Vibrationally excited H2 in the outer planets thermosphere: Fluorescence in the Lyman and Werner bands

Plnnef.SpoceSci, Vol. 39, No. 11pp.1591-1606,1991 Printedin Great Britain.

0032-%33/91$3.00 + 0.00 PergamonPress plc

VIBRATIONALLY EXCITED FLUORESCENCE

TARIQ

MAJEED’,

Hz IN THE OUTER PLANETS IN THE LYMAN AND WERNER

JOHN

C. McCONNELL2

THERMOSPHERE: BANDS

and ROGER

V. YELLE’

~LUNAR AND

PLANETARY LABORATORY, GOULD-SIMPSON BUILDING, UNIVERSITY OF ARIZONA, TUCSON, AZ 85721, U. S. A 2D~~~~~~~~~ OF EARTH AND ATMOSPHERIC SCIENCE, YORK UNIVERSITY, NORTH YORK, ONTARIO, CANADA M3J lP3

(Camera-ready

copy received 25 September, 1991)

AbstractWe have considered the impact of fluorescence of ground state Hz on the distribution of the vibrational levels of Hz in the upper atmospheres of Jupiter and Saturn for non-auroral latitudes. For v 2 3, for the conditions studied, this is the most important source of vibrationally excited Hz compared with other sources, such as photoelectron induced fluorescence, dissociative recombination of Hi ions, and direct vibrational excitation of Hz by photoelectron impact. Combining the Voyager limb observations of Hz band emissions on Saturn, theoretical calculations of the Hz fluoresence distribution, and column constraints of Jovian Hz airglow, we estimate that some of the higher vibrational levels may have effective temperatures > 3000 K on both Jupiter and Saturn. In turn, the vibrational population of v 2 4 levels are sufficiently increased by the fluorescence source that the chemical sink for the ionization is enhanced. As a result, ionospheric densities may be greatly affected. We also show that the vertical ion flows induced by horizontal neutral winds or dynamo electric fields must play some role in maintaining the plasma peaks at higher altitudes.

the above mentioned

1. Introduction

of vibrational of the Lyman

Observation inferred

and Werner

from the analysis

indicates

of the Voyager

that Hz molecules

are excited

atmospheres

of Jupiter (Shemansky,

(Shemansky

and Ajello, of energetic

of magnetospheric latitude

regions,

of Hz

UVS

data

Hz, is excited

precipitating

origin.

However

Hz is excited

the results of Cravens,

In

induced

by

bands of Hz, rather than electron-induced (Shemansky,

in low and mid-

and mid-latitude

excitation

Cravens (1987)

performed

density distribution in the Jovian

(McGrath

et al., 1990).

model calculations

of vibrationally

thermospheric

of the

excited Hz, Hz(v),

regions

based

on vibra-

tional sources reported by Waite et al. (1983). He confirmed earlier simpler calculations by Butler and McElroy (see McElroy,

1973) that enhanced

populations

concerned latitude

mostly sources

with aurora1 excitation. that he included

The mid-

did not incorporate

(Yelle et

that photo-

of Lyman and Werner fluorescence

1985), is the major contributor Hz band emissions. of these sources,

to either or both (as evidenced will give rise to substantial

to the low

Regardless

of the

fluorescence

due

from the airglow signal)

sources of Hz(v)

although

the altitude distribution of each source is likely to be somewhat different. Model calculations, including fluorescence recently

source of Hz (v), have been obtained and preliminary

results for Saturn’s

sphere have been reported 1990).

elsewhere

To interpret the Voyager 1 (Vl)

of

Hz(v) may be large enough to have a significant impact Cravens calculations were on ionospheric densities.

fluorescence

relative importance

of solar

UV radiation (Yelle et al., 1987; Yelle, 1988) and perhaps by other sources which may have an origin due to electron

resonance

charged particles

by absorption

Yelle and co-workers

al., 1987; Yelle, 1988) have demonstrated

1985) and Saturn

hydrogen,

At the

time there was some confusion as to the energy source of these emissions. However, since the publication of

in the upper

1983; Yelle et al., 1986).

aurora1 regions molecular the impact

bands

Lyman and Werner band sources

quanta at the observed strengths.

(Majeed

Linda1 et al., 1985), current ionospheric Connell and Majeed, 1987 for references)

1591

of Hz vibrational

et al.,

and Voyager 2 (V2)

electron density, ner profiles (Eshleman

a combination

by us

thermo-

et al., 1979a,b; models (Mchave invoked

excitation

and verti-

1592

T.

MAJEED

cal plasma drift to reduce the differences between the simple photochemical diffusive models and the measured electron densities. These models parameterize the effects of vibrational excitation by varying the H+ + Hz (~24) reaction rate coefficient (cf. section 2) to reduce the magnitude of the peak in the electron densities. The vertical drift induced either by the neutral winds or dynamo electric fields is introduced to raise the altitude of the n, peak (~cConnel1 et al., 1982; Stobel and Atreya, 1983). This has an impact because of the long lifetime for radiative recombination of H+ ions. In this paper we present results of the model density distribution of Hz(v) molecules and associated vibrational temperatures for each of the 14 excited levels as a function of altitude for the upper atmospheres of Jupiter and Saturn. The results indicate that fluorescence of Hs creates Hs(v24) densities sufficiently abundant that they may have a substantial impact on ionospheric densities. These results are suggestive and by no means are definitive given the number of uncertainties in the model inputs such as atmospheric composition and temperature, sources of Hz(v) and rate coefficients of reactions that control the vibrational distribution.

2. Model A one dimensional model to calculate the density distribution of vibrationally excited molecular Hs has been developed in conjunction with an ionospheric model for the thermospheres of both Jupiter and Saturn. The model uses the neutral temperature structure and composition measurements from the Voyager WVS solar and stellar experiments. For Jupiter the atmosphere model is characterized by an exospheric temperature of 1000 K (> 1600 km) above the 1 mb level and is based on the Jovian solar occultation analysis of G. Smith (see Figure 2 in McConnell et al., 1982) and is also matched to the stellar occultation results of Festou et al. (1981). For Saturn the exospheric temperature is N 420 K (> 1500 km) above the 1 bar level (cf. Smith et al., 1983). The model allows for molecular diffusion of vibrationally excited Hs in the background atmosphere, composed of Hs and H. The values of molecular diffusion coefficients, Dt, for Hz(v) are taken from Cravens (1987). Vertical transport by eddy diffusion, K, is also included in the model although, given the values of IC used, it is of minor importance for the altitude range considered in this study. The eddy diffusion coefficients were taken from McConnell et al. (1980) for Jupiter and Smith et al. (19831 \ I for Saturn.

et

al.

2.1 Ionospheric model The ionospheric model adopted is the same as that recently developed by Majeed and McConnell (1991) and concentrates on the thermosphere where the impact of hydrocarbons may be neglected. The solar ionization rates and other chemical rate coefficients used are unchanged from the earlier work. The main source ions produced in the model are Hz and Hf produced by ionization of-Hz and H by solar EUV photons and photoelectrons; H+ is also produced by photodissociative and electron impact dissociative ionization of Ha molecules. H+ may react with Hz(v) molecules, with ~14, as originally suggested by (McElroy, 1973) H++Hs(v>4)-+Hz++H

(1)

Since no experimental or theoretical analysis is available todate, the rate coefficient for this reaction, kr, is assumed to be 2 x lo-’ cm3 s-l, equivalent to the gas kinetic rate, measured by Huntress (1974). As we mentioned in the introduction kr may be used as free parameter in the ionospheric models to explain the n, measurements. In that case, the estimated vibrational temperature, T,, for a specified value of kr would then represent a single value for all vibrational levels in the thermosphere. The values of estimated T, obtained, recently, by Majeed and McConnell (1991) for reproduction of the Voyager n, profiles will be compared with those calculated in this study (see section 4). Radiative recombination is an important, but slow, sink for the protons produced H++e-+H+hv

(2)

with a recombination rate coefficient, ks, (lO_” cm3 s-l). Hz ions produced in the upper ionosphere, by the reaction of Hz ions with ground state Hs molecules, are vibrationally excited and rapidly radiatively relax to the ground state prior to recombine with electrons (McConnell and Majeed, 1987). The ground state Hz ions then dissociatively recombine via H$(v=O)+e+H+H+H -+H;+H

(3a) (3b)

We adopt a rate coefficient of kz = 2 x lo-’ (300/T)‘.’ cm3 s-l, consistent with some experimental and theoretical results (see Majeed and McConnell, 1991 for details). However, except for the very low values proposed by Adams and Smith (1989) the results presented herein are not sensitive to the rate of ks The * indicates that Hz produced in channel 3b may be electronically or vibrationally excited. Further detail of the ionospheric model is described in Majeed and

1593

Vibrationa~yexcited3 in theouterplanets~e~osphere

McConnell (1991). L2 VibTation~l model 22.1

Sources

of vibrationaUy

ezcited

I&

The most important sources of vibrationally excited Hz are: a) photon- and electron- induced fluorescence, b) electron impact excitation of ground state Hl(v = 0) by photoelectrons or other sources of energetic electrons, and c) dissociative recombination of Hz ions. Three body association of atomic hydrogen aa a source of Hz (v) is of minor importance but is included for completeness in the model according to (4)

H+H+M-+Hz(v)+M

with a rate coefficient kq = 8 x 10-ss(T/300)-0*6 (Ham et al., 1970). It is assumed that all vibrational levels of Hz (v) are excited with equal probability by this reaction. Fluorescence source : The vibrational levels of ground state Hz may be populated via cascading from the B *Cf3 and C ‘III, states ,

Hz(B ‘C:

or C ‘II,,

v’) -+ Hz(X ‘C;,

v) + hv

which have been excited by either absorption of solar EUV radiation, hv + H2(X ‘Ci,v”

= 0) --P H2(B ‘Cp’ or C ‘&v’)

or electron impact,

In our calculations, it is assumed that the total excitation rates for the B and C states, as a function of altitude, are given by the volume emission rates inferred from the analysis of the Hz band emissions (Yelle et al., 1986) observed by the Voyager limb drift experiment on Saturn. The scale heights of these emissions are estimated to be a factor of 5 to 10 larger than the scale height of neutral atmosphere (- 200 km). Initially it had been thought that the excitation was due to energized particles (Yelle et al., 1986) but lately it has been shown that there is a major contribution from solar induced resonance fluorescence (Yelle et al., 1987; Yelle, 1988). Although there remains some disagreement regarding the relative contributions of electron and photon mechanisms (McGrath et al., 1990) the total rate of production used in the model is independent of the excitation mechanism. On Jupiter, the limb drift experiment was compromised by the intense radiation environment (Broadfoot et al., 1981). Thus to obtain the Jovian volume emission rates the observed values of Saturn were scaled

by a factor of 3.3 and the height scale was adjusted so that the same column of Hz gave the same emission rate. The absolute values were adjusted to give 2.4 kR intermediate in value between the estimated intensity from photo-induced fluorescence (e.g. 2.1 kR, see Yelle et al., 1987) and the total Hz Lyman and Werner band intensity inferred from the analysis of the Voyager airglow data of N 3 kR (e.g., Shemansky, 1985 and Yelle et al., 1987). The relative production rates for each v level, shown in Table 1, have been estimated by calculating the solar EUV flux absorbed by a column of Hz at the ambient temperature. The atmosphere used in these radiative transfer calculations is modeled as isothermal at 200 K and homogeneous with a total Hz column depth of 1 x 10” cm-‘. We calculate the absorption rate of solar photons and subsequent reemission rate in this atmosphere. Molecular parameters fox the Hz Lyman and Werner bands are taken from Allison and DaIgarno (1970). Rotational levels up to 7 are included and are assumed to follow a Boltzmann distribution at the local temperature. Vibrational levels up to 2, also redistributed thermally are included but levels other than v=O contribute very Iittle. The solar spectrum used is based on AE solar maximum reference spectra, appropriate for the time of the Voyager encounters. Scattering of solar radiation is treated as monochromatic (i.e frequency redistribution within a line is neglected) and emergent intensities are calculated with H functions. From the emergent intensities we caiculate the column integrated vibrational excitation rates. In principle, the vibrational excitation rates will vary with altitude, while the technique employed here yields only a column average. We believe that this approximation is justified considering the exploratory nature of these calculations. Based on the results of Cravens (1987), the much smaller photo-electron fluorescence source has not been included for the calculations carried out in this study. Direct electron impact excitation: The direct electron impact excitation of molecular hydrogen in its ground electronic state is an important source for the levels v = 1 and 2, but becomes less important as the value of v increases. h This source is included in the model for v = 1,2 and 3 only e+Hz(v=O)+e+Hs(v)

v = 1,2,3

(5)

The cross sections for energy less than 10 eV for this mechanism (Erhardt et af., 1968) indicate that vibrational excitation by energetic primary particles is less important than that by low-energy photoelectron or by low-energy secondary electrons. The ratios of the direct production rates for v = 1,2,3 can be estimated from the ratios of the respective cross sections at their

1594

T. MAXED et al. Table 1: Relative production of Hz(v) Lyman and Werner system.

maximum near 1 to 2 eV (Erhardt et al., 1968): 1 : 0.1 : 0.007 respectively. These ratios are almost constant for electron energies greater than a few eV. The direct production of vibrational quanta in the model is adopted from Waite et al. (1983). They calculated a source strength of 3.4 x 10’ cm-* 5-l for Ha (v) associated with the production by low energy photoelectrons produced by solar EUV radiation for solar maximum conditions. Our model uses a Chapmantype function to represent this source assuming that Hs (v = 1) peaks at an altitude of N 750 km on Jupiter and N 1250 km on Saturn with the peak excitation rate adjusted so that the column excitation rates were consistent with the above estimates. Using the above ratios for the production rates of vibrationally excited Ha with v = 1, 2 and 3, the estimated production rate of vibrational quanta as a function of altitude is shown in Figures la and lb for Jupiter and Saturn, respectively. Ionospheric source: The strength of the source of vibrational quanta associated with dissociative recombination of H$ ions depends on the relative efficiency of k3, versus ksb. For the calculations performed in this study it is assumed that ksa = 0. Thus this provides a maximum source of vibrational quanta. In addition to the uncertainty regarding the relative rates of kh and ksb, the distribution of energy among the different vibrational levels of H*(v) is currently not known. For most of the calculations it has been assumed that each level is excited with equal probability. However to check the sensitivity of the distribution of this source on the vibrational distribution a calculation has also been performed with all the source of Hz(v) in the v = 14 level rather than distributed equally (see section

4). Although recent investigations (see Majeed and McConnell, 1991 for references) have signalled a substantial uncertainty in the value of kg, this will not greatly impact the column r~ombination rate of Hz (Majeed et al., 1990) since recombination is the only loss process for Hz ions, implying that production of vibrational quanta from reaction 3b is limited by the production rate of H$. Figures la and lb show vibrational production rates from the sources discussed above. The source for the v = 1 level is dominated at all altitudes by direct electron impact excitation. The production of vibrational

quanta for v = 2 is dominated by the electron impact process between 600 km and 1450 km on Jupiter and 1100 km and 2300 km on Saturn. At other altitudes the fluorescence source is more important. For v 2 3 the fluorescence source is more important than any other source at all altitudes. Q&.2 V~bratia~al chemistry

ad

~~te~hunge

coll~io~

This section briefly discusses various processes responsible for the redistribution and the loss of vibrational quanta and follows the discussion by Cravens The processes included are Vibrational(1987). Translational (VT) and Vibrational-Vibrations (VV) interchange collisions. The vibrational energy may be converted to translational energy during the VT collisions. The energy of vibrational levels during the VV collisions is redistributed among the other levels. Vibrational quanta may be lost by VT collisions with atomic hydrogen H,(v) + H --+ Hs(v - 1) -t H

Qv-l(T) (6)

or by VT collisions with molecular hydrogen Hs(v) +

Hz + Hz(v - 1) + H2

P,v-l(T)

(7)

The vibrational quanta may be redistributed v-levels via VV collisions with Hs

Vibrational production rate (cm-3

s-l)

Figure la: Production rates due to direct electron impact excitation for vibrational levels v = 1, 2, 3 are shown as a function of altitude (dashed curve), photon-induced fluorescence,v = 1 (soiid curve), ionospheric source, v = 1 (dotted curve) for Jupiter.

Vibrationally excited H, in the outer planets thermosphere

Hz(v) + Hz(w) +

boundary

P:;.:l

Hs(v - 1) + Hz(w + I)

is chosen

(8) Here QY,Y-I(T), P,,,_r(T) and P:,::,(T) are the temperature dependent reaction rate coefficients for the

3000 km on Saturn.

forward

reactions.

good approximation

reaction

rate coefficients

Using

these

from the principle

Experimental

rate coefficients VT

collisions

are no measurements for the processes retical

with H and Hz. Since there for the rate coefficients the model uses theo-

reported

by Billing a functional

for VT-H2

and VT-H

the rate

coefficients by Capitelli

can

balancing.

1 levels

For the v >

the

for v = 1 levels are used

of VV collisions,

rate coefficients

reactions

of detailed

available

(1976). described

coefficients,

for the reverse

be obtained to describe

rate

and Dilonardo

and Fisher

(1977)

form

chemical

and Cac-

to be at 2400 km on Jupiter At the lower boundary

time constants

constants,

are shorter

the photochemical

and all excited involving

levels of Hz(v).

vertical

drift,

boundary

condition. Diffusive

the upper boundary

condition

in other

cluded in the present include

spontaneous

study.

contexts

but

are not in-

Such loss processes

emission

of quadrupole

may

radiation,

electronic excitation or ionization of Hz (v) either by solar radiation or by electron impact, and vibrational quenching glected

by hydrocarbons.

the possibilities

brational

quanta

2.3 Boundary The lmbar

We have

of VV collisions

likewise

as

and neutrals. The density are carried

calculations

of vibrationally

out self-consistently

tron densities difference eralized

as the vibrational

(1987).

model and ionospheric

equation

method

steady

solutions

by carrying

times

using a gen-

to that used for the

by McConnell

state

are obtained

and flux equations

molecules

similar

of ion densities

for long enough species

of the continuity

Newton’s The

Hz

The coupled model solves the finite

versions

solutions

excited

with the ion and elec-

such that

and Majeed

to the continuity the calculations

the solutions

out for all

are converged.

ne-

when two vi-

3.

Results

are exchanged. 3.1

conditions

lower

is taken

(i.e +* = 0) for all ions

for ions and all 14 levels of H,(v)

may be important

is not an appropri-

equilibrium

(1987). for the loss of Hz (v) that

is a

for ions

(i.e 4; = 0) as the lower

condition.

model are coupled.

are other processes

(PCSS)

equation

For such calculations

ciatore et al. (1978) has been used. Further details of these vibrational rate coefficients are given in Cravens There

state

For the calculations

wn, PCSS

the zero ion flux is assumed

and

since the

than diffusion time

steady

to the continuity

ate lower boundary

for

processes

1595

boundary

is set

level, with a neutral

at 550

km above

temperature

the

of 336 K, on

Jupiter

and at 1000 km above the 1 bar level, with a

neutral

temperature

of 120 K, on Saturn.

The upper

Vibrationally

Hs vibrational Figure

excited Hz on Jupiter densities

2 shows the calculated

each of the 14 vibrationally standard

parameters

atmosphere, efficients

described

production

etc.).

number

excited

without

flects the structure

of the production

The H,(v=l)

rate.

energy deposi(see Figure

the larger electron

In addition,

level is controlled

re-

2a).

is much larger than the densities

of any other levels reflecting excitation

for

source

rate for level v =

solar EUV radiation

density

rate co-

densities

using fluorescence

1 and occurs in the region of maximum tion for incoming

for

in section 2 (e.g. model

rates and vibrational

The peak in the Hz(v=l)

the calculations

densities

levels of Hz with

impact

the de-excitation

by VT collisions

gen and the rate coefficient

of this

with atomic

for this process

hydro-

is slower

at lower temperatures. Normally, formed

lo*

101

lo“

101 Production

101 l(r 1v Rata Km-3 S-11

10'

l(r

Figure lb: Production rates due to direct electron impact excitation for vibrational levels v = 1, 2, 3 are shown as a function of altitude (dashed curve), photon-induced fluorescence, v = 1 (solid curve), ionospheric source, v = 1 (dotted curve) for Saturn.

stant,

a peak

in the

at an altitude rd, (= Hz/D,

where

density

distribution

con-

where H, is the scale height

and

equal to the chemical

diffusion time

coefficient)

constant,

T,, (=

where kvt is the loss rate and nn is the atomic gen density). to the particular the case.

is

time

Dt is the total molecular

the diffusion

However

l/&nn, hydro-

for the level with v = 1, due

form of sources

For Hs(v=l)

becomes

vertical

and sinks, this is not diffusion

controls

the

1596

T.

distribution the peak In fact

for altitudes is formed

the vertical

distribution steady

process

for vibrational

atomic

hydrogen.

decreases

than

1050 km, but

at N 200 km below

quasi-photochemical

of Hs(v=l)

greater

below

state

quanta

assumes

this

height.

1050 km is in

where the main loss is VT

In the diffusive

collisions

region

the atmospheric

in the same manner

~~AJEED

with

titudes

scale height

and

as the background

Hs

the Jovian

thermosphere

Hs number

= 2 and v =

densities

5 are mainly

The downward

more important intermediate

for the levels

cascading

than

controlled

Thus

by VV

cascading

the contribution

v

colli-

due to VV collisions

the upward

levels.

between

is

for these to the to-

The H,(v)

density obtained

model

of vibrationally the excitation

is shown in Figure

densities

at an altitude an altitude

1987;

Majeed

of Hs(v > 5) decrease cascading

from

to the total

higher

production

et al., 1990) sharply

with increasing

vibrational rates

and the densities levels

of these

the chemical chemistry

region,

and the transition

and diffusion

occurs

contributes

levels.

the v = 1 level the peak in the distribution

v. The As for occurs

in

region between

at somewhat

higher al-

by

peak that occurs

of ++ 850 km in quasi-photochemical

Diffusion

does not compete

re-

with chemistry

until

of 1050 km is reached.

The H,(v)

densities

cur at an altitude

Cravens,

2b. In this case the

N 10% at and above the distribution gion.

excited source due

of v = 1 level are only increased

v > 5 VT

(see

to those obtained

distribution

rable and the density

with Hz are more important

are similar

by including

tal production rate for these levels due to cascading from higher levels is important. For the levels with collisions

for the levels v

(1987).

to fluorescence

The

2a). For example,

(see Figure

= 2, 4, 8, and 14 the transition region occurs at an altitudes of N 1250, 1300, 1550, and 2200 km, respectively. These results for the distribution of Hz(v) in by Cravens

the density

density.

sions.

et al.

with v = 2, 3, and 4 are compapeaks in the chemical

region oc-

of N 1150 km. The altitude

sition

region

between

diffusion

about

150 km higher

than

of tran-

and chemistry

this.

Below

occurs

this altitude

the distribution of vibrational densities is controlled primarily by VV interchange processes. For the levels with v 2 5, due to extended

nature

of the excitation

source, the peaks in the density distribution the altitude

of transition

with increasing reflecting

region.

These

density downwards

away from the peak

the fact that the loss process,

Hz, has a smaller

scale

height

occur near levels fall off

than

quenching

via

the fluorescence

source whose scale height is much larger than that for Hs (see Figures

la and lb).

Loss of H2( v 2 4) with H+ The

model

including

Hz vibrational densities calculated by sink are H+ ions as a possible vibrational

shown in Figure consistently

3. These

densities

with the ionospheric

dard parameters. and without Density (cm-3)

ions

The model vibrational

the fluorescence

3b and 3a, respectively.

acteristics

of these vibrational

shown

vibrational

in Figures

self-

using stan-

densities

with

source of Hz(v) are shown

in Figures those

are calculated densities

The general

densities

2a and 2b obtained

loss of Hs(v 2 4) molecules

char-

are similar

to

with no

with H+ ions

via ki. The Hz(v) densities are reduced by including the loss of Hs(v 14) molecules with protons in the reaction, ki. The impact

of this reaction

Hz(v) densities (cf. Figure

calculated

is more pronounced

on the

with no fluorescence

source

3a) and less pronounced

on the Hs(v) den-

sities with fluorescence source included (cf. Figure 3b). A detailed comparison of Hz(v) densities shown in Figure

3a with those shown in Figure

the densities by a factor Figure 2: Densities for all 14 levels of Hz(v) in the thermosphere of Jupiter with no H+ (or kl) are shown (a) without fluorescence source (b) with fluorescence source.

2a indicates

that

for levels v = 4, 5, and 6 have decreased of about

10, 5, and 2, respectively

respective

peaks.

decreased

by less than

also influences

The

densities 20 %.

the vibrational

at their

for levels v > 6 have The impact densities

of H+ ions

for levels with

1597

V~~ration~lyexcitedHzin theouterplanets~~e~o~bere v = 3 and v = 2, since downward cascading due to the VV-Hz collisions is important as a source of vi” brational quanta for these levels. The peak density of I&(v = 3) in Figure 3a has decreased by about 6 times the peak l&(v = 3) density in Figure 2a. Similarly a decrease of about a factor of 2 is obtained for the peak density of Hz(v = 2). The densities for v = 1 level are unchanged because electron excitation is still the major source. When the fluorescence source is included the impact of Hf ions via kl on the population of v 2 2 levels (see Figure 3b) is less important than for the case shown in Figure 3a. This reflects the fact that, for this case, the budget for the vibrational levels is determined by the strength of the Ha emission source (in our case, by the solar flux in the region of absorption) and VT and VV collisions and the smaller ion source of H+ is overwhelmed. But, as can be seen later, although there is little effect on the vibrational distribution the ionospheric densities are greatly affected. In contrast, with no fluorescence the other sources of vibrational quanta (v 2 4) are inadequate to completely overwhelm the column source of protons and decrease when proton loss is included. The peaks in the density distribution for these levels

occurs at an altitude > 1000 km. At these heights the density of level v = 4 is reduced by a factor of 2 and that of level v = 5 is reduced by N 30 % compared to those shown in Figure 2b with na H+ ions included (lc, = 0). The change in densities for the ievels with v > 5 is calculated to be < 10 %. The densities of levels with v < 4 are also affected by kl due to downward cascading of Ha(v) via VV-H2 process. This gives it decrease in the peak Ha fv = 3) density by a factor of about 2 followed by a decrease of < 40 % in the peak Hz fv = 2) density. No change in the Hzfv = I) densities is noted. The Hz(v 1 4) densities maximize in the region of 1100 km and are larger by a factor 2 50 when fluorescence source is included. The results of such an impact on the Jovian ionospheric densities will be described later, 3.2 Vibrational temperatures in Jupiter’s thermoqhem A vibrational temperature, T,, may be associated with each level, defined by the following equation: kT,

= -I&

-

~)ln(n~/n~~)

where E, is the energy of the vth vibrational level for which we have used the following expression E, = El0 {(v + 0.5) -

Density (cm-3)

Figure 3: Densities for all 14 levels of Ha(v) in the thermosphere of Jupiter including H+ (or kl) are shown (a) without fluoresceme source (b) with fluorescence smrce.

6 (v -t 0.5)2}

with Elo = 8.726 x lo-I3 ergs and 6 = 0.0278 (Capitelli and Dilonardo, 1911) for an aharmonic OScillator. n, is vibrational density for the level v and n~$ is the density for v = 0 level. Thus as an alternative to density distributions the information associated with each v level can be displayed as a vibrational temperature. The vibrational temperatures for all 14 levels corresponding to Ha(v) densities shown in Figures 3a and Figure 3b are shown in Figure 4, aiong with the neutral temperature, T,, used in the model. For the case when no fluorescence source is used (Figure 4a), the vibrational temperatures for all levels with v > 3 are significantly higher than the neutral temperature, T,, through the region considered. However the neutral temperature in the upper therm~pheri~ regions exceeds vibrational temperatures for the levels with v = 1 and 2. In the lower thermospheric regions, below an altitude of 1000 km, T, for the level with v = 2 becomes larger than T, while for the level v -= 1 becomes equal to neutral temperature. Figure 4a also shows the temperatures for vibrational levels v > 8 are about 2.5 times laxger than the neutral temperature in the Jovian exosphere. The results for vibrational temperatures shown in Figure 4b are obtained by including the fluorescence source of vibrational excitation. Since the fluorescence source enhances the densities for vibrational levels with v > 1 as illustrated in Figure 3b, the vibra-

1598

T. WED

tional

temperatures

compared

for levels with v > 2 are much larger than

temperature,

T,.

tional

temperatures

than the neutral

which are N 4 to 4.5 times larger

lower thermospheric have exceeded exospheric

regions

T,

the magnitude

In the

of some of the levels of measured

T,

in the

of Hz(v) on Jupiter

lifetimes

calculations

tionally

in the exosphere.

regions.

3.3 Chemical The

levels (v > 8) have vibra-

temperature

excited

of

chemical

H*(v)

lifetimes

molecules

of

until an altitude

negligibly

small

of 1350 km is reached.

excited

as the value of v increases

vibra-

may help in under-

standing

1200 km and for these lo*

x

cmv3.

determined

occur

heights

since the

at altitudes

H+ densities

>

are < 3

Thus for these levels the lifetimes are by deactivation processes associated with

VT and VV collisions

only. Table

2 lists the chemical

lifetimes,

T=,, for all 14 levels of vibrationally

molecular

Hz.

3.4 Effect

on Jupiter’s

Figure 5 compares of scenarios

The

Hz with H+ ions becomes

peaks in the Hz(v > 4) densities

In the upper thermospheric

regions the higher vibrational

important

loss of vibrationally

to those shown in Figure 4a. The vibrational

temperatures neutral

for these levels are also enhanced

et al.

electron

excited

densities

the model n, profiles for a number

using standard

ionization

rates

with the

the relative importance of various chemical The lifetimes for all 14 levels of vibraprocesses. tionally excited Hz molecules have been calculated at

RSS entrance n, profile (see Eshleman et al., 1979a,b for data analysis) for a latitude of 12’S, Curve A.

the altitude

of the Hz(v) density

brational

in chemical

region, for the model that includes

orescence protons.

peak which is formed the flu-

source and loss of Hz(v 2 4) molecules For this model the calculated

are shown in Figure

with

Hz (v) densities

3b and the chemical

lifetimes

for

Curve

B is the model n, profile C is the model

tional

excitation

oc-

brationally

curs at an altitude of 850 km with a density of 1.8~10~ at this altitude is close to cm -3. The gas temperature

the levels

600 K. For this

creased

tant,

level only

and VT deactivation

more important the Hz density

than

VT

collisions

by atomic

by molecular

is much greater

cm3 s-l

+ klnH+, cients

chemical neutral

At

for v = 1 level are

lifetime,

where k, represents

for either

H is N 15 times Hz, even though

for Hz and 4.3 x lo-l3

H. The calculated

are impor-

than the H density.

this height the VT rate coefficients 2.1 x lo-l5

densities

VT

cm3 s-l

T= (= l/(x

for

k,ni)

or VV rate coeffi-

gas, H or Hz, designated

by

impact excited

is illustrated

to reduce to about

the peak

factor

of 2 too large compared

than VT collisions

by H or by Hz. The estimated in Table

2. For the calculations

levels v 2 4, the contribution ing via kl becomes

important.

either

T= for these levels are of lifetimes

of vibrational

for

quench-

For the level with v

= 4 the peak in the Hz(v = 4) densities

is formed

at

an altitude of 1200 km where the density of H+ ions At this height the VT deactivais 3.4 x lo* cme3. tion by H is still

a factor

of 2 greater

than

that

due

to Hz. VT and VV collisions are equally important. The quenching of Hz(v = 4) by H+ ions of the above magnitude contributes less than 10% to the total loss rate for this level. This gives a chemical lifetime of N 270 seconds,

which is much less than the transport

time since diffusion

for v = 4 level does not become

This

strong

range,

that

electron

dena

to the peak n, observed curve

A. Per-

of model peak n, one. H+ is The source

from the fluorescence

convert

protons

combine.

is

and the electron

to Hi

ions

Simultaneously,

is sufficiently

are largely

large

unaffected.

effect of this is that in this altitude are increased

is still

kl, in the 1000 - 1500 km al-

rapidly source

in-

kl is

the ionosphere.

can rapidly

Hz(v > 4) densities

for

that

value

experiments,

of Hz(v 2 4) arising

to about peak Hi

source

the altitude

ion throughout

the fluorescence

with Hz are more important listed

titude

densities

1000 km lower than the measured

the major

which subsequently

with v = 2 and 3 the VV collisions

RSS

haps more importantly,

of vi-

densities

3b) have been

in the model

4 x IO5 cme3.

onds.

5 (see curve D). For the levels

Figure

by fluorescence

by the W-entrance

Cravens,

source

on the ionospheric

able

sufficiently

used are those shown in Figure

H,(v)

sities

strength

of N 2 (cf.

of the fluorescence

by curve D. The vibrational

ns, and kl is the reaction rate coefficient for Ha(v 1 4) with H+) for the v = 1 level is about 2.5 x lo3 secThe H+ densities

In this case the model electron by a factor

with v 2 4 (cf.

sufficiently

is about

(WD = 0). with vibra-

and loss via lcl, but with no fluores-

are reduced The

with no vi-

drift

n, profile obtained

cence source included. densities

obtained

and no vertical

Curve

1987).

all v levels are listed in Table 2. For v = 1 level the peak in the Hz(v=l)

excitation

that

the

The

net

range Hi densities

densities

are reduced

lo* cmv3 in the vicinity of 1200 km. The density in this case is about 10 times larger

in magnitude

than

the fluorescence

that

calculated

As noted above, the fluorescence a significant

effect

tron densities.

without

including

source. source of H,(v)

on the calculated

However,

this electron

ionospheric density

has elec-

profile is

unable to explain the measured RSS n, profile, curve A. The model densities can be modified and the peak in the densities

can be raised to higher altitudes

posing a vertical drift associated with dynamo fields or strong meridional winds. In Figure

6 the H+, Hz and n, densities

by imelectric

are shown

1599

VibrationalIy excited fi2 in the outer planets thermosphere

for a model that includes a fluorescence source of H,(v)

2000 1000 Vibrational Temperature

. 3t

(K)

0

0

4500

Figure 4: Vibrational temperatures for all 14 levels of Hz(v) in the thermosphere of Jupiter including H+ (or Iri) itse shown (a) without fluorescence source (b) with fluorescence source.

Table

The calculated chemical lifetimes for each vibrational the thermosphere

Peak density 1.77 1.15 7.43 6.27 4.85 2.86 1.50 6.77 3.10 1.31 5.97 2.79 1.05 1.68

and an upward vertical drift, wn, of 25 m 8-l. In this case the peak n, is located at an altitude of 1600 km, consistent with the peak altitude measured by the Vlentrance experiment. However the magnitude of the peak n. has increased from 4 x lo5 cmv3 to N lo6 crne3 compared to that shown in Figure 5. This increase in n, is a result of the H+ being flowed to a region where the densities of H~(v 2 4) are not sufficient to destroy most of the H+ produced (cf. Figure 3b) . Basicaliy the column of H+ produced has been lifted to the ion peak by the drift velocity but the column production of vibrationally excited quanta above this level is less than that in the lower thermosphere and is inadequate to supply the loss of H+ required to reduce ionospheric densities. Thus, in this case, the production of vibrational quanta is rate limiting and Hz(v) densities are affected more than the H+ densities. The level most affected is v = 4 at and neas the ionospheric peak, where the loss of I&(v = 4) molecules with protons is about a factor of 3 greater than the total vibrational loss via VT and VV interchange collisions. Similarly the levels with v = 5 and 6 are also affected by increased proton densities. The loss of Hz (v = 5) molecules with protons is about a factor of 2 greater than the total loss associated with VT and VV quenching. However the loss of Hl(v = 6) molecules is almost the same as the total vibrational loss. For the higher levels such &s v 1 7, the loss of Hz(v) with protons contributes less than 30% to the total loss rate for these levels. Thus

x x x x x x x x x x x x x x

106 lo4 103 lo3 lo3 lo3 lo3 lo2 lo2 lo2 lOI 10’ 10’ loo

Peak altitude

‘-i!may-densityj H2 density

(km)

850 1150 1200 1200 1250 1300 1400 1500 1600 1700 1800 1950 2050 2100

1.95 1.59 1.59 1.31 1.08 7.52 5.31 3.80 2.75 2.01 1.27 9.44 8.15

x x x x x x x x x x x x x

108 108 108 108 108 lo7 107 lo7 lo7 107 lo7 10” lo6

1.77 1.21 1.21 8.33 5.81 2.90 1.48 7.78 4.15 2.25 9.15 5.09 3.81

x x x x x x x x x x x x x

109 109 109 108 lo* 10s 108 lo7 107 lo7 106 10” lo6

1

2.50 3.30 6.46 2.70 3.00 2.70 1.85 1.14 7.77 4.92 3.10 2.45 1.50 9.10

7,

(4 x x x x x x x x x x x x x x

lo5 102 lo2 lo2 102 lo2 lo2 102 10” 101 101 10’ 101 100

T. KNEEDet al.

1600

H,(v) densities for v = 4, 5, and 6 levels am reduced near the ionospheric peak (see Figure 6b) compared to those shown in Figure 3b. This also reduces the associated H$ densities in the ionospheric regions. Due to reduced Hz(v > 4) densities (or rate of supply) the effect on the ionospheric electron densities is negligibly small at and above 1000 km altitude (cf. Figure 6a). For fluorescence to cause an impact at these levels with a concurrent upward drift a stronger source of vibrational quanta would be required at and above the level of the n, peak.

500

Density

(cm-3)

Figure 5: Model n, profile for 12*S compared with the RSS Vl-entrance profile, curve A. Curve B is the model fit with kr = wn = 0. Curve C is the model fit with kr included but no fluorescence source added. Curve D is the model fit with Auorescencesource.

3.5 Vibrationally He ~bFatio~a1

excited Hz on Saturn densities

The calculated density distribution for vibrationally excited Hz(v) in the thermosphere of Saturn has also been obtained using similar sources as those used for Jupiter. The results with and without Auorescence source are shown in Figures i’b and 7a, with no H+ loss via kr. The general characteristics of these results are similar to those obtained for the Jovian thermosphere. For Hz(v = 1) the density peak is > 10’ cme3, and is located at an altitude of - 1300 km; it occurs in the region where energy deposition associated with solar photons maximizes the excitation rates. These peak densities are similar to those obtained for Hs(v = 1) in the thermosphere of Jupiter, even though the source for this level is reduced by a factor of - 3 on Saturn. The reason is that the main loss of Hs(v = l), due to VT quenching by H, is reduced by a factor of - 3 both as a result of the lower temperatures that obtain for Saturn and since the H densities in lower thermospheric regions of Saturn are more than an order of magnitude smaller than the H densities in

Figure 6: (a) Model n, profile for 12’S compared with the RSS W-entrance profile, curve A. Curve B is the model fit with fluorescencesource and WD = 25 m s-l. (b) The correspondingHz(v) densitiesfor all 14 levels used in (a).

Jupiter’s lower thermospheric regions. As for Jupiter, the Hz number densities for the levels between v = 2 and v = 5 on Saturn are mainly controlled by VV collisions involving exchange of a single vibrational quanta between the neighbouring vibrational levels. All these levels have comparable densities with peaks - lo3 cmm3 near an altitude of 1700 km. Chemistry controls vibrational distribution below - 2200 km altitude with diffusion controlling the distribution above this level. Thus the transition region occurs - 500 km above the altitudes where the peaks occur. For the Hz(v) densities with v > 5, vibrational quenching via VT processes with Hs is important and very rapid for higher vibrational levels. As a result, the H&v 1 5) densities decrease sharply with increasing vibrational level, (cf. Majeed et al., 1990). The altitudes of the peaks in the density distribution occur higher in thermosphere since chemistry becomes faster as the value of v increases. Thus the peaks in the distribution for v > 5 levels occur in the chemical region and diffusion becomes important several hundred kilometers above the altitudes of these peaks. For example for v = 7, 10, 14 the transition region occurs at an al-

VibrationallyexcitedH, in theouterplanetsthermosphere titude of N 2200,2500, and 3100 km, respectively (see Figure 7a). Figure 7b shows the impact of fluorescence source of Hz(v) on the density distribution shown in Figure 7a. The densities for the v = 1 level are only increased by N 10% except at the bottom boundary where increased densities reflect the stronger fluorescence source (cf. Figure lb). The densities for the levels between v = 2 and v = 5 are increased by a factor of N 30 and those for the levels with v > 5 are increased more than 10 to 20 times at their respective peaks compared to vibrational densities obtained with no fluorescence source (cf. Figure 7a). In this case, due to extended nature of source, the peaks in the density distribution for the levels v 2 6 occur near an altitude where the chemistry is balanced by diffusion and for the levels v < 6 occur several hundreds of kilometers lower that altitude. Loss of Hz(v 2 4) with HS ions Figure 8 shows results of the impact of reaction lcl

1601

on the Hz(v) density distribution with and without the fluorescence source. Similar to the caSes shown above, the peaks in Hz(v) densities obtained in Figure 8 are in chemical region and the altitudes where diffusion begins to compete with chemistry occurs N 1 to 2 scale heights above the altitudes of the peaks. Comparing Hz(v) densities shown in Figure 8a with those shown in Figure 7a (with k, = 0), the densities of Hz(v = 1) are almost unchanged. The densities for v = 2 level are reduced by about lo%, and those for v = 3 level are reduced by about a factor of 2 at all altitudes. The largest change has occurred for the H~(v = 4) densities, which are reduced by about an order of magnitude at the peak. The H,(v) densities with v = 5 and v = 6 are reduced by about a factor of 7 and 3, respectively. For the levels with v > 6 the change in the densities is less than 20%. The comparison of Hz(v) densities shown in Figure 8b with those shown in Figure i’b (with kl = 0) indicates almost no change in the Hz(v = 1) densities.

omsityIt-31 Figure 7: Densities for all 14 levels of Hz(v) in the thermosphere of Saturn including no H+ (or kl = 0) are shown (a) without fluorescence source (b) with fluorescence source.

Figure 8: Densities for all 14 levels of Hz(v) in the thermosphere of Saturn including Ht ions via kl are shown (a) without fluorescence source (b) with fluorescence source.

T.

1602

The

Hz(v)

densities

decreased factor

with

20 - 25%.

However,

level v = 4 are decreased

the Hz(v) by about

of 2 near the peak and the densities

v = 5 are decreased v > 5 the Hz(v) than

10%.

by about densities

As for Jupiter

loss indicates

vibrational

quanta

30%.

For the levels with by more

the small changes

that

with the introduction

that

the column

is greater

a

with level

are not changed

cur in the Hz(v) densities proton

et at.

with levels v = 2 and v = 3 are

by less than

densities

MAJEED

oc-

of the

production

of

than the column produc-

tion of protons. 3.6 Vibrational

temperatures

The calculated thermosphere and without

vibrational

of Saturn fluorescence

tral thermospheric comparison.

in Saturn’s

thermosphere

temperatures,

T,,

0

in the

looo

530

Vibratlonl

are shown in Figure 9 with source. The measured neu-

temperature,

T,

the temperatures

are greater

than the neutral

the higher

vibrational

2ooo

hpu&,r.

Moo

.mo

IKI

is also shown for

For the case when no fluorescence

is present,

lsoo

source

for all vibrational temperature

levels

and some of

levels reach temperatures

of N

2500 K in the exospheric regions. These temperatures T, are N 6 times larger than the neutral temperature, (see Figure 9a). Similar results atures tion

are obtained

when fluorescence is included

fluorescence tional

(cf.

9b).

source enhances

the higher

regions

vibrational

in comparison K obtained

case since

the population

for vibra-

vibrational

the temperatures

lifetimes

The calculated sity distribution

of -

420

UVS data.

on Saturn

lifetimes

level at the peak in the Hz(v) den3. The calculated

for these levels are shown in Figure

As noted above for the v = 1 level only VT colli-

sions are important,

and that VT deactivation

4 times more important

thermosphere. calculated For the important by Hs and the loss of tivation increases.

The

by H is

than by Hs in the Saturn’s

chemical

lifetime

for this level is

to be - 2 x lo4 seconds. levels with v 2 6, VT collisions are more than VV collisions. Thus VT deactivation H are the main processes that account for H,(v) molecules with v 2 6. But VT deac-

by H becomes For example,

less important

as the value of v

the removal of Hz(v) molecules

with v = 6, 9, 12, and 14 by VT-H

deactivation

Figure 9: Vibrational temperatures for all 14 levels of Hz(v) in the thermosphere of Saturn including H+ ions via kr are shown (a) without fluorescence source (b) with fluorescence source. peaks in the density

of Ha(v) molecules

are shown in Table

density distribution

in

for some of

temperature

of the Voyager

of H,(v)

chemical

for each vibrational

tem-

Thus

levels are as high as N 3500 K

with the neutral

by the analysis

9.7 Chemical

excita-

In this

for these levels are also enhanced.

the exospheric

-

Figure

temper-

of vibrational

levels with v > 1, the resulting

peratures

8b.

for vibrational

source

con-

tributes about 40%, 20%, lo%, and 3% to the total loss rate for these levels. As noted above the altitude of the

of v increases,

ing via VT processes > 6) molecules

distribution

and as a result

increases

as the value

the vibrational

with Hz enhances

at those altitudes.

quench-

the loss of Hs(v

Thus the chemical

lifetimes for these levels become smaller and smaller as the value of v increases (see Table 3). For the intermediate levels 2 5 v 2 5 the VV processes involving exchange of a single vibrational quanta between the neighbouring vibrational levels are very important (cf. Cravens,

1987; Majeed

3.8 Effect The Figure

et al., 1990).

on the Saturn’s

model

calculations

10 for a number

with the n, profile, sis of the Voyager

electron

density

of n, profiles of scenarios

curve A, obtained radio occultation

are shown in

and are compared from the analy-

data for a latitude

of 31‘S (See Lindal et al., 1985 for data analysis). The model n, profile with no vibrational excitation is shown

1603

VibrationallyexcitedH, in theouterplanetsthermosphere

Table 3: The calculated chemical lifetimes for each vibrational level in the thermosphere of Saturn. V

i

2 3 4 5 6 7 8 9 10 11 12 13 14 -

Peak density (cmm3) 2.24 x lo6 6.74 x lo3 7.16 x 103 1.15 x lo3 8.19 x lo3 3.99 x lo4 1.65 x lo3 6.28 x lo2 2.39 x lo2 8.24 x 10’ 2.86 x 10’ 9.37 x loo 2.13 x loo 1.51 x 10-l

Peak altitude

04

1350 1800

1800

1800 1900 2000 2100 2250 2400 2500 2600 2750 2850 2950

H density ( cmp3) 7.87 x 107 2.74 x lo7 2.74 x lo7 2.74 x lo7 2.15 x lo7 1.68 x lo7 1.31 x lo7 8.96 x lo6 6.11 x 10” 4.72 x lo6 3.65 x 10” 2.48 x lo6 1.91 x lo6 1.68 x lo6

by curve B; this yields a peak n, of N 2 x IO5 crnm3 at an altitude of N 1200 km. Curve C shows the effect of vibrational excitation but with no fluorescence source included. The calculated electron densities are reduced by a factor of = 2 at and above the ionospheric peak. Similar results are also obtained by Atreya et al. (1984). The impact of the fluorescence source of B,(v) on the ionospheric densities is shown by curve D. In this case the source of vibrational quanta for the levels with v 2 4 has been increased sufficiently by fluorescence that the reaction with protons via kr is able to

/

j

Figure 10: Model n, profile for 31’S compared with the RSS VS-exit profile, curve A. Curve B is the model fit with kr = wn = 0. Curve C is the model fit with kr included but no fluorescence source added. Curve D is the model fit with Auorescencesource.

H2 density ( cmT3) 3.04 x 1o’O 2.67 x 10’ 2.68 x log 2.68 x log 1.61 x lo9 9.70 x lo8 5.86 x lo8 2.76 x lo* 1.31 x 10s 7.96 x lo7 4.86 x lo7 2.32 x lo7 1.42 x lo7 1.11 x lo7

rc 2.SE 1.15 1.67 1.93 2.24 1.82 9.25 5.56 3.29 1.52 6.90 4.00 1.50 6.00

x x x x x x x x x x x x x

104 lo3 lo3 lo3 lo3 lo3 lo2 lo2 lo2 lo2 lo1 10’ lo1 loo

reduce the peak in the model n, to a value of 1.4 x lo4 cme3, comparable to that shown by the measured n, profile, curve A. However the altitude of the peak n, is still N 1000 km lower than the measured one. H+ is the major ion at the ionospheric peak but Ht dominates the electron densities in the 1500 - 2500 km altitude range due to increased loss of El+ ions with Hs(v 2 4) molecules. However, for different Hg recombination rate coefficients (cf. Mitchell, 1990) the relative distribution of H+ and Hz will change but without changing the main features of the curve. An attempt to obtain a n, peak at the similar height to that of the RSS data, using vertical drift, is shown in Figure lla. The ionospheric densities, H”, Hz, and n, are those calculated self-consistently with the fluorescence source included. A vertical drift of 15 m s-l raises the ionization peak from an altitude of w 1200 km (cf. Figure 10) to an altitude of N 2200 km in the presence of enhanced population of Hz (~24) molecules. The calcuIated density distribution for these levels is shown in Figure llb. The magnitude of the model n, peak at an altitude of 2200 km is nearly the same as that suggested by the RSS measurements, curve A. The model n, scale height above the peak is greater than the measured one. H+ is the main ion at and above the n, peak. Below 2000 km altitude the Hi ion becomes the main ion with a secondary peak of N lo4 cmm3 in the source region. Thus using the measured fluorescence source and measured H densities it seems possible to approximately reproduce the main features of one of the RSS

T. MAED

1604

3000

1000 I

‘,‘,...’

“..,..I

.‘,.,.,I

I “...,,I

“..“’

a

Density (cm-@

Figure 11: (a) Model n, profile for 31°S compared with the RSS VZexit profile, curve A. Curve B is the model fit with fluorescencesource and WD= 15 m s--I. (b) The correspondingHZ(V) densitiesfor all 14 levels used in (a). n, profiles, i.e. its height and peak density using only a modest vertical drift as an adjustable parameter. However, the topside scale height calculated is much too large suggesting control by processes other than diffusion. 4. Discussion

4.1 Vibrational temperatures: A comparison As mentioned in section 1, the Voyager n, measurements can be reproduced by using the estimated T, for a given value of kI. For this case a single value of T, is obtained for all levels with v > 4 at all altitudes. Based on the detailed calculations presented in this paper, it seems that a Maxwell-Boltzmann distribution cannot accurately describe the vibrational distribution of Hz, although vibrational temperatures provides a concise way of representing the H,(v) densities. The single vibrational temperatures for the thermospheric regions of Jupiter and Saturn, required to fit the measured n, profiles, are given in a recent paper by Majeed and McConnell (1991). As one can see in section 3, the most important levels of H,(v) that affect the ionospheric densities are

etai. those with v = 4, 5, and 6; levels with v > 6 have almost, no impact on the ionospheric electron densities because proton loss associated with these levels is not important due to their low densities,. The T, at the measured ionospheric heights (1600 km for the Vlentrance) for the levels 3 < v < 7 is calculated to be in the range 1300 K - 1800 K on Jupiter when no fluorescence source of Hz(v) is assumed (cf. Figure 4a). The inclusion of the fluorescence source increases T, for these levels to 1700 K - 2800 K at the same heights (cf. Figure 4b). Comparing these vibrational temperatures with those estimated for a specified value of kl, to explain the measured Jovian n, profiles (cf. Majeed and McConnell, 1991), we find that they are in the range of vibrational temperatures calculated above, particularly when the fluorescence source of Hz(v) is included. Similar results obtain for the Saturn’s thermosphere. The calculated vibrational temperatures for the levels with v = 4 to v = 6 near the measured ionospheric peak are in the range 1300 K - 2000 K with no fluorescence (cf. Figure 9a) and 1800 K - 2600 K (cf. Figure 9b) with the fluorescence source included, The value of T, estimated from an equivalent valuepf kl used in the standard ionospheric model of Majeed and McConnell (1991) is also within the range of vibrational temperatures calculated above. 4.2 Uncertainties

in vibrationally excited Hz

The model calculations presented in this study confirm and extend the work of Cravens (1987) on Jupiter and Majeed et al. (1990) on Saturn. These authors demonstrate the existence of significantly enhanced populations of vibrationally excited Hz in the upper atmospheres of Jupiter and Saturn due to the strong source of vibrational quanta provided by the fluorescence of Hz. They aIso show that Hz(v 2 4) densities are very important in enhancing the chemical sink for IIt ions and, as a result, ionospheric structure may be extensively modified if the standard rates described in section 3 are used. However, there are uncertainties associated with the vibrational sources and with the VT and VV rate coefficients. These uncertainty are addressed in the remainder of this section. The photon-induced fluorescence source of vibrationally excited Hz on Saturn was inferred from the analysis of the limb profile of Hz band emissions, observed by the Voyager limb drift, experiments on that planet (Yelle et al., 1986). This experiment was unsuccessful on Jupiter due to intense radiation environment (see Broadfoot et al., 1981). Thus for Jupiter’s thermosphere the fluorescence source of Hz vibrational excitation was appropriately scaled by using an altitude dependent volume emission rates observed on Saturn (cf. Yelle et al., 1986) but at the same time constraining the column emission of Ha bands to agree with the

Vib~tion~y

excited H, in theouterplanetsthermosphere

observed intensities (Shemansky, 1985 and Yelle et al., 1987). Thus although the column source rate should be reasonable this procedure represents a source of uncertainty in the volume emission rates. There are also uncertainties as to how the various vibrational levels are populated for some of the production processes. The vibrational distribution for production of vibrationally excited Hs via electron excitation fluorescence of Lyman and Werner bands is reasonably well known (cf. Waite et al., 1983), but the distribution of vibrational production from dissociative recombination of Hi ions is not yet known. It is only suspected that the product Hs molecules would be highly excited the vibrational levels if this channel is open (Mitchell, 1990). Thus the model was used to calculate the H,(v) densities assuming that the vibrational quanta were all produced in the v = 14 level. The results (not shown) are similar to the model calculations carried out by Cravens (1987). The results suggests that there could be larger enhancements in Ha(v) for higher v values, but for lower levels the enhancement would seem less important. Since the source of vibrational production is located in v = 14th level, the VV cascading brings down all the vibrational production from the higher levels to the lower levels whatever is the initial vibrational distribution of the production. Many of the chemical rate coefficients adopted in these model calculations are not well known. But the results presented in this study are certainly suggestive although by no means definitive. The rate coefficient, k,, for the reaction of H+ + H&v 2 4) has not been measured. However it is assumed that the measurements for ki will not be too different from the gas kinetic rate adopted in these calculations. Although the VT and VV rate coefficients for the relaxation of the v = 1 level used in this study are largely based on experimental evidence, the remaining rates are based on theoretical extrapolations as described in section 2. Some of the rate coefficients for the upper levels are much larger than gas kinetic rate. Thus test calculations were done to check the sensitivity of the H,(v) density results for reasonable variations of the rate coefficients for the VT-HZ and VV-Hs processes and confirmed the exploratory calculations of Cravens (1987).

5. Summary We have presented model calculations for the density distribution of H,(v) molecules and related vibrational temperatures (TY) of ground electronic state of Hs (X*C:), in the thermospheres of Jupiter and Saturn. The calculations of Hz(v) and the ionospheric densities are coupled seif-consistently in a ID chemical

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diffusive model. The calculations confirm and extend the work of Cravens (1987) and Majeed et al. (1990). We find that the most important source of Hs(v 2 3) is the fluorescence of ground state Hs induced either by absorption of solar photons or by electron excitation. In our calculations we have assumed the details of the distribution of quanta given by the calculations of Yelle (1988). For both Jupiter and Saturn the strength of the source is firmly based on experimental evidence. Further, for Saturn the details of the height variation of the source is based on the Voyager limb observation of Hz band emission (cf. Yelle et al., 1986). For Jupiter the column production is constrained by the observations of Hz Lyman and Werner band emission (e.g., Shemansky, 1985 and Yelie et al. 1987). For levels v 5 2 electron excitation of Hs is the most important source of I&(v) molecules (Cravens, 1987). The fluorescence source is so strong that Hs(v 1 4) densities are enhanced sufIlciently that under conditions of no plasma drift they can control the plasma density on both Jupiter and Saturn. The model calculations still cannot reproduce the ionospheric vertical structure without invoking vertical plasma drift due either to electric fields or meridional neutral winds. With the inclusion of vertical drift we find that our model cannot reproduce electron densities of the correct magnitude at Jupiter. However, for Saturn the model results can account for the correct magnitude and height of an observed ionospheric profile, although the topside scale height is not well reproduced. We have also compared T,, calculated in this study, for the levels v 2 4 with the values of T, estimated, for a specified value of ki, by Majeed and McConnell (1991) to explain the n, measurements. We show that these estimated values of T, are in a reasonable accord with the calculated T, for the thermospheres of Jupiter and Saturn.

A~~n~w~~~~~e~~~. TM and RVY have been ported from JPL contract 957763 under NASA contract NAGW-918 to the University of Arizona. TM also wishes to acknowledge partial support for this work by the Space and Terrestrial Physics Laboratory (STPL ) of the Institute of Space and Terrestrial Science (ISTS) in Ontario, Canada. JCM wishes to thank the Natural Science and Engineering Research Counsil (NSERC) of Canada for continuing support. JCM would also like to thank the Institut d’Astrophysique Spatial, CNRS, at Verrieres le Buisson for support. s

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T. MAJ~ et al.

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