GEOPHYSICAL RESEARCH LETTERS, VOL. 32, L02204, doi:10.1029/2004GL021327, 2005
Fine-structure physical chemistry modeling of Uranus H2 X
quadrupole emission
J. T. Hallett, D. E. Shemansky, and X. Liu
Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, California, USA
Received 23 August 2004; revised 10 December 2004; accepted 3 January 2005; published 29 January 2005.
[1] A new hydrogen physical chemistry model has been
developed at the fine-structure level for application to the
giant outer planet thermospheres. The model is applied to
Uranus because observations of dayglow H2 X 1S+g (v)
quadrupole and H+3 vibration-rotation emission made at
NASA IRTF and UKIRT provide critical constraints for
thermospheric modeling. The observed H+3 vibration-rotation
emission infers an H+3 dominant ionosphere, predicted only
for non-LTE H2 X (v : J). Excitation mechanisms explored
are solar and non-solar electron energy deposition. Non-solar
electron forcing is constrained by the EUV H2 Lyman and
Werner band emission measured by Voyager UVS. Analysis
indicates that non-solar electrons are dominant in the energy
budget required to predict the observed thermospheric
temperature profile. The modeled H 2 X quadrupole
emission infers that an additional mechanism is required to
excite the H2 X (v = 1) population. Non-thermal H produced
in dissociative excitation of H2 X is a primary candidate.
Citation: Hallett, J. T., D. E. Shemansky, and X. Liu (2005),
Fine-structure physical chemistry modeling of Uranus H2 X
quadrupole emission, Geophys. Res. Lett., 32, L02204,
doi:10.1029/2004GL021327.
1. Introduction
[2] The primary outer planet thermospheric heat source is
a major target of investigation. At Uranus, the Voyager 2
UVS atmospheric occultation experiments determined a
peak thermospheric temperature of (850 ± 100)K [Herbert
et al., 1987], compared to a predicted peak temperature of
150 K based on direct solar energy deposition [Strobel et al.,
1991]. The thermospheric temperature profile infers a high
altitude heat source (5000 km above 1bar), depositing a
globally-averaged heat flux of .06 (+.02, .04) erg cm2 s1
[Stevens et al., 1993]. Proposed thermospheric heat sources
include the sun, non-solar energetic electrons, gravity wave
dissipation, and auroral heating [see Yelle, 1988; Shemansky,
1985; Matcheva and Strobel, 1999; Achilleos et al., 1998].
Each source encounters difficulties in predicting the wide
array of observational results. The non-solar energetic electron source has not been identified, but may plausibly
involve an electron acceleration mechanism. The existence
of a non-solar energetic electron population is inferred from
the H2 Lyman and Werner band dayglow emission observed
from the outer planets. Non-solar electron populations have
been used to predict the Jupiter H2 EUV band emission
observed by Voyager UVS and Cassini UVIS [Shemansky,
1985; Shemansky et al., 2001].
Copyright 2005 by the American Geophysical Union.
0094-8276/05/2004GL021327$05.00
[3] A fine-structure hydrogen physical chemistry model
has been applied to the Uranus thermosphere to examine
solar forcing (solar photons + photoelectrons) and non-solar
energetic electron forcing as potential heat sources. Results
illustrate that non-LTE H2 X vibrational partitioning is
critical to predicting the Uranus thermospheric state and
can only be calculated self-consistently from fine-structure
chemistry and the inclusion of detailed H2 X (v : J) excitation
processes. In addition, calculations of fine-structure emission spectra (both IR and EUV) constrain the imposed
forcing function and non-LTE H2 X excitation through
comparison to dayglow observations.
[4] Uranus is the target of this analysis because its
observational data set is unique, due to recent observations
of H2 quadrupole and H+3 vibration-rotation emission carried out by Trafton et al. [1999] using the United Kingdom
Infrared Telescope (UKIRT) and the NASA Infrared Telescope Facility (IRTF). An averaged H2 X 1S+g (v = 1)
quadrupole emission spectrum is shown in Figure 1. Using
the derived Voyager UVS temperature profile [Herbert et
al., 1987], the observed quadrupole line intensity is a factor
of 300 to 400 greater than calculated in LTE at the base of
the emission system (2600 km above 1bar). The ionosphere
is constrained by the electron density profiles measured by
Lindal et al. [1987], and by the H+3 abundances inferred
from the H+3 vibration-rotation emission intensity [Trafton
et al., 1999]. The Trafton et al. [1999] abundances (1.5 1011 cm2 to 4.3 1011 cm2) correspond to the electron
abundances calculated from the Voyager radio science
ingress occultation (2. 1011 cm2 to 7. 1011 cm2),
indicating that H+3 is the primary plasma ion. The non-LTE
H2 X (v : J) distribution and ionospheric partitioning are
constrained directly by these observations.
2. Model Calculation
[5] A summary of the model is given here, with a detailed
description deferred to J. T. Hallett et al. (A rotation-level
hydrogen physical chemistry model for general astrophysical
application, submitted to Astrophysical Journal, 2004). H2,
H, H+3 , H+2 , and H+ are the model constituents. H2 chemistry
includes all electronic and rovibrational fine-structure. H+2
includes ground rovibrational fine-structure. H, H+3 , and H+
are currently treated as single states. The model calculates
steady-state constituent density distributions and volumetric
emission rates. Steady-state photoelectron (ehn) density distributions (monoenergetic grid: 2 eV to 32 eV) are calculated
in a multi-scattering energy loss procedure that tracks H2 X
(v : J) and H photoionization and inelastic photoelectron
collisions with constituents. The model ambient plasma is
internally compatible with the ion partitioning and the
L02204
1 of 4
L02204
HALLETT ET AL.: URANUS H2 X (v) EMISSION MODELS
imposed forcing functions. The ambient electron density
([ea]) and gas kinetic temperature are imposed on the
hydrogen volume as predetermined components from observation-derived density and temperature profiles [Lindal et
al., 1987; Herbert et al., 1987]. The neutral and ion gas
constituents are iterated in distribution and total particle
density to reach charge neutrality and statistical equilibrium,
controlled by the process rate coefficients. Thermal balance
is confirmed through comparison of ambient electron energy
deposition and loss rates. Imposed parameters are varied to
match the observed H2 densities at the given altitude.
[6] The imposed parameters include the two forcing functions and neutral diffusion. Solar forcing is limited by solar
flux attenuation by the foreground gas. Non-solar electron
forcing (Maxwellian distribution with user-defined temperature and density) is constrained by observed H2 EUV band
emission [Broadfoot et al., 1986]. Neutral diffusion is the free
parameter primarily used to predict H2 densities. The volumetric calculation necessarily limits examination of vertical
transport effects. Neutral diffusion is treated as equilibriated
mass flow that allows H to diffuse out and H2 to diffuse into
the volume at a rate defined by the user-prescribed loss
probability (s1). After convergence to observed H2 and
electron densities, the predicted emission is compared to
observed H2 IR and EUV band emission [Trafton et al.,
1999; Broadfoot et al., 1986]. The comparisons determine
the viability of the forcing function as the primary thermospheric heat source and the chemistry accuracy.
Figure 1. H2 X (v = 1) modeled quadrupole emissions
(3500 km – 5500 km) compared to the observation obtained
from Trafton et al. [1999].
[1968]. Analytic fits to the cross sections extend the work to
energetic electron energies.
H þ H þ M ! H2 X vj : Jj þ M
ð5Þ
H2 B; C; ðvi : Ji Þ ! H2 X vj : Jj þ hn
ð6Þ
3. Critical Model Chemistry
[7] The critical results in the analysis include the production of H+3 dominant ionospheres through the development
of non-LTE H2 vibrational distributions (allowing for the
prediction of low observed ambient electron densities), and
the energy deposition and emission spectra produced from
the forcing functions. The primary chemistry involved with
these results is discussed here. The critical fine-structure
ionospheric chemistry is given by Reactions 1 to 4.
L02204
e þ H2 X ðvi : Ji Þ $ e þ H2 X vj : Jj
ð7Þ
þ
H þ þ H2 X 1 Sþ
g ðvi : Ji Þ ! H2 þ H
ð1Þ
H2þ þ H2 ! H3þ þ H
ð2Þ
[8] The primary model heating mechanism is the thermalization of kinetically hot atomic hydrogen (H*), produced primarily from electron excitation of H2 X to the
repulsive H2 b 3S+u state (Reaction 8). Heating processes
initiated by energetic electron collisions with ambient electrons are minor sources in comparison. The H* heating
mechanism is examined for both solar forcing (ehn) and
non-solar electron forcing (es). The H* population excites
H2 X 1S+g (v : J) and heats the thermosphere through
Reactions 9 and 10.
e þ H3þ ! H þ H þ H
ð3Þ
es =ehv þ H2 X ! es =ehv þ H2 b ! es =ehv þ 2H*
e þ H3þ ! H2 X 1 Sþ
g vj : Jj þ H
ð4Þ
H* þ H2 X ðvi : Ji Þ ! H þ H2 X vj : Jj
Reaction 1 is the primary reaction limiting the ionospheric
density and is rapid and exothermic for H2 X (v > 3). NonLTE H2 X 1S+g (v) produces a significantly faster proton
sink than LTE H2 X 1S+g (v). Reactions 3 and 4 are the
primary electron sinks, with rate coefficients and product
partitioning obtained from Larsson et al. [1993] and
Strasser et al. [2001]. The primary sources of vibrational
excitation are Reactions 4 to 6, and energetic electron
excitation (Reaction 7). These processes compete with
ambient electrons (ea) (Reaction 7), which tend to relax the
distribution toward statistical equilibrium with the electrons.
Electron excitation is a controlling factor for the H2 X (v : J)
distribution. Reaction cross sections were developed at USC
from the experimental measurements of Erhardt et al.
H* þ M ! H þ M *
ð8Þ
ð9Þ
ð10Þ
Reactions 9 and 10 are not included in the current hydrogen
chemistry model for lack of accurate vibration-rotation
cross sections. The H* population component is currently
treated as thermal. Estimates of energy deposition are
calculated from the H* production mechanism (Reaction 8).
H* has an average energy of 4.6 eV, and a fraction of the
population will escape the volume of calculation at low
collision densities. The user-defined H loss probability, d
(s1), is quantitatively limited by the loss of H* out of the
volume of calculation at high thermospheric altitudes,
2 of 4
2f ½e½ H2 X k8 ffi ½ H d
ð11Þ
HALLETT ET AL.: URANUS H2 X (v) EMISSION MODELS
L02204
Figure 2. Solar forced constituent density distributions.
The imposed kinetic temperature is 600 K from 2500 km to
4500 km, and 450 K at 1000 km. H2+ and ehn (minor
components) are off-scale.
where [N] is the constituent (N) density (cm3), k8 is the
rate coefficient (cm3 s1), and f is the fractional loss of H
(from H* velocity and altitude of calculation).
4. Thermospheric Constituent Partitioning
[9] Figure 2 shows the constituent density distributions
for the thermospheric altitude range (1000 km to 4500 km)
examined for solar forcing. The solar flux transmitted
through the foreground H2 X 1S+g (v : J) gas is calculated
at each altitude. A minimum loss probability of 107 s1 is
required for the entire altitude range to predict the observed
H2 and electron densities. The loss of hot atomic hydrogen
(H*) from the top of the thermosphere (4500 km) can be
estimated from Equation 11. For the photoelectron source,
the solar forced H* loss probability is 5.5 1010 s1,
compared to the imposed loss probability of 1. 107 s1.
The modeled constituent density distributions for the two
loss probability cases at 4500 km are compared in Table 1.
With the estimated (5.5 1010 s1) loss probability, pure
solar forcing predicts an H+ dominant upper ionosphere and
a suppressed H2 (1.18 104 cm3) population compared to
the Voyager H2 result (1.8 108 cm3). Solar forcing
cannot account for the observed H2 densities and H+3
dominant environments at the top of the thermosphere,
unless an approximately two orders of magnitude greater
loss probability than the estimate is used. Large H loss is
required because the non-LTE H2 X 1S+g (v) distribution is
not sufficient for Reaction 1 to deplete the dominant proton
population. Protons then meet the charge neutrality condition through electron ionization and photoionization of H.
L02204
[10] Given the H* loss probability discrepancy, non-solar
energetic electron forcing is applied to the top of the Uranus
thermosphere (3500 km to 5500 km). The non-solar electron
population is estimated from the Voyager H2 EUV emission.
Non-solar electron forced excitation (Maxwellian: Ts =
30,000 K) is applied for all model altitude calculations and
provides the best fit to the Broadfoot et al. [1986] dayglow
results. The imposed electron density ([es] = 229 cm3)
required to predict the observed intensity is partitioned
within the four altitude zones to predict observed H2 and
electron densities. A loss probability of 4 106 s1 is
imposed on the model for the altitude range and is consistent
with the predicted H* loss probability from the top of the
Uranus thermosphere for the non-solar electron source. The
constituent density distributions for the altitude range are
given in Figure 3. The imposed parameters predict an H+3
ionosphere and an H2 atmosphere compatible with the
Voyager observational results.
[11] H+3 dominant ionospheres result directly from the
production of non-LTE H2 X 1S+g (v : J). The normalized
H2 X (v) distributions are compared in Figure 4a for solar
forcing (2500 km) and non-solar electron forcing (4500 km).
Both cases exhibit multi-orders of magnitude deviations
from a 600 K (kinetic temperature) thermal distribution.
Deviations from LTE for H2 X (v > 3) result in fast proton
loss rates (Reaction 1), leading to the H+3 electron sink.
Differences between the distributions are attributed primarily
to differences in the electron populations. The 2500 km solar
photoelectrons have a density of 6.2 103 cm3 with a
normalized distribution shown in Figure 4b. The 4500 km
non-solar electrons have a density of 120 cm3 (Maxwellian:
Ts = 30,000 K). The non-solar electron density produces
faster H2 X (v) electron excitation rates (Reaction 7).
5. H* Energy Deposition and H2 Modeled
Emissions
[12] The energetic electron density required to predict the
observed H2 and ambient electron densities at the top of the
thermosphere has implications for thermospheric heating.
Solar forcing predicts a total H* energy deposition of 7.6 Table 1. Solar Forcing Diffusion Comparison at 4500 km
Loss Prob. s1 [H2] cm3 [H] cm3 [H3+] cm3 [H+] cm3 [H2+] cm3
1.0 – 07a
5.5 – 10
Voyagerb
1.86 + 8
1.18 + 4
1.8 + 8
9.11 + 5
8.91 + 3
3.0 + 6
7.82 + 2
6.82 3
1.74 + 1
8.00 + 2
1.0 107, corresponds to Figure 2.
b
From Voyager UVS Observations [Herbert et al., 1987].
a
1.68 1
2.31 2
Figure 3. Non-solar energetic electron forced constituent
density distributions. The kinetic temperature is 600 K for
the altitude range. H2+ (a minor component) is off-scale.
3 of 4
L02204
HALLETT ET AL.: URANUS H2 X (v) EMISSION MODELS
L02204
observed thermospheric temperature profile, but is at least a
dayglow chemistry catalyst. A non-solar energetic electron
population is required to predict the observed H+3 dominant
ionosphere at high thermospheric altitudes. The non-solar
electron heat source predicts the observed H2 EUV band
emission intensity and the inferred global energy deposition
rate, but does not account for the total observed H2 IR
quadrupole band emission intensity measured by Trafton et
al. [1999]. H* excitation of H2 X (v), is a plausible source
for the shortfall. Future modeling will include a 1D atmospheric model (with vertical transport), multi-scattering
excitation of H2 X (v) by H*, and H+3 fine-structure for
comparison of modeled and observed H+3 emission.
[15] Acknowledgments. The authors wish to thank Professor Larry
Trafton for discussion of observational detail and manuscript review. The
reported results are based on the Ph.D. dissertation of J. Hallett. This work
has been supported by National Science Foundation ATM-0131210.
Figure 4. (a) H2 X 1Sg+ (v) normalized density distribution
for the 4500 km (electron) and the 2500 km (solar) cases.
(b) Normalized photoelectron energy distribution for the
2500 km (solar) case.
105 erg cm2 s1 (peak = 2500 km). The magnitude is a
factor of 800 below the required globally-averaged heat
flux, and the peak is 2000 km below the peak deposition
altitude inferred by Stevens et al. [1993]. Matching the
Stevens et al. [1993] result requires non-solar electrons with
a total energy deposition of 3. 102 erg cm2 s1 (peak
4000 km).
[13] The total H2 EUV band intensity (750 to 1550)Å was
calculated for both forcing functions over the thermospheric
altitude ranges explored. The total photoelectron-driven
EUV H2 band emission is 7.9 R, a factor of 30 below the
observed intensity (250 R, from Broadfoot et al. [1986]).
The corresponding H2 X (v = 1) quadrupole intensity is two
orders of magnitude below the Trafton et al. [1999] result.
The non-solar electron model gives a total EUV H2 band
intensity of 150 R. The non-solar electron H2 quadrupole
emission (model 4.5) is compared to the Trafton et al.
[1999] result in Figure 1. The modeled H2 X 1S+g (v = 1)
state population is already a factor of 650 above the thermal
distribution (Figure 4) at 4500 km. The deficit may be
covered by H* excitation of H2, given that the H* energy
pool generated by non-solar electrons (.03 erg cm2 s1) is
consistent with the derived thermospheric energy deposition. H* thermalization must be examined to determine the
capability of Reaction 9 to excite H2 X (v = 1) sufficiently to
resolve the discrepancy in IR intensity.
6. Conclusions
[14] Modeling of hydrogen fine-structure chemistry is
necessary to accurately predict the Uranus thermosphere.
Initial results indicate that solar forcing cannot predict the
References
Achilleos, N., S. Miller, J. Tennyson, A. D. Aylward, I. Mueller-Wodarg,
and D. Rees (1998), JIM: A time-dependent, three-dimensional model of
Jupiter’s thermosphere and ionosphere, J. Geophys. Res., 103, 20,089 –
20,112.
Broadfoot, et al. (1986), Ultraviolet spectrometer observations of Uranus,
Science, 233, 74 – 79.
Erhardt, H., D. L. Langhans, F. Linder, and H. S. Taylor (1968), Resonance
scattering of slow electrons from H2 and CO angular distributions, Phys.
Rev., 173, 222 – 229.
Herbert, F., B. R. Sandel, R. V. Yelle, J. B. Holberg, A. L. Broadfoot, and
D. E. Shemansky (1987), The upper atmosphere of Uranus: EUV occultations observed by Voyager 2, J. Geophys. Res., 92, 15,093 – 15,109.
Larsson, M., et al. (1993), Direct high-energy neutral-channel dissociative
recombination of cold H+3 in an ion storage ring, Phys. Rev. Lett., 70,
430 – 433.
Lindal, G. F., J. R. Lyons, D. M. Sweetnam, V. R. Eshleman, D. P. Hinson,
and G. L. Tyler (1987), The atmosphere of Uranus: Results of radio
occultation measurements with Voyager 2, J. Geophys. Res., 92,
14,987 – 15,001.
Matcheva, K. I., and D. F. Strobel (1999), Heating of Jupiter’s thermosphere by dissipation of gravity waves due to molecular viscosity and
heat conduction, Icarus, 140, 328 – 340.
Shemansky, D. E. (1985), An explanation for the H Lya longitudinal asymmetry in the equatorial spectrum of Jupiter: An outcrop of paradoxical
energy deposition in the exosphere, J. Geophys. Res., 90, 2673 – 2694.
Shemansky, D. E., P. Gangopadhyay, X. Liu, J. Tew, and the Cassini UVIS
Team (2001), Analysis of the Cassini UVIS observations of Jupiter dayglow, paper presented at 33rd DPS Meeting, Am. Astron. Soc., New
Orleans, La.
Stevens, M. H., D. F. Strobel, and F. Herbert (1993), An analysis of the
Voyager 2 ultraviolet spectrometer occultation at Uranus: Inferring heat
sources and model atmospheres, Icarus, 101, 45 – 63.
Strasser, D., J. Levin, H. B. Pedersen, O. Heber, A. Wolf, D. Schwalm, and
D. Zajfman (2001), Branching ratios in the dissociative recombination of
polyatomic ions: The H+3 case, Phys. Rev. A., 65, 010702, doi:10.1103/
PhysRevA.65.010702.
Strobel, D. F., R. V. Yelle, D. E. Shemansky, and S. K. Atreya (1991), The
upper atmosphere of Uranus, in Uranus, edited by J. T. Bergstarlh, E. D.
Miner, and M. S. Matthews, pp. 65 – 110, Univ. of Ariz. Press, Tucson.
Trafton, L. M., S. Miller, T. R. Geballe, J. Tennyson, and G. E. Ballester
(1999), H2 quadrupole and H+3 emission from Uranus: The Uranian
thermosphere, ionosphere, and aurora, Astrophys. J., 524, 1059 – 1083.
Yelle, R. V. (1988), H2 emissions from the outer planets, Geophys. Res.
Lett., 15, 1145 – 1148.
J. T. Hallett, X. Liu, and D. E. Shemansky, Department of Aerospace and
Mechanical Engineering, University of Southern California, Los Angeles,
CA 90089-1191, USA. (jtew@usc.edu)
4 of 4