The Astrophysical Journal, 624:448 –461, 2005 May 1
# 2005. The American Astronomical Society. All rights reserved. Printed in U.S.A.
A ROTATIONAL-LEVEL HYDROGEN PHYSICAL CHEMISTRY MODEL
FOR GENERAL ASTROPHYSICAL APPLICATION
J. T. Hallett, D. E. Shemansky, and X. Liu
Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089; jtew@usc.edu
Received 2004 October 4; accepted 2005 January 19
ABSTRACT
A physical chemistry model has been developed to predict the non-LTE state of hydrogen-dominated astrophysical
þ
+
objects under electron and photon forcing. The model is composed of five constituents, H2, H, Hþ
3 , H2 , and H , and is
unique in the application of physical chemistry at the rotational level. The range of behavior is explored for electron
and solar deposition. Application of solar forcing includes a prediction of the steady state photoelectron energy
distribution, calculated from the interaction of solar photons and photoelectrons with the fine structure. The model is
applied to a wide range of physical conditions, including those appropriate to the outer-planet upper atmospheres,
from the exobase to the hydrocarbon homopause. Steady state partitioning is found to vary by multiple orders of
magnitude in response to variation of neutral diffusion, ambient electron density, and gas kinetic temperature. The
model is particularly sensitive to neutral diffusion. The non-LTE H2 X 1 þ
g (v : J ) partitioning exhibited for the range
of explored physical conditions and forcing is critical to the prediction of the states of the outer-planet ionospheres. The
determination of rotational-level H2 partitioning allows the prediction of discrete and continuum emission features
running the entire spectral range for comparison to observations of astrophysical phenomena, including outer-planet
aurora and dayglow, comet coma environments, and stellar atmospheres.
Subject headingg
s: atomic processes — comets: general — diffusion — molecular processes —
planets and satellites: general — stars: atmospheres
perature, and vibrational development of H2 X 1 þ
g (v : J ) was
not tracked in response to the energy deposition mechanisms
imposed on the model. The H2 rovibrational detail is tracked
with this self-consistent ionospheric chemistry model.
The heating mechanism required to elevate thermospheric
temperatures to match observations continues to be unresolved.
Several mechanisms have been identified as possible sources of
thermospheric temperature elevation, including solar forcing, nonsolar energetic electron forcing, gravity-wave dissipation, auroral heating, and Joule heating (Yelle 1988; Shemansky 1985;
Shemansky et al. 2001; Young et al. 1997, 1998; Matcheva &
Strobel 1999; Waite et al. 1997, 2004; Achilleos et al. 1998). Each
theory has encountered difficulties in predicting the wide range of
observational results.
Inclusion of rotational-level physical chemistry provides additional constraints to imposed thermospheric heating mechanisms
through the prediction of ultraviolet and infrared H2 emission for
comparison to outer-planet dayglow results (Shemansky et al.
2001, 2003; Hallett 2004; Hallett et al. 2004). The H2 groundstate distribution is particularly sensitive to imposed heating mechanisms because of the long-lived excited H2 states. Application
of excitation mechanisms to the hydrogen chemistry model produces unique H2 X 1 þ
g (v : J ) distributions that can constrain
heating mechanisms through comparison of calculated H2 IR
quadrupole emission features to observations. The current model
has been initially applied to the Uranus atmosphere ( Hallett et al.
2004, 2005). The non-LTE conditions of the outer-planet thermospheres emphasize the importance of rotational-level H2 chemistry for predicting constituent densities, constraining energy
deposition mechanisms, and accurately predicting ionospheric
structure.
The hydrogen chemistry model can be applied to other astrophysical phenomena in general, such as comet comas, outer-planet
auroral excitation, accretion disk theory, and stellar atmospheres
because of the built-in large dynamic range. High-resolution
1. INTRODUCTION
The behavior of hydrogen chemistry deviates from local thermodynamic equilibrium for a range of astrophysical conditions.
The excitation of H2 produces activated, homonuclear molecules
that do not readily relax to a thermal distribution. Rotational-level
H2 physical chemistry modeling is critical for self-consistent analysis of hydrogen-dominant systems. A model at this structural
level is presented here. The model has been applied to a range
of physical conditions and forcing functions to demonstrate the
importance of rotational-level reaction chemistry to predicting
steady state constituent partitioning and determining the critical
reaction processes in the hydrogen volume. The importance of
rotational-level chemistry is illustrated by the examination of
the outer-planet thermospheres. Convergence of thermospheric
models to observational results is a complex problem. Previous
attempts to model the Jovian dayside ionosphere have failed
to reproduce the electron densities and altitude distributions
measured by Galileo and Voyager ( Hinson et al. 1997, 1998;
McConnell et al. 1982). Modeled peak electron densities are at
least an order of magnitude greater in density and higher in altitude than the measured results (Majeed & McConnell 1991;
Kim et al. 1992; Perry et al. 1999). Discrepancies result from the
lack of self-consistent, rotational-level H2 ionospheric chemistry
models. The development of non-LTE H2 X 1 þ
g (v) is particularly critical to the prediction of outer-planet ionospheric partitioning through an increased efficiency of several ion-molecule
reactions (Majeed et al. 1991; Shemansky et al. 2003). Jovian ionospheric models produced by Achilleos et al. (1998) predicted
electron densities approaching observational results (Hinson et al.
1997). However, a single rate coefficient was used to predict
the important proton charge-capture reaction with H2, which is
the critical step to producing Hþ
3 , the primary electron sink in the
Jovian ionosphere. The Achilleos et al. (1998) work assumed a
rate coefficient temperature elevated above the gas kinetic tem448
449
ROTATIONAL-LEVEL HYDROGEN PHYSICAL CHEMISTRY
observations of comet comas using the FUSE satellite have revealed numerous unidentified emission lines in the EUV region
(Weaver et al. 2003). A potential source of the emission lines
is highly excited H2 X 1 þ
g (v) interaction with solar radiation.
The excited H2 X (v) may be produced through one dissociation
channel of H2O. Application of solar forcing to a suitably modified chemistry model can provide predicted H2 ultraviolet emission features for comparison to observations.
The Jovian auroral ionosphere has been modeled assuming
a range of energetic electron precipitation 1–100 keV ( Waite
et al. 1983, 1988; Perry et al. 1999). Perry et al. (1999) examined
the ionospheric partitioning as a function of altitude for precipitating electrons at energies from 20 to 100 keV. Modeled electron densities were 2 orders of magnitude greater than Voyager
radio occultation results (Hinson et al. 1998). When an artificially
high H2 X vibrational temperature was applied, models predicted
Hþ
3 -dominant ionospheres, with electron densities approaching
observed results (Perry et al. 1999). However, the elevated H2
X (v) distribution was an ad hoc assumption. The present model
calculates the non-LTE state of the gas. Modeling of the Jovian
auroral H2 EUV-band emission intensities has required significant H2 X (v ¼ 2) self-absorption ( Wolven & Feldman 1998).
This indicates a non-LTE H2 X (v) distribution in the Jovian
aurora, consistent with energetic electron excitation of the H2
ground state.
The present chemistry includes five reacting species, H2, H,
þ
+
Hþ
3 , H2 , and H . The model predicts steady state constituent
density distributions, tracks detail in the energy budget, and predicts all H2 continuum and discrete emission in the converged
volume. The chemistry has been applied to the state of the outerplanet thermospheres (Shemansky et al. 2003; Hallett 2004;
Hallett et al. 2004, 2005). This paper examines steady state constituent density distributions in response to two heating mechanisms, solar forcing and energetic electron forcing, for a range of
physical parameters, including those applicable to the outer-planet
upper atmospheres. The parameter space exploration demonstrates the importance of applying non-LTE hydrogen chemistry
to the analysis of astrophysical phenomena when hydrogen is a
dominant component.
2. FORCING FUNCTIONS
The constituent density distribution and energy budget of the
modeled hydrogen gas are dependent on the imposed forcing
functions. In the outer-planet upper thermospheres, diffusion and
electron energy deposition are the primary drivers of the hydrogen reaction chemistry. The current volumetric calculations allow
diffusion of the neutral constituents (H2 and H), energetic electron
forcing, and solar flux forcing. Variation of these parameters and
subsequent analysis of the converged state of the gas provide insight into the critical reaction processes.
Neutral diffusion is a controlling factor for the prediction of
measured outer-planet H2 and H densities as a function of altitude. Diffusion is complex in the outer-planet upper atmospheres
and may involve electric field acceleration of ionospheric components. The diffusion process is also complicated by the production of energetic atomic hydrogen, leading to excitation and
scattering outside the volume of calculation. The model is currently specialized to the outer-planet thermospheric diffusion
processes, where the loss of kinetically hot atomic hydrogen
from the volume and gain of H2 from lower altitudes are primary
factors driving the constituent density distribution. Because the
current model is limited in its prediction of vertical transport
effects by a volumetric calculation, the diffusion process is treated
as equilibrated mass flow. The process allows net atomic hydrogen diffusion out of the volume,
H ! diAusion;
ð1Þ
and net H2 diffusion into the volume,
diAusion ! H2 ;
ð2Þ
at a user-prescribed loss probability Pdiff (s1). The loss probability is a free parameter in the calculation and is limited by
observed outer-planet H2 and H density profiles. For different
astrophysical phenomena, the loss probability parameter must
be altered given the conditions appropriate to the object under
consideration.
Solar radiation deposits energy into the hydrogen volume primarily through ionization. The resulting photoelectrons (eh) deposit energy into the volume through subsequent dissociation
and ionization reactions. Modeled solar forcing includes both
photoionization of the neutral constituents,
h þ H ! Hþ þ eh ;
ð3Þ
! Hþ
2
ð4Þ
h þ H2 X (v : J )
X (v : J ) þ eh ;
and photoexcitation of H2,
h þ H2 X (v : J ) ! H2 (X ; B; C; B 0 ; : : :);
ð5Þ
in an optically thin environment. Solar photoionization probabilities, Ah (s1), are integrated from the ionization threshold to
the short-wavelength limit of the imposed solar radiative flux.
Solar radiative flux is included in a tabulated form as a function
of wavelength at 2 m8 resolution for the wavelength range of
þ
2 þ
300 8 to 1.2 m. H2 X 1 þ
g (v ¼ 0, 14) to H2 X g (v ¼ 0, 18)
photoionization cross sections were derived from the calculations of Flannery et al. (1977). The development of a non-LTE
H2 X (v) distribution in the hydrogen volume increases the efficiency of H2 photoionization compared to a thermal H2 X (v)
distribution through exposure to expanded photoionization flux
thresholds. Effective H2 photoexcitation and de-excitation cross
sections are calculated from the fine-structure Einstein coefficients of spontaneous emission [A(vi , vj : Ji , Jj)] (Liu et al. 2002,
2003; Abgrall et al. 1997, 1993a, 1993b, 1993c; Jonin et al. 2000).
Solar photoexcitation and de-excitation transition probabilities
(Ah , s1) are calculated over the solar flux frequency range of
absorption, assuming Doppler broadening of H2 transitions in
a Maxwellian velocity distribution with the gas kinetic temperature (Tg).
The energetic photoelectrons (eh) produced through photoionization have an energy distribution dependent on the solar
radiative flux, the rovibrational distribution of H2 X 1 þ
g (v : J ),
and the constituent photoionization cross sections. The steady
state photoelectron energy distribution is established through an
iterative multiple-scattering energy-loss calculation that tracks
the deposition of photoelectron energy in the hydrogen volume.
The initial photoelectron energy is calculated from the relation
Eeh ¼ Eph Eij ;
ð6Þ
where Eph is the solar photon energy and Eij is the photoionization threshold energy. Photoelectrons lose energy in the volume primarily through excitation, ionization, and dissociation
of the neutrals. The model assumes only the threshold energy
450
HALLETT, SHEMANSKY, & LIU
Vol. 624
TABLE 1
Electron Reaction Chemistry
Label
Reaction
Reference
1A.........................
1B.........................
1C.........................
1D.........................
1E .........................
1F .........................
1G.........................
1H.........................
e þ H ! Hþ þ 2e
þ
e þ H2 X 1 þ
g (v : J ) ! H þ H þ 2e
þ
1 þ
e þ H2 X g (v : J ) ! H 2 X 2 þ
g (v : J ) þ 2e
1 þ
e þ H2 X 1 þ
g (vi : Ji ) $ e þ H2 X g (vj : Jj )
1 þ
1 (v : j )
(v
:
J
)
$
H
B
/C
e þ H2 X 1 þ
i
i
2
u j j
g
u
0
00 1 þ
0 1
e þ H2 X 1 þ
(v
:
J
)
$
H
B
;
B
i
i
2
g
u ; D; D u (vj : jj )
1 þ
e þ H2 X 1 þ
(v
:
J
)
$
e
þ
H
EF;
GK;
:
:
:
g (vj : jj )
i
i
2
g
3 þ
(v
:
J
)
!
e
þ
H
b
e þ H 2 X 1 þ
i
i
2
g
u
H2 b 3 þ
u !H þH
þ
2 þ
e þ H2 X g (v : J ) ! H þ H
þ
2 þ
e þ Hþ
2 X g (v : J ) ! H þ H þ e
e þ Hþ
3 !HþHþH
1 þ
e þ Hþ
3 ! H2 X g (vj : Jj ) þ H
e þ Hþ ! H þ h
1
2
3
4
5, 6, 7
8
9
10
11, 12
13
14
15
16
17
1I ..........................
1J ..........................
1K.........................
1L .........................
1M ........................
References.—(1) Shah et al. 1987; (2) Krishnakumar & Srivastava 1990; (3) Flannery et al. 1977;
(4) Erhardt et al. 1968; (5) Liu et al. 1995; (6) Liu et al. 1998; (7) Liu et al. 2002; (8) Jonin et al. 2000;
(9) Liu et al. 2003; (10) Stibbe & Tennyson 2000; (11) Khakoo & Segura 1994; (12) Nishimura &
Danjo 1986; (13) Peart & Dolder 1974; (14) Shemansky 1985; (15) Jensen et al. 2001; (16) Strasser
et al. 2002; (17) Seaton 1960.
loss for each photoelectron during the collisional process. Each
photoelectron is placed in a monoenergetic grid, where each bin
has a user-prescribed interval of energy. Photoelectrons are lost
completely to ion recombination reactions, particularly in the
lower energy bins. Electrons produced by photoelectron ionization of the neutrals are treated as part of the ambient electron
population. As photoelectrons gain and lose energy in the volume, their locations in the energy bins vary, until a steady state
population is achieved.
Additional energetic electron populations can be imposed on
the hydrogen chemistry as forcing functions that are nonsolar
in origin. These energetic electron populations can have both
monoenergetic ([es], Es) and Maxwellian ([es], Ts) energy distributions as user-selected forcing functions. The imposed populations do not vary during the model convergence to statistical
equilibrium and charge neutrality. Instead, the constituent population is forced to vary in total particle density and distribution in response to the imposed electron population. The charge
neutrality condition ensures that the physical chemistry produces
the imposed total electron density. Electron reactions included in
the hydrogen chemistry architecture are listed in Table 1.
Energetic electron and photoelectron reactions are the primary
energy deposition mechanisms in the operational hydrogen chemistry architecture. The dominant heating process in the hydrogen
volume is energetic electron excitation of the H2 X 1 þ
g (v : J )
states to the repulsive triplet-b state (H2 b 3 þ
u ),
es =eh (Ei ) þ H2 X ! H2 b þ es =eh (Ej );
ð7Þ
leading to dissociation of H2 into kinetically hot atomic hydrogen ( H ),
H2 b 3 þ
u ! H þH :
ð8Þ
Reaction cross sections for reaction (7) at the vibrational level
were obtained from Stibbe & Tennyson (1998). The reaction cross
section is detectable when the dissociated products have a total
kinetic energy greater than 2 eV. Excess energy above the excitation threshold can be divided between the outgoing electron
(Ej) and the dissociated hydrogen atoms. The division of energy is dependent on the incoming electron energy and the initial
H2 X 1 þ
g vibrational energy level (Stibbe & Tennyson 1998).
According to Trevisan & Tennyson (2002), the majority of the
remaining energy is converted to kinetic energy of the dissociated hydrogen atoms for H2 X 1 þ
g (v ¼ 0). Applied to all vibrational energy levels, this assumption provides an upper limit
to H energy deposition.
Kinetically hot atomic hydrogen heats the hydrogen gas
through momentum transfer collisions:
H þ M ! H þ M :
ð9Þ
H excites H2 X 1 þ
g (v : J ),
H þ H2 X (vi : Ji ) $ H þ H2 X (vj : Jj );
ð10Þ
contributing to a non-LTE distribution in the hydrogen volume.
Reactions (9) and (10) are currently not included in the hydrogen chemistry architecture. Future chemistry will include
the reactions, which will further alter H2 X (v : J ) from an LTE
distribution with the gas kinetic temperature. At high outerplanet thermospheric altitudes, the user-prescribed loss probability P (s1) is limited by the escape of nonthermal H from the
volume,
P½H ¼ 2 f ½e½H2 k7 ;
ð11Þ
where [N ] is the density (cm3) of constituent N, k7 is the rate
coefficient (cm3 s1) for reaction (7), and f is the fractional loss
of H from the top of the thermosphere. The fraction of H
escaping from the top of the atmosphere is calculated from the
energy distribution of H predicted from reactions (7) and (8)
and the altitude of the model calculation.
2.1. H2 Non-LTE Partitioning
Hydrogen chemistry partitioning is critically dependent on
the non-LTE distribution of H2 X 1 þ
g (v). For outer-planet
No. 1, 2005
ROTATIONAL-LEVEL HYDROGEN PHYSICAL CHEMISTRY
451
Fig. 1.—Rate coefficients for vibrational de-excitation of H2 X (v : J ) as a
function of the perturber temperature. H2 X (0 :1) and H rate coefficients were obtained from the work of Flower (2000) and Martin & Mandy (1995), respectively.
Fig. 2.—Rate coefficients for rotational de-excitation of H2 X (v : J ) as a
function of the perturber temperature. H2 X (0 : 1) and H rate coefficients were obtained from the work of Flower (2000) and Martin & Mandy (1995), respectively.
thermospheric temperatures, an H2 X 1 þ
g (v) thermal distribution results in proton-dominated ionospheres, corresponding to
high predicted electron densities when compared to observation. Hþ
3 -dominant ion partitioning is obtained through two ionmolecule reactions:
and de-excitation by ambient electrons is defined symbolically
by
e þ H2 X (vi : Ji ) ] e þ H2 X (vj : Jj ):
ð17Þ
Spontaneous quadrupole emission is defined by
þ
Hþ
2
H þ H2 X (v : J ) ! H þ
X (v : J );
þ
H2 X (v : J ) þ H2 X (v : J ) ! Hþ
3 þ H:
ð12Þ
ð13Þ
Reaction (12) is exothermic for H2 vibrational energy levels
greater than 3. H2 rovibrational reaction cross sections were
obtained from the theoretical work of Ichihara et al. (2000).
þ
Hþ
2 reacts rapidly with H2 to form H3 (reaction [13]). Reaction
cross sections were obtained from Cordonnier et al. (2000).
Reaction (12) is an important proton sink, given the comparably slow proton recombination rate with ambient electrons
(ea),
ea þ Hþ ! H þ h:
ð14Þ
The rate coefficient for electron recombination with protons at
1000 K (reaction [14]) is 2:1 ; 1012 cm3 s1, compared to 1:7 ;
109 cm3 s1 for proton charge transfer with H2 X 1 þ
g (v ¼ 4).
Hþ
3 is a sink for the ambient electron populations through the
following dissociative recombination reactions:
ea þ H þ
3 ! H þ H þ H;
ea þ
Hþ
3
! H2 X
1
þ
g
(v) þ H:
ð15Þ
ð16Þ
The total dissociative recombination cross section and product
partitioning measured by Larsson et al. (1993) were used to determine collision strengths for reactions (15) and (16). At low
relative energies, the partitioning for the two product branches,
3H : H2 X 1 þ
g (v) þ H, is 3 : 1. Product H2 vibrational partitioning for reaction (16) was determined experimentally by
Strasser et al. (2002). The partitioning has a broad distribution,
with a peak at approximately H2 X 1 þ
g (v ¼ 4). This H2 X (v)
product partitioning is applied in the model.
Ambient electrons play an important role in the vibrational
distribution of the ground-state H2 population. Direct excitation
H2 X (vj : Jj ) ! H2 X (vi : Ji ) þ h:
ð18Þ
H2 quadrupole transition probabilities for reaction (18) were
obtained by Wolniewicz et al. (1998). Calculations based on the
work of Ehrhardt et al. (1968), Nishimura et al. (1985), Gibbson
(1970), Linder & Schmidt (1971), and Houfek et al. (2002)
resulted in direct electron excitation cross sections greater than
previously determined, establishing the importance of these reactions in determining the ground-state vibrational distribution
( D. Shemansky 2004, private communication). Additional H2
X thermalization reactions include H and H2 excitation and
de-excitation:
H þ H2 X (vi : Ji ) ] H þ H2 X (vj : Jj );
H2 þ H2 X (vi : Ji ) ] H2 þ H2 X (vj : Jj ):
ð19Þ
ð20Þ
Reactions (19) and (20) involve thermal H and H2 populations, respectively. These reactions compete with non-LTE H2
X (v) excitation processes to relax the vibrational distribution to
a thermal distribution with the gas kinetic temperature. The two
reactions are currently not included in the hydrogen chemistry.
Reaction (19) is not included because of the lack of fine-structure
cross sections for the range of H temperatures needed in the
model. Reaction (20) cross sections have been obtained by
Flower (2000) but have yet to be incorporated into the chemistry.
Reaction (17) is an effective H2 X (v) thermalization process for
the majority of outer-planet thermospheric conditions, and inclusion of reactions (19) and (20) will not significantly alter the
predicted H2 X (v) non-LTE distributions.
Comparisons of the rate coefficients for electron, H, and H2
de-excitation of H2 X (v : J ) are given in Figures 1 and 2 for vibrational de-excitation and rotational de-excitation, respectively.
Rate coefficients for H de-excitation were obtained from the theoretical calculations of Martin & Mandy (1995) and are accurate
for the temperature range 600 to 1 ; 104 K. H2 de-excitation
452
HALLETT, SHEMANSKY, & LIU
rate coefficients were obtained from the theoretical calculations
of Flower (2000). The calculated H2 X (v ¼ 1) to H2 X (v ¼ 0)
de-excitation rate coefficient underestimates the measured value
at low temperatures (Flower 2000). At 300 and 500 K, the theoretical calculations are a factor of 2 and 3 below the experimental values, respectively. Flower (2000) suggests further
experimental measurements and theoretical calculations to resolve the discrepancy.
For the range of temperatures, the ambient electron deexcitation rate coefficient is faster than both the H and H2 X (0 : 1)
de-excitation rate coefficients. The difference is most significant
at low temperatures, corresponding to the outer-planet thermospheric temperature range of 500–1350 K. For a typical thermospheric temperature of 1000 K, the ambient electron H2 X (v ¼ 1)
to H2 X (v ¼ 0) de-excitation rate coefficient is a factor of 1100
greater than the H de-excitation rate coefficient and a factor of
1:1 ; 105 greater than the H2 X (0 : 1) de-excitation rate coefficient. At H2 to electron density ratios greater than 105, H2 relaxation of H2 X (v) will compete with ambient electron relaxation, resulting in a faster thermalization process than the current
chemistry model. This will primarily affect the H2 X (v ¼ 1)
population. H2 thermalization of H2 X vibrational levels greater
than 1 is less effective than that of ambient electrons. For example, ½H2 /½ea density ratios of 109 would be required for H2
to compete with ambient electrons at 1000 K for H2 X (v ¼ 3) to
H2 X (v ¼ 2) de-excitation. Inclusion of H2 vibrational excitation
and de-excitation cross sections will not critically alter the results
presented here, because the ambient electron population is effectively controlling the H2 X thermalization process. H excitation is expected to play an important role in non-LTE excitation
of low- and midrange H2 X vibrational energy levels.
For rotational de-excitation of H2 X (0 : 2) to H2 X (0 : 0), the
electron de-excitation rate coefficient is only a factor of 20
greater than the H2 X (0 : 1) de-excitation rate coefficient and a
factor of 1200 greater than the H de-excitation rate coefficient
( Fig. 2) at 1000 K. For most outer-planet thermospheric conditions, H2 and H relaxation of the ground-state rotational energy
levels will be a faster process than that of ambient electrons. This
is mitigated somewhat for higher rotational energy levels, as
illustrated by the H2 X (0 : 12) to H2 X (0 : 10) de-excitation rate
coefficients shown in Figure 2. In the current chemistry, ambient
electron excitation and de-excitation dominate the rotationallevel population distributions, and H2 and H will contribute
to the control of H2 X (v : J ). The current omission of H2 and
H (including H ) excitation of the ground-state H2 X (v : J ) population must be taken into account when examining the modeled
rotational energy level distributions, particularly at large ½ H2 /½ea density ratios.
Solar EUV photons, photoelectrons, and energetic source electrons excite the H2 X 1 þ
g (vi : Ji) states to the Lyman, Werner, and
higher electronic bands:
h=e þ H2 X (vi : Ji ) ! H2 B; : : : (vj : Jj ):
ð21Þ
Energetic electron excitation of H2 to the singlet gerade excited
electronic states is quadrupole allowed:
e þ H2 X (vi : Ji ) ! H2 EF; GH ; : : : (vj : Jj ):
ð22Þ
Fluorescence from these bands to the Lyman and Werner states,
H2 EF; : : : (vj : Jj ) ! H2 B; C (vj : Jj ) þ h 0 ;
ð23Þ
Vol. 624
contributes to the non-LTE distribution of H2 X 1 þ
g (v : J )
through fluorescence from these bands to the ground state,
H2 B; : : : (vj : Jj ) ! H2 X (vj : Jj ) þ h 0 :
ð24Þ
Fluorescence to the continuum is also included in the chemistry
architecture:
H2 B; C; : : : (vj : Jj ) ! H þ H þ h 0 :
ð25Þ
Transition probabilities for reactions (23), (24), and (25) were obtained from the work of Liu et al. (2002) and Abgrall et al. (1997).
Electronic band fluorescence and three-body recombination,
H þ H þ M ! H2 X (vj : Jj ) þ M ;
ð26Þ
primarily populate the higher vibrational levels of H2 X 1 þ
g
(vj : Jj). Inclusion of these reaction processes at the rotational
level results in non-LTE distributions of H2 X 1 þ
g (v : J ).
Rotational-level reaction modeling is required to accurately determine the volumetric partitioning of the hydrogen chemistry
neutral and ion constituents.
3. HYDROGEN CHEMISTRY MODEL CALCULATION
The hydrogen chemistry architecture includes over 3000 states,
each associated with several physical reactions quantitatively
described by multicoefficient quantities that determine the absolute collision strengths for the specific transition process. The
multicoefficient analytic shape functions are referenced to a dimensionless energy scale, allowing for the calculation of rate
coefficients over a wide range of temperatures and energies. The
use of shape coefficients adds flexibility and computational speed
to the model and allows the application of the hydrogen chem+
istry to a wide range of imposed physical conditions. Hþ
3 , H , and
includes
the
rovibrational
strucH are treated as single states. Hþ
2
.
H
is
the
most
significantly
developed,
including
ture of X 2 þ
2
g
all electronic states and rovibrational structure.
The hydrogen chemistry is applied to a FORTRAN code that
calculates rate coefficients and transition probabilities for the reactions given in the formatted hydrogen chemistry architecture
file. The code can be applied to any chemical system, given the
appropriate architecture file. The code performs an iterative volumetric calculation to conform to the charge neutrality and statistical equilibrium conditions. A flow diagram of the calculation
process is given in Figure 3.
The code forces the ambient (ea) and energetic forcing (es)
electron densities and temperatures to remain constant throughout the iteration procedure, allowing ambient and energetic electron loss probabilities (Pa and Ps) to be calculated before the
iteration procedure from the imposed electron densities and rate
coefficients (k). The diffusion loss probability (P, s1) is imposed
on the chemistry and can be varied depending on the object of
study. If the Sun is included as a forcing function, the photoelectron populations ([eh]) are binned into a monoenergetic grid
of a user-prescribed energy bin size. The photoexcitation and
photoionization transition probabilities (Ah) are calculated before the iteration cycle from the imposed solar radiative flux and
effective cross sections. Photoelectron production rates are calculated by multiplying the varying constituent H2 and H densities by the photoionization probability (s1) within the iteration
cycle. Each monoenergetic electron component population is
treated as a separate species (m). As the photoelectrons interact
No. 1, 2005
453
ROTATIONAL-LEVEL HYDROGEN PHYSICAL CHEMISTRY
Fig. 3.—Flow diagram of the iteration procedure in COREQH5A7. Here Rj, i (cm3 s1) is the production rate of constituent i at iteration j, and Pj, i (s1) is the
constituent loss probability. The parameter Ah represents the transition probabilities for photoexcitation and photoionization (s1). The ambient and source electron
loss probabilities (Pa and Ps) remain constant throughout the iteration procedure. Neutral and ion impactor loss probabilities are calculated from the rate coefficient
(k, cm3 s1) and iterating densities (cm3).
with the constituent population, the density distribution of the
energy grid varies to track photoelectron energy gain and loss.
The constituent number densities [Njþ1; i ] are calculated during
one iteration ( j þ 1) using the relation
Nj þ1; i
Rj;i
;
¼
Qj;i
½e ¼
ions
X
q½Ni ;
ð29Þ
i
ð27Þ
which defines the constituents in statistical equilibrium. Here Ri
is the production rate (cm3 s1), and Qi is the loss probability
(s1) for all reactions involving species i. The production rates
and loss probabilities are calculated from the previously converged constituent densities [Nj,i] and the reaction rate coefficients (cm3 s1). The initial calculation is performed assuming
that the imposed total particle density [Ntot ] is split between H2
X (0 : 0) and H2 X (0 : 1) according to the ortho : para statistical
weight. If statistical equilibrium is not achieved, then the code
normalizes the constituent populations and repeats the procedure with the scaled previous constituent densities through the
relation
½Nj;i ;
½Njþ1; i ¼ ½Ntot P
i ½Nj;i be converged to statistical equilibrium. After this condition is
reached, the code tests the charge neutrality condition given by
where [e] is the total electron charge density and [Ni] is the
number density of an ion species with charge q. If the gas is not
charge neutral within a given tolerance, the total number of
particles ([Ntot]) is varied and the iteration procedure is repeated
until the population conforms to statistical equilibrium and
charge neutrality. The convergence condition for total particle
statistical equilibrium is given by the relation
Ntot P Nj;i i
Ntot
105 :
Statistical equilibrium convergence is further checked for the
H2 X (v ¼ 0 : J ¼ 0) state,
j½H2 (0 : 0) j ½H2 (0 : 0) jþ1 j
ð28Þ
where [Njþ1; i ] is the particle number density of constituent i for
iteration j þ 1. When the total particle number density forced on
the system is equal to the sum of the calculated particle number density within a given tolerance, the system is considered to
ð30Þ
½ H2 (0 : 0) j
106 ;
ð31Þ
106 ;
ð32Þ
and for the H2 X (v ¼ 0 : J ¼ 1) state,
j½H2 (0 :1) j ½H2 (0 :1) jþ1 j
½H2 (0 :1) j
454
HALLETT, SHEMANSKY, & LIU
TABLE 2
Outer-Planet Thermospheric Parameter Space
Parameter
Range
Reference
500–1350
1 ; 106 –1 ; 1012
1 ; 103 –1 ; 105
5.2
1
1
2
...
500–800
1 ; 106 –1 ; 1014
1 ; 102 –1 ; 104
19.1
3
3
4
...
Jupiter
Kinetic temperature (K)..................
H2 density (cm3) ...........................
Electron density (cm3) ..................
Sun-planet distance (AU) ...............
Uranus
Kinetic temperature (K)..................
H2 density (cm3) ...........................
Electron density (cm3) ..................
Sun-planet distance (AU) ...............
References.— (1) Seiff et al. 1998; (2) Hinson et al. 1997; (3) Herbert et al.
1987; (4) Lindal et al. 1987.
to ensure that the appropriate (ortho : para) H2 ground-state distribution (3 : 1) is achieved through the H2 formation reactions.
The H2 X (v ¼ 0 : J ¼ 0; 1) checks are critical for low collision rate, hydrogen-dominant astrophysical objects. The specific
convergence conditions can be varied for other astrophysical
phenomena. The photoelectron steady state population has the
convergence condition
j½eh j ½eh jþ1 j
106 ;
½eh j
ð33Þ
where ½eh j is the total photoelectron density for iteration j.
Charge neutrality has the convergence condition
j½e Pions
i
½e
q½Ni j
106 :
ð34Þ
The total electron charge density ([e]), including imposed ambient electrons, energetic forcing electrons, and photoelectrons,
must equal the total steady state ion charge density within the
tolerance to meet the charge neutrality convergence condition. In
reality, the imposed forcing function interacts with the constituent population, leading to the production of an ambient electron
population. In the model calculation, the steady state ambient
electron population is forced on the hydrogen chemistry, and the
constituent particle populations vary from the imposed forcing
function in distribution and total density to ensure that the reaction chemistry produces the required steady state electron
density through ionization and recombination. The steady state
Vol. 624
ion calculation is internally consistent. At the point of convergence, the production and loss rates of the electron population
are in equilibrium. The code outputs the converged constituent
þ
+
number densities (H2, H, Hþ
3 , H2 , and H ) and volumetric emis3 1
sion rates (photons cm s ) for all H2 rovibrational states.
4. RESULTS AND DISCUSSION
The hydrogen chemistry behavior is examined for a range of
parameters that include conditions applicable to the outer-planet
thermospheres (Table 2). A summary of the physical conditions
applied to the chemistry model is listed in Table 3 for both solar
forcing and energetic electron forcing. Solar forcing is applied
only to the Jupiter orbital distance because of extended model
convergence time. In general, trends in constituent partitioning
for the parameters listed in Table 3 are similar for solar and energetic electron forcing, because both forcing functions deposit
energy through electron impact. The parameter space explored
demonstrates the flexibility of the model and illustrates the H2
non-LTE response to a wide range of imposed forcing functions.
To fit an atmospheric volume in the outer-planet thermospheres, the loss probability P (s1) and the imposed forcing
function are applied to the chemistry, given the observed ambient
electron population. The steady state H2 density is then compared to the observed result at the altitude of application. The
imposed loss probability is then varied to match the predicted
and observed H2 densities. The altitude of the calculation fixes
the solar forcing function through attenuation of the flux by the
foreground. Nonsolar energetic electrons are constrained in density and temperature by observations of dayglow and aurora
H2 EUV Lyman and Werner band emission. At forcing function
extremes the code does not converge to the statistical equilibrium
and charge neutrality conditions, indicating an unrealistic state
of the gas.
4.1. Solar Forcing
The behavior of the hydrogen chemistry in response to solar
forcing is examined first. The model produces detailed calculations of constituent density distributions given the imposed
solar radiative flux and diffusive loss probability. Solar flux is an
obvious candidate for the expanded states of the outer-planet
equatorial thermospheres, given that H2 EUVemission is evident
only on the planetary daysides. The electron population inferred
from the observed dayglow emission is capable of heating the
thermosphere through reactions (7) and (8) (Shemansky 1985).
However, recent observations by the Cassini Ultraviolet Imaging Spectrograph (UVIS) of the Jupiter dayglow indicate that an
additional heating mechanism is required to predict the observed
H Rydberg series emission (Shemansky et al. 2001). Solar radiative flux is expected to be at least a catalyst for thermospheric
TABLE 3
Parameter Space Variation
Forcing Function
Parameter
Sun .........................................
Kinetic temperature ( K)
Ambient electron density (cm3)
Diffusive loss (s1)
Sun-planet distance (AU)
Kinetic temperature ( K)
Ambient electron density (cm3)
Energetic electron density (cm3)
Energetic electron temperature (K)
Energetic electron ..................
Range
1350
5 ; 10 2 –1
1 ; 1010 –1
5.2
5 ; 101 –1
104
1 ; 102 –1
2.5 ; 104 –1
; 10 5
; 107
; 104
; 10 2
; 1010
No. 1, 2005
ROTATIONAL-LEVEL HYDROGEN PHYSICAL CHEMISTRY
Fig. 4.—Response of hydrogen chemistry to solar forcing. The loss probability is constant for the range of ambient electron densities imposed on the
chemistry volume. Here Ta and Tg are 1350 K.
chemistry. The response to solar radiation is explored for the
Jupiter orbital distance. Solar radiation and solar photoelectrons
are the drivers for ionospheric partitioning and energy deposition. The response to solar forcing is examined for variations in
ambient electron population density and neutral loss probability.
A gas kinetic temperature of 1350 K was imposed for all model
calculations. The behavior of the constituent density distribution
with ambient electron density variation (5 ; 102 –1 ; 105 cm3)
is shown in Figure 4.
The ambient electron density range corresponds to electron
densities typically observed at Jupiter and Uranus (Table 2). The
loss probability is the free parameter in the calculation, and a
value of 107 s1 is applied for the range of imposed ambient
electron population densities. The loss of atomic hydrogen to H2
through the 107 s1 loss probability is sufficient for H2 to be the
dominant neutral for all conditions included in Figure 4. The H2
density varies by 5 orders of magnitude for the range of electron
densities (factor of 200) explored, although the neutral and ion
partitioning does not vary significantly throughout the electron
density parameter space. The ion chemistry is driven primarily
by the ion-molecule reactions (reactions [12] and [13]). The H2 X
vibrational development and total density are sufficient to proþ
duce Hþ
2 through reaction (12) for each case, resulting in H3 is
removed
from
the
volume
dominant ion distributions. Hþ
2
through reaction (13), as evident through the depleted Hþ
2 populations in Figure 4. Protons are at least an order of magnitude
below the Hþ
3 populations for the range of ambient electron densities imposed on the system. To produce the ion densities required by the increasing ambient electron densities, higher H2
densities are needed to increase both ion-molecule reaction rates
(reactions [12] and [13]) to meet the charge neutrality condition
through Hþ
3.
The relative neutral and ion partitioning does not vary significantly for the fixed diffusive loss case. Similar examinations
of the electron density parameter space at diffusive loss probabilities of 108 and 109 s1 exhibit approximately fixed constituent density distribution ratios for variation in electron density,
as with the 107 s1 case. For the 109 s1 case, the net gain of
H2 through the H loss probability is insufficient for the proton
sink (reactions [12] and [13]) to overcome solar photoionization
and electron ionization. H and H + are the dominant constituents
for the range of ambient electron conditions explored for the low
loss probability case. At large outer-planet scale heights, the chem-
455
Fig. 5.—Normalized H2 X (v) distributions, predicted for solar forcing at the
Jupiter-Sun distance. Distributions are given for three imposed ea populations
and are compared to the thermal distribution at Tg .
istry will tend to produce an H +-dominant ionosphere with solar
forcing. At these high thermospheric altitudes, additional (nonsolar) electron forcing is required to predict Hþ
3 -dominant ionospheric partitioning. The 108 s1 diffusive loss probability case
represents a transition region, where the H2 is approximately
25% of the total neutral population and Hþ
3 is approximately 5%
of the total ion population for the range of ambient electron
conditions. The H loss probability and H2 X (v) non-LTE partitioning allows the proton sink to become competitive with proton production.
The non-LTE vibrational energy level distributions of H2
X 1 þ
g (v) are given for three of the imposed ambient electron
populations in Figure 5 for the 107 s1 diffusive loss case. The
three conditions predict populations in agreement with a thermal
distribution at the kinetic temperature for H2 X 1 þ
g (v ¼ 0, 1).
The model with an ambient electron density of 103 cm3 departs most significantly from thermal equilibrium, illustrating the
reduced effectiveness of the ambient electron population in controlling the distribution. The H2 X 1 þ
g (v) vibrational development beyond LTE is produced from electron recombination with
Hþ
3 , solar fluorescence from the excited, singlet-ungerade states
of H2, and photoelectron excitation. Proton charge capture from
H2 (reaction [12]) is a more efficient reaction as the imposed
ambient electron density increases, because more protons are
produced by the physical chemistry. The effect of this reaction
in depleting midrange vibrational energy levels of H2 X 1 þ
g (v) is
evident in the predicted partitioning for the imposed 104 and
105 cm3 ambient electron populations (Fig. 5). Despite the depletion, the H2 X 1 þ
g (v ¼ 4) density is a factor of 30 greater than
the normalized thermal density for the imposed ½ea ¼ 105 cm3
case and is a factor of 1:4 ; 104 greater for the imposed ½ea ¼
103 cm3 case.
As discussed previously, H2 excitation of H2 X (v : J ) is currently not included in the model calculation. Given the converged
H2 densities for the vibrational distributions given in Figure 5, inclusion of H2 excitation and de-excitation rate coefficients would
thermalize H2 X (v ¼ 1) faster for the 104 and 105 cm3 electron
cases. However, the ambient electron population is already effectively thermalizing the H2 X (v ¼ 1) populations for the two cases,
and the addition would not significantly alter the constituent
density distributions and total particle densities. At 1350 K, ambient electron rate coefficients are significantly larger than H2
456
HALLETT, SHEMANSKY, & LIU
Vol. 624
Fig. 6.—Response of hydrogen chemistry to solar forcing for applied loss
probability variation. Here [ea] and Tg are 104 cm3 and 1350 K, respectively,
for all models.
rate coefficients for H2 X vibrational de-excitation originating
from vibrational energy levels greater than 1 ( Fig. 1). The ratio
of ambient electron to H2 rate coefficients at 1350 K for deexcitation of H2 X (v ¼ 3) to H2 X (v ¼ 2) is 1:6 ; 107 , illustrating a dominant ambient electron thermalization process for
the three cases examined in Figure 5. Thermal H de-excitation of
H2 X (v ¼ 1) is comparable to electron excitation for the three
cases illustrated in Figure 5. However, nonthermal H excitation
is not included in the current model and will result in further
vibrational-level deviation from a thermal distribution (average
H : 4.6 eV ). Despite the lack of this excitation process, deviations from a thermal distribution for H2 X (v 2) result in Hþ
3dominant ion partitioning, given the sufficiently fast diffusive
loss probability (107 s1) applied for these cases. The steady
state populations produced for this selection of parameters
produce ( H2 : Hþ
3 )-dominant chemistry. The ambient electron
density affects the total neutral and ion densities in this computational methodology but does not alter the overall component
distribution ( Fig. 4).
As a free parameter, the diffusive loss probability can be varied to predict H2 : H partitioning observed at various outer-planet
thermospheric altitudes. The effect of the loss probability on the
hydrogen chemistry model is illustrated in Figure 6. H2 densities
vary by 7 orders of magnitude over the diffusive loss range explored. The diffusive loss probability is a critical parameter in
determining the partitioning of the hydrogen species.
Two stable partitioning regimes exist given variations in the
loss probability: an (H : H +)-dominant partitioning regime and
an (H2 : Hþ
3 )-dominant partitioning regime. Within these two regimes, the loss probabilities primarily control the H2 : H partitioning. The ionization mixing ratio is an indicator of response
to variation in the diffusion rate (Fig. 7).
Diffusive loss probabilities less than 108 s1 produce
( H : H +)-dominant partitioning at lower total particle densities
compared to cases produced by faster diffusion processes. The
flow of H2 into the volume is not sufficient to overcome solar
photoionization and electron ionization. Three-body recombination of atomic hydrogen to form H2 is slow at the predicted
total nuclear densities. Atomic hydrogen becomes the dominant
neutral. The charge neutrality condition is met through equilibrium in production and loss of the ambient electrons. The partitioning of H and H + is determined by the total H ionization and
H + recombination rates. At a diffusive loss probability of 2:5 ;
108 s1, the H2 density is high enough (7:8 ; 108 cm3) for
Hþ
3 to dominate ( Fig. 6). Here, the ion-molecule reactions (reactions [12] and [13]) control the ion constituent density parti-
+
Fig. 7.—Fractional ionization of Hþ
3 and H relative to the two neutral
constituents ( H2 and H ) for variation in the neutral diffusive loss probability.
Here [ea] and Tg are 104 cm3 and 1350 K, respectively, for all models.
tioning. The ion-molecule reactions require larger H2 densities to
meet charge neutrality than the dominant H ionization process
active in the H : H + regime.
The total photoelectron density in the modeled hydrogen
volumes increases by a factor of 85 from the 107 s1 loss
10 1
s loss probability case
probability case (H2 : Hþ
3 ) to the 10
(H : H +; Fig. 6). The photoelectron multiscattering energy-loss
process is complex, involving numerous reactions. Differences
in the photoelectron energy distribution are illustrated in Figure 8.
The differences in photoelectron energy distributions for the
two diffusive loss probability cases are associated primarily with
the differences in H2 : H partitioning. The photoelectron population distribution and density are tied to the imposed diffusive loss
probability parameter, which controls the total particle density and
distribution. The majority of the energetic electron loss processes
(Table 1) depend on the H2 density and ground rovibrational state
distribution. In an H : H + regime, the total neutral density and the
H2 : H ratio must be lower for equilibrium to be physically established, reducing the effectiveness of the photoelectron sink.
Therefore, the total photoelectron population is larger for the
1010 s1 diffusive loss case.
Fig. 8.—Normalized, steady state photoelectron distributions produced from
the imposed loss probabilities of 107 and 1010 s1. Panel a illustrates the
photoelectron distribution below 10 eV. Panel b illustrates the photoelectron
distribution above 10 eV.
No. 1, 2005
ROTATIONAL-LEVEL HYDROGEN PHYSICAL CHEMISTRY
Differences in the photoelectron energy distribution are also
attributed to the solar photoionization reactions. The entire H2 X
1 þ
g (v : J ) non-LTE distribution is exposed to the solar flux
compared to the single atomic hydrogen ground state, altering
the photoelectron energy distribution and total density for the
two regimes. Multiple–order-of-magnitude differences in distribution at photoelectron energy bins greater than 12–13 eV are
primarily associated with threshold differences between H2 and
H. Given the short-wavelength threshold of 300 8 for the imposed solar flux, the maximum photoelectron energy is approximately 28 eV for H. The H2 X (v ¼ 14) state gives the maximum
H2 photoelectron energy of approximately 31 eV. In the H2 : Hþ
3
regime, the photoelectron distribution has more high-energy
photoelectrons compared to the distribution in the H : H + regime.
A higher eh 2–3 eV bin density for the 1010 s1 diffusive loss
case relative to the 107 s1 loss probability case is attributed to
the reduced H2 X (v : J ) densities. H2 X rovibrational excitation is
a more efficient photoelectron sink in the H2 : Hþ
3 regime given
the larger H2 densities. The low-energy photoelectron distribution for the 107 s1 loss probability case is controlled by vibrational excitation.
H2 ground-state rotational-level chemistry is a critical component in the prediction of ionospheric partitioning and electron
density profiles in outer-planet thermospheres. The loss probability is the primary driver of constituent density distributions,
with a loss probability of approximately 108 s1 representing
+
the transition point between the H2 : Hþ
3 and the H : H constituent density distribution regimes. Inside these regimes, the loss
probability affects H2 : H partitioning, enforcing the dominant
ion component. The ambient electron density controls the total particle density, with constituent density distributions minimally affected when compared to loss probability variations. The
rotational-level H2 partitioning allows for the prediction of the
steady state photoelectron population. Significant differences are
illustrated in distribution and total density given the two primary
constituent density distribution regimes. The rotational-level H2
chemistry allows for the detailed examination of photoelectron
energy deposition, which leads to the accurate determination of
solar heating in the hydrogen volume.
An examination of H2 X rotational-level distributions is given
for the H2 : Hþ
3 chemistry regime, with conditions appropriate to
the Jupiter thermosphere. The ambient electron density and
temperature are 104 cm3 and 1350 K. The H2 X (v ¼ 0 : J ) and
H2 X (v ¼ 4 : J ) distributions are shown in Figure 9, compared to
thermal distributions at the gas kinetic temperature (Tg). The H2
X (v ¼ 0, 1) rotational-level distributions agree with the expected
thermal distributions within 15%, indicating the ambient electron control of the H2 X rotational-level distributions for low
vibrational levels. Inclusion of thermal H2 and H excitation and
de-excitation rate coefficients for H2 X (v : J ) will further thermalize the v ¼ 0 and v ¼ 1 states. Energy levels greater than
v ¼ 1 exhibit deviations from the thermal distribution similar to
those illustrated by the H2 X (v ¼ 4 : J ) distribution shown in
Figure 9. The high rotational energy level tail of the distribution
deviates from the thermal distribution by a factor of 2 for rotational energy levels greater than 8. This component of the distribution will be altered for models in which the ½H2 /½e density
ratio is greater than 105 when H2 relaxation of the ground state
is included in the chemistry. The H2 X (v ¼ 4 : J ¼ 5) state deviates by a factor of 1:5 ; 103 from the thermal distribution. A
similar deviation exists for vibrational energy levels 2–6. This
trend does not occur for nonsolar energetic electron excitation
and is a result of solar flux interaction with the ground state. The
solar forcing functions produce unique steady state non-LTE H2
457
Fig. 9.—H2 X (v ¼ 0 : J ) and H2 X (v ¼ 4 : J ) distributions compared to
thermal distributions at Tg . Model conditions are appropriate for the Jupiter
equatorial thermospheric region.
rovibrational distributions that can be compared at various wavelength ranges to observations through calculations of rotationallevel volumetric emission rates. The comparisons allow detailed
examination of critical reaction chemistry and heating mechanisms in the astrophysical object under consideration. Inclusion
of more detailed H2 X excitation chemistry is required to accurately predict transitions originating from high rotational levels
for vibrational energy levels greater than 1.
4.2. Nonsolar Energetic Electron Forcing
Energetic electrons that are nonsolar in origin also drive hydrogen chemistry in the outer planets. These electrons may have
magnetospheric origins, such as energetic electrons (T 106 K)
depositing energy in the auroral regions of the outer planets
( Perry et al. 1999). Nonsolar energetic electrons (T 3 ; 104 –
1 ; 105 K) have been used to predict the H2 EUV Lyman and
Werner and H Ly and Ly dayglow emission observed at
Uranus and Jupiter by the Voyager ultraviolet system (UVS) and
Cassini UVIS, respectively (Shemansky et al. 2001; Hallett
2004; Hallett et al. 2004, 2005). The state of the gas is examined
in response to imposed energetic electron populations with
Maxwellian energy distributions. Awide range of energetic electron temperatures is examined to predict the state of the gas for a
range of outer-planet conditions. The loss probability and ambient electrons are important drivers of the constituent density
distributions, as with solar photoelectrons ( Figs. 4 and 6, respectively). Similar effects are predicted for independent variations
of loss probability and ambient electron density. The loss probability continues to control constituent density distributions, while
the ambient electron density continues to control total particle
density. Therefore, the parameter space variation is limited here
to energetic electron density and temperature. Steady state results
are produced for conditions typical of the Uranian thermosphere
(ea ¼ 104 cm3, Tg ¼ 600 K), with an additional examination of
behavior for a range of gas kinetic temperatures (Tg). The imposed energetic electron populations drive energy deposition and
partitioning confined by the user-prescribed density and temperature. Variations in these parameters affect the reaction rates
of the electron chemistry listed in Table 1.
Energetic electron populations (es), with varying densities (1: ;
101 –1 ; 102 cm3), are imposed on the gas with a constant energetic electron temperature (Ts) of 5 ; 104 K. The variation in
458
HALLETT, SHEMANSKY, & LIU
Vol. 624
Fig. 10.—Variation of steady state constituent partitioning with [es]. Here
[ea] and Tg are 104 cm3 and 600 K, respectively, for all models. The value of
Ts is 5 ; 104 K.
Fig. 11.—Variation of steady state constituent partitioning with Ts. Here [es]
is 1.0 cm3 for all results. Ambient electron parameters correspond to those
discussed in Fig. 10.
steady state constituent densities is given in Figure 10. The loss
probability for atomic hydrogen is constant for this set of chemistry models (107 s1) and does not affect the variations in
neutral and ionospheric partitioning. H2 densities vary by 10
orders of magnitude for the set of energetic electron densities
explored. The ionospheric partitioning is driven by the hydrogen
chemistry production of Hþ
3 through the ion-molecule reactions
(reactions [12] and [13]). At energetic electron to ambient electron density ratios greater than 5 ; 103 , the es production of
protons through ionization of H2 and H overwhelms the proton
sink (primarily reaction [12]). A smaller total neutral density is
required for the ionospheric population to meet the forced ambient electron density (104 cm3), because protons are the dominant ionospheric component. H2 densities below 105 cm3 are
predicted for these cases (Fig. 10). As with solar forcing, higher
density energetic electron (or photoelectron) populations predict
constituent density distributions in the H : H + region. At lower energetic electron densities (½es /½ea < 5 ; 103 ), the proton charge
exchange reaction (reaction [12]) competes efficiently with the
production of protons, and Hþ
3 is the dominant ion. This process
requires larger H2 densities, as illustrated in Figure 10. The region at ½es /½ea ¼ 5 ; 103 represents the sharp transition region
+
between the H2 : Hþ
3 regime and the H : H regime. Variations in
the atomic hydrogen loss probability will vary the location of this
transition but not the overall trend of the constituent density distribution. At electron ratios (½es /½ea ) greater than 1 ; 102 , the
distribution depends entirely on the relative efficiency of H electron ionization to proton recombination.
Variation of the constituent density distribution with energetic
electron temperature is illustrated in Figure 11 for a temperature range (Ts) of 104 –109 K. A source electron density (es) of
1.0 cm3 was chosen for the parameter space variation. The point
corresponds to an H2 : Hþ
3 regime in the electron density variation shown in Figure 10. The variation in H2 density (10 orders
of magnitude) with energetic electron temperature depends on
the variations in the non-LTE H2 X (v) partitioning and the thermally averaged rate coefficients for electron reactions in the
volume.
At energetic electron temperatures greater than 105 K, neutral
ionization and dissociation overwhelm the proton charge transfer
sink, resulting in a shift from predominantly Hþ
3 ion partitioning
to predominantly H + ion partitioning. This shift in ion distribu-
tion occurs despite the significant deviations from LTE H2 X (v)
predicted for high Ts ( Fig. 12). At the 600 K kinetic temperature,
the energetic electron excitation rate of H2 X (v) corresponds
within a factor of 2 with the ambient electron excitation rate for
the range of energetic electron temperatures explored. This results in significant H2 X vibrational development beyond LTE for
all states except H2 X (v ¼ 0) (Fig. 12). Given the large variations
in H2 and H de-excitation rate coefficients at low temperatures
(Fig. 5), ambient electrons are the primary H2 X (v) thermalization component for energetic electron forcing cases greater than
2:5 ; 104 K. Given the large H2 density for the 2:5 ; 104 K case
(1012 cm3), the H2 de-excitation rate for H2 X (v ¼ 1 to 0) is a
factor of 10 faster than the ambient electron (104 cm3) deexcitation rate. For the imposed energetic electron density and
range of temperatures explored, the loss probability is sufficient
to maintain H2 as the dominant neutral. Neutral partitioning is
more sensitive to the imposed loss probability and energetic electron density than the energetic electron temperature. At temperatures greater than 1 ; 106 K, the steady state solutions trend
back to higher H2 densities, producing the same H2 density for
Fig. 12.—Steady state H2 X (v) distributions predicted for the listed Ts.
Deviation from LTE at 600 K is predicted for all H2 X vibrational energy levels
greater than zero.
No. 1, 2005
ROTATIONAL-LEVEL HYDROGEN PHYSICAL CHEMISTRY
459
Fig. 13.—Variation of steady state constituent partitioning with Tg . Here [es],
Ts, and the loss probability (107 s1) are constant for each calculation.
Fig. 14.—Steady state H2 X (J ) distributions predicted from energetic electron
forcing. Distributions are compared to thermal distributions at Tg ¼ 600 K.
different energetic electron populations (Fig. 11). At higher temperatures, the energetic electron populations sufficiently excite
the H2 X 1 þ
g (v : J ) distribution beyond LTE for the charge
exchange proton sink (reaction [12]) to once again produce Hþ
3dominant ion partitioning.
The gas kinetic temperature (Tg) also affects the constituent
density distribution and total particle density through variations
in the H2 X 1 þ
g (v) population distribution, particularly in the
temperature range in which the H2 X (v) rate coefficients are
varying rapidly (Fig. 1). Variations in partitioning for a range of
temperatures from 50 to 104 K are examined in Figure 13, given a
constant energetic electron population (5 ; 104 K, 1.0 cm3) and
diffusive loss probability (107 s1). The energetic electron population corresponds to the populations used to predict H2 Lyman
and Werner band emission at Jupiter and Uranus. Over the range
of temperatures corresponding to the outer-planet thermospheres
(400–1500 K), neutral densities vary by approximately 40%,
which is relatively low when compared to the other parameter
space variations examined at a kinetic temperature of 600 K.
Order-of-magnitude variations in neutral density and ionospheric
partitioning occur at the low-temperature end of the parameter
space variation. In this low temperature range, the electrons control the H2 X (v) distribution. H2 and H de-excitation rate coefficients for H2 X (v : J ) drop significantly compared to electron
de-excitation (Figs. 1 and 2) in this range, although the H2 and
H rate coefficients are uncertain below 600 K ( Flower 2000;
Martin & Mandy 1995). At temperatures less than 100 K, the H2
ground-state partitioning is sufficiently suppressed for protons to
overwhelm the charge exchange sink (reaction [12]). At higher
gas kinetic temperatures, the fraction of the H2 population in
H2 X (v 4) increases to allow for faster proton charge capture
(reaction [12]), leading to Hþ
3 -dominant ion partitioning. At a
kinetic temperature of 4 ; 103 K, the non-LTE H2 X (v) distriþ
+
bution is sufficient to allow Hþ
2 and H3 to exceed the H density
through reaction (12).
Ground-state rotational energy level distributions are given
for energetic electron forcing in Figure 14. The H2 X (v ¼ 0 : J )
distribution conforms to the thermal distribution calculated for
the same total H2 X (v ¼ 0) density. The H2 X (v ¼ 0) state is
most heavily influenced by interaction with the ambient electron
population. Deviations from a thermal distribution occur for
vibrational energy levels greater than 1, as illustrated by the H2 X
(v ¼ 4) case. A factor of 2 increase from the thermal population
occurs at J ¼ 7. The J ¼ 12 state deviates by a factor of 42 from
the thermal distribution, which is attributed to energetic electron
excitation. Similar trends in rotational distribution are exhibited
for higher temperature energetic electron populations. At the
H2 to ambient electron density ratio of 105, thermal H2 and H
relaxation will lessen the high rotational energy level deviation
from a thermal distribution, as with the solar case. Nonthermal
H excitation will contribute to the deviation. Inclusion of thermal H and H2 and nonthermal H is required to examine the
relative effects on the rotational energy level distributions, primarily for vibrational energy levels greater than 1 and for the
high rotational energy levels (J 7). As illustrated, the H2 X
state is particularly sensitive to imposed heating mechanisms.
Observations of H2 X quadrupole emission can be used to constrain hydrogen chemistry through comparison to the modeled
distributions. Recent IR H2 X (v ¼ 1) quadrupole emission measured at Uranus by Trafton et al. (1999) has been used to constrain
potential thermospheric heating mechanisms and determine critical ground-state excitation mechanisms (Shemansky et al. 2003;
Hallett et al. 2004, 2005) using the current chemistry code. Predicted rotational-level H2 UV emission can also be used to constrain reaction chemistry and forcing functions in the outer
planets and other astrophysical objects.
The constituent partitioning is sensitive to imposed energetic electron temperature and density. Observations of Hþ
3 IR
vibration-rotation emission (Trafton et al. 1999; Miller et al.
1997; Drossart et al. 1989) and subsequent modeling indicate
that the outer-planet upper ionospheres are dominated by Hþ
3
(Shemansky et al. 2003; Hallett 2004; Hallett et al. 2004; Majeed
& McConnell 1991; Achilleos et al. 1998; Perry et al. 1999).
Modeled energetic electron excitation in the equatorial outerplanet thermospheres is limited to the low-energy region of energetic electron excitation, given the results illustrated in Figures 10
and 11 and energetic electron populations predicted from Lyman
and Werner band dayglow excitation. Predictions of energetic
electron populations from the observed Jupiter and Uranus dayglows (Shemansky et al. 2001, 2003; Hallett 2004; Hallett et al.
2004) fall below a temperature of 105 K, corresponding to the
modeled ionospheres predicted here. Hþ
3 auroral emission observed at Jupiter more likely corresponds to the high energetic
electron temperature regime (temperatures greater than 106 K).
Variations in kinetic temperature do not produce the multiple–
order-of-magnitude variations in partitioning seen by energetic
460
HALLETT, SHEMANSKY, & LIU
electron parameters for the range of temperatures corresponding
to the outer-planet thermospheres (400–1500 K). Variations in
neutral density and ionospheric partitioning outside this range
may have implications for other astrophysical phenomena.
5. CONCLUSIONS
A hydrogen physical chemistry model has been developed to
predict non-LTE behavior of hydrogen-dominated astrophysical
phenomena. The model produces steady state constituent partiþ
+
tioning for H2 (v : J ), H, Hþ
2 X (v : J ), H3 , and H . The state of
the gas is examined for a range of imposed parameters and forcing functions expected for the outer-planet upper atmospheres.
H2 X 1 þ
g (v : J ) partitioning, deviating multiple orders of magnitude from LTE, is predicted for both solar forcing and nonsolar
energetic electron forcing, given the significant number of H2
ground-state excitation mechanisms included in the chemistry
architecture. The non-LTE H2 X (v) distribution critically affects
the ion partitioning in the volume through the ion-molecule reactions (reactions [12] and [13]). The H2 X (v) distribution and loss
probability are the primary parameters determining ion partitioning.
Solar forcing at Jupiter produces two distinct partitioning re+
gimes, H2 : Hþ
3 and H : H , dependent almost entirely on the loss
of H to H2 in the volume. Energetic electron forcing exhibits a
larger range of state partitioning when compared to solar forcing,
which is limited by the reaction chemistry through the production of photoelectrons. A duality of converged density distributions exists for the energetic electron parameter space analysis.
At sufficiently high electron temperatures, the ion-molecule proton sinks overcome the high rate of neutral ionization to produce
an H2 : Hþ
3 partitioning regime that is predicted for orders-ofmagnitude lower electron temperatures. This duality may be seen
in comparison of the auroral and dayglow chemistry in the outer-
Vol. 624
planet thermospheres. Observational results from both regions
infer Hþ
3 -dominant ionospheres, but with widely differing electron energy deposition predictions.
Results presented here demonstrate the importance of
rotational-level H2 physical chemistry to the modeling of
hydrogen-dominant systems and its potential applicability to
additional hydrogen systems, such as solar forcing of comet
coma chemistry. Modeling of the outer-planet ionospheres requires internally, self-consistently calculated non-LTE H2 vibrational partitioning to predict the observed electron density
profiles. In addition, rotational-level H2 chemistry allows for
modeling of H2 emission for comparison to high-resolution
observations in both the IR and UV regions for astrophysical
phenomena, including the outer planets and comet comas. Modeling of emission features provides constraints for the imposed
energy deposition mechanisms applied in the model. Future
updates to the chemistry will include Hþ
3 fine structure to allow
prediction of observed IR vibration-rotation emissions at Jupiter
and Uranus. A multiscattering model of energetic H energy deposition will be included in future codes to track the thermalization process of H and its effect on non-LTE reaction chemistry.
Thermal H2 and H relaxation of H2 X (v : J ) will also be included
in future chemistry, particularly for accurate modeling of H2 X
quadrupole emission originating from high rotational energy levels for H2 X vibrational energy levels greater than 1.
The research described in this paper was carried out at the
University of Southern California and is based on the Ph.D.
dissertation of J. T. Hallett. The research was supported by
NASA (NAG5-8939) and the National Science Foundation
(ATM-0131210).
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