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10-1-2001
Hot Carbon Densities in the Exosphere of Mars
Andrew F. Nagy
Michael W. Liemohn
Jane L. Fox
Wright State University - Main Campus, [email protected]
Jhoon Kim
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Nagy, A. F., Liemohn, M. W., Fox, J. L., & Kim, J. (2001). Hot Carbon Densities in the Exosphere of Mars. Journal of Geophysical
Research-Space Physics, 106 (A10), 21565-21568.
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Physics
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 106, NO. A10, PAGES 21565-21568,
OCTOBER 2001
Hot carbon densitiesin the exosphere of Mars
Andrew F. Nagy and Michael W. Liemohn
Departmentof Atmospheric,Oceanicand SpaceScience,Universityof Michigan,Ann Arbor, Michigan,USA
J.L.
Fox
Departmentof Physics,Wright StateUniversity,Dayton, Ohio, USA
Jhoon Kim
Korea AerospaceResearchInstitute•Taejon,Republicof Korea
Abstract. Theoreticalresultsof hot carbondensitiesin the exosphereof Mars arepresented.The
calculationis a two-stepprocess:First a two-streamtransportcodeis usedto solvefor the
distributionfunctionat the exobase,andthentheseresultsareusedin a Liouville equationsolution
abovethe exobase.It is foundthat photodissociation
of carbonmonoxideis the largestsourceof
hotcarbon
atomsin theupperatmosphere
of Mars,largerthandissociative
recombination
of CO+
andmuchlargerthanthe creationof hot carbonthroughcollisionswith hot oxygenatoms.It is also
foundthatthe high solaractivitydensitiesare aboutan orderof magnitudelargerthanthosefor the
low solar activity case.
1.
Introduction
The changesin the carbondioxidecontentof the atmospheres
of
Mars and Venus over time are determinedeither by the atmospheric escapeof carbon via CO2, CO, or C or by the surface
processesassociatedwith carbon-bearing
materialsin the regolith
and carbonatedeposits(and the polar cap at Mars). The escape
energies
of •2C at VenusandMarsare •6.38 and 1.48 eV,
respectively.The presenceof a hot carbon exosphereat Venus
has been established[Paxton, 1983] by the UV spectrometer,
carried aboard the Pioneer Venus orbiter [e.g., Stewart, 1980],
butit hasbeenshown
thatthe•2Cescape
fluxesat Venusare
negligiblysmall.However,becauseof the lower escapeenergyat
Mars, an examination of this issue is in order. The observed
emissionsat 165.1 nm have been identifiedas coming from hot
carbonatoms,andan exobasemixing ratio of C/O was estimatedto
be on the order
of
1% at Venus.
There
tion processwere calculatedby assumingthatthe productswere in
their groundstateandby usingthe photodissociation
crosssections
presentedby Fox and Black [1989]. The solar flux values used
were the 79050 and the SC21REFW Hinteregger et al. [1981]
EUV fluxes,for high andlow solaractivity,respectively,combined
with the X-ray valuesgiven by Ayres[1997]. The thermospheric
modelsusedwere similarto thoseusedpreviously[e.g.,Fox, 1997;
Kim et al., 1998]. The high solar activity model is basedon the
Mars ThermosphericGeneral CirculationModel (MTGCM) of
Bougheret al. [1990], and the specificvaluesusedwere for near
the equatorat 1600 LT. The low solaractivity,neutralatmosphere
is that from the Viking neutral mass spectrometerresults,which
correspond
to a solarzenithangleof 44ø [NierandMcElroy,1977;
Fox and Dalgarno, 1979].
The dissociative
recombination
of CO+,
is no observational
CO+ q-e -• C(3p)q-O(3p)q-2.90eV,
(2a)
CO+ + e • C(1D)q-O(3p)q-1.64eV,
(2b)
CO+ + e --•C(3p)q-O(1D)-Jr0.94eV,
(2c)
oxygen atoms with cold, thermal carbon. In this brief note we
presentthe resultsof our calculationof hot carbon densitiesat
CO+ + e -• C(1S)q-O(3p)q-0.22eV,
(2d)
Mars, due to all three of these sourcemechanisms.
CO+ + e --•C(1D)q-O(1D)--0.33
eV,
(2e)
informationregardinghot carbon densitiesat Mars available at
this time.
There are three potentiallyimportantsourcesof hot carbon at
Venus and Mars: They are the photodissociationof CO, the
dissociative
recombination
of CO+, and the collisionsof hot
2.
Calculated Densitiesand Escape Fluxes
The photodissociation
of CO,
COq-hv(•1116•,)• Cq-O,
(1)
resultsin an excesskinetic energy,the amountof which depends
on the electronic excitation state of the products,as indicated
above. In a recentpaper,Fox and Hac [1999] have carried out
detailed Monte Carlo calculations of the altitude-dependent
velocity distributionsof the C atomsresultingfrom reaction(2),
for both high and low solarcycle conditions.In thesecalculations
they usedthe latestavailablerate coefficientsandbranchingratios
[Rosenet al., 1998]. The total dissociativerate coefficientusedwas
resultsin excesskinetic energybecomingavailableto the atomic
products,the amountof which dependson the wavelengthof the 2.76 x 10-7 (300/Te)
ø'55.
At 0-eVrelative
energy
thebranching
dissociatingphoton and the electronicstate of the dissociation ratiosgivenby Rosenet al. [1998] are 0.761, 0.145, 0.094, and 0.0
products.The hot C productionratescausedby thisphotodissocia- for channels(2a)-(2e), respectively.At 0.4 eV the endothermic
channel (2e) is now energeticallypossible, and the measured
branchingratiosare 0.53, 0.34, 0.08, 0.0, and 0.05, respectively.In
Copyright2001 by the AmericanGeophysicalUnion.
the calculationsbelow, a linear interpolation between these
branching ratio values was used, which depended on the
Papernumber2001JA000007.
0148-0227/01/2001JA000007 $09.00
temperaturescorrespondingto a given altitude. Fox and Hac
21565
21566
NAGY
ET AL.:
BRIEF
[1999] assumedthat the rotational and vibrationaltemperatures
were the sameas the adoptedion temperatures.
They did take into
account
the
decrease
in
the
cross
section
for
REPORT
240
dissociative
recombinationdue to the relativevelocity of the ionsand electrons
(a)
Flux
220 Upward
[Rosen
etal.,1998].
Theassumed
ionospheric
densities
forthelow
and high solaractivity conditionsare presentedby Fox and Hac
DownwardFlux
[1999],andtheelectron
andiontemperatures
canbefoundin the • 200
Escoping
Upword Flux
work of Kim et al. [1998].
E
Collisionsbetweenenergeticoxygen atomsand cold, thermal •-
carbonatomscanresultin hotcarbonproduction:
Ohotq- Ccold•
/
(3)
We usedthe hot oxygendistributionfunctionscalculatedfor Mars
[Kim et al., 1998] to obtainthe productionrate of hot carbondueto
thisprocess.
Weadopted
a cross-section
valueof 1.2x 10-Is cm2,
/
160
140
, ,., v",•l
et al.
,
105
[1997].
model to calculate the hot C fluxes as a function
blaximum
Solar
Minimum
....
240
(b)
Upward Flux
220
Downward
200
Flux
Escaping
Upword Flux
180
iI
160
•'
:'
140
/,-'
......
i
105
..........
106
107
NumberFlux(cm-2s-•)
i
,
,
,
108
Figure 2. Hot carbonnumberflux versusaltitudefor (a) high
solar activity conditionsand (b) low solar activity conditions.
Upward and downward flux values are integrated over all
energies,while the escapingupward flux values are integrated
above
1.48 eV.
Having calculatedthe distributionfunctionsat the exobase,we
usedLiouville's theorem[cf. Schunkand Nagy, 2000] to calculate
the hot carbondensitiesin the exosphereof Mars, aswe havedone
for hot hydrogenand oxygencasesbefore [e.g., Cravenset al.,
1980b; Nagy and Cravens, 1988]. The resulting hot carbon
densitiesare shownin Figure
3. The
densityvaluesdecreasefrom
2
3
100.00
Solar
,,i
108
of
altitude.This two-streammodel [cf. Schunkand Nagy, 2000] has
been used widely and successfullyto calculateelectron,ion, and
neutral particle fluxes [e.g., Cravens et al., 1980a; Nagy and
Cravens, 1988; Kim et al., 1998]. Specifically,it has been used
to calculatehot oxygen densitiesat both Venus and Mars; the
calculateddensitiesat Venusagreedwell with the observedvalues,
and the Mars results[Nagy and Cravens,1988; Kim et al., 1998]
are in reasonablygood agreementwith the valuescalculatedby
Lainmet and Bauer [1991] andHodges [2000], who useda Monte
Carlo method.(There is a factor of •13 differencein the escape
fluxes given in Table 1 of Kim et al. [1998] and Hodges [2000],
which is due to an errorin compilingthat table;the densitiesand
the distribution function presentedby Kim et al. [1998] are
correct.)Using thesecalculations,we obtainedthe hot C fluxes
at the exobase.The classicaldefinitionof the exobase,namely,the
locationwherethe meanfree pathequalsthe scaleheight,placesit
at •195 and 215 km for low and high solar cycle conditions,
respectively.The exact choice of the exobasealtitude does not
impactour calculateddensitiesto any significantdegree,aslongas
that choice is "reasonable" (see Figure 5 and two paragraphs
below).The calculatedenergydistributionfunctionsat thenominal
exobases,
for the two solarcycleconditions,are shownin Figure 1.
The upward,downward,and escapehemisphericfluxesareplotted
in Figures2a and 2b, for the high and low solar activity cycle
conditions,respectively.
......
- , ', ',"i,
106
107
NumberFlux(cm-2s-•)
We combinedthesethreehot C productionratesas a functionof
altitude and energy.We then used theseproductionrates in our
two-stream
,
//
N 180
Chatq- Ocold-
a reasonable choice based on the calculations of Kharchenko
iI
ii
•4.7 x 103 and3.6 x 10 cm- neartheexobase
forthehigh
10.00
and low solaractivityconditions,respectively,andremaina minor
constituent
throughoutthe exosphere,comparedto hydrogenand
oxygen.
o
1
2
Energy(eV)
3
4
We found that photodissociation
is the most importantsource
mechanism,followed by dissociativerecombination,while the hot
oxygenimpactsourceappearsto be negligiblysmall at Mars. To
demonstratethis conclusionwe plotted in Figures4a and 4b, for
the high solar activity conditions,the exosphericdensitiesand
hemisphericescapefluxes,respectively,due to the threepossible
sourcesseparately.
In Figure5 we plottedthe calculatedhigh solar
activity densities,as a function of altitude, for four different
assumedexobasealtitudes,in order to demonstratethat the choice
of the exobasealtitudehasonly a smallinfluenceon our calculated
hot carbon densities.
Figure 1. Hot carbondifferentialnumberdensityversusenergy
We also calculatedthe hemispheric
escape
fluxes and found
5
2
1
for thehigh andlow solaractivitycases.Spectraarefor the 192-km themtobe7.7 x 106and5.3 x 10 cm- s- forhighandlow
altitudebin, and eachenergy"box" has a width of 0.02 eV.
solar cycle conditions,respectively.Note that the escapeflux
NAGY
X•X
5000
ET AL.:
BRIEF
ß - -Solar
Maximum
.
............
REPORT
21567
5000
Minimum
4000
4000
..
•
..,,.x,• ....... 248km
_
•'3000
-
'..•
\\
ß
•'3000
N
2000
2000
lOOO
lOOO
........
•
........
10
i ....... ;'";",
.....
1 O0
,
.......
1000
.... I
10000
10
Density(era-3)
........
I
........
1 O0
I
'
,• -,
,''-', ,,
1000
10000
Density(cm-3)
Figure 3. Hot carbondensitiesin the exosphereof Mars versus Figure 5. Hot carbondensitiesin the exosphereof Mars for the
altitude for the high and low solar activity cases.The exobase high solar activity case using various altitudesfor the exobase
altitude was chosen to be 192 km for these calculations.
height.
valuesare obtaineddirectly from the two-streamcalculationsand
thus do not dependon the choice of the exobaselocation. This
calculatedescapeflux can be comparedto the sputteringrate of
between
1-5 x l0s cm-2 s-1 [Luhmann
et al., 1992;Jakosky
et
al., 1994; Kass, 1999]. There are indirectindicationsof "heavy"
ionescape
(O+, O2+, CO2+, CO+, andC+) fromtheionosphere
of
from the Phobosspacecraft[Lundinet al.,
CO2,CO,andC byO+ ions,whichisestimated
tofallsomewhereMars by measurements
) '5
5000
.......
•
4000
".,.
-_-
-Collisions
WifhHof0
•'3000
N
2000
lOOO
....
I
........
I
10
,
, '•'
1 O0
.....
I
.......
1000
10000
Densify(cm-s)
1990; Veriginet al., 1991] and by model calculations[Fox, 1997;
Liu et al., 1999, 2001]. Thesedirection escapefluxesmay carry
more carbon than the escapedue to hot carbon, but both the
measurements
and three-dimensional
modelscan only provide an
estimate
of thetotalionescape
flux(3-14 x 1025
s-1).
The various possibleescapemechanismsmust have certainly
changedover the historyof the planet.It has been suggestedthat
the escapedue to sputteringwas more than 3 ordersof magnitude
largerthanthe presentrate 3.5 Gyr beforethe present[Luhmannet
al., 1992; Kass and Yung, 1995, 1996], but of course large
uncertaintiesare associatedwith these estimates.The currently
calculatedescapefluxeswould alsohavebeengreaterin an earlier
epochwhen the solarfluxeswere higher.The ion escapemechanism must also have been significantlydifferent,becauseof the
presenceof an intrinsicmagneticfield. This all meansthat while
these calculatedescapefluxes are of intellectualinterest, it is
difficult to estimate their significancein terms of the overall
evolution of the atmosphereof Mars, especiallysince some of
the atmospheric
carbonmay be tied up in carbon-beating
materials
in the regolithand carbonatedeposits.
Our calculations
24O
220
200
180
(b) ,,,,' //
•)'•
o•-•'d
Js
soc
iafio
n /
and assumed mean iono-
/
Dissoclohve
/iII
:,
ingfromthedayside
oftheplanet
is•6.3 x 1024and4.3 x 1023
atoms
s-1 forthehighandlowsolaractivity
cases,
respectively.
ß'•........
;..
Recombination
•/
/
•3(•lffsTo-ns
Wifh/•
•"
are one-dimensional
spheric conditions.If one assumesthat this result is a good
representation
of daytimefluxes and that the nighttimeescapeis
negligiblysmall,thenthe estimateof thetotalescaperateoriginat-
Acknowledgments. JanetG. LuhmannthanksR. RichardHodgesand
anotherrefereefor their assistance
in evaluatingthis paper.
/
/
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J. Kim, Korea AerospaceResearchInstitute,52 Eoun-dong,P.O.B. 113
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(ReceivedJanuary10, 2001; revisedApril 1,2001;
acceptedApril 1, 2001.)