JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 89, NO. A1, PAGES 85-90, JANUARY
1, 1984
The Thermosphereof Titan
A. JAMES FRIEDSON AND YUK L. YUNG
Divisionof Geologicaland Planetary Sciences,California Institute of Technology
The diurnal variation of the vertical structure of Titan's thermosphereis calculatedthrough simultaneous solution of the equations of heat transfer and hydrostaticequilibrium. The temperatureand
densityprofilesare found above the mesopause.The dynamicalresponseof the thermosphereto heating
is for the most part neglected.Nevertheless,we are able to draw some interesting qualitative and
quantitative conclusionsregarding the vertical structure. Heating of the upper thermosphereoccurs
primarily through absorption of solar Lyman • radiation by methane, with an additional amount of
heating(•< 20%) due to low-energymagnetosphericelectronprecipitation.The heat is conducteddownward to the mesopause,where it is removedby IR cooling due principally to acetylene.The mesopauseis
foundto occurwherethe densityis 2.2 x 10x2cm-3 (736km), and hasa temperature
of ,-•110K. The
exospherictemperatureis unlikely to exceed225 K in the courseof a Titan day. The diurnally averaged
exospherictemperatureis in the range 187-197 K dependingon the amount of magnetosphericelectron
heating that is includedin the model. The amplitude of the diurnal variation is found to be <•28 K. We
find that the verticalextent of the hydrogencloud is too large to be explainedin terms of simplethermal
escapeof hydrogenfrom a ,-•225-K exosphere,and we concludethat other processesmust be important
for populatingor heatingthe neutral torus.
1.
INTRODUCTION
the orbit of Titan are complexand highly variable.While the
Voyager
1 UVS observationprovided usefulinformation on
As Voyager 1 passed through Titan's shadow, an occultation of the sun was observedat the morning and evening the energyflux of electronsincidenton Titan at the time of the
terminators by the ultraviolet spectrometer(UVS). Analysisof observation, the electron flux at other points along Titan's
the occultation data has yielded the temperature and density orbit is poorly constrained.Hence a model of the diurnal
near the exobase.The temperatureat 3840 km (measuredfrom variation of the thermospherewhich incorporates electron
the center of Titan) has been inferred to be 176 + 20 K at the heating must make someinitial, arbitrary assumptionabout
eveningterminator and 196 + 20 K at the morning termina- the plasmaconditionsalong the orbit.
The lack of any data concerningthe rotation rate of the
tor, while the N 2 density at the same altitude is seen to be
becomesan additionalsourceof uncertaintyfor
nearly the same at each terminator and equal to 2.7 + 0.2 thermosphere
the modeling. The Voyager 1 infrared interferometer specx 108cm-3 [Smithet at., 1982].
It is apparent from the UVS observationthat the morning trometer (IRIS) experimentershave inferred the presenceof
but there is no comand evening exospherictemperaturesdo not differ by much superrotatingwindsin the stratosphere,
and may in fact be equal.This suggests
that there may be little pellingreasonto believethat this superrotationextendsall the
diurnal variation of the exospherictemperature. It should be way up to the thermosphere.In view of the complexityof
pointed out, however, that the exospherictemperature at the plasmaconditionsat Titan's orbit and of our lack of knowlmorning and eveningterminatorsof Venus was also measured edge of the thermosphericrotation rate, we cannot hope to
quantitativemodel of the thermoto be quite similar [Keating et at., 1980], yet the exospheric presenta comprehensive
structure,
temperaturethere exhibitsa strong dependenceon local time. sphere.However,someaspectsof the thermospheric
such
as
the
location
and
temperature
of
the
mesopause,
are
Consequently,it would be ill advisedto concludea priori that
above.In addiTitan's exospherictemperature does not substantially vary fairly insensitiveto the uncertaintiesdiscussed
tion, we can set an upper limit to the exospherictemperature
during one rotation period.
Our aim in the present study is to calculate the vertical that can be achievedduring a Titan day.
The thermal time scales that characterize the diurnal behavstructure of the thermosphere,down to the mesopause,as a
ior of the thermosphereare discussed
in section2. In section3
function of local time. In so doing we have ignored any dynamical responseof the thermosphereexcept that associated we presentthe input model atmosphereusedto calculatethe
with the "breathing velocity" of constant-pressuresurfaces. temperatureprofile and discussthe dominant heating and
in the thermosphere.The temperature
Hence the amplitude of any diurnal variation predictedby our cooling mechanisms
model must be interpreted as an upper limit. In addition, the profilesobtainedby integratingthe heat transferequation
calculation of the vertical structure is appropriate only for with and without electronheatingare presentedand discussed
in section4. In section5 we investigatewhat implicationsthe
Titan's equator.
Our task of modeling the temperatureprofile in the upper derived exospherictemperatureshave for the neutral hydrogen torus.
thermosphereis complicated by the fact that it is difficult to
accurately quantify the heating due to precipitating magnetosphericelectrons. Results of the Plasma Scienceexperiment on Voyagers 1 and 2 [Bridge et at., 1981, 1982] have
shown that conditions in the magnetosphericenvironment at
2.
Two
THERMAL TIME SCALES
The way in which thermospherictemperaturesvary in time
can be understood in terms of two time scales, which are
relatedto the two principalcoolingmechanisms.
The first time
scaleis the responsetime associatedwith nonlocal thermodynamic equilibrium (NLTE; vibrational relaxation) coolingdue
to acetyleneand methane.It is roughly the time requiredfor a
given level in the thermosphereto relax to a new steadystate
Copyright 1984 by the American GeophysicalUnion.
Paper number 3A1663.
0148-0227/84/003A-1663505.00
85
86
FRIEDSON
AND YUNG' TITAN'STHERMOSPHERE
1500
3.
1400
MODEL
For our model of the thermospherewe usethe resultsof the
UVS solaroccultationexperiment,
as reportedby Smithet al.
[1982], togetherwith the photochemical
modelproducedby
Yunget al. [1982].Only threeconstituents
of theupperatmo-
1300
'-• 1200
r• I100
sphereare importantto the energybalance'N2, CH½,and
k-I000
exobase
andfallsoff to --•3% in thelowerthermosphere.
The
C2H 2. The mixing ratio of methaneis taken to be 8% near the
acetylenemixing ratio drops from a value of 2% near the
<r 900
exobaseto only 0.2% in the lower thermosphere,
in accordancewith the best fit model presentedby Smith et al. The
800
initial input altitudeprofilesof theseconstituents
are shownin
700
105 106 10
7 I08 I09 i0© i0II i0121013
1014
CONCENTRAT ION (crrF3)
Figure 1.
Two sourcesof energy are available to heat the thermo-
sphere'solarenergyand energeticmagnetospheric
electrons
Fig. 1. Altitudeprofilesof N 2, CH,•, and C2H• chosenas initial
[Strobel and Shemansky,1982]. The solar flux used in our
input for modelcalculations.
Theseprofilesare recalculated
simulta- modelis taken from Mount and Rottman[1981]. The flux in
neouslywith the temperature
profile.
Lyman • incidenton Titan is 5.5 x 109 photonscm-: s-•.
The bulk of the solarheatingoccursthroughabsorptionof
in response
to a changein the heating,if the only cooling Lyman o•by methane.Acetylenealso contributesto the heatmechanism
is NLTE cooling.Thisresponse
timeis givenby
ing throughits absorptionat wavelengths
lessthan 2000
=
pCe
(o/OT)i
T
(1)
Althoughnitrogenis an order of magnitudemore abundant
than methane,it only absorbsat wavelengths
shortwardof
1000,&,where
thesolarfluxislow.Hence
it contributes
only
where
p isthemass
density
atthelevel
ofinterest,
Cvisth•
--•10% to the solarheating.
Methane is dissociatedat Lyman • via three channels
[Slanger, 1982]'
specificheat at constantpressureof N2, R is the total NLTE
cooling rate, and T is the temperature.At all altitudes consideredin our models,the responsetime z •> 3 years.Sincethe
40%
CH½+ hv-• •CH2 + H 2
longestthe thermosphericrotation period is likely to be is
5O%
CH 4 + hv-• CH 2 + 2H
only 16 days,we may concludethat the temperatureprofileat
any local time is not a steadystateprofilebut containsa good
8%
CH½+ hv--} CH + H 2 + H
deal of memoryof the temperaturesat pastlocal times.
dueto CH½absorptionis calculatedfor
The secondtime scaleof interestis simply the conduction The heatingefficiency
and the weightedaverageover the
relaxation time for the thermosphereabove a given altitude eachchannelseparately,
channels
is thentakento yielda meanheatingefficiency.
In
level.It is given by
whereL is a characteristic
scalelengthof the systemand •cis
the effectiveheatdiffusivity.It is not immediatelyclearhow to
chooseL and • for an inhomogeneous
medium,but it is natural to chooseL to be equal to the scaleheightat a given
altitudeand to choose• to be the heat diffusivitythere.The
time scaleZcis then roughlythe time requiredfor conduction
to bring the atmosphereabove the altitude of inte est into
equilibriumwith the lowerlayers.
We may estimatethe densityof the level where the conduction relaxationtime is comparableto the thermospheric
rotation period.It is givenby
n • Pk/mCeH2
(2)
eachchannel,the kineticenergyof the dissociation
fragments
as well as 50% of the CH2 (or ell) recombination
energy
contributesto the local heating.Once the •CH2 radicalis
formed,it is rapidlyquenched
in collisions
withN 2 to 3CH2.
Subsequently,
two 3CH2radicals
combine
to produce
C2H2
andH 2 [Yunget al., 1982].SinceC2H2 is chemically
stablein
the thermosphere,
the reactionsequenceterminatesat this
point. This set of reactionsreleases2.8 eV of heat, and we
include50% of thisrecombination
energy,or 1.4eV, with the
kineticenergyof thedissociation
fragments
whenthe heating
efficiency
is calculated.
The recombination
energyof H, however,doesnot contributeto the localheating,as H is slowto
react comparedwith the transporttime scale.The average
heatingefficiencyover the three methanechannelsis found to
be 0.35 at Lyman •. It variesfrom a maximum of 0.47 at 1000
,&to 0.32at 1300,&.A similaranalysis
donefor acetylene
yieldsa meanheatingefficiencyof 0.45 between1300and 2000
where n is the number density, P the thermosphericrotation
period, k the heat conductivityof N2, m the mass of an N2
molecule,and H the local scaleheight. If P is taken to be 16
days(corresponding
to rigid corotation),then n--• 8 x 10•ø
cm-3, corresponding
to an altitudeof --•860km abovethe
surface.Therefore we expectvery little diurnal variation of the
temperature below this altitude. The amplitude of the diurnal
variation
need not be small above this level. In our numerical
calculations, we find that the actual level where the diurnal
amplitudeis --•5 K liesat n -• 5 x 10•ø cm-3, whichtendsto
support the scalingargumentsusedhere.
A.
The solarheatingis givenby
H(r,
0)=
•/ni(r
)•d2i•i(•) o'i(•)Fov(•) e-•(";øz(ø) (3)
wherer is the radialdistancefrom Titan'scenter;ni is the
concentration,
ei the heatingefficiency,
and ai the absorption
crosssectionfor constituent
i; Foo(2)is the incidentsolarflux
per unit wavelength;
r is the total normalopticaldepth;and
Z(0)is the Chapmanfunctionfor solarzenithangle0. The
FRIEDSONAND YUNG' TITAN'S THERMOSPHERE
is the absorption path length for electron scattering, a is an
"absorption"crosssection,e is the electronheating efficiency,
<pis the hemisphericallyaveragedelectronflux incidentbelow
the exobase,and // is the angle between the Saturn-sun line
and the position of Titan in its orbit. The cross section a is
chosen to put the peak in the electron heating above the
1!00-km level. The value used for a is 4.2 x !0- •7 cm2. We
consider the electron flux to have reached its peak during
Voyager 1 closestapproach(//= 0) and allow <p(//)= 0 on the
nightside magnetosphere.This model is intended to roughly
account for the dayside-nightsideasymmetry in the plasma
flux tube content observedby the Plasma Scienceexperiments
on Voyagers 1 and 2 [Bridge et al., 1981, 1982]. It is a crude
approximation in that it ignores the longitudinal asymmetry
in the electron depositionat Titan observedby the UVS experiment [Broadfoot et al., 1981' $trobel and Shemansky,
1500
t
1300 -
I100-
-
900
-
_
700
i
iO-Ia
87
io-ii
!982]. The value of e•p(fl= 0) is taken to be 6 x 10-3 erg
cm-2 s-•. Admitting a larger electronenergyflux at the
I
io-iO
10-9
morning terminator causes the exospheric temperature to
exceedthe range allowed by the UVS observation.
The solar heating at a zenith angle of 60ø is plotted as a
function of altitude in Figure 2. The peak electronheating as a
integration
overwavelength
is performed
between
50 ,&and
function of altitude is shown in Figure 3.
2000 A.
Heat can be removed from the thermosphere by NLTE
Another energy source for heating the thermosphereis
cooling. The cool-to-space approximation [Chamberlain and
derivedfrom electronimpact on N2. Some featuresof Titan's
McElroy, 1966; Strobel and Smith, 1973] is quite adequate at
EUV emissionspectra obtained during the Voyager 1 enall levelsin our model. The 13.7-#m band of acetyleneand, to
countersuggestthat someof the emissionoriginatesbelowthe
a smaller degree,the 7.7-#m band of methane are responsible
exobase[Strobeland Shemansky,1982]. The emissionis confor the bulk of the NLTE cooling. Although methane is more
sistentwith beingcausedby a secondaryelectronenergydisabundant than acetylenein the thermosphere,acetylenedomitribution that is roughly a Maxwellian with an electrontemnates the NLTE cooling. This is true for two reasons'(1) the
peratureof Te = 2 x 105K. This temperature
corresponds
to
relaxation rate of the 13.7-#m acetylene band in collisions
an averageelectronenergy of -•26 eV. Observationof the
with N2 is an order of magnitude greater than that of the
emissionfrom the bright limb constrainedthe sourcealtitude
methane 7.7-#m band, for the same temperatureand pressure
to be above -• 1100km. If photoelectronsproduced-• 25 R of
[Yardley et al., 1970; Hager et al., 1981], and (2) the lower
N2 Lyman-Birge-Hopfieldemission,then the hemisphericenergyassociatedwith the 13.7-#m transition givesit a higher
averaged
energyfluxbelowtheexobase
was-•0.0! ergcm-•
probabilityof excitationrelativeto the 7.7-#m transitionby a
s- • at the time of the observation[Strobel,1983]. The altitude
SOLAR HEATINGRATE (erg crrf3se½
i)
Fig. 2. Solar heatingprofilefor solarzenithangleof 60ø.
at which the source of this emission occurs, however, is still
uncertain.Clearly, the actual electronenergyflux incidenton
Titan shoulddependon the positionof the satellitealong its
orbit. It is possible,in view of the complexityof the Saturnian
magnetosphereat Titan's orbit, that this flux fluctuatessubstantially.
factor of >• 100.
If we denote the total NLTE cooling rate per unit volume
as R(r, T), then
R(r,T)= • •ihvirh(T)e-n'•/krfi[n(r)]2Y•(r
)
(5)
i
Here vi is the frequencyof a 13.7-#m or 7.7-#m transition, T is
It is very difficultto calculatedirectlyan effectiveheating the kinetic temperature of the ambient gas,f• is the mixing
efficiencyfor electronimpact on N2 that would correctlytake ratio of acetyleneor methane,n is the total density,rh is the
into account the numerousphysical and chemical processes
that determinethe fraction of energythat is ultimately dissipated as heat. Generally,this quantity will lie somewherebe1500
tween 0.3 and 0.7. Since the electron energy flux below the
exobaseis probably uncertainby a factor of 2 or so, it seems
pointlessat this time to specifya uniquevaluefor the electron
heatingefficiency.
We will lump the uncertaintyin the electron
energyflux and the heatingefficiencytogetherand treat their
product,e•b,as an adjustableparameter.The valueof e•bis not
well constrainedby the data. Nevertheless,
we have includeda
model run which incorporatesa plausibleamount of electron
heatingfor illustrativepurposes.We model the electronheating in the simpleparametrizedform
E(r, ,•)= ecp(l•)n(r)•
exp [--z(r)]
(4a)
where
1400
1300 -
1200-
I100IOO09OO
8OO
7OO -
10-14
z(r) =
n(r')adr'
(4b)
10-13
i0-12
i0-11
i0-10
HEATINGRATE (ergsc•sec7 •)
Fig. 3. Peak electronheatingprofile.
10-9
88
FRIEDSON AND YUNG'
TITAN'S THERMOSPHERE
collisionalrelaxation rate for the appropriate transition, •i is
the ratio of the statisticalweightsof the first excitedstate to
the ground state, and Y• is the net collisionalbracket for the
transition.For a transitionwhoseoptical depth is •<1% of its
thermalizationdepth, Y•_• 1 [Avrett and Hummer,1965]. This
conductionand dynamical advectionof heat are neglectedin
equation(9). Theseprocesses
must reducehorizontal and vertical temperaturegradientsin the thermosphere,so the diurnal
amplitude predictedby equation (9) must be consideredas an
upper limit.
is the case, at all altitudes of the model, for individual lines in
Equation (9) must be supplementedwith boundary conthe methane 7.7-#m band. Some lines in the acetylene13.7-#m ditions at the upper and lower boundaries of our model as
band, however,will have optical depthsof • • 100, or as much well as with an initial temperatureprofile specifiedat a particas • 10% of the thermalization depth, at the lowest altitudes ular local time. The upper boundary condition is that the
of the model. For theselines the value of Y•may differ sub- vertical temperaturegradient must vanish above the exobase
stantially from unity. The value of Y•for the strongestlines is for all local times. We set the temperature to a constant value
approximately0.7 at the mesopause(740 km), and it decreases at the lower boundary,which occursat an altitude of 680 km.
almost linearly to •0.1 at the lower boundary of the model Choosing the temperature at 680 km to be independentof
(680 km). We have determined,by numerical calculation,that time is supportedby the scalingargumentspresentedin secthe effect of setting Y•= 1 in equation (5) is to underestimate tion 2. Numerical solution of equation (9) has shown that the
the mesopausetemperature by 7 K and to overestimatethe vertical structure obtained at and above the mesopauseis
lapse rate in the vicinity of the mesopause.(In particular, the insensitiveto the particular value chosenfor the temperature
temperature gradient at the lower boundary of the model, as at the lower boundary. Specifically,the vertical temperature
shown in Figure 5, is slightly superadiabatic.Allowing Y• to profile was found to be the samefor lower boundary temperdiffer from unity in equation (5) causesthe lapse rate to aturesin the range 100-160 K.
become subadiabatic.)For simplicity, we have set Y•= 1 in
To guessan initial temperatureprofile for the morning terequation (5). Uncertaintiesassociatedwith other aspectsof the minator, we impose a steady state profile with a slightly remodel are potentially more important.
ducedheating efficiencyto accountfor the thermal inertia of
The collisionalrelaxation rate of the 13.7-#m band of C2H2 the system.The validity of the initial guessis determinedby
by N 2 has beendeterminedat room temperature[Hager et al., the degreeto which the solution returns to the initial profile
1981]. We have not located any experimental data for this after one rotation. Below 860 km, where the diurnal temperrate at other temperatures.Consequently,we have used data ature variation is expectedto be negligible,the initial profile
for the temperature dependenceof C2H 4 vibrational relax- shouldbe that associatedwith diurnally averagedheating conation in N: [Wang and Springer,1977] and expect that these ditions. A model run with diurnally averagedheating showed
data should give an adequate descriptionof the temperature that the initial guessfulfilled this requirement.
dependenceof the C:H:-N: system.The collisionalrelaxation
The densityprofile at eachlocal time is found simultaneousrate for C:H:-N: is taken to be
ly with the temperatureprofile by integratingthe equationof
hydrostaticequilibrium.The densityat the lower boundary is
r/c•a•(T
) = 5.08x 10-•'•T•/2e-28/T1/3
cm3/s
(6) chosenin order that the vertical profile at the morning termiThe collisionalrelaxation rate of the CH,• 7.7-#m transition in nator predictsa densityat 1270km of 2.6 x 108 cm-3, in
agreementwith the UVS observation.The mixingratios of the
N2 is given by [Wang and Springer,1977]
minor speciesare held fixedduringthe diurnal run.
r/c.•(T) = 1.02x 10-i3Ti/2e-56/T•/3cm3/s
(7)
Equation (9) is integratednumericallyby a finite difference
relaxation technique.The vertical resolution is 8 km; hence
Heat is transportedin the thermosphere
by molecularcon- there are at least six stepsper scaleheight in the model. The
duction. For the conductivityof N 2 we use
ks•(r) = 42.7r ø'69+ 2.61r-
355.6
(8)
which fits the data to within 5% between 80 K and 500 K
[Weast, 1967]. We neglecteddy heat conduction,sinceit is
validity of the numericalsolutionsis checkedby requiring
energyto be conserved
bothlocallyandglobally.
4.
RESULTS AND DISCUSSION
The verticalstructureof the thermosphereis found through
simultaneoussolution of the heat transfer equation and the
viscousdissipation[$choeberlet al., 1983' Walterscheid, equation of hydrostatic equilibrium. The value of the total
densityat the lower boundary is fixed by the condition that
1981].
Given the heatingand coolingrates,we calculatethe verti- the densityat 1270 km on the morning terminator agreeswith
not clear to what extent the downward transport of heat due
to eddiesis able to balanceor overcomethe heat generatedby
cal temperatureprofileas a functionof local time by solving
the time-dependent
heat transferequation
•C3T)
= H(r,t)+ E(r,t)+ R(r,T)
c3T
1c3
(r2
kN2
(T)
pCvr3t r2r3r
(9)
where H(r, t) is the total solar heating rate, E(r, t) is the
electronheatingrate, and R(r, T) is the NLTE coolingrate.
The specificheat at constantpressure,Cv, is usedrather than
Cv in equation(9) in order to take accountof the general
expansionor contractionof constant-pressure
surfaces
in responseto heatingand cooling.This thermospheric
"breathing"
acts to reducethe diurnal temperaturevariation. Horizontal
the UVS solar occultation
observation.
We have consideredtwo modelruns which differ only in the
sourcesof heating for the thermosphere.Both modelsassume
the rotation period of the thermosphereto be equal to Titan's
orbital period (16 days).The first model considersthe effectsof
solar heating alone, while the secondintroducessomeamount
of magnetospheric
electronheating which might be representative of the conditions at Titan's orbit. The product
e4•(/•= 0) for the electronheatingis takento be 6 x 10-3 erg
cm-2 s-•. For a hemispherically
averaged
electronenergyflux
belowthe exobaseof 0.01erg cm-2 s-• this corresponds
to
an electronheating efficiencyof 0.6. It must be emphasized
here that the actual amount of electronheating at Titan and
its diurnal variation are highly uncertain.The true value of
FRIEDSON AND YUNG' TITAN'S THERMOSPHERE
same in both models and are therefore insensitive to the as-
20
10
oo
8:32
km
992
km
90
i
i
i
i
80
70
60
-'--
50
i
i
i
i
LLI210
or' 190
1152km
I-- 170
i
i
i
17o
i
_---
1501I
i
170•
I
1270 km
•
•
I
12
LOCAL
I
18
TIME
I
0
sumptionsmadeconcerningelectronheating.
Superrotationof the thermospherewould tend to reducethe
amplitude of the diurnal variation and tend to increasethe
time lag of the responseto the heating. If there is a diurnal
temperaturevariation in the thermosphere,the averagecooling rate at each level is greater than the cooling rate in a
thermospherewith the sameaveragetemperaturebut no diurnal variation. This arisesfrom the nonlineardependenceof the
cooling rate on temperature.As a consequence,
a superrotating thermosphere with little diurnal temperature variation
should exhibit a slightly higher diurnally averagedexospheric
temperature than a slower rotator. In the limit where Titan's
thermosphereis consideredto rotate so fast as to not experi-
<i: 15o
150•
6
89
1472
km
I
ence any diurnal variation, the average exospherictemperature is -• 190 K when only solar heating is included.If these
modelscome closeto describingthe actual heatingconditions
at Titan, it appears unlikely that the exospherictemperature
exceeds225 K. A fluctuationin electronheating conditions(a
local magnetospheric"storm,"for example)could temporarily
raise the exospherictemperature above this limit; however,
the diurnal averageof the exospherictemperatureshouldstay
below 225 K.
6
5.
(hrs)
Fig.4[ Diurnal
temperature
variation
atfivealtitudes,
solar
heating only. The dashed curve for 1270 km is for the model which
includeselectronheating.
e•b(//= 0) could be negligible,or it could be twice the value
usedin the model. Our purposein includingthis model is to
determinewhat, if any, effectthe inclusionof an electronheat
sourcehas on the conclusionswe make in this study.
Figure 4 showsthe diurnal temperaturevariation at five
altitudeswhen solar EUV radiation is the only sourceof heat-
ing. The data pointsshownon the curvefor the 1270-kmlevel
representthe UVS solar occultationmeasurementsat each
terminator. The peak exospherictemperatureis 216 K and
occurs at • 1600 hours local time, while the minimum of 159
K occursat •0400 hours. The diurnal amplitude of the ex-
ospherictemperatureis AT • 30 K. Alsoshownin Figure4 is
THE HYDROGEN TORUS
The neutral hydrogen torus orbiting Saturn has been reported to extendradially between8 Rs and 25 Rs and to have
a vertical half thicknessof 6-8 Rs [Sandel et al., 1982]. It is
interestingto considerto what extent the morphologyof the
torus is determinedby simpleJeansescapeof hydrogenfrom
Titan.
In order to understandthe torus geometryit is necessaryto
know first whether or not collisionsbetweenatoms are important to the dynamics of the cloud. Recent data of the flux of
neutral particles,detectedby the low-energychargedparticle
detector aboard Voyager 2 during the preencounterphase,
havebeenusedto setan upperlimit of 100cm-3 for the total
neutral densityin the torus (W. H. Ip, unpublisheddata, 1982).
The meanfreetime for collisions,
Zc,is of orderzc .• (nat))-•,
where n is the torus density,a is the collisionalcrosssection,
and v is the averagerelative velocitybetweenatoms.The rela-
the diurnal variation at 1270 km when electron heating is
included.The peak exospherictemperatureis •6 K warmer
for this case than for the solar heating case. Both models
DENSITY (crff•)
I08 I09 I0© I0II i012 I013 I014
1500
predicta temperatureat 1270 km on the eveningterminator
which is 15 K warmer than the highesttemperatureallowed
1400
by the UVS observation.The dynamicalresponseof the thermosphereor superrotationwould be expectedto reducethe
1300 diurnal amplitude of the temperaturevariation. Hence it is
possiblethat winds or superrotationof the thermosphere
E
._x:1200 couldexplainthe discrepancy
at the eveningterminator.
The diurnal averagetemperatureand density profiles for
solarheatingonly are shownin Figure 5. Theseprofileswere
found as solutionsto the diurnal averageof equation(9) and
i-- ioooJ
to the equationof hydrostaticequilibrium.In orderto fit the
900 observeddensityat 1270 km on the morningterminator,we
find that the density at the mesopausemust be n= = 2.3
\
_
8OO
x 10t2 cm-3. The mesopause
is locatedat an altitudeof 736
km and is quitecold,T= = 104K (110K if we includeopacity
700
•
•
I
•
I xq
• effects;seeequation(5)). The diurnallyaveragedexospheric
I00
I10
120 130 140 150 160 170 180 190
temperatureis 187 K. The diurnallyaveragedexospheric
temTEMPERATURE
(K)
peratureis • 10 K warmerthan thiswhenelectronheatingis Fig. 5. Diurnal average temperature (solid curve) and density
included.The mesopauselocation and temperatureare the
(dashedcurve)profilesfor solarheating.
I
I
I
-
•
\xX
90
FRIEDSON AND YUNG: TITAN'S THERMOSPHERE
Bridge,H. S., J. W. Belcher,A. J. Lazarus, S. Olbert, J. D. Sullivan, F.
tive velocity betweenatoms is approximately •e•a, where fl
Bagenal,P. R. Gazis, R. E. Hartle, K. W. Ogilvie, J. D. Scudder,E.
is the orbital frequency,e the eccentricity,and a the semimajor
C. Sittler,A. Eviatar, G. L. Siscoe,C. K. Goertz, and V. M. Vasyaxis of a typical particle orbit. Adopting values for a and fl
liunas.Plasmaobservations
near Saturn:Initial resultsfrom Voyappropriate for particlesnear Titan, a-• 10-•5 Cm2, and
ager 1, Science,212, 217, 1981.
n-• 100 cm-3, the meanfreecollisiontimeis of order•:c•
Bridge, H. S., J. W. Belcher, A. J. Lazarus, R. L. McNutt, J. D.
2 x 10? 1/e s. Thusfor eccentricities
of •<0.2,the collision Sullivan,P. R. Gazis,R. E. Hartle,K. W. Ogilvie,J. D. Scudder,E.
C. Sittler,A. Eviatar,G. L. Siscoe,C. K. Goertz,and ¾. M. ¾asyliunas,Plasmaobservations
near Saturn:Initial resultsfrom VoyBridge et al. [1982]. A collisionlesstreatment for the torus
ager 2, Science,215, 563, 1982.
would then be appropriate. Due to the uncertaintiesinvolved Broadfoot,A. L., B. R. Sandel,D. E. Shemansky,
J. B. Holberg,G. R.
Smith,D. F. Strobel,J. C. McConnell,S. Kumar, D. M. Hunten, S.
in this analysis,however, the question of the importance of
K. Atreya, T. M. Donahue, H. W. Moos, J. L. Bertaux,J. E. Blacollisionsin the torusmustbe left openfor the present.
mont, R. B. Pomphrey,and S. Linick, Extreme ultraviolet observa$myth [1981] useda detailed computermodel to study the
tions from Voyager1 encounterwith Saturn,Science,212, 206,
structureof a collisionless
torus.For a mean emissionvelocity
1981.
time is greaterthan the toruslifetimeof 108s estimatedby
for H atomsof 2.0 km s-•, corresponding
to an exospheric Chamberlain,J. W., and M. B. McElroy, Martian atmosphere:The
temperatureof ,-•240 K, the vertical half thicknessof the torus
was found to be 1.5 Rs.This is considerablylessthan the 6-8
Rs inferred from the Voyager 1 and 2 UVS data. Therefore if
the torus is collisionless, it is much thicker than can be ex-
plained by simplethermal escapefrom a ,-•225-K exosphere.
The same conclusion can be reached if the torus is collision
Mariner occultationexperiment,Science,152, 21, 1966.
Hager, J., W. Krieger, and J. Pfab, Collisional deactivation of laserexcitedacetyleneby H, HBr, N 2, and CO, J. Chem.Soc.Faraday
Trans., 77, 469, 1981.
Keating, G. M., J. Y. Nicholson III, and L. R. Lake, Venus upper
atmospherestructure,J. Geophys.
Res.,85, 7941, 1980.
Mount, G. H., and G. J. Rottman, The solar spectralirradiance12003184 angstrom near solar maximum: July 15, 1980, J. Geophys.
dominated. A vertical scale height of 8 Rs implies a cloud
Res., 86, 9193, 1981.
temperature of 260 K [Sandel et al., 1982]. This is warmer Sandel,B. R., D. E. Shemansky,A. L. Broadfoot,J. B. Holberg, G. R.
than the 225-K upper limit we have set for the exospheric
Smith, J. C. McConnell, D. F. Strobel, S. K. Atreya, T. M. Don-
temperature.,
More complicated
processes
than thermalescape
mustbeiriV•ølved
in forming
a toruswithhalfthickness
•8
ahue,H. W. Moos, D. M. Hunten, R. B. Pomphrey,and S. Linick,
Extreme ultraviolet observationsfrom the Voyager 2 encounter
torus, or perhaps a source of neutral hydrogen other than
with Saturn, Science,215, 548, 1982.
Schoeberl,M. R., D. F. Strobel, and J.P. Apruzese, A numerical
model of gravity wave breaking and stressin the mesosphere,J.
Geophys.Res.,88, 5249, 1983.
Titan.
Slanger,
T. G., Photodissociation
channels
at 1216/!•for H20, NH3,
Rs.Among the viablealternativesare nonthermalescapefrom
Titan, gravitationalscatteringin the torus,local heatingin the
The diurnal variation of Titan's thermospherictemperature
and density profiles has been calculatedby simultaneously
solving numericallythe heat transferequation and the equation of hydrostaticequilibrium. It is found that the exospheric
temperatureis unlikely to exceed225 K during a Titan day.
Its diurnally averagedvalue lies in the range 187-197 K. The
amplitude of the diurnal variation is •<30 K. The mesopause
is fairlycold, • 110K, andis locatedat a densityof 2.3x 10•2
cm-3 (736 km). This densityis greaterthan that expected
at
736 km if Titan's upper atmospherewere isothermal above
190 km with a temperatureof 170 K. This suggeststhat the
temperature reaches a local maximum, warmer than 170 K,
somewhere
between 200 km and 700 km altitude.
The vertical
extent of the hydrogen torus is too large to be explainedby
simple thermal escapefrom a • 225-K exosphere.We conclude that other mechanismsmust be more important in
populating the torus.
and CH,•, J. Chem.Phys.,77, 2432, 1982.
Smith, G. R., D. F. Strobel, A. L. Broadfoot, B. R. Sandel, D. E.
Shemansky,and J. B. Holberg, Titan's upper atmosphere:Composition and temperaturefrom the EU¾ solar occultation results,J.
Geophys.Res.,87, 1351, 1982.
Smyth,W. H., Titan's hydrogentorus,Astrophys.J., 246, 344, 1981.
Strobel, D. F., Upper atmosphereand torus, in Saturn,edited by T.
Gehrels,Universityof Arizona Press,Tucson,in press,1983.
Strobel, D. F., and D. E. Shemansky,EU¾ emissionfrom Titan's
upper atmosphere:Voyager 1 encounter,J. Geophys.Res.,87, 1361,
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Weast, R. C. (Ed.), Handbookof Chemistryand Physics,CRC, Cleveland, 1967.
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Acknowledgments.The authorswish to thank A. P. Ingersoll,M.
nitrogen and carbon monoxide on Titan: Abiotic synthesisof orAllen, M. E. Summers,and G. R. Gladstone for helpful discussions.
ganic compounds, paper presented at the First Symposium on
This researchwas supportedby NASA grant NSG 7376 to the CaliChemical Evolution and the Origin and Evolution of Life, NASA
fornia Institute of Technology.Contribution 3907 from the Division
AmesResearchCenter, Moffett Field, Calif., Aug. 2-4, 1982.
of Geological and Planetary Sciences,California Institute of Technology.
The Editor
thanks R. E. Hartle
and D. Strobel for their assistance
in evaluatingthis paper.
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A. J. Friedson and Y. L. Yung, California Institute of Technology,
Division of Geologicaland Planetary Sciences,
Pasadena,CA 91125.
(ReceivedAugust 30, 1982;
revised October 10, 1983;
acceptedOctober 11, 1983.)