CO2(0110)+N2(v=xx,J)→CO2(0000)+N2(v=xx,J+4)+ΔE
is near-resonant, with |ΔE|≤50 cm-1 for seven rotational
levels 36–42. This process has the potential to be the sought-after
mechanism, provided rotational levels relax in small steps (ΔJ=-2,ΔE≈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
CO(v=1)+H2(v=0,J=2)→CO(v=0)+H2(v=0,J=6)+88cm-1.
Conclusions
A large value of kx requires the rate coefficient of
the unknown mechanism to be equal to kx × (M VMR)/(O
VMR), where M is the species participating in the unknown mechanism. While
kx 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 N2; its VMR, while not increasing, stays nearly constant
at about 0.78. It is shown that the CO2(v2)–N2 near-resonant 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 N2,
produced by collisions of fast O atoms with N2 or by the N + NO
reaction or any other mechanism, hold out hope if these rotational levels
relax in small steps (ΔJ=-2,ΔE≈230 cm-1) with
a small rate coefficient.
The 15 µm (bending mode v2) emission from CO2 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 % CO2, a few percent of
N2) and, in these atmospheres, direct excitation of CO2 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 SCIAMACHY 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 space-based (Sharma and Dao, 2005)
Raman lidars proposed earlier.