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Advances in Geosciences
Vol. 19: Planetary Science (2008)
Ed. Anil Bhardwaj
c World Scientific Publishing Company
THE SATURN HOT ATOMIC HYDROGEN PLUME:
QUANTUM MECHANICAL INVESTIGATION OF H2
DISSOCIATION MECHANISMS
XIANMING LIU∗,§ , D. E. SHEMANSKY†,¶ , P. V. JOHNSON∗, ,
C. P. MALONE‡ , H. MELIN† , J. A. YOUNG∗ and I. KANIK∗,∗∗
∗ Jet Propulsion Laboratory, California Institute of Technology,
Pasadena, CA 91109, USA
† Planetary and Space Science Division,
Space Environment Technologies, Pasadena, CA 91107, USA
‡ Department
of Physics, California State University,
Fullerton, CA 92834, USA
§ xianming@jpl.nasa.gov
¶ paul.v.johnson@jpl.nasa.gov
isik.kanik@jpl.nasa.gov
∗∗ dshemansky@spacenvironment.net
The Cassini/Huygens Mission to Saturn has provided new observations of
thermospheric processes that emphasize the need for further work on the
properties of weakly ionized hydrogen. The Cassini UVIS experiment has
obtained high spatial resolution images of atomic and molecular hydrogen
in the atmosphere and magnetosphere of Saturn. The images show atomic
hydrogen flowing out of the top of the sunlit thermosphere in a confined,
distinct plume in ballistic and escaping orbits, and reveal a continuous
distribution of atomic hydrogen from the top of the Saturn atmosphere,
measurable to at least 45 Saturn radii in the satellite orbital plane, and
measurable to 30 Saturn radii latitudinally above and below the plane. Possible
processes for the fast atomic hydrogen formation include the excitation of H2
singlet-ungerade states, doubly excited states by photons and electrons, the
excitation of the singlet-gerade and triplet states by electrons, and chemical
reactions involving the formation and dissociative recombination of H+
3 .
Based on the available laboratory measurements and quantum mechanical
calculations, the various mechanisms for H2 → H production are examined
here, especially those producing H atoms with sufficient energy to escape from
Saturn. It is found that electron excitation of vibrationally excited H2 X 1 Σ+
g
to the dissociative b3 Σ+
u state, as well as excitation to the doubly excited states
and dissociative ionic states by solar photons and electrons, are mechanisms for
the production of the observed hot hydrogen plume, and extended distribution
in the magnetosphere.
405
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1. Introduction
In 2005, virtual images of the Saturn system were obtained using the
Cassini UVIS (Ultraviolet Imaging Spectrograph) experiment at a pixel
resolution of 0.1 × 0.1 Saturn radii (RS ) in a unique geometry in which the
rings were edge-on to the spacecraft, eliminating scattering or obscuration
effects. The image pixel content is composed of spectral vectors containing
the accumulated exposure to the emission in a multiply scanned systemcentered matrix. The image data shows H Lyman-α (Ly-α) in ballistic and
escaping trajectories sourced at the top of the thermosphere, mainly in
the southern sunlit hemisphere.1, 2 Earlier low spatial resolution images
were obtained by the Voyager UVS (Ultraviolet Spectrograph) experiment.3
Emission spectra of the H2 singlet-ungerade Rydberg series show strong
deviation from local thermodynamic equilibrium (LTE) in the main source
region and the X 1 Σ+
g state is found to be highly excited. Fig. 1 shows
a contour plot of the H Ly-α image. The main feature in the image is
2
1
RS 0
-1
-2
-5
-4
-3
-2
-1
0
RS
1
2
3
4
5
Fig. 1. Cassini UVIS image of the Saturn system in a surface contour plot in H
Ly-α emission showing the escape of atomic hydrogen in a non-uniform asymmetric
distribution from the top of the Saturn atmosphere. Image accumulated 2005 DOY
74–86 at spacecraft-planet range of 24–44 RS . The image pixel size is 0.1 × 0.1 RS .
The edge-on view of the rings is indicated; sub-spacecraft latitude is 0◦ . The 1 bar
level and terminator (Sun on right side of image) is indicated by white dots. Range
in the virtual image is indicated at the frame of the image in units of RS , where 0,0
is the position of the planet center. Contour lines of constant brightness are shown
on the plot with Rayleigh brightness values given at selected locations. The locally
confined emission structure contains a foreground/background signal broadly distributed
throughout the magnetosphere with magnitudes indicated near the north and south
frames of the image. The core of the plume is at −13.5◦ planetocentric latitude. Subsolar latitude is −22.3◦ . Auroral emission is apparent at the poles extending over the
terminator. Solar phase is 77◦ .
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a distinctive plume structure with a FWHM of 0.56 RS at the exobase
sub-solar limb at ∼−13.5◦ planetocentric latitude constituting the core
of the distributed outward flow of HI from the sunlit hemisphere, with
a counterpart on the anti-solar side peaking near the equator above the
exobase limb. The structure of the image indicates that part of the
out-flowing population is sub-orbital and re-enters the thermosphere in
∼5 hour time scale. A larger and more broadly distributed component
fills the magnetosphere to beyond 45 RS in the orbital plane and 20
RS FWHM latitudinally in an asymmetric distribution in local time.1–3
The phenomenon of escaping atomic hydrogen is unique to Saturn in two
properties. First, the magnitude of the gravitational potential is small
enough to accommodate the loss of the atomic dissociation products
produced in the activated thermosphere. Secondly, Saturn is the only planet
showing a remarkably confined low latitude region in the sunlit atmosphere
away from auroral influence from which a large fraction of out-flowing
hydrogen originates. The auroral zones are in fact not a significant source
of escaping atomic hydrogen and are not a measurable source on the
magnitude scale of the low latitude outflow. It has also been found that
the emission spectra of H2 singlet-ungerade states in the primary atomic
hydrogen source region are highly non- LTE.1 The spectra in both extreme
and far ultraviolet (EUV and FUV) regions collected along with the H Ly-α
into the image mosaic show a distinctive H2 resonance property correlated
with the location of the H Ly-α plume. Figure 2 shows an image of the H2
band resonance emission in the 1,220–1,370 Å spectral region, corresponding
to the same data set shown in Fig. 1. This figure shows the confinement
of H2 EUV/FUV band emission mainly to the southern hemisphere, with
a ridge of emission roughly aligned with the atomic hydrogen plume and
relatively strong emission crossing the terminator into the dark-side in the
southern hemisphere. These properties infer electrodynamic electron impact
excitation in the vicinity of the exobase. Emission in the H2 resonances
shown in Fig. 2 show no detectable polar enhancement associated with the
auroral zones, and in the north polar region the emission in these features is
not detectable. Escaping hot atomic hydrogen is also not measurable above
the foreground/background resident magnetospheric H Ly-α signal in the
polar regions (Fig. 1). Heating at the poles by dissociation of H2 in auroral
deposition in these observations must therefore be deeper and closer to the
local heat sink.
Contemporaneous published global model calculations4 assuming
auroral deposition to be a major source of thermospheric heating show
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408
.5
R 0
S
-.5
-1.5
-1.0
0.0
RS
1.0
1.5
Fig. 2. Cassini UVIS image of Saturn in a surface contour plot in H2 band emission in
the 1,220–1,370 Å region from the same data set shown in Fig. 1. The 1 bar level and
terminator (Sun on right side of image) is indicated by white dots. Range in the virtual
image is indicated at the frame of the image in units of RS (Saturn radii), where 0,0 is
the position of the planet’s center. Contour lines of constant brightness are shown on the
plot. Rayleigh brightness values are indicated at selected locations on the image. The
image shows a bright emission ridge roughly aligned with the plume feature in Fig. 1,
and emission crossing the terminator in the southern hemisphere. Resonance emission is
not strong in the auroral regions.
very hot polar thermosphere temperatures, but slow meridional transport
leaves cold low latitude temperatures in the absence of additional processes.
While the inferred approximate globally averaged energy deposition at the
top of the thermosphere from the production of the hot atomic hydrogen
can account for the measured atmospheric temperature,1 the mechanisms
of the production of hydrogen atoms with sufficient kinetic energy to escape
the gravitational potential are not fully delineated.
The present paper explores mechanisms for the production of fast
atomic hydrogen atoms responsible for the observed plume. The dominance
of H2 in the atmosphere dictates that any plausible processes of hot HI
atom production must involve H2 , which can be ro-vibrationally excited as
inferred from observed H2 emission spectra of the singlet-ungerade states.
The escape energy of a hydrogen atom at 2,000 km above the 1 bar level
varies from 5.7 eV at the equator to 7.0 eV at the poles. The task of
the present paper reduces to the examination of chemical reactions and
excitation-dissociation processes of H2 and hydrogenic plasma products
that produce HI with kinetic energy in the range up to and above 5.7 eV.
The present work examines the kinetic energy distribution of HI produced
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from excitation into continuum levels of singlet-ungerade states, singletgerade states, triplet states, ionic states, and doubly excited states.
2. Method
This section describes calculations of the photodissociation cross sections
and discrete-continuum Franck-Condon factors. Both quantities are
differential, and display the relative magnitude of dissociation in terms of
the kinetic energy of the hydrogen atom product. Visual inspection of both
quantities, in many cases, is sufficient to give a qualitative assessment of the
importance of the process for energetic atom production. Both quantities
are important for quantitative modeling of the hot hydrogen outflow on
Saturn. Throughout the paper, we use indices i and j to denote levels of H2
X 1 Σ+
g and the excited electronic state, respectively.
2.1. Photodissociation cross section
Under irradiation by photons with energy of Eph = hcν, the dissociation
cross section for excitation from (vi , Ji ) to the continuum level (Ek , Jj ) is5
σ(vi , Ji ; Eph ) =
8π 3 ν Hji (Jj , Ji )
ρ(Ek )Υj,i (R)
3hc
2Ji + 1
(1)
Jj
where
Υj,i (R) = |χEk ,Jj (R)|D(R)|χvi ,Ji (R)|2 ,
Hji (Jj , Ji ) and D(R) are the Hönl-London factors and the electric dipole
transition moment. χvi ,Ji (R) and χEk ,Jj (R) are the radial wave functions of
initial level i and the continuum level j, respectively. ρ(Ek ) is the densityof-states normalization factor at energy Ek = hcνk above the dissociation
limit of state j:
δ(Ek − Ek )
ρ(Ek )
(2)
Ek = Eph + E(vi , Ji ) − Vj (R → ∞),
(3)
χEk ,Jj (R)|χEk ,Jj (R) =
where Vj (R → ∞) is the asymptotic potential energy of state j.
It is convenient to convert internuclear distance, R, to a dimensionless
quantity z = R/R0 where R0 is an arbitrarily selected scale length. Two
convenient values for R0 are 1 Å or 1 a0 (bohr).5, 6 In the present work, the
amplitude of the continuum wave function is asymptotically normalized
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410
to unity:
lim χEk ,Jj (z) = sin[kz + ηJj (Ek )],
z→∞
(4)
where ηJj (Ek ) is the phase shift and k = 2πR0 2µcνk /h, with µ
and normalization give
being the reduced mass of H2 . The conversion
a density of states factor of ρ(Ek ) = 2R0 2µc/hνk (states per cm−1 ).
The photodissociation cross section in equation (1) in units of Mb can be
re-written as:6
2 4µEph
Hji (Jj , Ji )
Υj,i (z),
σ(vi , Ji ; Eph ) = 25.936
(5)
mH Ek
2Ji + 1
Jj
where Eph and Ek are in hartree, D(z) is in au, R0 in bohr (a0 ), and mH
is HI mass.
2.2. Franck-Condon factors
The discrete-continuum Franck-Condon factor is the square of the overlap
integral of χvi ,Ji (z) and the energy normalized continuum vibrational
wave function. However, since the amplitude of χEk ,Jj (z) is asymptotically
normalized to unity, an energy normalization factor, ρ(Ek ), must be applied.
The differential Franck-Condon factor, in units of per hartree, is
µ
F CF (vi , Ji ; Ek , Jj ) = 19.289
|χEk ,Jj (z)|χvi ,Ji (z)|2
(6)
mH Ek
where Ek is in hartree and R0 in bohr.
2.3. Potential energy curves and transition moments
The discrete and continuum nuclear wave functions, χvi ,Ji (R) and
χEk ,Jj (R), are obtained by numerical solution of the Schrödinger
equation. For the X 1 Σ+
g state, the Born-Oppenheimer (BO) potential
of Wolniewicz et al. ,7 along with adiabatic, relativistic and radiative
corrections of Wolniewicz,8 is used. For the npσ 1 Σ+
u states, BO and
adiabatic potentials calculated by Staszewska and Wolniewicz,9 and
Wolniewicz and Staszewska10 are used. In addition, relativistic and
radiative corrections, wherever available, are also applied.11 Similarly,
BO and adiabatic potentials calculated by Wolniewicz and Staszewska12
along with appropriate relativistic and radiative corrections are used for
the npπ 1 Πu states. Ab initio transition moments, D(R), calculated by
Wolniewicz and Staszewska 10, 12 are utilized for the photodissociation cross
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1
1 +
sections of the npσ 1 Σ+
u and npπ Πu −X Σg transitions. Finally, ab initio
potentials and transition moments are not available for the high n Rydberg
states. The approximate method via quantum defect theory outlined by
Glass-Maujean et al.13 can be utilized to derive the estimated BO potentials
and transition moments.
3 +
3
For the triplet states, adiabatic potentials of the a3 Σ+
g , b Σu , c Πu ,
3 +
3 +
3 + 3
3
3
3
e 3 Σ+
u , f Σu , g Σg , h Σg , i Πg , k Πu , r Πg and w Πg states and electronic
transition moments between these states have been accurately calculated by
Staszewska and Wolniewicz.14, 15 In addition, the nonadiabatic coupling of
16
Results obtained
the a3 Σ+
g state has recently been treated by Wolniewicz.
from these ab initio calculations are sufficient to evaluate the adiabatic
transition probabilities of the triplet states and Franck-Condon factors
between the X 1 Σ+
g state and the triplet states.
For the singlet-gerade states, the EF 1 Σ+
g adiabatic potential of
1 +
1 +
,
P
Σ
and
O
Σ
Orlikowski et al.,17 the GK 1 Σ+
g
g
g potentials of Wolniewicz
18
19
and Dressler and Dressler and Wolniewicz, and the H H̄ 1 Σ+
g potential
refined by Wolniewicz20 are used. Ab initio potentials of other singletgerade states21 are also utilized. The discrete transition probabilities
between singlet-gerade and singlet-ungerade states have been reported by
Liu et al.22, 23
For the doubly excited states, the potential curves for the Q1 and Q2
series by Sánchez and Martı́n24, 25 and the Q3 and Q4 series by Fernández
and Martı́n26 are utilized to calculate Franck-Condon factors. Except for
the lowest states of the Q1 and Q2 series calculated by Guberman27
and Borges and Bieloschowsky,28 electronic transition moments to the
remaining doubly excited states are not available.
The potential energy curves of H+
2 calculated or tabulated by Hunter
29
30
et al. and Sharp are used to calculate Franck-Condon factors for
dissociative ionization. The Flannery et al.31 transition moment is used to
+
2 +
calculate the photoionization cross section of the H2 X 1 Σ+
g to H2 X Σg
transition.
3. Results
3.1. Excitation to singly excited states
3.1.1. Singlet-ungerade excitation
Dissociation of H2 via singlet-ungerade Rydberg states can take place by
either photon or electron excitation. Excitation of H2 to the continuum
levels of the singlet-ungerade states results in direct dissociation that
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produces one hydrogen atom in the ground state and one in the
excited state. Apart from direct dissociation, predissociation, arising from
excitation to the ro-vibronic levels that are coupled to the continuum levels,
also takes place.
A number of theoretical calculations6, 32–34 have shown that
photoexcitation to the continuum levels of singlet-ungerade states produces
very few hydrogen atoms with kinetic energy greater than 3.5 eV. Figure 3
1
displays photodissociation cross sections of the B 1 Σ+
u and D Πu states
1 +
from various (vi , Ji ) levels of the X Σg state as a function of the kinetic
energy of outgoing hydrogen atom.
1
1 +
The B 1 Σ+
u , C Πu and B Σu states are not predissociated by other
singlet-ungerade states, though excitation to the H(1s) + H(2) continuum
1 +
is significant. Predissociation is possible for the other npσ 1 Σ+
u and npπ Πu
states. A number of experimental and theoretical investigations by GlassMaujean and co-wokers have shown that the predissociation in the npσ 1 Σ+
u
and npπ 1 Π+
u states is primarily caused by direct or indirect coupling to the
35–38
The D1 Π+
B 1 Σ+
u continuum.
u levels above the H(1s) + H(2) limit
are directly predissociated by the B 1 Σ+
u continuum. The predissociation
(n
>
4)
takes
place
by
homogeneous
coupling with the B 1 Σ+
of npσu1 Σ+
u
u
36
1 +
continuum levels. The predissociation of npπu Πu (n > 3) takes place by
1 +
1 +
1 +
either npπu1 Π+
u −D Πu homogeneous coupling followed by D Πu −B Σu
1 +
1 +
Coriolis coupling or npπu Πu − npσu Σu Coriolis coupling followed by
1 +
1 −
1 −
npσu1 Σ+
u −B Σu homogeneous coupling. The D Πu and npπu Πu states
1 +
1 +
are not coupled to the B Σu or other npσu Σu states. They can only
1 −
couple to a dissociating 1 Π−
u state. Among the npπu Πu states below
1 −
the H(1s) + H(n = 3) limit, C Πu is the only dissociative 1 Π−
u state.
1 −
Since npπu1 Π−
states
are
only
weakly
coupled
to
the
C
Π
state,
their
u
u
predissociation rates are negligibly small.
The kinetic energy distribution of hydrogen atoms produced by
predissociation of the singlet-ungerade states is similar to that from direct
dissociation. Fig. 3 shows the photodissociation cross sections from various
1 +
1
vi levels of the X 1 Σ+
g state to the continuum levels of the B Σu and D Πu
states as a function of the HI kinetic energy. From vi = 0, singlet-ungerade
excitation can only generate hydrogen atoms with Ek < 1 eV. While more
energetic hydrogen atoms can be produced from vi > 0 levels, very few
hydrogen atoms with Ek > 3.5 eV are produced from H2 singlet-ungerade
continuum levels.
Electron excitation of H2 singlet-ungerade states above ∼20 eV is
dominated by the dipole component.39 Electron impact excitation in
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1
Fig. 3. Photodissociation cross sections of the B 1 Σ+
u and D Πu state as a function
of the kinetic energy of outgoing hydrogen atoms.6,33 Top panel: excitation from (vi =
1 +
0−7, Ji = 1) levels of the X 1 Σ+
g state to the B Σu continuum. Bottom panel: excitation
1
from (vi = 0 − 7, Ji = 0) levels of the X 1 Σ+
g state to the D Πu continuum. Note that
in both cases very few, if any, hydrogen atoms with Ek > 3.5 eV are produced.
the high energy region is equivalent to photoexcitation. Electron impact
dissociation cross sections of singlet-ungerade states is obtained from
the corresponding photodissociation cross sections and the measured
electron excitation functions.6 The kinetic energy distribution of hydrogen
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atoms produced by electron-impact is similar to photodissociation, shown
in Fig. 3.
3.1.2. Singlet-gerade excitation
Electron–electron exchange excitation of X 1 Σ+
g to singlet-gerade states
is significant in the low energy region.22, 23 In the asymptotic limit, the
relative value of the electronic form factor is nearly independent of rovibrational quantum number and the Franck-Condon factor gives an
accurate representation of relative differential cross sections with respect
to kinetic energy of the outgoing HI from different initial (vi , Ji ) levels.
The discrete-continuum Franck-Condon factor thus represents the relative
kinetic energy distribution of H atoms from various (vi , Ji ) levels of the
X 1 Σ+
g state.
1 +
1 +
and X 1 Σ+
Franck-Condon factors for X 1 Σ+
g −EF Σg
g −H H̄ Σg
22
discrete-continuum excitations are very small. The dissociation of H2
is thus dominated by the second member of the singlet-gerade series, the
GK 1 Σ+
g state. Fig. 4 shows Franck-Condon factors to the continuum levels
1 +
of the GK 1 Σ+
g state from several X Σg (vi , Ji ) levels. In general, more
energetic atoms are more efficiently produced from higher initial vi levels.
The continuum levels of higher singlet-gerade states such as J 1 ∆g , O1 Σ+
g,
Fig. 4. Franck-Condon factors from various vi levels of the X 1 Σ+
g state to the
continuum levels of the GK 1 Σ+
g (Ek ) state. Note the negligible value for Ek > 3.5 eV.
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and P 1 Σ+
g all have small Franck-Condon overlap integrals with the vi = 0
1 +
1
level of the X 1 Σ+
g state, but are significant for vi > 1. The X Σg −I Πg
transition has a large discrete-continuum overlap integral for all vi . The
excitation cross sections of the high lying states, however, are generally
small.22, 40 The HI kinetic energy from these states is also mainly below
3.5 eV. We note, however, that production of <3.5 eV atoms at the exobase
produce observed sub-orbital atoms shown in Fig. 1.
Another mechanism of HI formation is via the continuum of the X 1 Σ+
g
state. This primarily involves direct excitation of the singlet-ungerade
states, followed by spontaneous decay to the continuum of the X 1 Σ+
g state.
1 +
1 +
Excitation from low vi levels of X Σg gives the strongest B Σu −X 1 Σ+
g
band system continuum emission. Continuum transitions of the B 1 Σ+
u,
1
1 +
C 1 Πu , B 1 Σ+
u and D Πu −X Σg band systems have been investigated
41
by Stephens and Dalgarno, and Abgrall et al.,42 who found that these
transitions produce hydrogen atoms with low kinetic energy.
Nonadiabatic coupling among the singlet-gerade states leads to
predissociation of some discrete levels.43, 44 Given that predissociation is
ultimately caused by direct or indirect coupling with the continuum, the
energy distribution of HI arising from predissociation should be similar to
those of the continuum levels.
3.1.3. Triplet excitation
Excitation to the triplet states by low energy electrons is a very important
dissociation channel. Except for a few rotational levels of the c3 Π−
u (0)
state, excitations to all other triplet levels eventually end in dissociation
or predissociation resulting in the production of fast H(1s) atoms. The
lowest triplet state is the repulsive b3 Σ+
u . The next higher triplet state is
,
the
lowest
triplet
gerade
state.
Excitation
of the a3 Σ+
a3 Σ+
g
g state produces
3 +
3 +
the so-called a Σg −b Σu continuum. Hydrogen molecules excited to other
3 +
higher triplet states either cascade to b3 Σ+
u or a Σg and dissociate into
3 +
fast H(1s) atoms via b Σu . Some rotational levels of c3 Πu (0) are lower in
3 +
energy than counterparts of v = 0 of a3 Σ+
g . Spontaneous decay to a Σg is
3 +
not possible for these levels. The c3 Π+
u state can be predissociated by b Σu
3 +
3 +
3 −
via Σu − Πu coupling. These levels of c Πu (0) are metastable.
The normalized kinetic energy distribution of H atoms from several
3 +
ro-vibrational levels of the X 1 Σ+
g state excited to b Σu at asymptotic
excitation energy is shown in the top panel of Fig. 5. Significant populations
of atoms with kinetic energy above 5 eV can be produced by excitation of
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Fig. 5. Top panel: relative H(1s) kinetic energy distribution from the X 1 Σ+
g (v, J)
−b3 Σ+
u dissociative excitation at asymptotic energy as determined by Franck-Condon
factors. Note that a significant portion of H(1s) atoms with Ek > 5 eV can be produced
via direct excitation from the vi ≥ 2 level of the X 1 Σ+
g state. Bottom panel: H2
3 +
a3 Σ+
g −b Σu continuum transition probabilities as a function of the kinetic energy of
3 +
3 +
outgoing hydrogen atom. In contrast to direct excitation to b3 Σ+
u , the a Σg −b Σu
transition produces low energy atomic hydrogen with negligible HI formed with Ek >
3.5 eV.
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3 +
H2 X 1 Σ+
g (vi ≥2). In contrast, the indirect excitation of b Σu by cascade
from higher triplet states through a3 Σ+
g produces hydrogen atoms with
moderate kinetic energy. The bottom panel of Fig. 5 shows the kinetic
3 +
45
The kinetic energy
energy distribution produced via a3 Σ+
g −b Σu cascade.
3 +
3 +
distribution of HI from somewhat less important g Σg and h3 Σ+
g −b Σu
3 +
3 +
transitions is similar to that of a Σg −b Σu . The highest possible kinetic
3 +
3 +
3 +
energy of HI formed from the a3 Σ+
g , g Σg and h Σg −b Σu transitions is
limited to 5.1 eV.
3.2. Excitation to doubly excited and ionic states
Doubly excited states of H2 can be viewed as a Rydberg series converging to
the excited electronic states of H+
2 (Fig. 6). The Q1, Q2, and Q3 series refer
2
2 +
to Rydberg states converging to the 2pσu2 Σ+
u , 2pπu Πu , and 2sσg Σg ionic
1 +
2
states, respectively. The excitation from the X Σg (1sσg ) state to doubly
excited states requires simultaneous change of two electron configurations
and is forbidden within the independent electron model. Photoexcitation to
the doubly excited states takes place through electron correlation. The cross
section of doubly excited states is very small. Figure 6 shows the potential
energy curves of Q1, Q2, Q3 and Q4 doubly excited states that can be
accessed by photons from the X 1 Σ+
g state. Since most doubly excited H2
states autoionize to form HI and H+ , the total excitation cross sections
to doubly excited states by electrons or photons can be estimated from
the measured dissociative ionization cross section after the contributions
2 +
of the H+
2 ionic states are removed. X Σg is the only bound state of
+
+
H2 . Excitation to the continuum levels of X 2 Σ+
g produce H(1s) and H
+
with low kinetic energy. All excited electronic states of H2 are repulsive
and excitation to these states produce fast H(n) and H+ . Figure 7 shows
Franck-Condon factors for excitation from the vi = 0 and 1 levels of X 1 Σ+
g
2 +
+
to H+
2pσ
Σ
as
a
function
of
the
kinetic
energy
of
outgoing
H(1s)
or
H
.
u u
2
The upper horizontal axes indicate the required minimum energy of the
excitation from the vi = 0 level to produce H(1s) or H+ with indictated
kinetic energy Ek . It is clear that excitation to the dissociative ionic states
can produce H(1s) atoms with sufficient kinetic energy to escape Saturn.
Glass-Maujean and Schmoranzer46 have shown that the combined
photoexcitation cross sections of the doubly excited states is only a few
hundredths of a Mb, nearly two orders of magnitude smaller than the
1 +
B 1 Σ+
u −X Σg photodissociation cross section shown in the top panel
of Fig. 3.
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Fig. 6. Potential energy curves of the H+
2 and H2 Q1, Q2, Q3, and Q4 states. Dashed
colored lines refer to the 1 Σ+
u state while continuous colored lines denote states with
1 Π symmetry. Adapted from Aoto et al.47
u
Electron impact excitation of H2 X 1 Σ+
g to the doubly excited states
takes place by interaction beyond electron correlation. Moreover, the
doubly excited states accessed by electron impact are not limited to
1 +
Σu or 1 Πu symmetry. Thus, the excitation to doubly excited states by
electrons, relative to those of singly excited states, is more significant than
photoexcitation. Experimental measurement48 and model analysis49 have
shown that the total excitation cross section of the excited ionic states and
doubly excited states−depending on electron energy — can be 5–10% of
the total singlet-ungerade excitation cross section.6, 13, 39 Electron impact
excitation can be collectively significant in the production of fast hydrogen
atoms because all the doubly excited states and excited ionic states are
repulsive.
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+
2 +
Fig. 7. Calculated Franck-Condon factors for the H2 X 1 Σ+
g (vi = 0, 1)−H2 2pσu Σu
as a function of kinetic energy, Ek , of the outgoing H(1s) or H+ fragments. ∆E at the
top of the horizontal axis refers to the minimum energy (i.e. threshold energy) required
to produce the indicated Ek from the vi = 0 level. The corresponding threshold of the
vi = 1 level is about 0.5 eV lower than that from vi = 0. The kinetic energy of the
outgoing electron is assumed to be negligible. The solid line represents excitation from
the vi = 0 level while the dotted line is excitation from vi = 1.
In addition to dissociation, autoionization rates of doubly excited
H2 are significant. The second member of the Q1 1 Σ+
u series, the Q1
1 +
Σu (2) state, has been shown to dissociate to H(1s)+H(2s) and autoionize
into H+ +H(1s) with 50% and 48% yields, respectively.46 Figure 8 shows
the atomic kinetic energy distribution for dissociation and autoionization
channels resulting from high energy electron impact excitation. In the case
of autoionization, it is assumed that the kinetic energy of the outgoing
electron is negligible and the energy is equally distributed between H+
and H. It can be seen that both channels are capable of producing
energetic hydrogen atoms and the initial vibrational quantum number has
a significant effect on the kinetic energy distribution.
4. Discussion
In addition to the production of fast HI from dissociation of H2 , dissociative
recombination of H+
3 also forms fast hydrogen atoms. As discussed
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Fig. 8. Normalized relative kinetic energy distribution of atomic hydrogen from e + H2
1 +
X 1 Σ+
g (vi = 0, 1)→Q1 2 Σu excitation at asymptotic energy. The solid line represents
the dissociation channel, which produces H(1s)+H(2s), while the dotted line represents
the autoionization channel, which forms H(1s)+H+ . Note that either channel is capable
of producing energetic hydrogen atoms and the initial vibrational quantum number has
a large effect on the kinetic energy distribution. Each production channel has been
separately normalized to unity. In the case of autoionization, it has been assumed that
the kinetic energy of the electron product is negligible.
+
elsewhere,1 H+
3 chemistry starts with the formation of H2 via charge
+
exchange of H with vibrationally excited H2 , which can be formed with
electron excitation of ground state H2 . H+
2 , produced via charge exchange
or H2 ionization, reacts with H2 to form H+
3 . Dissociative recombination
with
ambient
electrons
results
in
the
production of fast hydrogen
of H+
3
atoms.
These reactions can be summarized as:
1 +
e + H2 X 1 Σ +
g (vi : Ji ) ↔ e + H2 X Σg (vj : Jj )
(7)
H + + H2 X (vj : Jj ) → H + H2+ X (v : J)
(8)
e/hν + H2 X(vi , Ji ) → H2+ X(v, J) + 2e/e
H2+ X (v : J) + H2 X (v : J) → H3+ + H
ea +
H3+
→ H +H +H
ea + H3+ → H2 X 1 Σ+
g (v : J) + H
(9)
(10)
(11)
(12)
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The Saturn Hot Atomic Hydrogen Plume: Quantum Mechanical
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where ea refers to ambient electrons. Note that reaction (8) is exothermic
only for X 1 Σ+
g (v ≥4). The three-body channel (11), having a branchingratio of 0.64 ± 0.05,50 produces HI atoms with kinetic energy of ∼1.59 eV.
Depending on the H2 X 1 Σ+
g vibrational quantum number, the two-body
breakup reaction (12), with a branching-ratio of 0.36 ± 0.05, can produce
HI with kinetic energy ranging from 3.15 to 6.15 eV. Both measurement51
and calculation53 show that the vibrational population distribution of H2
peaks near v = 5–6, which corresponds to the most probable HI kinetic
energy of 4.4 eV to 4.5 eV.
Preliminary analysis1 has shown that the energy deposition rate of H+
3
dissociative recombination is not a significant channel on Saturn, because
of the small plasma mixing ratio. The possibility of a large number of H+
produced from excitation to the ionic states and doubly excited states was
not considered in the analysis by Shemansky et al.1 Photoabsorption cross
sections of doubly excited and ionic states are quite small. Electron impact
excitation of ionic and doubly excited states is much more efficient. If a
sufficient population of electrons with energy greater than 28 eV is present,
a significant number of H+ will be produced, increasing the formation of H+
2
by reaction (8), making reaction (12) significant. The observed H2 singletungerade emission rate and overall energy deposition will constrain the
number of electrons with Ek > 13 eV. Modeling of H2 emission and the
hydrogen plume will provide a more definitive answer.
Figure 9 compares the cross sections for formation of energetic HI
from X 1 Σ+
g (0) by electron impact excitation. The solid trace represents
the production cross section of energetic H(n) and H+ by excitation to
the excited ionic and doubly excited electronic states.49 The formation of
H(1s)+H(n) (n > 1) is a minor channel.52 The dissociative ionization
cross section shown in the figure can therefore be taken as the total
cross section of energetic HI from ionic and doubly excited states. The
3 +
dot trace with filled circles is the X 1 Σ+
g (0)−b Σu cross section derived
54–57
Note that it has been reduced by a factor
from several measurements.
3 +
20 in the figure. While the threshold of the the X 1 Σ+
g (0)−b Σu starts
at ∼4.5 eV, only cross sections above 9 eV have been reliably measured.
The b3 Σ+
u cross section peaks sharply near 15 eV, and declines rapidly
with excitation energy, with the value at 60 eV being 16 times smaller
than that at 15 eV. In contrast, the lowest threshold for double excitation
is ∼28 eV. The cross section for H(n)+H+ does not peak until ∼90 eV.
It also decreases more slowly than the b3 Σ+
u cross section, even though
both are forbidden excitations. The peak cross section near 90 eV is about
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Fig. 9. Comparison of HI production cross sections by electron impact excitation of H2
1 +
3 +
X 1 Σ+
g (0). The dotted line with circles denotes the cross section for the X Σg −b Σu
54−57
transition derived from various experimental measurements.
Note that the b3 Σ+
u
cross section has been reduced by a factor of 20. The solid line represents total dissociative
ionization cross sections from excitation to the doubly excited states and excited ionic
states, as determined from the difference between the measured total H+ cross section48
49 The * symbol
and the inferred H+ cross section from continuum levels of X 2 Σ+
g .
emphasizes that the cross section represents the formation of energetic H+ and H(n)
(see Figs. 7 and 8). The dot-dash line with filled squares refers to the electron impact
6
dissociation cross section via the continuum levels of the B 1 Σ+
u state.
a factor of 28 lower than b3 Σ+
u excitation near 15 eV. For comparison,
the dot-dash line with filled squares in Fig. 9 shows the HI production
6
cross section via the B 1 Σ+
u continuum, the largest component of singletungerade series.
Figures 7 and 8 show that the production of HI or H+ with Ek > 5.5 eV
does not require the presence of vibrationally excited H2 . The production of
HI with Ek > 5 eV via b3 Σ+
u excitation practically cannot take place from
the vi = 0 level, and requires significant population at vi ≥ 2 levels. In the
region where the intense HI plume was observed, the H2 emission spectra
did show a significant population in vibrationally excited levels.1 Several
theoretical calculations58–60 have predicted significant enhancement of the
3 +
X 1 Σ+
g (vi )−b Σu cross section with larger vi . Figure 9 clearly shows the
relative importance of the b3 Σ+
u channel and the ionic and doubly excited
channels depends on the energy distribution of the primary electrons.
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The confinement of the Saturn atomic hydrogen plume phenomenon to
a relatively small region of the southern hemisphere, correlated spatially
to the presence of enhanced non-LTE H2 EUV/FUV singlet-ungerade
emission at the base of the source of escaping atoms is indicative of an
unexplained electrodynamic extrasolar excitation process. It is not clear if
the confinement of the plume is the result of the altitude of a more generally
spatially distributed region of excitation, electron temperature, latitudinal
dependence of the escape energy or a combination of these physical factors.1
The image in Fig. 1 shows a bifurcated distribution of atomic hydrogen,
one localized observationally to within approximately 4 RS of the center,
and another constituting a background broadly distributed throughout
the magnetosphere showing a longitudinal structure fixed to local time
with substantial mass loss from the system.1–3 The confined distribution
inside 4 RS of center is much shorter lived than the broad extended
component, so that rates of atomic flux from the top of the atmosphere
are disproportionally represented in the observed steady state populations
occupying the magnetosphere. The range of processes considered in this
work are apparently needed to explain the observed distributions because
the large production of atomic hydrogen from the excitation of the b3 Σ+
u
state produces very little flux at the escape energy. The higher energy flux
from the weaker doubly excited states may be necessary to explain the
broader distribution of escaping and orbiting gas.
The present exploration of the range of transitions in H2 that end in the
conversion of the molecular binding energy and excitation of repulsive states
into atmospheric heating and escape of the dissociation products shows
that the more confined considerations by Shemansky et al.1 underestimate
the efficiency of heat deposition in giant planet atmospheres relative to
the observed EUV/FUV Rydberg system and infrared emissions. This
efficiency factor has not been accurately quantified to date, and detailed
model calculations are needed so that the relationship between energy in the
forcing process and heating from deposition can be accurately determined.
The present work provides additional relevant physical rate processes for
incorporation into these calculations.
Acknowledgments
The analysis reported in this paper was carried out at Space Environment
Technologies (SET) and Jet Propulsion Laboratory (JPL), California
Institute of Technology. XL acknowledges the support of a NASA/JPL
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424
Senior Fellowship, administered by Oak Ridge Associated Universities
through contract with NASA. DES acknowledges support by a Cassini
UVIS contract with the University of Colorado. We acknowledge financial
support through NASA’s Outer Planets Research, Planetary Atmospheres
Research and Cassini Data Analysis programs.
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