Experimental and coupled-channels
investigation of N2 radiative
properties for analysis of FUSE
dayglow observation
Xianming Liu and D. E. Shemansky
Space Environment Technologies
A. Heays and B. N. Lewis
Australian National University
P. D. Feldman
Johns Hopkins University
Outline
• N2 background
• Electron-impact induced emission
• Coupled-channels Schrödinger Equation
(CSE)
• Results of experimental and CSE
investigation
• Application to FUSE terrestrial
thermospheric dayglow observation
N2 Electronic Structure
• Ground X 1Σg+ state electron configuration
– (1σg)2 (1σu)2 (2σg)2 (2σu)2 (1πu)4(3σg)2
• Excited states
– Triplet states (FUV, spin-forbidden from X 1Σ g+)
– Singlet-gerade states (FUV, dipole-forbidden from X 1Σg+)
– Singlet-ungerade states (EUV, dipole-allowed)
• Ionic states (EUV)
– Single hole states (nondissociative ionization)
• (3σg)-1 X 2Σ g+
• (1πu)-1 A 2Πu
• (2σu)-1 B 2Σu
Classification of N2 singlet-ungerade states
• 2 valence states: b’1Σu+ and b 1Πu states.
• 3 Rydberg series: npσ, npπ and nsσ.
– npσ and npπ series converge to the N2+ X 2Σg +
state and are designated as c’n+11Σu+ and cn 1Πu.
– nsσ series converges to the N2+ A 2 Πu state and
is designated as on 1Πu.
Experimental measurement of
c’1Σu+ - X 1Σg + band system
• Accurate relative intensity measurement
– Enhancement of apparatus efficiency (B4C grating)
– Low resolution (0.3Å) for transition moment
measurement
– High resolution (36mÅ) for model accuracy
– Optical thin for accurate raw intensity measurement
• Pressure dependence, swarm vs cross beam measurement
– Accurate instrumental relative sensitivity calibration
with e+H2 model (error less than 7% in relative
intensity 900-1630Å)
Experimental measurement of
c’1Σu+ - X 1Σg + band system
• Accurate relative intensity measurement
– Enhancement of apparatus efficiency (B4C grating)
– Low resolution (0.3Å) for transition moment
measurement
– High resolution (36mÅ) for model accuracy
– Optical thin for accurate raw intensity measurement
• Pressure dependence, swarm vs cross beam measurement
– Accurate instrumental relative sensitivity calibration
with e+H2 model (error less than 7% in relative
intensity 900-1630Å)
Theoretical calculation
• Coupled-channel Schrödinger equation (CSE) model
– 2005 model: interactions between b, c, and o 1Πu and C and C’3Πu
states (9-channels)
– present model: interactions between b’ and c’1Σu, b, c, and o
1Π , and C, C’, F, G 3Π states
u
u
– Ab initio potential energy refined by experimental term values.
– Transition moments refined by photoabsorption and electron impact
induced emission results.
– Capable of calculating line oscillator strengths, predissociation and
photodissociation cross sections
• Example of N2 CSE (2005 model, taken from J. P.
Sprengers’ Ph. D. Thesis)
CSE model
• Three levels of interactions
– Homogeneous electrostatic interactions among the states
within the 1Σu,1Πu, and 3Πu Rydberg-valence manifolds
– Homogeneous spin-orbit interactions between 1Σu+, 1Πu,
and 3Πu manifolds
– Heterogeneous L-uncoupling interactions between 1Σu+
and 1Πu manifolds
– All interactions depend on internuclear distance, R
• Continuous photodissociation CSE spectrum
– Fit CSE cross section to Fano profile to obtain resonance
energy, width and oscillator strength
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LIU ET AL.: N2 c04 1+u X 1+g RADIATIVE PROPERTIES
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Figure 2. Comparison of calibrated experimental (solid lines) and CSE-model (dotted lines) e + N2
low-resolution emission spectra for the c04 1Su+(0) X 1Sg+(03) transitions. The experimental spectra
were obtained concurrently in cross-beam mode, with 100 eV excitation energy and a spectral resolution
of 0.3 Å FWHM. The model spectra were generated assuming a rotational temperature of 300 K. All
y-axes refer to calibrated intensity in counts, with appropriate indicated scales, while all x-axes refer to
wavelength in Å, with indicated offsets. An upper limit of 3% was estimated for the resonance
absorption in the c04 1Su+(0) X 1Sg+(0) band, i.e., had the resonance absorption been absent, the solid
trace for the c04 1Su+(0) X 1Sg+(0) transition would have been 3% stronger. The emission intensity
drops by a factor of 300 from vi = 0 to vi = 3. See section 4 for a discussion of the discrepancy for l 1026.6 Å.
validating the CSE treatment of the c04 1S+u state and its
coupling. For the (0,3) band, which is weaker than the (0,0)
band by a factor of 300 and the measured intensity has an
estimated uncertainty of 18%, mainly because of the
relatively large uncertainty in the background subtraction,
intensities on the R-branch (shorter-wavelength) side are
reproduced to within the experimental uncertainty. However, the model underestimates significantly the intensity on
the P-branch (long-wavelength) side of this band. While the
reason for this is not clear, it is most likely due to weak
atomic nitrogen emission that is not included in the current
model, since the discrepancy applies only to one side of the
band. Emission from the b0 1S+u (1) state is unlikely to be
responsible, since it is known to be weak in this region, and,
in any case, the b0 1S+u X 1S+g electronic transition
moment employed in the CSE model is well constrained
by the experimental oscillator strengths for the b0 1S+u (vj) X 1S+g (0) bands [Stark et al., 2000, 2008]. As mentioned
above, the c3 1Pu(1) X 1S+g (vi+1) band emissions overlap
with the P-branch side of the c04 1S+u (0) X 1S+g (vi) band
emissions, and, indeed, the c3 1Pu(1) X 1S+g (4) band lies
in the correct position to explain the additional emission on
the P-branch side of the c04 1S+u (0) X 1S+g (3) band.
However, the calculated emission, which is included in
the model spectrum of Figure 2, is too weak to fully explain
the discrepancy. In principle, a change to the R-dependence
of the model c3 1Pu X 1S+g electronic transition moment
might improve matters, but, considering that good agreement is found between the model and experimental spectra
for the c3 1Pu(1) X 1S+g (0) band, and that the model c3
1
Pu(1) X 1S+g (3) band emission is somewhat too large
compared with experiment, it is unlikely that a
realistic R-dependence will simultaneously explain the
observations for all three bands. Possible atomic nitrogen
emissions in the region are the 2s22p2(3P)12d2D 2s22p3 2Do5/2 and 2s22p2(3P)12d 2D 2s22p3 2Do3/2 transitions, at 1026.69 and 1026.78 Å, respectively,
and spin-forbidden transitions, 2s22p2(3P)12d 4P 2s22p3 2Do5/2 and 2s22p2(3P)12d 4P 2s22p3 2Do3/2, at
1027.15 and 1027.24 Å, respectively. The c04 1S+u (0) 7 of 17
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LIU ET AL.: N2 c04 1+u X 1+g RADIATIVE PROPERTIES
Figure 3. Adopted CSE-model diabatic c04 1Su+ X 1Sg+
electronic transition moment (white curve), including
uncertainty range (shaded area), compared with ab initio
calculation of Spelsberg and Meyer [2001] (black curve).
The reader is cautioned against using equation (7) for
R-values outside its range of applicability. In such regions,
the R dependence calculated ab initio by Spelsberg and
Meyer [2001] is likely to be significantly more realistic.
The CSE-model transition moment is compared with that
of Spelsberg and Meyer [2001] in Figure 3. While the general
forms of the transition moments are similar, the average
magnitude of the adopted CSE moment is 15% less than
the ab initio value. Discrepancies of similar magnitude and
sign have been found in the case of the diabatic transition
moments for the b, c3, and o3 1Pu X 1S+g transitions of N2
[Haverd et al., 2005].
[38] The CSE-model calculated line transition probabilities
for the c04 1S+u (0) X 1S+g (0– 3) and b0 1S+u (1) X 1S+g (0 – 3)
bands are listed in Tables 5 and 6, respectively, along with
the estimated total radiative transition probabilities of the
c04 1S+u (0) and b0 1S+u (1) levels, obtained by summing line
transition probabilities up to vi = 29 of the X 1S+g state. The
transition frequencies of c04 1S+u (0) X 1S+g (0 – 3) and
b0 1S+u (1) X 1S+g (0-3) bands are listed in Tables 5 and
Table 6. In the case of the c04 1S+u (0) X 1S+g (vj) transition,
the listed bands represent the strongest emissions from the
c04 1S+u (0) level. Because the potential-energy curve for the
diabatic c04 1S+u state is very similar to that of the X 1S+g
state, the diabatic Franck-Condon factor for the c04 1S+u (0) X 1S+g (0) band is on the order of 0.9 [Stahel et al., 1983;
Whang et al., 1996]. Thus a very substantial proportion of
the c04 1S+u X 1S+g electron-impact excitation normally
ends up in the c04 1S+u (0) level, with most emission back to
the X 1S+g (0) level. The diabatic b0 1S+u (1) X 1S+g (0 –2)
Franck-Condon factors are very small, but rotational lines
involving b0 1S+u (1) levels in the region of the b0 1S+u (1) c04 1S+u (0) level crossing borrow significant strength from
the corresponding c04 1S+u (0) X 1S+g (0-2) transitions,
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through the b0 1S+u (1) c04 1S+u (0) homogeneous coupling.
The overall b0 1S+u (1) X 1S+g (vi) emission becomes more
significant in the far-ultraviolet region. Estimated uncertainties in the calculated transition probabilities for the strong
and moderately strong transitions in Tables 3 and 4 are
12%.
[39] The accuracy of the line transition probabilities listed
in Tables 3 and 4 can be examined for each band. Reliable
absolute transition probabilities for the b0 1S+u (1) X 1S+g (0)
and c04 1S+u (0) X 1S+g (0) bands can be inferred from the
high-resolution photoabsorption experiments of Stark et al.
[2000]. Of the 64 measured P- and R-branch transitions,
57 calculated transition probability values agree with the
experimental ones within the experimental uncertainties. All
remaining 7 transitions agree within twice the experimental
uncertainties. Overall, the agreement for the R-branch
transitions is better than for the P branches, where the
calculated values are generally smaller than their experimental counterparts.
[40] In the case of the (0,1) and (0,2) bands, where no
absolute experimental data exist, apart from those inferred
indirectly from the present work, the relative CSE-model line
intensities can be compared with those from the high-resolution experimental spectra. Because of the Jj-dependent
predissociation of the c04 1S+u (0) levels [Ubachs et al.,
2001; Liu et al., 2005a], the calculated relative emission
intensity depends somewhat on the predissociation rate for
each Jj level. Ubachs et al. [2001] measured the lifetimes of
several groups of unresolved Jj levels of the c04 1S+u (0) state in
the time domain. By interpolation and extrapolation of the
results of Ubachs et al. [2001], Liu et al. [2005a] derived a set
of lifetimes in order to analyze the emission spectrum of the
c04 1S+u (0) X 1S+g (0) band. As shown by Lewis et al. [2005a,
2005b], the predissociation rate can also be computed using
the CSE model. The predissociation rates and lifetimes for
various rotational levels of the c04 1S+u (0) state will be
examined in a future joint experimental and theoretical paper.
It is sufficient to point out here that a set of lifetimes,
estimated from the preliminary CSE predissociation linewidths provided by the current model, has been used to aid
the calculation of the emission spectra. These CSE lifetimes
are consistent with those of Liu et al. [2005a] for Jj 20. For
Jj > 20, the estimated CSE lifetimes are somewhat longer,
leading to greater calculated emission intensities. The differences in overall relative intensities, however, are small
because emissions from levels with Jj > 20 are weak. The
primary effect is that the estimated CSE lifetime leads to a
slightly lower inferred rotational temperature [e.g., 260 K
versus 270 K for the (0,1) band].
[41] Figures 4 and 5 compare experimental and CSEmodel emission spectra at the rotational level for the c04
1 +
Su (0) X 1S+g (1) and c04 1S+u (0) X 1S+g (2) bands,
respectively. Higher backing N2 pressures were utilized in
the experiments to compensate for the decrease in the (0,1)
and (0,2) band emission intensities. The increase in rotational cooling results in temperatures of 260 and 150 K,
respectively, for the high-resolution spectra of the (0,1) and
(0,2) bands. With an N2 pressure of (0.90.1) 104 Torr
and 20 mm slit widths (in second order), the (0,1) band
emission remains reasonably strong, and a single scan with
an integration time of 220 s per channel and 14.5 h total
acquisition time is sufficient. As a result, only very small
9 of 17
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LIU ET AL.: N2 c04 1+u X 1+g RADIATIVE PROPERTIES
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Figure 4. Comparison of high-resolution experimental (solid line) and CSE-model (dotted line) e + N2
emission spectra for the c04 1Su+(0) X 1Sg+(1) transition. The transition is labeled in standard notation
DJ(Ji) with appropriate upper electronic state designation. When the electronic designation is omitted, the
transition is assumed to be from the c04 1Su+(0) X 1Sg+(1) band. When electronic label is b0, the transition
is from the b0 1Su+(1) X 1Sg+(1) band. The experimental spectrum was obtained under essentially the
same conditions as those described by Liu et al. [2005a], except that the N2 pressure was (0.9 ± 0.1) 104 Torr. The spectral resolution is 33 mÅ FWHM. A factor of 14 increase in N2 pressure from that
of Liu et al. [2005a] results in a decrease in rotational temperature from 300 K to 260 K. The
overlapping b0 1Su+(7) X 1Sg+(3) emission, which peaks near the R-branch band head at 980 Å, is much
weaker that the c04 1Su+(0) X 1Sg+(1) emission. Atomic nitrogen 2s2p4 2D 2s22p3 2Do emission lines,
at 980.632 and 980.706 Å, are either absent or negligible.
tion [Lefebvre-Brion and Field, 2004]. In the equivalent
local-perturbation picture, the b 1Peu(4), b 1Peu(5) and c3
1 e
Pu(0) levels are the primary rotational perturbers of the c04
1 +
Su (0) level [Liu and Shemansky, 2006]. The 1S+u 1Peu
coupling also provides the c04 1S+u (0) levels with a primary,
Jj-dependent, predissociation mechanism by 1Pu(e levels,
which, in turn, are predissociated by the C 3Pu and C0 3Pu
states via spin-orbit coupling [Lewis et al., 2005a, 2005b;
Haverd et al., 2005]. The lifetime of the Jj = 0 level of the
c04 1S+u (0) state, therefore, is the predissociation-free lifetime.
[46] High-resolution photoabsorption measurements by
Stark et al. [1992, 2000, 2005] have shown, in many cases,
large deviations of the R:P-branch oscillator-strength ratio
from the corresponding Hönl-London factor ratio, and very
strong J-dependence of some Q-branch oscillator strengths.
The CSE calculation of Haverd et al. [2005] has achieved
very good agreement with experimental Q-branch oscillator
strengths for transitions to the 1Pfu states. They attributed
any strong J-dependence of the vibronic oscillator strength
to the quantum interference caused by strong electrostatic
coupling within the 1Pu manifold. In addition to the
electrostatic coupling, the P- and R-branch transitions are
affected by 1S+u 1Peu coupling. Liu and Shemansky
[2006], by considering the localized coupling among the
b0 1S+u (1), c04 1S+u (0), b 1Peu(4), b 1Peu(5) and c3 1Peu(0)
levels, have obtained accurate P- and R-branch oscillator
strengths for transitions between these levels and the X 1S+g (0)
level. Because of the strong J-dependence of the vibronic
oscillator strength for the three 1Peu levels, it was necessary
to use dipole matrix elements derived from the experimental
Q-branch oscillator strengths for the b 1Pfu(4), b 1Pfu(5), and
c3 1Pfu(0) X 1S+g (0) bands. However, as the dipole matrix
elements of the b 1Pfu(4), b 1Pfu(5), and c3 1Pfu(0) X 1S+g (vi
> 0) transitions cannot be computed from their diabatic
vibrational overlap integrals, the local-coupling model of
Liu and Shemansky [2006] cannot be extended to the vi > 0
levels of the X 1S+g state. In this regard, the more sophisticated CSE model employed here provides a more accurate
and versatile representation of the experimental results.
[47] The present experimental investigation has not
addressed the predissociation rate of the c04 1S+u (0) level,
which is another important quantity for atmospheric modeling. Even though the c04 1S+u (0) level is known to be
predissociated by 1S+u 1Peu coupling, no systematic
measurements on individual rotational levels have been
carried out, although Ubachs et al. [2001] have detected
14 of 17
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LIU ET AL.: N2 c04 1+u X 1+g RADIATIVE PROPERTIES
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Figure 5. Comparison of high-resolution experimental (solid line) and CSE-model (dotted line) e + N2
emission spectra for the c04 1Su+(0) X 1Sg+(2) transition. The transitions are labeled in terms of DJ(Ji)b
vj vi, where b represents the upper electronic state. When the vibronic label, bvj vi, is omitted, the
transition is from the c04 1Su+(0) X 1Sg+(2) band. When only b (i.e., no vj vi) is specified, the transition
belongs to the b0 1Su+(1) X 1Sg+(2) band. The experimental conditions are similar to those of Figure 4,
except that the N2 pressure was 3.3 104 Torr and a much longer integration time was employed to
compensate for the weaker signal. A factor of 3 increase in N2 pressure from that of Figure 4 results in a
decrease in rotational temperature to 150 K. The very weak b0 1Su+(7) X 1Sg+(4) emission, between
1001.9 and 1002.5 Å, is also well reproduced by the model. However, intensities for the peaks at longer
wavelengths than 1003.63 Å, primarily from the c3 1Pu(1) X 1Sg+(3) band, are somewhat overestimated
in the model. See section 4 for discussion of the discrepancy.
some J-dependence in the lifetime by using pump-probe
laser techniques without rotational resolution. While Liu et
al. [2005a] provided a crude estimate of the c04 1S+u (0)
predissociation yields, their results were based on interpolation and extrapolation of the experimental lifetimes
of Ubachs et al. [2001] and application of the c04 1S+u (0)
X 1S+g (0) Franck-Condon factor of Whang et al. [1996],
both of which can lead to significant errors. In principle, the
predissociation yield of a (vj, Jj) level can be obtained as the
fraction of the total emission cross section from the level to
the excitation cross section to the level. The excitation cross
section of the c04 1S+u (0) state can be obtained from the
excitation function measured by Ajello et al. [1989] and the
photoabsorption oscillator strength measured by Stark et al.
[2000, 2005], or calculated by the CSE method in the present
study. It can also be obtained directly from electron energy
loss work of Khakoo et al. [2007]. If the absolute emission
cross section of the c04 1S+u (vj, Jj) level to the X 1S+g (0) level,
or an X 1S+g (vj > 0) level, can be measured accurately, the
transition probabilities calculated in the present study enable
a reliable evaluation of the total emission cross section. In this
way, both predissociation yield and total transition probability, A(vj, Jj), can be determined. Work is in progress to
measure the absolute emission cross section of the c04
S+u (0) X 1S+g (0) band under high-resolution and optically
thin conditions. After the measurements are completed, a
forthcoming article will present excitation cross sections and
compare the measured and CSE calculated predissociation
yields and emission cross sections of the c04 1S+u (vj = 0, Jj)
levels.
[48] In summary, relative emission intensities for
the c04 1S+u (0) X 1S+g (1-3) bands of N2 have been de
termined accurately, using low-resolution electron-impactinduced emission spectroscopy. A CSE-model analysis of the
experimental relative intensities and photoabsorption oscillator strengths [Stark et al., 2000, 2005] has allowed the
determination of the diabatic c04 1S+u X 1S+g electronic
transition moment and calculation of the c04 1S+u (0) X 1S+g (vi) and b0 1S+u (1) X 1S+g (vi) line transition probabilities. The accuracy of the calculated transition probabilities
has been further verified by comparison with high-resolution
experimental emission spectra.
1
[49] Acknowledgments. This work has been partially supported by
NSF ATM-0131210 and the Cassini UVIS contract with the University of
Colorado. It has also partially been supported by the National Aeronautics
and Space Administration (NASA) under grant no. NNG06GH76G issued
15 of 17
Results of Experiment and CSE Investigation
• Summary of Results
– accurately reproduced measured relative vibrational band
intensity
– accurately reproduced relative intensities of c’1Σu+ - X
1Σ + (0,0), (0,1), and (0,3) bands at rotational levels
g
– calculated line oscillator strengths agree with highresolution photoabsorption measurement
• Conclusion
– accurate c’1Σu+ - X 1Σg+ diabatic transition moment
– Reliable transition probabilities and predissociation rates
of the c’1Σu+ (0) and b’1Σu+ (1) - X 1Σg+ transitions.
Application to interpreting FUSE observation
• Anomaly of c’1Σu+(0) - X 1Σg+(0) band
– Largest vibrational excitation and emission cross section (lab)
– Very weak in spacecraft observation of Earth and Titan dayglow
• c’1Σu+(0) - X 1Σg+(0) vibrational band, f=0.14, brightness <40 R
• N2+ B 2Σu - X 2Σg electronic band, f=0.76, 3~4 times larger
excitation cross section at 100 eV, brightness 1~5 kR (more than
25 times brighter !)
• Known cause of the anomaly
– Optical thickness & multi-cycle resonance absorption and
emission
– Radiative escape via emission to v” > 0 level of the X 1Σg+ state
Far Ultraviolet Spectroscopic Explorer (FUSE)
• Instrumentation
–
–
–
–
4 co-aligned telescopes-2 SiC and 2 LiF coated
Low-resolution aperture (LWRS, 30”x30”, FWHM ~0.4 Å)
Medium-resolution aperture (MDRS, 4”x20”, FWHM ~0.07 Å)
High-resolution aperture (1.25”x20”, rarely used)
– 905-1184 Å spectral range
• N2 dayglow emission data
–
–
–
–
Observation made with LWRS in 1999
Data processed by CalFUSE v3.2
Error in total absolute flux <5%
Error in individual N2 band emission 10%~15%
Brightness (R/Å)
10
0
1047
5
1048
1049
1050
Wavelength (Å)
15
1051
1005
1052
1006
1053
0
1024
0
1072
1025
Fig 1c. c4'(0) & b'(1) - X(4)
1073
1026
Wavelength (Å)
1074
1027
10
1075
1028
1076
Wavelength (Å)
O I (1027.431)
N I (1027.15, 1027.24)
N I (1026.69, 1026.78)
O I (1028.157)
N I (1028.357, 1028.449)
c4'(1,4)
1077
N I (1029.500, 1029.592)
c4'(3,6)
c4'(2,5)
5
c4'(3,8)
c4'(1,6), c4'(2,7)
40
H I (1025.722)
O I (1025.762)
15
CO 3p E(0)-X(0)
1004
b'(4,6)
1003
10
b'(7,5)
50
b'(7,7)
30
Brightness (R/Å)
c4'(1,3)
10
Brightness (R/Å)
1002
N I (1051.867, 1051.964)
N I (1052.050,1052.149,1052.22
1001
b'(4,5)
b'(7,4)
20
b' (7,6)
N*
0
1000
Ar I (1048.220)
b(5,4)
Brightness (R/Å)
Fig 1a. c4'(0) & b'(1) - X(2)
Fig 1b. c4'(0) & b'(1) - X(3)
1029
1030
Wavelength (Å)
Fig 1d. c4'(0) & b'(1) - X(5)
15
5
1078
Brightness (R/Å)
10
5
0
1153
1154
1101
1155
1102
1103
1156
Wavelength (Å)
1157
1104
1158
1105
15
1159
Brightness (R/Å)
5
0
1181
5
1126
1182
1127
15
10
1183
1128
1184
1129
1185
Wavelength (Å)
O II (1130.147)
O II (1129.251)
P(1) (1128.507)
O II (1128.081)
10
O III (1185.961)
N I (1101.291)
15
P(1) (1185.048)
1100
0
1125
O III (1184.174)
0
1099
P(1) (1101.687)
4
O III (1183.150)
6
O III (1182.770)
8
N I (1100.360; 1000.465)
20
b'(4,10)
O III (1181.748)
c4'(3,12)
10
Brightness (R/Å)
12
P(1) (1156.28)
14
O II (1154.096)
16
N I (1098.954, 1099.152)
18
c4'(4,12)
O II (1153.357)
b'(4,9)
Brightness (R/Å)
Fig 2a. c4'(0) & b'(1) - X(6)
Fig 2b. c4'(0) & b'(1) - X(7)
2
1130
Wavelength (Å)
Wavelength (Å)
Fig 2c. c4'(0) & b'(1) - X(8)
Fig 2d. c4'(0) & b'(1) - X(9)
1186
1131
1187
Summary I. Neutral N2 Excitation mechanisms in
thermospheres of Earth and Titan
• Excitation by Photoelectrons
– Principal mechanism for every singlet-ungerade levels except where
resonant solar photoexcitation coincident with N2 excitation
• Resonant photoexcitation by solar radiation
–
–
–
–
–
b(3) by H Ly-γ (complete predissociation)
b(6) by H Ly-δ, b(10) by H Ly (n=9)
b’(4) by H Ly-ε, b’(6) by H Ly (n=8), b’(7) by H Ly (n=12)
b’(8), o(2), and b(12) by H Ly (n>15)
b(12) also by H ionization continuum
• Resonant photoexcitation by strong N2 emission
– b(2) from v”=0 by c’1Σu+ (0)-X 1Σg +(1) transition
– b’(4) from v”=1 by c’1Σu+ (0)-X 1Σg +(0) transition [non-LTE
X(v”)]
01 +
1 +
LIU ET AL.: N2 c04 1 Σ+
u (0) & b Σu (1)−X Σg DAYGLOW EMISSION
X - 26
1 +
01 +
Table 1. Brightness of the c04 1 Σ+
u (0)− and b Σu (1)−X Σg (vi ) bands (R)
Modela
vi
1 +
c04 1 Σ+
u (0)−X Σg
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
v
i
P >20
P(vi ≥2)
(vi ≥0)
2101.6
312.4
35.2
6.00
2.55
1.98
2.80
4.12
5.00
5.31
5.00
4.03
2.53
1.14
0.290
0.021
0.107
0.186
0.099
0.008
0.020
∼0.4
76.8
2491
Modela
b
01
1 +
Σ+
u (1)−X Σg
13.7
2.12
0.40
0.39
0.80
1.65
2.93
4.44
5.80
6.50
6.20
4.92
3.10
1.40
0.328
0.002
0.111
0.216
0.128
0.011
0.018
∼0.4
39.7
55.6
Modela F U SE
Sum Observedb
2115.4
314.6
35.6
6.39
3.36
3.63
5.73
8.56
10.8
11.8
11.2
9.0
5.63
2.53
0.619
0.023
0.218
0.403
0.227
0.019
0.037
∼0.8
116.6
2547d
24±7c
100
35.3
5.2
7.3
11.1
11.6
a
Absolute optically-thin model brightness inferred by using a normalization constant averaged over the emission bands terminating
on vi = 2, 8, and 9 (see text), and an N2 temperature of 500 K.
b
Estimated from FUSE spectrum after removing the contributions from atomic, ionic, and other overlapping N2 emissions.
Due to severe distortion of its shape, the brightness of this band cannot be partitioned accurately between c04 1 Σ+
u (0)− and
1 Σ+ (0) emission and any overlapping features.
b0 1 Σ+
(1)−X
u
g
c
d
If the FUSE-measured brightnesses of 24 and 100 R are adopted for emission to vi = 0 and 1, the total modeled brightness of
emission to all ground-state levels is ∼241 R, only 10% of the model-predicted optically-thin brightness.
Summary II. Model Results
• Inferred thermospheric temperature 500 ±50 K
• Model reproduces observed brightness of v”=2-9
within FUSE observation error (10~15% )
• Reliable estimate for v”>9 level
• Model-total, column averaged, optically thin
emission rates 2.5x109 and 6.6x107 cm-2 s-1 for
c’1Σu+(0) and b’1Σu+(1), respectively
• Upper limits of electron-impact excitation rate to
c’1Σu+(0) and b’1Σu+(1) levels are 3.3x109 and
1.2x108 cm-2 s-1
Radiation loss of c’1Σu+-X 1Σg+
(0,0) and (0,1) bands
• 98% for v”=0 level (2115 R expected for optically thin vs
24±7 R observed)
– Multiple scattering, predissociation, radiative escaping to
v”>0
– Reduction of emission rate and distortion of band shape
• 68% for v”=1 level (315 R expected vs 100 R observed)
– By predissociative b(2)-X(0) absorption
– By self-absorption of c’(0)-X(1) itself (require significant
population at v”=1 level -> non-LTE N2(v”) population!
Analysis of b(1)-X(v”) will provide definitive answer!)
Predissociation & multi-scattering on
(0,0) and (0,1) band shapes
• Predissociation yields of c’1Σu+(0) and b’1Σu+(1)
– Negligible at J’=0, increase rapidly with J’
• Mechanisms of radiation loss
– I. Multi-cycle resonance absorption and emission and
radiative escape to v’> 0
– II. Predissociation, drastically enhanced by multi-cycle
absorption and emission
– P(1) lines of c’ (0,0) and b’(1,0) band take place by I only
– All other lines takes place by both I and II, and observed
intensities rapidly decrease with J’
Fig 3b. c4'(0) & b'(1) - X(1)
Fig 3a. c4'(0) & b'(1) - X(0)
80
100
FUSE
Model (opt. thin) x 1/30
Brightness (R/Å)
50
80
70
Brightness (R/Å)
60
40
30
20
FUSE
Model (opt. thin) x 2/7
P(1) (980.502)
P(1) (958.602)
70
90
60
50
40
30
20
10
10
-0
-10
957
0
958
959
Wavelength (Å)
960
961
-10
979
980
981
982
Wavelength (Å)
983
Numerical Example
• J’ = 0 level [P(1) line of c’1u+(0)- X 1g +(0)]
– No predissociation, (0,0) band emission branching ratio 0.843.
– 15.3% loss for each absorption-emission cycle
– After 20 absorption-emission cycles, P(1) line intensity drops by a
factor of ~30
• J’=7 level [R(6) and P(8) lines of c’1u+(0)- X 1g +(0)]
– Significant predissociation, (0,0) band emission branching ratio
0.716
– 28.4% loss for each cycle of absorption-emission
– After 20 absorption-emission cycles, the apparent intensity of
P(8)&R(6) lines drops by a factor of ~800.