Electron-driven excitation of O2 under night-time auroral conditions: Excited state densities and band emissions

ARTICLE IN PRESS

Planetary and Space Science 54 (2006) 45–59 www.elsevier.com/locate/pss

Electron-driven excitation of O2 under night-time auroral conditions: Excited state densities and band emissions D.B. Jonesa, L. Campbella, M.J. Bottemab, P.J.O. Teubnera, D.C. Cartwrightc, W.R. Newelld, M.J. Brungera, a

School of Chemistry, Physics and Earth Sciences, Flinders University, GPO Box 2100, Adelaide, SA 5001, Australia b School of Informatics and Engineering, Flinders University, GPO Box 2100, Adelaide, SA 5001, Australia c 700 Lewis Avenue South, Rush City, MN 55069, USA d Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK Received 17 January 2005; received in revised form 26 August 2005; accepted 29 August 2005 Available online 1 December 2005

Abstract Electron impact excitation of vibrational levels in the ground electronic state and seven excited electronic states in O2 have been simulated for an International Brightness Coefficient-Category 2+ (IBC II+) night-time aurora, in order to predict O2 excited state number densities and volume emission rates (VERs). These number densities and VERs are determined as a function of altitude (in the range 80–350 km) in the present study. Recent electron impact excitation cross-sections for O2 were combined with appropriate altitude dependent IBC II+ auroral secondary electron distributions and the vibrational populations of the eight O2 electronic states were determined under conditions of statistical equilibrium. Pre-dissociation, atmospheric chemistry involving atomic and molecular oxygen, radiative decay and quenching of excited states were included in this study. This model predicts relatively high number densities for the 1 þ 0 1 X 3 S
g ðv p4Þ; a Dg and b Sg metastable electronic states and could represent a significant source of stored energy in O2* for subsequent thermospheric chemical reactions. Particular attention is directed towards the emission intensities of the infrared (IR) atmospheric (1.27 mm), Atmospheric (0.76 mm) and the atomic oxygen 1S-1D transition (5577 A˚) lines and the role of electron-driven processes in their origin. Aircraft, rocket and satellite observations have shown both the IR atmospheric and Atmospheric lines are dramatically enhanced under auroral conditions and, where possible, we compare our results to these measurements. Our calculated 5577 A˚ intensity is found to be in good agreement with values independently measured for a medium strength IBC II+ aurora. r 2005 Elsevier Ltd. All rights reserved. PACS: 34.80.Gs Keywords: Electron-driven; Excited state densities; Band emissions; O2; Aurora

1. Introduction Understanding processes in the atmosphere is of both technological and fundamental interest. The atmosphere itself can be roughly divided into various layers, including the troposphere, stratosphere and thermosphere, with the relative roles of various physical and chemical processes often differing markedly between these layers. Thermospheric atoms and molecules experience both solar radiaCorresponding author. Tel.: +61 8 82012958; fax: +61 8 82012905.

E-mail address: michael.brunger@flinders.edu.au (M.J. Brunger). 0032-0633/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2005.08.007

tion and charged particle impact, resulting in their excitation and ionisation. Because O2 in metastable excited states may well have enhanced chemical reactivity, as well as characteristic radiation, the influence of electron interaction with O2 needs to be understood. While there have been extensive studies, both measurement and modelling, into the behaviour of atoms, molecules and ions under auroral conditions (Strickland et al., 1999), only a small subset of these have been devoted to the role of molecular oxygen (O2) (Strickland et al., 1999). Of these studies, an even smaller fraction has concentrated on the effect of electron-driven processes in

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E3Σu-(9.960)

B3Σu-(6.170)

A3Σu+(4.340) A'3∆u (4.263)

X3Σg- (0.00)

Tanaka’s Progression I

Shumann-Runge

Herzberg I

Herzberg III

Herzberg II

a1∆g (0.980)

Atmospheric

Noxon

b1Σg+(1.630)

Chamberlain

c1Σu-(4.050)

Infrared Atmospheric

the electronic–vibrational behaviour of O2 under auroral conditions. Indeed the only major self-consistent study that has explored this behaviour was by Cartwright and coworkers some 32 years ago (Cartwright et al., 1972). At least part of the reason for this apparent neglect was that estimates of the electron impact integral cross-sections for the a1 Dg and b1 Sþ g electronic-states were too small (e.g. Noxon, 1970; Witt et al., 1979) to explain the respective observed infrared (IR) atmospheric and Atmospheric band intensities. As a consequence, much of the subsequent analysis (Bates, 1994) has been based around three-body atom recombination chemistry (Watanabe et al., 1981). However, the electron impact integral cross-sections (Cartwright et al, 1972; Noxon, 1970; Witt et al., 1979) used in these early studies of the 1.27 and 0.76 mm emissions have been superceded (Brunger and Buckman, 2002), with new a1 Dg and b1 Sþ data g (Brunger et al., 2003) indicating significantly larger cross-sections, particularly near-threshold, than reported earlier. We have recently identified the importance of resonant behaviour, in which an electron is temporarily captured by an atom or molecule, in our studies of IR fundamental band emissions from NO (Campbell et al., 2004) under auroral conditions. In that work the inclusion of new integral excitation cross-sections led to an improved understanding of the origin of these IR lines. That is, the previously used electron-impact excitation cross-sections were too small to explain the measured intensity emissions and, as a consequence, the observed IR lines were thought to arise only from chemiluminescent effects. However, with the inclusion of the new resonance enhanced cross-sections (Josic et al., 2001; Jelisavcic et al., 2003) our work (Campbell et al., 2004) showed that some 25% of the emitted (1,0) radiation is due to electron-driven processes, with the remainder originating from chemiluminescent effects. Similarly, the recently determined larger electron impact cross-sections for O2 represents one of the major rationales for the present study in general and for the 1.27 and 0.76 mm emissions in particular. The original statistical equilibrium investigation of Cartwright et al. (1972) focused on a three-level model 1 þ 1 ðX 3 S
g ; a Dg and b Sg Þ for O2. In the present study we extend this model to encompass eight electronic states, which allows us to examine the well-known IR atmospheric, Noxon, Atmospheric, Herzberg I, II and III, Schumann–Runge and Tanaka’s Progression I band systems, as well as their cascade contributions to population of the lowest three electronic states. A schematic diagram of the energy levels of molecular oxygen, showing the radiative emission transitions we consider, is given in Fig. 1. Our statistical equilibrium model (Cartwright et al., 2000) includes pre-dissociation, selected atmospheric chemistry involving O2, and quenching. The details of the enhanced statistical equilibrium model used in this study are discussed in greater depth in this paper.

Energy above Ground State (eV)

46

Fig. 1. Schematic diagram of the energy levels of O2, showing the radiative emission transitions for which transition probabilities have been sourced.

2. Collisional-radiative model for night-time auroral excitation of O2 The model employed here to predict the absolute vibrational population densities in the O2 ground and excited electronic states is based on the concept of statistical equilibrium (Jefferies, 1968), in which the balance between electron impact excitation–de-excitation, population and depopulation by radiation, heavy particle deactivation (quenching and/or chemical reaction) and predissociation, determines the excited state number densities. This model has been used successfully to characterise excitation of N2 under auroral conditions (Cartwright et al., 1971; Cartwright, 1978; Morrill and Benesch, 1996; Campbell et al., 2005c) and in the dayglow (Campbell et al., 2005c), and the behaviour of NO under auroral conditions (Cartwright et al., 2000; Campbell et al., 2004), and is used here to study O2 under night-time International Brightness Coefficient-Category 2+ (IBC II+) auroral conditions (Hunten et al., 1956). If it is assumed that excitation occurs only from the lowest vibrational level v00 ¼ 0 of the O2 ground electronic state, the equations for statistical equilibrium for each vibrational level (v0 ) of electronic state (a) are (Cartwright

ARTICLE IN PRESS D.B. Jones et al. / Planetary and Space Science 54 (2006) 45–59

et al., 2000; Campbell et al., 2005c): # ! " X X ba nb X aj na0 a 0a ak i ð1
Q v0 Þ kv0 0 þ Aiv0 x ¼ ðAv0 i þ Qv0 Þ vx , n0 n0 i b i;j;k (1) where kav0 0 ¼

Z

1

F ðEÞsav0 0 ðEÞ dE

0

(2)

is the electron impact excitation rate of vibrational level v0 in state a; E is the electron energy, F ðEÞ is the altitude dependent night-time auroral ‘‘secondary’’ electron distribution (assumed to be known—see later), nx0 is the number density of O2 molecules in the ground electronic–vibrational state (see also Fig. 2) (MSIS, 2004), nav0 =nx0 is the relative fractional density of vibrational level v0 in electronic state a (this ratio is the quantity of primary interest), sav0 0 (cm2) is the rotationally averaged electron impact excitation integral cross-section for the v0 th vibra
1 tional level in electronic state a, Aba iv0 (s ) is the transition probability connecting vibrational levels i and v0 in
1 electronic states b and a, respectively, Qak v0 (s ) is the 0 quenching rate of vibrational level v in electronic state a by a species k [O2, N2, O] and Q0 v0 is the pre-dissociation probability for the vibrational level v0 in electronic state a. Full details of the values, for the above parameters, we employed in our model calculations are given below. We note that in the present model we assume that the electron (IRI, 2004) and excited state number densities in ‘‘normal’’ aurora are sufficiently small so that super elastic and twostep excitation can be neglected, even for the long-lived vibronic (i.e. excited electronic–vibrational) states of O2.

2.1. Auroral secondary electron spectrum The auroral electron spectrum varies a great deal depending on a large number of geophysical parameters, so we attempted to obtain a ‘‘typical’’ auroral secondary electron spectrum as follows. The electron spectrum measured by Feldman and Doering (1975), approximately constant for the altitude range 120–162 km, and that measured by Lummerzheim et al. (1989) for 340 km were used as reference electron spectra for determining the electron spectra at the altitudes considered in this study. These two sets of measurements, although at different altitudes, appear to have been performed for about the same strength aurora because both authors reported a 5577 A˚ intensity of 40 kRayleighs, corresponding to a medium strength IBC II+ aurora. For the spectrum measured by Feldman and Doering (1975), no simultaneous measurement of the primary energy flux was made but it was estimated to vary over the range 1–31 erg/cm2/s. For the spectrum at 340 km, Lummerzheim et al. (1989) measured an energy flux of 27 erg/cm2/s with a characteristic energy of 3.1 keV. In the current study the shape of the distribution was taken from the model of Lummerzheim and Lilensten (1994), with their values scaled (  27) to roughly match the total energy to the specific measurements listed above. Our distributions for 130 and 350 km were set to those of Lummerzheim and Lilensten (1994) at 150 and 300 km, respectively, both multiplied by a factor of 27. The distribution for 130 km was extended below 1 eV using the shape of the low-energy (thermal) spectrum measured by Sharp and Hays (1974). The assumed secondary electron distributions at altitudes (h) between 130 and 350 km were obtained by interpolation using: F h ¼ F 130 þ

14

47

O2

E h
E 130 ðF 350
F 130 Þ, E 350
E 130

(3)

log10 [Number Density (molecules/cc)]

where 0

E h0 ¼ 1
e
0:027ðh
60Þ

12

(4)

O

and F h is the flux at height h (km). Extrapolation of the above formula (Campbell et al., 2005c) below 120 km was unphysical, so between 80 and 120 km we scaled the flux downwards using:

10

F h ¼ F 120 e
0:1ð120
hÞ . 8

6 80

134

188 242 Altitude (km)

296

350

Fig. 2. Population density (in molecules/cm3) of O2 and atomic oxygen, as a function of altitude (in km). See reference (MSIS, 2004) for further details.

(5)

We believe the extrapolation between 120 and 80 km is physical because of the model’s success in reproducing the column emission rate for the 5577 A˚ green-line of atomic oxygen, as discussed later in Section 3.7. An example of our auroral secondary electron spectrum at an altitude of 120 km is given in Fig. 3. A log/log plot is used in Fig. 3 to show clearly the details of the low-energy portion of the spectrum because that is the most effective region of the electron spectrum for exciting the characteristic O2 bands (see Fig. 4).

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0.0 10

B3Σulog10 [Cross section (Angstroms2)]

log10 [Electron Flux (cm2 s sr eV)-1]

9 8 7 6 5 4 3

-0.5 c1Σu-+A′3∆u+A3Σu+

-1.0

E3Σu-

0→1

0→3

-1.5

a 1 ∆g b1Σg+ 0→2

-2.0

2 1

0→4

-2.5

Altitude = 120km

-1

0 0.01

0.1

1

10 Energy (eV)

100

1000

10000

-0.5

(a)

0 0.5 log10[Energy(eV)]

1

1.5

8

Fig. 3. Present secondary electron flux distribution at an altitude of 120 km. Note the logarithmic x- and y-axis.

2.2. Chemical equilibrium model The thermosphere is a very complicated, dynamic, system which exhibits both spatial and temporal variations in behaviour. Along with the electron-driven processes that are the main focus of this study, chemical processes are occurring simultaneously. As a consequence a number of electron-impact and chemical processes compete to create and destroy atomic nitrogen, atomic oxygen, N2, O2 and NO (Barth, 1992). This study employed a model (as detailed in Table 1), based on that of Barth (1992) and includes most of the reactions involving electron impact used in Barth’s model, plus those involving vibrationally excited N2 (N2*) and N2 ðA3 Sþ u Þ. Photo-dissociation was excluded in this study because the focus is on the effects of night-time aurora. We have used our statistical equilibrium concept to solve the simultaneous continuity equations for these, thus ensuring the chemical processes are included. Full details of our procedure can be found in Campbell et al. (2005c). Note, however, that the incorporation of atmospheric chemistry into the present study represents a significant improvement in our model over that originally employed by Cartwright et al. (1972).

3. Model parameters In solving Eq. (1) electron impact integral cross-sections of O2, energy levels, transition probabilities, quenching rates, Franck–Condon factors (FCFs) and pre-dissociation rates are all required. Some of these data are directly available from the literature, whilst in other cases we had to perform our own calculations in order to determine the

Cross section (Angstroms2)

7 Elastic 6 5 4 Ionisation 3 2 B3Σuv′=0→1

1

Dissociation

0 0

20

(b)

40 60 Energy(eV)

80

100

Fig. 4. (a) Recommended integral cross-sections (A˚2) for various vibrational (0–1, 2, 3, 4) and electronic-state excitations (as labelled) in O2. (b) Recommended integral cross-sections (A˚2) for elastic scattering, ionisation and dissociation (as labelled) in O2 as well as for the 0-1 and B3 S
u excitation processes.

required parameter. These details are now discussed in relation to the appropriate component of the model. 3.1. Cross-sections for O2 The ground electronic state of O2 is denoted by X 3 S
g. The electron impact excitation processes needed to describe the electronic–vibrational behaviour of thermospheric oxygen include: 00 3
0 X 3 S
g ðv ¼ 0Þ ! X Sg ðv ¼ 1; 2; 3; 4Þ,

(6)

1 X 3 S
g ! a Dg ,

(7)

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Table 1 A listing of the reactions used, and their respective rates, in the present chemical equilibrium calculations Reaction

Rate (s
1)/calculation

Source


N2+e
s -N2*+es N2*-N2+hn N2*+N2, O2, O, NO-N2+N2 y +
O2+e
s -O2 +2 es
+ N2+es -N2 +2 e
s 4 2
N2+e
s -N( S)+N( D)+es 1 + 0 N2 [X Sg (n 411)]+O-NO+N 2 N2 [A3S+ u ]+O-NO+N( D) 3 + 1 N2 [A Su ]+O-O ( S)+N2 N (2D)+O2-NO*+O N (4S)+O2-NO+O NO+N (4S)-N2+O + NO+O+ 2 -NO +O2 NO+N (2D)-N2+O 2 NO++e
t -N ( D)+O 2 + N+ 2 +O-N ( D)+NO 2 4 N ( D)+O-N ( S)+O 4 NO++e
t -N ( S)+O + + N2 +O2-O2 +N2 4 2
N+ 2 +et -N ( S)+N ( D) 4 + + O2 +N ( S)-NO +O 4
N (2D)+e
t -N ( S)+et N (2D)-N (4S)+hn

Full cross-section used Individual levels Individual levels Full cross-section used Full cross-section used Full cross-section used 10
11 2  10
11 2.5  10
11 (Tn/298)0.55 9.7  10
12 exp (
185/Tn) 1.15  10
11 exp (
3503/Tn) 2.2  10
11 exp (160/Tn) 4.4  10
10 6  10
11 0.75  4.2  10
7 (300/Te)0.85 1.4  10
10 (Tn/300)0.44 1.4  10
12 exp (
259/Tn)/exp (
259/298) 0.25  4.2  10
7 (300/Te)0.85 5.1  10
11 (Tn/300)
0.8 1.8  10
7 (Te/300)
0.39 1.2  10
10 6.0  10
10 (Te/300)0.5 2.273  10
4

Brunger et al. (2003) Gilmore et al. (1992) Cartwright (1978) Brunger et al. (2003) Cartwright (2001) Cosby (1993a) Aladjev and Kirillov (1995) Kochetov et al. (1987) Herron (1999) Herron (1999) Swaminathan et al. (1998) Swaminathan et al. (1998) Barth (1992) Herron (1999) Barth (1992) Barth (1992) Herron (1999) Barth (1992) Barth (1992) Barth (1992) Barth (1992) Barth (1992) Cartwright (2001)

1 þ X 3 S
g ! b Sg ,

(8) 3

1
0 3 þ X 3 S
g ! c Su þ A Du þ A Su ,

(9)

3
X 3 S
g ! B Su ,

(10)

3
X 3 S
g ! E Su .

(11)

Direct vibrational excitation (Eq. (6)) of the ground electronic state was described using the cross-sections recommended in Brunger et al. (2003), extended to threshold with results from Allan (1995b). Excitation of the a1 Dg ; b1 Sþ g and Herzberg pseudo-continuum states 03 3 þ (Eqs. (7)–(9)) c1 Sþ u þ A Du þ A Su , again used the recommended cross-sections in Brunger et al. (2003), while excitation to the Schumann–Runge continuum, B3 S
u, (Eq. (10)) and the E 3 S
u state (Eq. (11)) used cross-section data from Shyn et al. (1994a, b). All these data are plotted in Fig. 4(a) and it should be noted that there is significant resonance enhancement (i.e. increased magnitude) of the excitation cross-sections in all of the vibrational channels (Noble et al., 1996) and to a lesser extent for the a1 Dg and b1 Sþ g electronic states (Middleton et al., 1992). Note that in these graphs a linear interpolation is plotted between the individual datum points. To complete the cross-section matrix the recommended elastic scattering cross-section of Brunger et al. (2003), the electron impact ionisation cross-section of Lindsay and Mangan (2003) and the dissociation cross-section of Cosby (1993b) are used. These latter cross-sections are shown in

Fig. 4(b), together with the cross-section for excitation to the first vibrational level of the ground electronic state and electronic excitation to the B3 S
u state. This enables comparison between the relative magnitudes of the vibrational and electronic state cross-sections with the elastic, dissociation and ionisation cross-sections. As can be seen from Fig. 4(b) (and as usually is the case) the individual electronic and vibrational cross-sections are significantly smaller than the elastic, dissociation and ionisation cross-sections although, as shown below, they remain fundamentally important to our understanding of thermospheric phenomena. Finally we note that the total ionisation cross-section we have employed (Lindsay and Mangan, 2003) is consistent, at 100 eV, with the sum of the very recent measurements for the first- and second-negative band systems of O+ 2 from Terrell et al. (2004). 3.2. Energy levels The absolute energies of all the vibronic levels are needed to perform our calculations. These values were generally sourced directly from the literature or calculated by us from published wavelengths, wave numbers or frequencies of transition between the vibrational levels of the relevant electronic transitions. We note that wavelengths were often provided by authors in conjunction with their transition probabilities (Lewis et al., 1999; Chan et al., 1993; Campbell et al., 2000; Klotz and Peyerimhoff, 1986). Our preferred data for the O2 vibrational energy levels are given in Table 2.

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50

3.3. Transition probabilities

where l is the wavelength (A˚), o ¯ is the statistical weight and Sji is the line strength. Here,

As we are primarily concerned with electronic–vibrational transitions between states for which reliable crosssections are available, we therefore also require transition 1 þ 1
03 1 probabilities between the X 3 S
g ; a Dg ; b Sg ; c Su ; A Du ; 3 þ 3
3
A Su ; B Su and E Su electronic states. To perform the statistical equilibrium simulations we initially collected a large amount of data for both transition probabilities and absolute band oscillator strengths, from various sources. The oscillator strengths were needed, in some cases, to calculate the relevant transition probabilities using the formulation of Hasson et al. (1970). A summary of the sources for the transition probabilities used in this study (Lewis et al., 1999; Chan et al., 1993; Klotz and Peyerimhoff, 1986; Newman et al., 1999; Krupenie, 1972; Schermaul and Learner, 1999; Bates, 1989; Allison et al., 1971; Minaev, 2000; Slanger, 1978) is given in Table 3. These data were typically selected on the basis of how many vibrational sub-levels were given and the accepted reliability of the source. In general, where multiple transition probabilities for a given transition were available, we found they were largely consistent. We also require the transition probabilities for the quadrupole transitions between the vibrational levels of the ground electronic state. The transition probability for a quadrupole transition is given by (Tatum, 1966):

Sji ¼ Q2ji ,

Aji ðs
1 Þ ¼

1:680  1018 S ji , l5 o ¯

(12)

(13)

where Qji is the change in electric quadrupole moment (in ea20 ) during the transition j ! i. The diagonal elements of the electric quadrupole moment for vibrational level v, Qv can be calculated for O2 using (Lawson and Harrison, 1997): Qn ¼
0:2530 þ 0:0257ðn þ 12Þ

(14)

with the off-diagonal elements being obtained from the method of Cartwright and Dunning (1974). Using Eqs. (12)–(14) and the method of Cartwright and Dunning (1974) we have calculated the transition probabilities between all vibrational levels in the ground electronic state up to v0 ¼ 14. A subset of these calculations for the fundamental (v ! v
1), first (v ! v
2) and second (v ! v
3) overtones is presented in Fig. 5. As expected all the quadrupole transition probabilities, for the fundamental, first and second overtones, are small relative to dipole (i.e. optically allowed) radiative transitions. Here we see that the quadrupole transition probabilities for the first overtone are larger than those for the second overtone, as is consistent with corresponding data for N2 (Cartwright and Dunning, 1974). The fact that the overtone transition probabilities are larger than that for the fundamental (for (v0 44)) is a direct result of the large anharmonicity in the potential energy curve for the O2 ground electronic state. Note that we extended the number of vibrational states

Table 2 Energy above the ground ðX 3 S
g ðv ¼ 0ÞÞ state, of the vibrational–electronic states of O2 (eV) n

X 3 S
g

a1 Dg

b1 Sþ g

c1 S
u

A3 Sþ u

A0 Du

3

B3 S
u

E 3 S
u

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

0.000 0.193 0.383 0.570 0.754 0.936 1.114 1.290 1.463 1.633 1.801 1.965 2.128 2.288 2.448

0.980 1.164 1.345 1.522 1.697 1.868 2.036 2.200 2.362 2.520 2.675 2.827 2.976 3.121 3.264

1.630 1.804 1.975 2.142 2.306 2.466 2.623 2.777 2.927 3.073 3.216 3.356 3.492 3.625 3.755

4.050 4.145 4.237 4.325 4.410 4.490 4.566 4.638 4.706 4.769 4.827 4.880 4.928 4.971 5.008 5.039 5.065 5.085 5.099

4.263 4.361 4.455 4.544 4.631 4.713 4.789 4.860 4.924 4.980 5.029 5.068 5.096

4.340 4.436 4.528 4.617 4.700 4.779 4.853 4.920 4.980 5.033 5.077 5.111 5.134

6.170 6.255 6.338 6.417 6.494 6.567 6.637 6.703 6.765 6.823 6.876 6.924 6.967 7.004 7.036 7.062 7.083 7.099 7.112 7.121 7.128 7.132

9.96 10.28 10.57 10.665a 10.775a

a

The energy range of the spectral line is given, so the energy reported is the average value taken over the energy range.

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Minaev (2000)

radiationless transition, caused by collisions with other atoms and molecules. Here they were the same as those used in the AURIC analysis by Strickland et al. (1999) for 3 þ 03 1
the b1 Sþ g ; c Su ; A Su and A Du electronic states by collisions with O, O2 and N2. In addition to these rates, the quenching rates of the a1 Dg state through collisions with O, O2 and N2, from Cartwright et al. (1972), were also 3
employed. Quenching rates for the B3 S
u and E Su states, to the best of our knowledge, were unavailable. However, due to the short lifetimes of their vibrational states we would expect quenching of them to be negligible for the altitudes in this study. The quenching rates used in our simulations are given in Table 4.

Slanger (1978) Bates (1989)

3.5. Franck–Condon factors

Table 3 Sources of the preferred transition probabilities as used in our simulations Transition designation

Source of transition probabilities

a1 Dg ! X 3 S
g

Newman et al. (1999)

3
b1 Sþ g ! X Sg

Krupenie (1972) and Schermaul and Learner (1999) Bates (1989)

3
c1 S
u ! X Sg 3

A0 Du ! X 3 S
g

Bates (1989)

3
A3 Sþ u ! X Sg

Bates (1989)

3

3
B S
u ! X Sg 3
E Su ! X 3 S
g 1 b1 Sþ g ! a Dg 1 c1 S
u ! a Dg 03 A Du ! a1 Dg 1 A3 Sþ u ! a Dg 03 A Du ! b1 Sþ g 1 þ A3 Sþ u ! b Sg 1 þ B3 S
u ! b Sg

Allison et al. (1971) Chan et al. (1993)

Klotz and Peyerimhoff (1986) Klotz and Peyerimhoff (1986) Klotz and Peyerimhoff (1986) Lewis et al. (1999)

-10.5 1st Overtone

log10[Transition Probability (s-1)]

-11.0

2nd Overtone Fundamental

-11.5

-12.0

-12.5 O2 2

4

51

6 8 10 Upper Vibrational Level

12

14

Fig. 5. Present calculated transition probabilities (s–1) for the fundamental, first and second overtones of the X 3 S
g ground electronic state in O2.

beyond those for which we have cross-sections, as by doing so it enables us to obtain a more accurate picture for the behaviour of the excited electronic states which can decay to higher vibrational levels in the ground electronic state. 3.4. Quenching rates Quenching rates in this study apply to processes by which excited atoms or molecules are de-excited, via a

The electron impact excitation rates, kan0 0 , from the ground state to the excited electronic–vibrational states are required in solving the statistical equilibrium Eq. (1). These rates are calculated with Eq. (2) using the atmospheric environment model discussed in Section 2.1 and the crosssections described in Section 3.1. Because the integral cross-sections do not provide any information about the excitation probability to the various vibrational sub-levels of a given electronic state, we used FCFs to assign the weighting that is to be given to each vibrational sub-level. In this study we obtained the FCFs for the 3 þ 03 1
a1 Dg ; b1 Sþ g ; c Su ; A Su and A Du states from Campbell et al. (2000), for the B3 S
u state from Krupenie (1972), and estimated the FCFs for the E 3 S
u state from the electron energy loss spectra measurements of Dillon et al. (1995). 0 For the E 3 S
u state only the v ¼ 0; 1 and 2 sub-levels are observable, implying that if the Franck–Condon approximation holds, the sum of their FCFs should be unity. Considering the data of Dillon et al. (1995) we note that there is a relative reduction in the intensity in the v0 ¼ 1 sub-level as the scattering angle increases. As a consequence of this behaviour we averaged the observed v0 ¼ 1 intensity (Dillon et al., 1995) over all the angles they reported, and then estimated the E 3 S
u state FCFs from the ratio of the observed intensity of each sub-level to the total intensity of all the peaks. In the above procedure we implicitly assume ideal Franck–Condon behaviour. Work by Campbell et al. (2005b), on vacuum ultraviolet (VUV) emissions from N2 under auroral conditions, explicitly showed that the model predictions were quite sensitive to the FCFs employed. Hence the assumption of ideal Franck–Condon behaviour is an important one. For the a1 Dg and b1 Sþ g states of O2, Teillet-Billy et al. (1988) reported results that indicated deviations from ideal Franck–Condon behaviour. However, those results were not supported by later work from Allan (1995a), Doering (1992) and our group (Middleton et al., 1992; Campbell et al., 2000). Note that in those cases where deviations from ideal Franck–Condon behaviour are established, the input FCFs are simply modified to account for these effects (Campbell et al., 2005b).

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Table 4 Quenching rates (s
1) as used in our calculation Reaction

O2 ða1 Dg Þ þ M ! O2 ðX 3 S
gÞþM 1

3
O2 ðb Sþ g Þ þ M ! O2 ðX Sg Þ þ M 3
1
O2 ðc Su Þ þ M ! O2 ðX Sg Þ þ M 3 O2 ðA0 Du Þ þ M ! O2 ðX 3 S
gÞþM 3 þ O2 ðA Su Þ þ M ! O2 ðX 3 S
gÞþM

Rate coefficient (cm3/s) for species, M N2

O2

O

0.11000E
18

0.24000E
17

0.13000E
15

0.22000E
14

0.40000E
16

0.80000E
13

—

0.26400E
12

0.13200E
09

—

0.17000E
10

0.17000E
10

0.75000E
12

0.22500E
10

0.15000E
10

3.6. Pre-dissociation Pre-dissociation of the higher lying (in energy) excited electronic states of O2 into atomic O, by electron impact, is known to be substantial (Cosby, 1993b) and is particularly true for the Herzberg pseudo-continuum, Schumann– Runge continuum and E 3 S
u states. Pre-dissociation rates are not, to our knowledge, directly available in the literature so they were estimated from the data in Cosby (1993b). It is data from that source that we have employed in the current simulation. Photo-dissociation of the Schumann–Runge (B3 S
u ) continuum into atomic O is also known (Cosby et al., 1993; Balakrishnan et al., 2000; Dooley et al., 1998) to be very important in atmospheric behaviour. As our present model does not account for photo-dissociation effects, our simulated population densities for the B3 S
u should be viewed as upper bounds to the physical situation. 3.7. Atomic oxygen Atomic oxygen is also a major constituent of the thermosphere (see Fig. 2) and because its interaction in thermospheric processes is important, it is included in the present study. Cross-sections for electron impact excitation between the ground (2p4 3P) state and the 2p4 1D, 2p4 1S, 2p3(4So)3s5So, 2p3(4So)3s3So, 2p3(4So) 3d3Do, 2p3 (2Do)3s3Do and 2p3(2Po)3s3Po excited states are taken from Kanik et al. (2001) and Johnson et al. (2003). The corresponding transition probabilities for the various transitions were obtained from the NIST database (NIST, 2004). The well-known atomic oxygen O(1S)-O(1D) green line at 5577 A˚ has been studied by many workers (e.g. Strickland et al., 1999; Takahashi et al., 1984, 1985; Yee and Abreu, 1987; Megill et al., 1970, 1971; Murtagh et al., 1990; Murtagh, 1995), at least in part from the view that the green line intensities are a means for remote sensing of atmospheric atomic oxygen densities. We note that excitation of the O-atom green line occurs by a process (i.e. ‘‘exchange’’) which is relatively more sensitive to the low-energy portion of the secondary electron distribution than the high energy portion. Hence, the predicted O green-line represents one qualitative check on our model

calculations. Quenching of the O(1S) state by O2 and O(3P) was included in our simulations using the respective rates from Strickland et al. (1999) and O’Neil et al. (1979). In Fig. 6 (lower panel) we compare our results for the altitude dependence of the 5577 A˚ emission rate produced by all processes with the data of Sharp et al. (1979). Good qualitative agreement is found between them, although there is a discrepancy in terms of absolute magnitudes of the emission rates. The data of Sharp et al. (1979) were produced by an aurora of energy 5.6 erg/cm2/s, whereas the present auroral energy is 28 erg/cm2/s. Hence we would expect a discrepancy between the calculated and measured values, with a scaling factor of 0.2 being applicable. However, the actual scaling factor required to obtain agreement is 0.03, indicating our predictions are about seven times too high for the quoted energy. To investigate this apparent discrepancy we re-ran our calculation using the measured electron spectrum of Sharp et al. at 143 km. In this case our calculated 5577 A˚ emission rate is found to be in very good agreement (see Campbell et al., 2005c) with the corresponding data of Sharp et al., indicating the discrepancy in Fig. 6 is not due to our model but is in the relationship between the electron spectrum of Sharp et al. (1979) and their quoted auroral energy. Finally, we note that the present model predicts a direct electron impact contribution of between 25% and 35%, depending on the altitude, to the total 5577 A˚ in Fig. 6. In Fig. 6 (upper panel) we compare the column emission rate predicted by our model, as a function of altitude, with measured data from both Sharp et al. (1979) and O’Neil et al. (1974). The results from our model are in very good agreement with the ascent (rocket) column emission rate measurement of O’Neil et al. (1974) but, as expected, are larger than the data from Sharp et al. (1979). Note that we expected this result because our auroral energy is five times greater than that of Sharp et al. Our total IBC II+ aurora emission rate of 50 kRayleighs is also in good agreement with the value from Feldman and Doering (1975) of 40 kRayleighs. So in spite of some inconsistencies with the results of Sharp et al. we predict a total green-line emission which is close to the expected value for an IBC II+ aurora, and suggests that our model contains the most important physical and chemical processes.

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D.B. Jones et al. / Planetary and Space Science 54 (2006) 45–59

200 150 100 100

1000 10000 Column Emission Rate (Rayleighs)

100000

220

200

Altitude (km)

180

160

140

corresponding value from Borst and Zipf. Our transition probability for the B ! X process is from Gilmore et al. (1992), while our respective reaction rates for production of B2S+ u by O and O2 are from Barth (1992). The results from our simulation of the altitude dependence of the 3914 A˚ emission rates are given in Fig. 7. Of particular interest is the upper panel of this figure where the present column emission rates are compared to the ascent rocket measurements of O’Neil et al. (1974). It is quite clear from Fig. 7 that our model calculations for the 3914 A˚ emission are in quite good agreement with the measurements of O’Neil et al. above about 90 km. Below 90 km we predict a significantly larger emission rate than is found experimentally, suggesting that our model, at the lower altitudes, is not representative of the conditions during the O’Neil experiment. Nonetheless the agreement at the higher altitudes, when coupled with what we previously found for the atomic O green-line emission (see Section 3.7) provides further evidence for the overall consistency of our model.

Altitude (km)

120

100

200 150 100

80

100 10

100 1000 555.7-nm emission rate (photons/cc/s)

200

180 Altitude (km)

The 3914 A˚ first negative band line for the B2 Sþ u ð0; 0Þ ! + X Sþ has also been studied g ð0; 0Þ transition in N2 extensively (Noxon, 1970; Megill et al., 1970, 1971; O’Neil et al., 1974). In contrast to the 5577 A˚ emission, which as noted above is more sensitive to the details of the lowenergy portion of the electron spectrum, the first negative band system is more sensitive to the high-energy portion of the spectrum. In the present study we have employed the direct 2 þ electron impact cross-section for X 1 Sþ g ! B Su ð0; 0Þ of Ohmori et al. (1988). This cross-section is from a database that has been used successfully (Campbell et al., 2001) to model gas discharge behaviour in N2, and it is different from the earlier data of Borst and Zipf (1970) which has been widely used. For instance, the Ohmori et al. crosssection at 30 eV is some 50% larger in magnitude than the

1000 10000 Column Emission Rate (Rayleighs)

220

Fig. 6. (lower panel) Altitude dependence of the emission rate (photons/ cm3/s) of the atomic O green-line (5577 A˚). The present simulation results for a IBC II+aurora (K) and the data for a weaker aurora from Sharp et al. (1979) (  ), are shown. (upper panel) Altitude dependence of the column emission rate (Rayleighs) of the atomic O green-line (5577 A˚). The present simulation results (—) and the data of Sharp et al. (1979) (B) and O’Neil et al. (1974) (J), are shown.

3.8. N+2

53

160

140

2

120

100

80 100

1000 10000 391.4-nm emission rate (photons/cc/s)

Fig. 7. (lower panel) Altitude dependence of the emission rate (photons/ cm3/s) for the B ! X transition (3914 A˚) in N+ 2 . The present simulation results (––––) are shown. (upper panel) Altitude dependence of the column emission rate (Rayleighs) for the B ! X transition (3914 A˚) in N+ 2 . The present simulation results (—) and the data of O’Neil et al. (1974) (J), are shown.

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4. Results and discussion Strickland et al. (1999) demonstrated that O2 plays a major role in atmospheric behaviour under night-time auroral conditions, as a consequence of atomic oxygen recombination. We have therefore mimicked this same environment to consider the role and relative importance of O2 electron-driven processes, for altitudes between 80 and 350 km. A selection of our most significant results, from the current statistical equilibrium simulation, are now presented and where possible compared to corresponding data from rocket or satellite measurements and other simulations. 4.1. Direct excitation rates

Log10 [Electron Impact Excitation Rate (excitations /s/O2 molecules)]

In Fig. 8 we present the direct electron impact excitation rates for transitions out of the ground state, as calculated using Eq. (2) with the auroral secondary electron spectra described in Section 2.1 (see also Fig. 2) and the crosssections discussed in Section 3.1 (see also Fig. 4). The excitation rates plotted in this figure are for an altitude of 120 km and, with the similar data at other altitudes between 80 and 350 km, are essential for the statistical equilibrium analysis to proceed. The present data represent the first time such an extensive set of computations for direct excitation rates in O2, under an IBC II+ night-time auroral environment, have been reported. While Cartwright et al. (1972) must have made the corresponding calculations in their earlier 1 þ 1 study, for the X 3 S
g ; a Dg and b Sg states, they did not report their results in that paper. As a consequence we

cannot compare the present data to those of Cartwright et al. It is clear from Fig. 8 that there is significant direct excitation into the v ¼ 024 vibrational sub-levels of the X 3 S
g ground electronic state, and the v ¼ 0 and 1 levels of the a1 Dg and b1 Sþ g excited electronic states. Important excitation into the E 3 S
u state is also noted. Direct excitation into the Herzberg pseudo-continuum and Schumann–Runge continuum states is, however, generally relatively small across all their vibrational sub-levels. The mechanism for the relatively strong direct excitation of the O2 ground state can be understood as follows. For the vibrational sub-levels of the ground electronic-state (v0 ¼ 1; 2; 3; 4), we see in Fig. 4a that there are two major peaks in the cross-sections at 0.58 and 10 eV. Both these peaks are the result of resonance phenomena due to the temporary capture of an electron by the O2 molecule. Fig. 3 shows that at an energy of 0.58 eV there are a relatively large number of electrons, while at 10 eV there still remains an appreciable number of electrons. Hence the predicted significant direct excitation rates for the vibrational sublevels of the X 3 S
g state are due in our model to resonant behaviour at the nanoscale. Similar, although less pronounced, resonance enhancements in the a1 Dg and b1 Sþ g cross-sections explain the relatively important excitation rates for these states (see Fig. 4a). On the other hand, as shown in Fig. 4a, the largest magnitude for an excited-state integral cross-section occurs for the B3 S
u state at around 20 eV, while Fig. 8 shows that the direct excitation rates for the vibrational sub-levels of the B3 S
u state are the lowest for the states studied. The reason for this is apparent in Fig. 3, where we see the relative number of electrons at 120 km with 20 eV energy is smaller than that at the lower energies.

-4

4.2. Excited state densities

-5

Having determined the relevant electron impact excitation rates, one can calculate the O2 excited state’s atmospheric densities under our night-time auroral IBC II+environment using Eq. (1). These equilibrium excited state densities, relative to the density of the X 3 S
g ðv ¼ 0Þ state (see Fig. 2), are shown in Fig. 9. It is apparent from 1 þ 0 Fig. 9 that the X 3 S
g ðv p3Þ and b Sg states are predicted to have large population number densities for the lower vibrational levels and that for the a1 Dg state is both large and extended. It should be noted that the X 3 S
g state the 0 population densities in Fig. 9 for X 3 S
ðv X5Þ are due to g cascade from higher lying electronic states, in particular the Herzberg pseudo-continuum. This is because the direct cross-sections for these levels are currently believed to be very small. Hence, the relative populations of v0 ¼ 5 ! 14 in the ground-state predicted by our model (Fig. 9) could be a lower limit if the higher level cross-sections are resonantly enhanced. The model predictions for relatively high number densities of both the a1 Dg and b1 Sþ g states is crucial as the a1 Dg
X 3 S
transitions give rise to the IR atmospheric g

-6 X3Σg-7 -8

E3Σu-

-9

a1∆gb1Σg+ c1Σu-

-10 -11

A′3∆u A3Σu+ B3Σu-

-12 Altitude = 120km -13 0

5 10 15 20 Upper State Vibrational Quantum Number

25

Fig. 8. Electron impact excitation rates (excitations/s/O2 molecule), as a function of the upper state vibrational quantum number, for the electronic states of O2 (as labelled) as calculated in the present study. The altitude is 120 km.

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-4

a1∆gX3Σg-

-6 -8

c1Σu-

b1Σg+

-10

A′3∆u

A3Σu+

-12 -14 E3Σu-

-16

B3Σu-

-18

Altitude = 120km -20 0

5

10 15 Vibrational Quantum Number

20

Fig. 9. Relative population density (per unit O2 molecules), as a function of the upper state vibrational quantum number, for the electronic states of O2 (as labelled) as calculated in the present study. The altitude is 120 km.

3
bands, the b1 Sþ g ! X Sg transitions give rise to the 1 Atmospheric bands and the b1 Sþ g ! a Dg transitions give rise to the Noxon bands (see Fig. 1). Because the predicted number densities of the a1 Dg and b1 Sþ g states are high, it is reasonable to anticipate that all the aforementioned bands will have quite strong emission intensities under night-time auroral conditions, a result that is at least qualitatively consistent with the rocket observations of Megill et al. (1970), which is explored in more detail below. These relatively high predicted a1 Dg and b1 Sþ g number densities may also be important because as these states are metastable and possess substantial amounts of internal energy (0.98 and 1.6 eV, respectively), they might be expected to play an important role in the chemistry occurring in the thermosphere under disturbed conditions.

4.3. Volume emission rates for the a1 Dg ðv0 ¼ 0Þ
00 X 3 S
g ðv ¼ 0Þ transition at 1.27 mm Having used our enhanced statistical equilibrium code to determine the altitude dependence of the excited state populations, we can now use that data to determine the altitude dependence of the volume emission rates (VERs) for specific transitions of interest. We look now at the IR atmospheric emission at 1.27 mm, due to the a1 Dg ðv0 ¼ 00 0Þ
X 3 S
g ðv ¼ 0Þ transition, which is known to be a prominent feature of night-time aurorae. Previous rocket-based measurements for the 1.27 mm line have been reported by Noxon (1970), Llewellyn et al. (1969) and Megill et al. (1970), while simulations using two different auroral environments were presented by Cartwright et al. (1972). The difficulty in comparing the present results and those of Cartwright et al. to the earlier

55

measurements, is that all those measurements show significant variations in 1.27 mm intensity as a function of either rocket spin (Megill et al., 1970) or latitude (Noxon, 1970). Therefore, in order to try and make a sensible comparison to the simulation results, in Fig. 10 we plot an ‘‘average’’ VER for the experimental data (Noxon, 1970; Megill et al., 1970). Note that this average is over either the rocket spin or latitude, as appropriate. It is apparent from Fig. 10 that the altitude dependent VERs for the 1.27 mm transition predicted by our model are significantly smaller in magnitude than those measured previously (Noxon, 1970; Megill et al., 1970; Llewellyn et al., 1969), suggesting that processes other than electrondriven might be responsible for the observed emission rates. One such process was suggested by Bates (1994), who speculated that O2(a) in the lower thermosphere might be formed by the deactivation of O2(b) and by direct entry in termolecular association. Notwithstanding this, from a qualitative perspective the VER measurements of Megill et al. (1970) and the present VER simulation results show good shape agreement over the common altitude range. Somewhat surprisingly the earlier simulations (Cartwright

106

Volume Emission Rate ( cm-3 s-1 )

Log10[Relative Number Density (nν,α)/n0X) per unit O2 molecule]

D.B. Jones et al. / Planetary and Space Science 54 (2006) 45–59

104

100

1

0.01 0

50

100

150 200 250 Altitude (km)

300

350

400

Fig. 10. Altitude dependence of the volume emission rate (cm–3 s–1) for the 1.27 mm line in O2. The present simulation result (—) is compared against the earlier model results from Cartwright et al. (1972) (- - - -) model 1 and (– –) model 2, and the measurements of Llewellyn et al. (1969) (J), Noxon (1970) (&) and Megill et al. (1970) (B). The error bars represent one standard deviation and reflect the VER variation during rocket rotation.

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et al., 1972), using two different auroral secondary electron energy distributions, are in better agreement with the experimental measurements than the present. We believe, however, this agreement between the earlier simulations and the data is fortuitous. This is because the present simulation employs a cross-section database that is significantly superior to that available to Cartwright et al. (1972) at that time. Campbell et al. (2005a) recently showed that model predictions for emissions from N2 in the wavelength range 1600–2900 A˚ were quite sensitive to the N2 cross-section database employed. Their study clearly indicated that the more physical the cross-section database was, the more accurate the model predictions were compared to the results from independent measurements. In addition, the environments we have used (i.e. the auroral secondary electron spectra) are more physical than both of the models that were employed by Cartwright et al. and we note our environments are also valid over a more extended altitude range than had been previously possible. 0 4.4. Volume emission rates for the b1 Sþ g ðv ¼ 0Þ
3
00 X Sg ðv ¼ 0Þ transition at 0.76 mm

In Fig. 11 we compare the predicted altitude dependence of the VER for the 0.76 mm emission, with the AURIC results from Strickland et al. (1999) and measured data from Burrage et al. (1994), Megill et al. (1970), Witt et al. (1979) and Murtagh et al. (1990). The current simulation predicts a peak in the VER at an altitude 88 km, in quite good agreement with the average experimental prediction (Witt et al., 1979; Murtagh et al, 1990; Burrage et al., 1994) of 92 km. However the present simulation also predicts a more extended VER for altitudes greater than about 92 km, than was found by Witt et al., Murtagh et al. and Burrage et al. All these measurements predict a very localised 0.76 mm VER at about 92 km. On the other hand the measurements of Megill et al., for altitudes in the range 100–150 km, indicate an extended VER consistent with our prediction. Indeed we would characterise the shape agreement between our VER simulation and the data of Megill et al. as being very good, over the common altitude range. It is interesting to note, similar to what we have just seen for the 1.27 mm emission, that the magnitude of the 0.76 mm VER from Megill et al. is systematically higher than the present result. It is also significantly larger than any of the other measurements (Witt et al., 1979; Murtagh et al., 1990; Burrage et al., 1994). If this observation was indicative for some systematic overestimation in the measurements of Megill et al., then it would have important ramifications to the discussion we gave earlier in Section 4.3. Namely, the extent of the discrepancy between our 1.27 mm VERs and those of Megill et al. might need to be reviewed and the mechanism proposed by Bates (1994) for the observed emission rates might need to be reconsidered. The AURIC calculation result, based on an atomic oxygen three-body recombination process, from Strickland

106

105

Volume Emission Rate ( cm-3 s-1 )

56

104

1000

100

10

1

0.1 0

50

100

150 200 250 Altitude (km)

300

350

400

Fig. 11. Altitude dependence of the volume emission rate (cm–3 s–1) for the 0.76 mm line in O2. The present simulation result (—) is compared against the scaled AURIC result from Strickland et al. (1999) (- - - -) and the measurements of Burrage et al. (1994) (n), Witt et al. (1979) (J), Murtagh et al. (1990) (&) and Megill et al. (1970) (B). The error bars represent one standard deviation and reflect the VER variation during rocket rotation.

et al. is also shown in Fig. 11. At first glance the agreement between this calculation and the measurements of Witt et al., Murtagh et al. and Burrage et al. appears outstanding. However, this level of agreement is in fact a little artificial as Strickland et al. scaled their atomic oxygen population up by about 60%, over the accepted values (see Fig. 2), to fit the data of Burrage et al. This is an interesting result as historically the three-body process was originally proposed because the then available electron impact integral crosssections could not explain the observed 0.76 mm intensity. However, with the current cross-section database it is obvious from Fig. 11 that electron-driven processes (and our defined chemistry—see Table 1) can at least now reproduce the maximum observed 0.76 mm VER, even though there clearly remains differences in other details with most of the measurements. If the AURIC calculated VER from Strickland et al. is scaled downwards by 60%, then it is apparent from Fig. 11 (particularly if one allows for the log scale) that, by itself, the three-body recombination process cannot explain the observed 0.76 mm emissions. We therefore believe that, in all likelihood, it is

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probably a combination of three-body and electron-driven processes that is causing the observed night-time aurora emissions for this line. 4.5. Herzberg bands I and II and chamberlain band emission spectrum Strickland et al. (1999) presented a calculated spectrum, as obtained from their AURIC model, for the Herzberg I, Herzberg II and Chamberlain bands for a tangent altitude of 95 km. This spectrum gives an indication of the relative population of the Herzberg pseudo-continuum of states, and so it is of interest to compare it with the corresponding spectrum from our model. Note that in making this comparison we have broadened our radiative line intensities so that they correspond to an instrument resolution of 10 A˚ (FWHM), consistent with that done in Strickland et al. (1999). The results of our simulation and those from the AURIC model are plotted in Fig. 12. The present simulation shows larger intensities from threshold up to about 2700 A˚, demonstrating a relatively higher population of 1
the A3 Sþ u and c Su upper vibational levels. Thereafter, however, results from the present simulation and the AURIC model are in semi-quantitative agreement. This result demonstrates that, under aurora-like conditions, direct electron impact excitation can be an important mechanism for production of the Herzberg pseudocontinuum.

HI+HII+Chm 1.5

Strickland

log10[Radiance (R/Angstrom)]

1.0

57

5. Conclusions We have reported results from a comprehensive study into the electronic–vibrational behaviour of O2 under night-time auroral conditions, using our statistical and chemical equilibrium model. This study combined the best secondary electron distributions and cross-section database to simulate the role of electron-driven processes under these conditions. Pre-dissociation, an important effect when dealing with O2 molecules, was also included in this model, as was heavy-particle quenching. As a consequence, we believe the present results supercede and extend those from the earlier simulation of Cartwright et al. (1972). Significant results were obtained from the present study. These include large and, in some cases quite extended, 1 þ 0 1 population densities for the X 3 S
g ðv X0Þ; a Dg and b Sg states, as well as quantitative descriptions for the altitude dependence of the 5577 and 3914 A˚ column emission rates. In addition, the important role played by electron-driven processes in understanding the altitude dependent VER for the 1.27 and 0.76 mm lines was demonstrated. Finally, the role of electron-driven processes in the origin of the Herzberg I, Herzberg II and Chamberlain bands was elucidated. Future work will involve the enhancement of the model to account for photo-dissociation. Acknowledgements We thank Marilyn Mitchell for typing this manuscript. This work was supported by a grant from the Australian Research Council. One of us (WRN) would also like to thank both Flinders University, for their financial support and hospitality during his visit, and the Royal Society for travel support. DBJ thanks the Ferry Trust and Complex System Sciences Division of CSIRO for financial support. References

0.5

0.0

-0.5

-1.0 2000

2500

3000 3500 4000 Wavelength (Angstroms)

4500

5000

Fig. 12. Wavelength dependence of the radiance for the Herzberg I, Herzberg II and Chamberlain band spectra observed at a tangent altitude of 95 km and for a band width of 10 A˚ (FWHM). The present simulation results (—) are compared against the results from Strickland et al. (1999) (- - - -).

Aladjev, G.A., Kirillov, A.S., 1995. Vibrational kinetics of molecular nitrogen and its role in the composition of the polar thermosphere. Adv. Space Res. 16 (l), 109–112. Allan, M., 1995a. Experimental differential cross sections for the electron impact excitation of the a 1Dg, b 1S+ u and the 6 eV states of O2. J. Phys. B: At. Mol. Opt. Phys. 28, 4329–4345. Allan, M., 1995b. Measurement of absolute differential cross sections for vibrational excitation of O2 by electron impact. J. Phys. B: At. Mol. Opt. Phys. 28, 5163–5175. Allison, A.C., Dalgarno, A., Pasachoff, N.W., 1971. Absorption by vibrationally excited molecular oxygen in the Schumann–Runge continuum. Planet. Space Sci. 19, 1463–1473. Balakrishnan, N., Jamieson, M.J., Dalgarno, A., Li, Y., Buenker, R.J., 2000. Time-dependent quantum mechanical study of photodissociation of molecular oxygen in the Schumann–Runge continuum. J. Chem. Phys. 112, 1255–1259. Barth, C.A., 1992. Nitric oxide in the lower thermosphere. Planet. Space Sci. 40, 315–336. Bates, D.R., 1989. Oxygen band system transition arrays. Planet. Space Sci. 37, 881–887. Bates, D.R., 1994. Some facets of the ionosphere and of the nightglow. J. Geophys. Res. 99, 19101–19112.

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