The zonal distribution of hydrogen in the Jovian atmosphere

I(

.xRI'S

611, 64!)

65"~ (19;~4)

The Zonal Distribution of Hydrogen in the Jovian Atmosphere ROSEMARY M. K I L I . E N ANn)JOSEPH W. C H A M B E R I . A I N l ) c p a r t m c n t ,?l.S'pacc I'hv~ic.~ and A.~tr, momy. Ri~ c I/nit'cr.~itv. tlo,.~ton. "lcu~.~ 77251

Received ()ctohcr 7. 198~: revi,,ed .,\ugtl,d 2!1. 1984 l h e Voyager udtraviolet '~pectrometer disclosed strong longitude variation in the midlatiludc I.yman alpha brighlnesn of Jupiter. Minimum brightnesnes of 16 and 14.4 kR were observed llonl Voyagers I and 2. respectively, v, ith the inten,,il.v rising to peaks ot" 21 ~,nd 19.6 kR at a longitude near I 1 0 . ()bscrvations of Jo,,ian I.ynlan alpha, nl.:Ldc with the International [Jhraviolel Explorer l i t / E ) beginning in l ) e c e m b c r 1978. and continuing lhrough January 1982. ab, o show it region of persistently e n h a n c e d but ,.affable flux near a longitude. A. of IIR); however, ll..JE mea,~ured brightne~,ses are consistently Iou.er than those of Voyager. A h h o u g h the l.yman alpha flux t'ron] Ihc " ' n o r m a l " region of the plant hclv,een h 200 and 300': remained nearl.,, constant during the period of lhe l[_i[:~ observations. Ihat fronl the "'perturbed" region centered on x I ll)' varied by ' 25',: from Ihc mean. The source,, of l..,, man alpha Ihnx include resonance xcatlermg of solar and interphmetau~, l . y m a n alpha, and excitation by charged particle precipitation, l'hal portion of Ihe day~,ide flux due to charged particle excitation ha', been variou,~l~, estimated at betv, een 2.3 and 7 kR. About I kR t~l lhc dayside flux i,, due Io rc~,onance , t a t t e r i n g of the sky background. It i', a~sunlcd that H and an absorber (('||a) are di~,tributcd above the h o m o p a u s e according Io tile local height distribution of temperature. The daytime equalion t)f radiative transfer is solved to determine the longitudinal distrihution of I're¢ly ,,tattering attomic h}drogcn Ihat would actor|n! for the observed flux. Tills daytime xolution s h o w s lhal it the h>duogen bulge is the ICMII! of localized heating :.md ;.t c~.Hl~,C quenl increase in ,,tale heighl, the temperature in Ihe perturbed region must he i|bont IIRYK ,aarmer than that in the normal region. The nightside l..vman alpha brightness exhibit', a hmgitude ',ariation very similar to thal on the dayhide. The tt diMribution derived from the dayxide solution is used with the nighlsMe llux to estima!e Ihe hmgilude variation of particle precipitation on the night Male. , I'JX4 '~cadcnu~Pie... Int,

INIRC)I)L 'CTION

The ultraviolet spectrometers on board the Voyager spacecraft discovered a pronounced kmgitudinal asymmetry in the l.yman alpha brightness of Jupiter (Sandel ~,t a/.. 1980). The observations show a peak intensity centered at about I I(F west longitude (System III, 1965) and corotating with the planet. It remained nearly constant in the 4 months between Voyagers I and 2. Observations of Jovian l,yman alpha made by the International Ultraviolet Explorer (IUE) covering a 3-year period bracketing the Voyager flyby also show a persistent l,yman alpha bulge centered at about am ~II0°; however, the IUE observations are consistently lower than those of Voyager and show that, while the flux from the nor-

nml sector remained nearly constant during the observation period, the flux from the perturbed region varied by ±25% from the mean (Skinner el al.. 1983). These observations are summarized in Table II. We have used the Lyman alpha intensities measured by Voyagers 1 and 2 (Sandel el a/.. 1980) and by IUE (Skinner e t a / . , 1983) to deduce the distribution of atomic hydrogen in the Jovian atmosphere, assunling that the sources of the dayside Lyman alpha include resonance scattering of solar Lyman alpha, resonance scattering of the interplanetary Lyman alpha radiation, and direct excitatkm by charged particles. We assume thai I kR of the dayside flux is due to resonance scattering of a sky background source (McConnell el al.. 1980L 1-arly attempts to estimate the cohnmn

¢~4q) 0 0 1 9 - I0 ~,5,'84 $:t.(X) ( op%rtJ2hl . l'JX4 h~ ~Litd{*llllk '%11 n l ~ t l l x ,11 icJ31odli~ll~lll

I'nc-,. Im

ill ;111% hlrlll ] ~ ' x ~ ' l ~ d

JOVIAN HYDROGEN DISTRIBUTION density of atomic hydrogen in the Jovian atmosphere employed the assumption that the observed dayside flux was entirely due to resonance scattering of solar Lyman alpha. Carlson and Judge (1971) computed the column emission rate as a function of the optical depth of H above a completely absorbing surface. Wallace and Hunten (1973) included a lower boundary in which H and CH4 were uniformly mixed by eddy diffusion from below. Clarke et al. (1980) investigated spatial variations in Lyman alpha using sounding rocket data obtained I December 1978. They employed a simple black-white model similar to the Carlson and Judge model with the added refinement of an empirical solar line profile. The nightside problem was solved by McConnell et al. (1980) by assuming that the flux observed on the nightside is due to resonance scattering of sky background Lyman alpha and direct excitation by precipitating protons or electrons. They also assumed a homogeneous conservatively scattering layer above a completely absorbing surface. Yung and Strobel (1980) evaluated a photochemical model of the Jovian atmosphere and concluded that the contribution to the dayside l,yman alpha flux due to direct particle excitation was insignificant compared with that due to resonance scattering of sunlight. More recently, however Shemansky and Ajello (1983) have analyzed the particle excitation of Lyman alpha using more accurate excitation cross sections and including higher Rydberg series band systems for H2 Lyman and Werner bands. Their analysis of Voyager 1 Saturn equatorial spectra indicates that about 1.4 kR, or 28% of the flux. is duc to direct particle excitation. We have scaled this estimate to the Jovian I,yman alpha flux, and have estimated that 2.3 kR of the IUE measured brightness is due to particle excitation. Gladstone and Shemansky (1983) reanalyzed the Jovian spectra and concluded that up to 7 kR of the dayside flux at the time of the Voyager encounter may be due to direct excitation by charged particles. We have assumed a minimum of 2.3 kR and a maxi-

641

mum of 7 kR of the dayside flux measured by the Voyager ultraviolet spectrometer (UVS) was due to direct excitation of I~yman alpha by charged particles. Temporal variations in Jovian Lyman alpha emission have been discussed by Skinner et al. (1983). We do not extensively discuss these variations except to give a range of values for the H column densities implied by the Voyager and IUE observations. Table I of Atreya et al. (1982) summarizes the Jovian Lyman alpha observations taken between 1967 and 1980. We have adapted the Chamberlain and McEIroy (1966) solution of the daytime transfer problem for an inhomogeneous atmosphere to an atmosphere with two constituents, H and CH4, in diffusive equilibrium. This analytic solution was used as a test for a multiple scattering program based on the doubling-adding method extensively developed by Hansen and Hovenier (1971) and initially coded by Hansen and Travis (1974) at the Goddard Space Flight Center. We used the multiple scattering program with the daytime albedo to derive the distribution of hydrogen with longitude. Finally, we used the distribution of freely scattering hydrogen with longitude, along with nightside Lyman alpha intensities measured by the Voyager spectrograph, to estimate the longitudinal distribution of particle flux on the nightside. ]'HE ANA1.YTIC SOLUTION If the CH4/H mixing ratios for the Jovian atmosphere were constant with height, we could find the l.yman alpha albedo directly from the solution of the transfer equation for reflection by a sunlit, homogeneous, semi-infinite atmosphere (Chandrasekhar, 1950): r-rcf ~" 7rr ,. = ~ (o,Fin~ H(l~o) f dp. p. l/(p.),

(i)

where H is the Chandrasekhar t l function, /~ is the cosine of the incidence or reflection angle, and k "me is the incident flux per unit frequency interval. We have defined the single scattering albedo, oSv, as

642

KII.I.I';N AND CHAMBERI.AIN N( H )czd t t )

o),. - IN(H)o¢,(H) + N(CH4)(~(CH4II.ya)I (2) where the N ' s are concentrations. The
(3)

where X is a scale factor to be determined and ~'1~) is the optical depth tit height :. We used their solution to derive tin equivalent t l function, ll(T~,l.t), tO describe the emergent radiation from the top of a two constituent a t m o s p h e r e in diffusive equilibrium. l)etails of the derivation arc given in the appendix. We used the analytic solution as a test for our c o m p u t e r program and obtained excellent agreement for those portions of the line that should be appropriate for the analytic approximation. The analytic solution ix inappropriate for the far wings of the line where the single scattering albcdo, o), is so small that only a few scatterings occur before a photon is absorbed or escapes from the a t m o s p h e r e .

] l i e NUMERICAl. S()IA.IION An exact solution of the radiative transfer problem for Jovian Lyman alpha has been obtained using a doubling-adding method. The method was extensively' developed for isotropic scattering by van de llulst (1963) and extended to include polarization by Hansen and Hovenier (1971). It was coded for computer in essentially' the form we use by Hansen and "]'ravis (1974). In addition to being accurate over the entire line. the numerical solution is not restricted to tin atmosphere in diffusive equilibrium. The Jovian atmosphere is essentially a semi-infinite conservative scattering layer at the line center in Lyrnan alpha. We as-

sume that the scattering is coherent and isotropic. It was first shown by Wallace (1971) that. although the physical processes obtaining in the Doppler core result in complete frequency redistribution (CFR) of the radiation out to about x = 3. where x is the variation from the line center in units of the Doppler width, the assumption of monochromatic radiative equilibrium (MRE) is not a bad approximation for the calculation of the flux radiated from the top of the atmosphere. The radiative transfer problem fi)r the Jovian I.yman alpha line was solved by Carlson and Judge (1971) for a homogeneous, isothermal a t m o s p h e r e using CFR for the Doppler core and MRE for the wings, and assuming isotropic scattering. Their results indicate that the contribution to the diffusely reflected flux from the wings dominates t~)r column densities greater than about 2 x 10" cm 2. For column densities derived in this paper, the contribution from the wings is significant and the error introduced by the assumption of MRE will be much less than the maximum 8(,~ error introduced in the l)oppler core of the line. An excellent discussion of the physical reasons for the reasonable ticcuracy' of the M R E approximation can be found in Wallace and Hunten (1973. p. 1(118). The polarized c o m p o n e n t of the radiation will be scattered anisotropically: however. for single scattered photons, the polarized c o m p o n e n t represents at most 27'~4 of the beam tBrandt and Chamberlain, 1959L and multiple scattering further reduces polarization (Hansen and Travis, 1974). For optical depths encountered at L y m a n alpha in the Jovian a t m o s p h e r e , an isotropic phase function is an excellent approximation. l.ine profiles were constructed assuming a Voigt profile: r(x) - r(O)Vrr(b(.v) and

(4) (6(x) =

I

I 4- ~l/(\Tr(tK~))

where we define ~'1 as

JOVIAN HYDROGEN DISTRIBUTION

~9 =

N(CH4)ot(CH4[Lya) N(H)a(H)

x < 3 x > 3.

TABI.E I

(5)

RESONANCE lANE DATA FOR H LYMAN AI.PHA

The Voigt profile is the same as that employed in the analytic solution: k/~b(.r) ~ exp(-x2), a/X/-~x 2,

643

(6)

Here, a is the ratio of the natural width to the Doppler width of the line. With the Doppler width, AVD = (2kT/ m) L'2` x is a function of the assumed temperature. We assumed a temperature in the scattering region of 170°K for the normal region. Profiles of albedo versus optical depth were constructed for various positions along the line. Then the reflectivity, I/F, was computed as a function of x. The computer solution was tested by comparing the monochromatic reflectivities obtained via the analytic and computer methods assuming the analytic o3(r) relation. The final solution was not restricted to an atmosphere in diffusive equilibrium, however. Although the analytic solution is not applicable to the far wings of the line, good agreement was found for the core and near wings. The total reflectivity was obtained by numerically integrating I/F over the line using an eight-point Gaussian quadrature (Abramowitz and Stegun, 1964). The reflected intensity at Lyman alpha is calculated for the Voyager I and 2 data reported by Sandel et al. (1980) and lbr the IUE data reported by Skinner et al. (1983). The Voyager measurements indicate that the disk center flux from the normal sector varied from 16.5 to 15 kR in the period between Voyagers I and 2, and that from the bulge varied from 21.5 to 20 kR in the same period. The IUE data, on the other hand, indicate that in the 3-year period between D e c e m b e r 1978 and January 1982 the Lyman alpha brightness from the normal sector remained nearly constant at about 8.5 kR, while that from the perturbed region varied from 10 to 15 kR. Thus, either the Voyager measurements indicate a period of unusually high H column density, or a call-

v (sec i) h (,~) F (sec ~) Av~ (sec ') A v o (sec i) a

2.466129 x I0 I~ 1215.67 6.265 x 10~ 4.986 x I(F 1.061 × 109 \ ' ~ : 4.06 × I0 ' ~ ( 1 " = 135°K1

ao(H) (cm-')

(5.057 x I0 ,~) ( 1~5)].':

a(CHall.yot) (cm 2)

1.9 X 10 I:

bration problem exists with one, or both, of the spectrometers. We have simply calculated column densities indicated by the published data. We use a minimum of 10 kR and a maximum of 15 kR for the perturbed region flux measured by 1UE. Two measurements of solar Lyman alpha flux are available for the period of the Voyager observations. A mid-July observation from the Atmospheric Explorer satellite yielded a line center flux of 7.1 × 10 ~t photons cm -2 sec i ~, i (McConneli et al., 1980) while a rocket-borne spectrometer measured a line center flux of 5 x I() ~ photons cm "-sec ~A J on June 5, 1979 (Mount et al., 1980). The difference between the two measurements is greater than either the published measurement error of 15% or the observed variation of about 10% from the mean (Hinteregger, 1981). We have chosen to use Mount's value. The published measurement errors for Mount's solar flux values result in a 5% uncertainty in the hydrogen column densities. With Hinteregger's fluxes, the column densities would be reduced by a factor of 2. At Jupiter, the solar flux is reduced from that at 1 AU by a factor of 0.037. We used a solar line shape at Lyman alpha published by VidaI-Madjar (1977). The solar phase angle was assumed to be 15° for the Voyager observations. The actual phase angle varied from 13 to 19° . Resonance line data for hydrogen Lyman alpha are given in Table I. The observed L y m a n alpha brightness and associated albedo are given in Table II for the normal and perturbed regions.

644

KIIJJ'~N A N I ) C H A M B E R I . A I N I A I H . I : 11 R I t I 1 ( 1 1 D I'1 I ' X 'v'o),a{,tel I n;ittlr{ll

x o ) a g c r _~ I1;llill;ll

.~',1) .Xl B I I)<)

\o),agcr I pcl'ltlr bed

Ill]

\"oyagCl 2 pc'rlllrbl2d

IUI'. perturbed

Iltll IIl';ll Mlnlnitlnl

4=/IkRi

16. <

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2914

2kll

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1+71)

() 29

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-

l

l

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; 14 l+#~(I

The line profiles derived lor the liitir Voyager observations are given in Fig. I. t h o s e for the three IUE cases are shown in Fig. 2. The IUE profiles correspond to the average normal sector and the minimum and maximum brightness observed over the perturbed region. The o)(r) rehitionship obtained from the computer sohltion along with the assumption that the atmosphere reaches diffusive equilibrium at great heights allows us to derive the abundance of hydrogen and methane versus height. Figures 3 and 4 show the integrated cohimn abundances of H and CH4 above a reference level defined by optical depth unity in CH4 for the Voyager arid I U[" models, respectively. The total vertical optical thicknesses in the line center, re, implied by the reflectivities with the assumption thai 2.3 kR of dayit)

:ll

t 19 flgl)

Ill

<"

t',"

i) 1i1%

I1 Ills

91

Ma'~Jnlum 15 I1" II. ]~

12 < I';7 '~

hhll

24l't 7*r,2

side flux is due to direct excitation h) charged paltJcles, along with lhe corresponding column density of hydrogen, n. arc given in Table 111. The cohimn density of hydrogen is given by n - rUn,u, where ~,~ is the cross section tk~r scattering l.yman alpha at the line center. The ratio o f the cohimn density of hydrogen in the perturbed to that in the normal region is aboul 2. If the hydrogen bulge is the result of localized heating arid a consequent increase in scale height, then the temperature in the scattering region is elevated by about 10(FK in the perturbed region o v e r that in the norreal region. With the minimum dayside particle flux. the Voyager data indicate that the column density' in the n o r m a l sector w a s 2 × Ill a: to 3 x I() F c m 3. while thai in the bulge was u tiictor of 2.5 larger, if the dayside particle

i 1

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+' 4 -'~"1 ' , f ' " ,ltJE Pe, tt+rbed(,T.m)

al

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7

4

0.~ ~f~\~ -+

2

I'I(A. I. I.ine profiles for the Vo)agers I and 2 normal region (solid linen). V I. and V2,. re,+pectivel+,,, and for the perturbed region (da',hed line'~L V I r :rod V2,.. re,+peclively.

>

\~,~" k' r

L 0

"Q-.

-1 JE No too+ , " -..

3.2

0.4 AX,~.

0.6

P'm. 2. l.ine proliles for the avm'age I U I + normal region (solid linel and for the nlinimurn and maxinmm IL'|- perturbed regions fl.lashed linesl.

JOVIAN

HYDROGEN

DISTRIBUTION

:j

~ , . ~ , ,H

"',,,,, , f / W F'erturl~l

E 2oC

,

'*,

645

/

nt..~~rrurbecl(max)

~ " , ¢ J / I U E P~turbed(min)

~

10C

-4'

-3 \ \ -2 '" k~ (~), atm-cm

-'t

-4

IUF NO¢n~ol

-3 -2 IOg(~/), otm-cm

-I

FIG. 3. Log of integrated column density versus height above a reference level delined by optical depth unity in CH4. The curve for CH4 is common to all cases. The curves for H correspond to the Voyagers I and 2 observations in the normal region (solid lines) and perturbed region (dashed lines), respectively.

F](;. 4. Log o f integrated column density versus height above a reference level defined by optical depth unity in CH4. The curve for CH4 is common to all cases. The curves for H correspond to the 1UE observations in the average normal region (solid linel and minimum and maximum perturbed region (dashed lines), respectively.

flux computed by Gladstone and Shemansky (1983) were correct, then the column densities would be reduced by a factor of 2.5. The total optical depth in Lyman alpha and integrated column densities computed with the assumption that 7 kR of the dayside flux is due to excitation by charged particles are given in Table IV. The column density in the normal sector indicated by the IUE observations was a factor of 10 less than that indicated by the Voyager data. The column density of freely scattering H in the perturbed region varied by a factor of 2.5 during the IUE observation period from a minimum of 9.7 × 10" to a maximum of 2.6 x 1017. The column density of hydrogen may have been unusually high during the time of the Voyager observations, but the long-term stability of the

normal sector over the 3-year period of the 1UE observations indicates a difference in calibration between the two spectrometers. On the other hand, if the global particle flux were unusually high at the time of the Voyager encounters, the column densities implied by the Voyagers and IUE observations would be more consistent. The Lyman alpha brightnesses measured by a sounding rocket on I December 1978 (Clarke et al.. 1980) were even greater than those measured by Voyager. These observations are not compatible with those obtained by IUE in December 1978. Assuming that 7 kR of the observed flux is due to excitation by charged particles, the sounding rocket observations imply column densities of 2 x 1017 c m -2 in the normal sector and 1 x 1018 cm 2 in the perturbed sector.

TABI,E Iii

OPTICAl. DEPTH.q AND COLUMN I)ENSITI[-S DERIVE[) ASSUMING2.3 kR OI- PARTICI.I! EX('ITATION AT I,YMAN AI.PIIA Voyager 1 natural

Tq) n

1.2E5 2.8EI7

Voyager 2 natural

9. I E4 2.1EI7

Voyager 1 perturbed

2.3E5 6.8EI7

Voyager 2 perturbed

2.0E5 5.9EI7

IUE natural

1. I E4 2.6EI6

IUE perturbed Minimum

Maximum

3.3E4 9.7E16

9.0E4 2.6EI7

KILLEN AND ('HAMBERI+AIN

646 'l'A Bl,l'~ IV ()PII(+AI

[)]-.Plll5,

.,'~kSSUMIN+; 7

r, n

AND

(_'()1 I.~MN D I N S I I I I

~, I ) I : R I V I

kR ( i v P A R I I(. I I [ ' X ( I l A l l ( I N I,YMAN AI l'llA

Voyager I natural

Voyager 2 natural

Voyager I pcrttlrbed

4.41"4 9.6E16

3.4E4 7.9E16

1.21IS 3.5EI7

l)

AI

Voyager 2 pcrttll'b,ad 1.0E'~ 2.91.117

Out results are similar to those obtained by Clarke et a/.. because, although our model yields larger column densities than a simple conservatively scattering layer, wc subtracted the flux prestimed to he duc to charged particle excitation, and w.'c assumed a lower t e m p e r a t u r e in the scattering region. Clarke c t a / . assumed a temperature of 1200°K, appropriate tk~r thc exospherc, whereas most of the scattering actually occurs near the h o m o p a u s e . NI(iH fSII)E I+YMAN A L P I I A I M I S S I ( ) N S ..\NI) I M P I . I C A T I ( ) N S F()R P A R I I ( ' I Ii PRE(+IPIIAI'I()N

The L y m a n alpha brightness observed on thc nightsidc of Jupiter exhibits a longitudinal variation very similar in shape to lhal Of the dayside. The brightness mea~,ured b} the Voyager UVS is nearly uniform at 750 R across the disk with a broad enhancement rising to a peak of 1000 R ccnlered al about I00:' west longitude (Mc('onncll ul a/.. 1980). (In the nightside, the only sources of I.x-

man alpha flux are resonance scattering of an interstellar wind (ISW) source of aboul g00 R and direct excitation by charged particles. A map of the sky backgrotmd as seen by Voyager 2 near Jupiter cncounter is given by McConnell el a/. in their I:ig. 5. The ISW is moving with a velocity Vis -- 20 km sec ~ at an angle with rcspccl to the terminator plane, 3' ~ 23:, and at an angle/3 -: -7 ° with respect to the Jovian equatorial plane. The g e o m e t r y of the poslencotmtcr view is shown in Fig. I of McConnell e¢ a/. For these calculations we used l'; 0, and

assumed an isotropic source of 800 R. For the l,yman alpha scattered by hydrogen in the ISW, we assumed a Doppler protile characterized by "/is - 12,0( X)°K. The equalions t\)r the Doppler shift as a function of zenith angle and azimuth are given in McConnell +,t a/. (p. 133). Our reflectivilies were obtained from our doubling-adding code and then convolved with the ISW profile. We integrated o v e r solid angle and frequency using eight-point Gaussian quadratures. We have used our dayside column densities to estimate the proportion of the nightside flux which is scattered ISW radiation. These tluxes are given in Table II. The remainder of the llux is assumed to be due to excitation of L y m a n alpha by particle precipitation. This is the flux labeled "'excess flux'" in Table 11. The nightside brightness shows little tentel to limb variation. McConnell e t a / . have s h o w n l h i t l the observed center to limb variation can be modeled by soft electrons which deposit their energy abovc thc homopause. Because ('Ha is a strong absorber at l,yman alpha, a stronger limb darkening would be produced if the charged particles depositcd thcir cnergy below the homopause. The fact that <500 R of He band emission is stimulated further constrains thc region of energy deposition to thc optically thin region in g y m a n alpha where [H ] [1|:] + I. We therefore assume that the prccipilating particlcs are soft electrons ( -5(I cV) or protons (--10 keV). Electron b o m b a r d m e n t of an a l m o s p h c r c consisting of H and 1-12produces both dissociative and direct excitation of Lyman alpha. Dissociative excitation of l.yman alpha can be produced by electrons ~ith energy greater than 14.67 eV its (' - H ~ - - ,

c

~ tl~:

H!: ,--, H ( 2 : I ' )

+ l- l( leS)

<7)

H(2-'P)--, II(12S) I hr. Alternatively. H~can be predissociated into 22,S" and be transferred to 221' by a thermal

JOVIAN HYDROGEN DISTRIBUTION collision. The total cross section (O'D) of H: for dissociative excitation of L y m a n alpha by 50-eV electrons is 1.2 x 10 ~7 cm 2 _+ I1% ( M u m m a and Zipf, 19711. The cross section for direct excitation of H by 50-eV electrons is o'5 = 4.0 x 10 -t6 cm 2 (Swartz et al., 1975). The range, R. of electrons in the a t m o s p h e r e can be estimated by the formula of Gun (Hunten and Dessler, 19771 R = 4.57 x 10-6/-'j/75 g c m

-"

(8)

where E0 is the initial electron energy in kilo-electronvoits. The range for 50-eV electrons is 2.4 x 10 - S g c m 2 or 7.2 x i() t5 molecules cm--'. The m a x i m u m energy will be deposited at 0.4R (Chamberlain, 19611. Using a scale height for H2 of 35 km, we find that the total n u m b e r density at 0.4R is about 1 × 10 9 c m 3 corresponding to an atomic hydrogen density of about 5 x 107 cm -" from A t r e y a and D o n a h u c ' s model. Following the analysis of Chamberlain (19611, we find that most of the energy will be deposited o v e r a height span of 40 km. We can make a crude estimate of the electron flux required to produce the excess L y m a n alpha emission as follows. The n u m b e r of collisions that produce a L y m a n alpha photon, C, per square centimeter per second is given by C = F[n(H2)m~ + n(H)o-~]

(9)

where F is the electron flux, n(H2) is the column a b u n d a n c e of H2 o v e r which the energy is deposited, ~ro is the cross section lbr dissociative excitation of L y m a n alpha, n(H) is the column a b u n d a n c e of atomic hydrogen, and o-c is the cross section tbr direct excitation of H. The n u m b e r of captures is 47rl/r. where r is the reflcctivity. The flux of electrons required to produce the o b s e r v e d emission depends strongly upon the atomic hydrogen density and the level of energy deposition. These calculations are based on our nominal a t m o s p h e r e model with 2.3 kR of dayside L y m a n alpha emission due to particle excitation. The Voyager results are consistent with a flux of 50-eV electrons of 0.040 erg cm -2 sec -j

647

o v e r the normal region and 0.06 erg cm -" sec -f o v e r the bulge. The models derived from the I U E o b s e r v a t i o n s imply a particle flux of 0.06 erg cm -2 sec-* o v e r the normal region and 0.06-0.08 erg c m - : sec 'j o v e r the bulge. Although the I U E data may be calibrated differently than the Voyager data, these o b s e r v a t i o n s show that the particle flux into the bulge region varies with time from a level equal to that o v e r the normal sector to a level enhanced by 0.02 erg cm -" sec J o v e r that deposited in the normal region. T h e s e values arc c o m p a r a b l e to the 0.04 erg cm -2 sec ~ calculated by McConnell et al. (19801 for the normal sector using V o y a g e r 2 data. We have not included the flux which is reflected from the a t m o s p h e r e . About half of the incoming flux is reflected from the top of the atmosphere (Mantas and Walker, 1976), so that the total incoming flux is double that computed. l~ct us a s s u m e that an additional 0.(12 erg cm 2 sec ~ is deposited above the homopause in the bulge region o v e r that deposited in the normal region. Up to 30%, of this energy would be available for thermalization. The remainder of the energy escapes as radiation. If the heat input, Q, is deposited at the t h e r m o p a u s e (z~) and conducted to the m e s o p a u s c (zm) where it is radiated a w a y , the difference between the exospheric and m e s o p a u s e t e m p e r a t u r e s can be calculated from Eq. (4) of Hunten and I)essler ( 19771: T'~ - TL =

Qsk In(pm/pl)

Alxg

(10)

With the thermal conductivity, x = A T L in e r g c m ~sec -~°K J,A = 2 5 2 a n d s = ( } . 7 5 1 . The mean molecular weight, /z, is that for H2. The gravitational acceleration, g, is 2322 cm sec 2 k is the Boltzmann constant, and p~ and Pm are the pressure at the thcrm o p a u s e and m e s o p a u s e , respectively. The heat required to raise the t e m p e r a t u r e in the t h e r m o s p h e r e to 1000°K a b o v e a mesopause at 170°K is 0.517 erg cm--" sec ~. The

64g

KILL, EN AND CHAMBERI,AIN "I'AITI.I.~ V PRO(

I!S~,FIS

WHI(It

MAY

F(IRMAIIOIN

l~Ic,.thmlran~,tu't

RFISUI (ll

II'

1 IN

Iltl

I1"

+ Ib

• II'

It;

'

II,

• 11'

I I . ¢21

II

'

H.

• tl'

It

II

'

It,

I1"

'

It,

• tl

• tl'

II

'

I1,

• II

I1'

II i . l a l

II,

• II

II

II

h n p a . . . t o l f a s t 11 o n II,

II

(11

I )1~xt~. l a l + x t + l.-~k+ll+lt it lit

b+

pl olon~

bx ~;i~l a t o [ l l ~

II

II t ~al

tl',

~u,

~ <4hi

II

'

tt,

.11

i

II

II

II

'

II,

• II

i

il'

• II

, . iI~+ ¢.ldt

heat input into the bulge region is one third of the excess particle flux, or 0.067 erg cm ' sec ~, greater than that input into the normal sector. If the heat input a b o v e the perturbed region is 0.524 erg cm : s e c t the results are consistent with a m e s o p a u s e t e m p e r a t u r e of 270°K and an exospheric t e m p e r a t u r e a b o v e the perturbed region of 1160°K. These values lkw the exospheric t e m p e r a t u r e , 1000°K o v e r the normal sector and .... 1200°K o v e r the bulge, are within the range of measured temperatures. Protons and hydrogen atoms traveling through tt_, produce i,yman alpha principally through sequential ionization and charge capture. Other processes which may result in the tkwmation of an excited hydrogen a t o m (H*) include impact of fast 1! atoms on H_,, and dissociative excitation of H, on impact with protons or fast hydrogen atoms. These processes are shown in Table V (Birely and McNeil, 1972), where It denotes a fast hydrogen atom and H* denotes an excited atom. The total cross section for emission of L y m a n alpha due to projectile and dissociative excitation of H(2p) in collisions of 10-keV protons and H atoms with He is
10-keY protons would be required to produce the o b s e r v e d emission in the normal region with 0.14 erg cm -" sec ~ in the bulge region. The total capture cross section t\)r protons in t-|,, is a factor of 3 less than the cross section in air; hence we have divided the n u m b e r of quanta/proton atm-cm obtained by Chamberlain (1961, p. 249), by 3. Thus, the proton flux we derive is greater than that derived by McConnell c't a/. even though we have a greater column density of hydrogen. The Voyager m e a s u r e m e n t s indicate that the exospheric t e m p e r a t u r e is on the order of 10(X)-12(X)°K (Atreya e t a / . , 1981). On the basis of the occultation of/3-Scorpii by Jupiter, French and Gierasch [1974) proposed thal the upper a t m o s p h e r e is heated by the vertical propagation of inertia gravity waves. Although Atreya and Donahue [1976) and Atreya e t a / . (1979) concluded that the energy flux calculated by French and Gierasch would be adequate to raise the exospheric t e m p e r a t u r e to 1000°K, the Voyager thermal data rule out inertia gravity waves as a primary source of upper atmospheric heating (Atreya et al.. 1981). Hunten and Dessler (1977) proposed that penetration of magnetospheric electrons would be responsible for heating the neutral gas. Atreya et ,/. (1981) objected to this explanation on the grounds that the energy spectrum is unknown, a planetwidc precipitation of 5(1- to 100-eV electrons in the equatorial region seems unlikely, and it fails to explain the o b s e r v e d diurnal and zonal variations m the [,yman alpha air glow. They propose that Joule heating in the main ionosphere may be of importance in heating the upper atmosphere. H o w e v e r . H: densities in the ionosphere may be too low for this m e c h a n i s m to be effective, and the upper atmospheric dynamics are uncertain. Regardless of the primary heating mechanism, we expect a 150+:K enhancement of the exospheric temperature over the H bulge due It) a zonal a s y m m e t r y in the particle precipitation. Dessler et a/. (1981) have proposed a

JOVIAN HYDROGEN DISTRIBUTION mechanism for the transport of magnetospheric electrons from the active sector associated with the foot of Io's flux tube to the region associated with the Lyman alpha bulge. They suggested that a two-cell convection pattern in the Jovian magnetosphere is driven by a longitudinal mass asymmetry in the Io toms. They propose that the incident electrons have energies of 100 keV and produce the excess hydrogen in the vicinity of the bulge through dissociation of H2 deep in the atmosphere. We propose that the asymmetry in the particle flux produces the bulge through heating. The electrons responsible for heating the mesosphere are not those responsible for the excess nightside Lyman alpha. It is likely, however, that the precipitating electrons have a wide range of energies. SUMMARY Our calculations show that, with the minimum assumed particle flux, column densities of 2 x l0 j7 cm 2 in the normal sector and 6 x 1017 c m -2 in the perturbed sector are compatible with the Voyager 2 Lyman alpha observations. The column densities implied by Voyage 1 observations are 25% larger. The difference between these column densities and those calculated by McConnell et al. (1980), I × 1017 and 3 × 1017 in the normal sector and bulge, respectively, is only partially due to the different models employed. McConnell et al. adopted a solar flux measured by Hinteregger which is 30% larger than that used here. After accounting for the difference due to the two values of the solar Lyman alpha flux, our column densities are only slightly larger than those calculated by McConnell et al. using a simple homogeneous model. Our model, with an absorber mixed with the scatterer, yields larger column densities than a simple conservatively scattering layer above an absorbing surface, as expected. We have assumed that i kR of the dayside emission is due to resonance scattering of an interstellar wind source, and 2.3 to 7 kR of the dayside Lyman alpha

649

brightness are due to direct excitation by charged particles. With the maximum assumed particle flux, the column densities are reduced by a factor of 2. The variation of Lyman alpha across the nightside disk implies that both a zonal variation in H column density and in particle flux must be present. This result lends support to the proposal that a corotating magnetospheric convection pattern preferentially deposits charged particles into the equatorial region in the vicinity of the perturbed sector (Hill et al., 1981). We show that the flux of soft electrons or protons into the bulge region is enhanced by about 0.04 erg cm 2 sec- J over that in the normal region. This estimate includes that portion of the particle flux which is reflectcd from the top of the atmosphere. The H2 l,yman and Werner band emission is a factor of l0 greater on the dayside than on the nightside (Broadfoot et al., 1981), implying a diurnal variation in the precipitation pattern in addition to a zonal variation. The IUE observations paint a somewhat different picture of the Jovian atmosphere. These observations indicate that in the 3year period between December 1978 and January 1982 the column density of H in the normal sector remained fairly constant at about 2.5 x 10 j6 cm 2, while that in the bulge varied from a minimum of 9.7 x l0 l~ cm 2 to a maximum of 2.6 x 10tTcm 2. The source of the bulge must, therefore, be persistent but extremely variable. The difference between the Voyager and IUE observations indicates that either the atmosphere was unusually perturbed at the time of the Voyager observations or that a calibration problem exists.

APPENDIX Chamberhdn and McEIroy start with the exact integral equation for the function, h(r,t.t), defined such that I i

d/z'

h0"4x) = 1 + 2 J0 ~

.

,

~S(r,/z,~ ),

(AI)

650

KII.LEN ANi) CHAMBERLAIN

w h e r e S describes the scattering function at depth r. It is assumed that h(r,/t) is a p p r o x i mated by the C h a n d r a s e k h a r t i f u n c t i o n , defined l b r a h o m o g e n e o u s atmosphere. c h a r a c t e r i s t i c o f some greater depth:

h(r./t) - H ( r + T~../t).

(A2)

H(7 ~ r~./t) is integrated o v e r / t and evaluated f o r a mean r - r,.. To use the C h a m b e r l a i n - M c l : ~ h o y solution. we write (b,.(r) - &(0) e x p ( - , ~ r ( : ) ) .

&,,(c)

I -

71,,(=,))

cxpl--(:

(;~,,(r) " ( b ( 0 ) l l - hr,.(::)],

h---I.

o),.(=)

II'0, (n,)l/lru(=.)"l}

I

~)

' I

o)(v) - e x p ( - A ¢ ' ) .

(14)

where c0 is s o m e reference height. Here !t~ is the scale height for h y d r o g e n and t t , i~ the scale height for m e t h a n e . At the tipper levels in the line center, o),. I or ~t,.(~) <~ 1. F o r the a p p r o x i m a t i o n tt~ ~-- ! 1 , . the ,+ingle scattering a[bedo can be written. ~b,(=)

l -

-

r/,.(=)

-.: l -

t

(b(r) I " - ~--

I' d l z / t .uI' ./t. . .+~

.,

, I

e~P I-':

-

:")iT,,

ii,)

rd=)

-

ru(.'.u)

, r~../t')ll

e x p l - ( = .... :,)illl] 4 r,(=,)exp[-(:--

2(I

Since I i , --> ! i , and ru ~- r,. we can use the

ll(r./t)-

I

ru(:,) expl-(=

(A6)

w h e r e rtl 'T(b'(i) due to H alone: r. - r(u.) due to H + ('Ha. - -

l f w e w r i t e p / t t j - I 1 , 1 .... t l j i o r p = l i t : l. the single scattering a l b e d o becomes tl,

I I

I

(AI0)

.~

d/t'

/t'(/t' .Ii,'/t : k' "(~/t ) we o b t a i n by i n t e g r a t i n g for r ,1

llir

~ q.,tt')

tl(r

/t

I

+ ;~.,l~)ll(r

\3h(blp(r

-

(1]1,

T i "EL.

d/t'

Il

2(I :,,)/llll.

Tc)l'

(b(r)

a p p r o x i m a t e solution,

r.(:)

Jr &j)l:

We have defined ( g / t ' ) / ( # f /t') - 6. Using the integral e q u a t i o n for C h a n d r a s e k h a r ' , , H function,

&(r)

: . ) / l i , I.

H ) d ' %1

\"3h(bl/tSp(7 ' T,.F I -2(I - &j)l_; . . . .

\..~)k(Oi/t'~p(T

• (15)

In the line c e n t e r the optical depth is

+ r~,/t)

tl(r

/t'

'1, ,//t/t u~ - ;-~,,~1 I,

I. -

lt(T I II

1

r/,.(cL~)

(A9)

the C h a m b e r l a i n - M c E I r o y Eq. ~9) b e c o m e s

(A3)

.

(A8)

For a m i x t u r e o f h y d r o g e n and methane.

i

I

rfi.

the value o t ' p is 15. With the a l b e d o r e p r e s e n t e d in the form

l.et r / b e the ratio o f a b s o r b e r n u m b e r density to scatterer n u m b e r density weighted by their respective a b s o r p t i o n cross secl i o n s . F o r t w o c o n s t i t u e n t s in diffusive cquilibrit,m we o b t a i n

exp I (: - =,,)(~,

(17)

t)l"

.u i t ( T -r 7c,l&)d/t

For small A we use the a p p r o x i m a t i o n

-- : , ) ( p / l l ~ ) J .

7

(Ol

~- --

Il

(0IT)

7-

d/t'#'

~ r,.,/t')

t ToY' I

.)l) I:

o)(r) -, [YUI&I) + 7"~((al)1.

~AI2)

The y ..... are definite integrals given by C h a m b e r l a i n - M c l - h ' o y I'q. (AIOL and we define o)t

&(r-

r~.).

JOVIAN H Y D R O G E N DISTRIBUTION

651

Second-order terms have been discarded. T h e i n t e g r a l s in Eq. ( A I 2 ) c a n be e v a l u a t e d in t e r m s o f the C h a m b e r l a i n - M c E i r o y y ..... functions o51 1"y2o(o51) + ~/11(~1)1 ~-

W e o b t a i n the e f f e c t i v e a l b e d o f r o m Eq. (A9). F o r a n y g i v e n v a l u e o f ~. in the line c e n t e r , w e c o n s t r u c t a line profile as foll o w s . At a n y p o i n t in the line the o p t i c a l d e p t h is r(x) = rH(X) + TCH4(X) = "I'H(0)~/"/T ~b(x) + rCHg0). C o n t r i b u t i o n s f r o m the natuII - e x p ( - X ~ > + X(-r + "r<)P)l ral w i n g s o f the line b e c o m e i m p o r t a n t as considerable multiple scattering occurs. = - 5_ ,tpv" L,/2ff~) e x p I - M u' + M r + "r<,)s>] C o n s e q u e n t l y , a Voigt f u n c t i o n has b e e n a s s u m e d for the line s h a p e . W e will use the 4(1 - - ~ 1 ) 1'2 1"/31(~i) .,I- "),22(o)1)1 approximation for the Voigt profile (l~ang, 1974) e x p l - h v " + g.(r + r~)~']. (A13) \ / - - ~ ( x ) ~ e x p ( - x 2) + alTrl"2x2. ( A I 9 ) T h i s e x p r e s s i o n is e v a l u a t e d for a m e a n ~" = If w e define ~'~ with ~.-r~ <~ I. F o r ~,~j + 7_'2 = ~o~i ( C h a m b e r l a i n N(CH4)a(CH4iLya) M c E I r o y ( A I 3 ) ) , the e f f e c t i v e o p t i c a l d e p t h (A20I "0o = N(H)oto(H) is the single s c a t t e r i n g a l b e d o at a f r e q u e n c y x z~i(~i) ( A I 4 ) D o p p l e r units f r o m the line c e n t e r c a n be ~'c - 4(I - o31)I/2 [oq~(~l) - I1 written F o r 03 ~ 1, C h a m b e r l a i n a n d M c E I r o y h a v e s h o w n that

and cl0(oSi) ~ 2 - 2(1 - ~bl) 1:2.

(A16)

Equation (Ai4} becomes

-

~1)]

1'2"

= (18.75/Ivs ~ h / "

'

(l/[dJi,(r)l)

-

I.

(AI7)

H e r e we h a v e e v a l u a t e d r~ for the u p p e r m o s t part o f the a t m o s p h e r e w h e r e r = 0 and ~i = ode. W e use the h o m o g e n e o u s H(<.h,lx) = H(-r~,/x) to r e p r e s e n t the a c c u r a t e h('c,lx) f u n c t i o n i n s o f a r as d e s c r i b i n g the e m e r g e n t r a d i a t i o n f r o m the t o p o f the a t m o s p h e r e . T h e f u n c t i o n h(r,/x) is a n a l o g o u s to C h a n d r a s e k h a r ' s (1950) HoS(kO f u n c t i o n s for hom o g e n e o u s a t m o s p h e r e s . By i n s e r t i n g the p r e s u m e d v a r i a t i o n o f a i b e d o with o p t i c a l d e p t h into Eq. ( A t 7 ) , w e o b t a i n the effective o p t i c a l d e p t h for the e q u i v a l e n t h o m o geneous atmosphere: ~'~

(A21)

H e r e a0(H) is the a b s o r p t i o n c r o s s s e c t i o n for h y d r o g e n at t h e line c e n t e r . T h e single s c a t t e r i n g a l b e d o at x is g i v e n by Eq. (A21) where ~ll

P r~ = 2[3(I

~h(.r) = I + ~J~'i"2~(x)'

(AI8)

We fit the resulting variation ot'¢b(x) with r(.r) to the expression eb = e x p ( - A ~ ' ) . With the resulting value o f A, the equivalent single scattering albedo can be found at each point x as in the line center. The monochromatic albedo, A, for the equivalent homogeneous atmosphere is given by A -- 1 - tt(/xo)(l - o)~)12.

(A22)

ACKNOWLEDGMENTS This research was supported by the Planetary Atmosphere program of the National Aeronautics and Space Administration under NSG-7043 and by the Division of Atmospheric Sciences of the National Science Foundation under ATM-80-06530. We acknowledge helpful comments by John C. Mc('onnell and an anony m o u s re['c Fee.

KILI,I':N

652

AN[) CHAMBERLAIN

REFERENCES AtlRAMOWITZ. M.. AND 1. A. S]EtiI'N ( E d n . ) t l g M ) . H , n d h o o l , o f M a t h e m u t i c , I I"unctitm,~. pp. 887.916. U . S . G o v l . Prinling Office, Washington. I ) . C . A I R I : Y A , ~. K., AND "1". M. DONAIIUI (1976). Model ionospheres o f Jupiter. In Jllpilcr (T. (;ehiel,< Ed. I, pp. 304-318. Univ. o f Arizona Press, Tucson. AI'RIE~ A, ~. K . . T. M. D O N A t l I ; I , B. R..~;kNDI-.I . A. 1.. BR(SADFOtSl. AND (i. R. SMIItt 11979). Jm, ian upper atmospheric tempel'att]i'e measul'el3aent by the Voyager 1 UV npectromeler. (it'~,phvL Rc~. l.ctt. 6, 795-798. At r P , a . S. K.. T. M. I)ONAllUl....X,',t) M. C. Ff SIOI 119811. Jupiter: Structure and compo,,ition of thc upper atmo,~pheic. A.~trophy.~..I. 247. 1,4~-1,47. AIRI.','A. S. K.. M. C. F I S l o t : . "1. M. [)ON.XHU~ . R. B. KI:Rr, E. S. BARKt..r, W. 1). (_'o( Ilr.xx. J. I.. BI:RIAUX. ANIS ~,". 1,. UPStSN II (1982). ('opcrnictr, meastlrClllCnl of the Jovian l.yman-alpha cmin,,ion and itn acronomieal significance. ,-t~m,phv~. J. 262, ~77-387. BIRI-I.','. J. H.. At',[.:, R. J. M( NI.:II 11972). I"ornu~lion of H(2p) and tl(2s) in collisions of plottms and tl',drogcn atoms v. ith hydrogen molcculc,L l'hv.~. R c r . .4 5. 692-71)1. BR..~NI)I. J. ('.. ,'~NI)J. ~,;. (_'IIAMIII Rl ,~,1% l ltlSt)l, lnIcrplanetary gan. I. |'lydrogen radiation in Ihe night ",ky. A~trophv,~. J. 130, 670-692 I { R o A I ) r ( ) o l . A. 1,.. I'1. R. S A N I ' . t i . I). I:. ,'gill MANSK't. J. ('. M('(-'ONNt!I I . (i. R. N,MII i t , J. I;I. I t o l Bl:Rt;. S. K. A lm.'r.,,, T. M. l ) o N o t t t I . I). I'. ,~IROBEI , AND J. [,. BERIAt X (19811. ( ) v e i v i e ~ of the Voyager tdti'aviolet spectrometry renults though Jupiter cnommlctn..]. (;eophy.~. R c s . 86, 8259-8284 (',xrl soN. R. W., ,xNI) 1). 1,. Jl_l)(il 11971). l h e cxlrcme ultraviolet dayglow of Jupiter. I'hu,.l..~,pa( ~" 5,~ i. 19, ~,27. 343. ('IIAMBI Rl &IN, J. ~/. 11961). l'hv,~i~ s ,q the ,4lit'ofit ,rid Aick, hm. Academic Pi'cns. Ne~ Y o r k , l , t m d o n . ('IIAMI:II-:RI AIN. J. ~/'., AND ~ . B. M( El R()'~ ( 19661. Diffuse reflection by an inholnogcncoun phmctar~ atmosphere. A.~trophy,s. J. 144, 1148--II 58. ('IIANI)RASI!KII,'~R. S. (195(1). Radiatiuc 'l?an.~Jl,r. ()xl\)rd Univ. Prc'+s (Clarendon). I.ondon.:Nc~ York. ('1ARKI.. ,I. T., ft. A. WE,xvliR. P. l). | ' ~ I t ) M A N , It. W. M o o s . ,XNI) W. G. FASlII-. (19g01. Spatial imaging o f hydrogen l,yrnan +~ emi,~,,ion from Jupilcr ..l.~tr+~pIIy~. J. 240, 696-701. I)I:SSIIR. A. J., B. R. ,~&NI)I l . AND .N.K. A I R I ~ . A 11981). The Jovian hydrogen bulge: t.xidence Ibr t2OI'Ol;ltiFIg magnetospheric convection, t'hm,.l. Spa, +c S,+'i. 29, 215. FRINCtl. R. G.. AND P. J. (il~-:RAS(.tt (1974). Wavc~ in the Jovian upper a t m o s p h e r e . . / . . - U m , . ~ . . ~ h i . 31, 171)7-1712. (JlAI)SIONI!, ( . i . R . . AND 1). t':. SIIt. Xl.-XNSK', (1983), Radiative transfer o f internal source',: Application It) the 1.yman ,+r dayglov,, of Jupiter. Bull. Amcr. A str,,n. 5,',,¢. 15, 832-833.

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DISTRIBUTION

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WHALING, W. (1958). The energy loss of charged particles in matter. In Handbuch der Physik (S. Flugge, Ed.). Vol. 34, p. 207. Springer-Verlag, Berlin/New York. YUNG, Y. L., AND D. F. STROBEL (1980). Hydrocarbon photochemistry and Lyman alpha albedo of Jupiter. Astrophys. J. 239, 395-402.