VOL. 76, NO. 28
JOURNAL OF GEOPHYSICAL RESEARCH
OCTOBER 1, 1971
Mariner6 and7 Ultraviolet
Spectrometer
Experiment.
Analysis
of Hydrogen
Lyman-Alpha
Data
DONALDE. AN•SON, J•., ANYCI•Am,•,SW. Holy
Laboratory ]or Atmosphericand Space Physics
University o] Colorado,Boulder 80502
Mariner 6 and 7 ultravioletspectrometers
that flewby Mars in 1969observed
the Lyman-,
dayglowof atomichydrogen.Data in the altituderange200 to 24,000km are analyzedto
determine
the structure
of the Martianexosphere.
The classical
evaporative
theoryis applied
to calculatea hydrogendensitydistribution.A sphericalmodel of the dayglowLyman-a
emission,usingradiative transfertheory, is usedto producetheoreticalintensitiesfor com-
parison
with the datain orderto determine
temperature
anddensityin the exosphere.
It is
foundthat the exospheric
temperature
is 350ø ___100øKandthat the numberdensityat 250
km is 3 ___1 X 10' cm'•. The existence
of a Lyman-acoronaimpliesa primarysourceof
hydrogenon Mars, probablythe photodissociation
of water vapor.
Determination of the atomic-hydrogendis-
tributionin a planetaryatmosphere
is important
in studying the evolution and structure of
planetary atmospheres.
In addition to implications of the mere existenceof a hydrogen
corona,measurement
of its distributionprovides
informationabout conditionsat the uppermost
boundary of a planetary atmosphere.This
upperboundaryis the baseof the exosphere,
or
critical level, and is defined as the altitude at
a densitydistribution
and effectivetemperature at the baseof the exosphere.
In additionit
is possible
to calculate
the escape
fluxandthe
escape
timefor hydrogen
andotheratmospheric
constituents.
If thistimeis lessthanthe ageof
the solar system there must be some mech-
anismproducing
thisconstituent.
Owingto the
sensitivityof the technique,the lack of a de-
tectableLyman-a signalwouldimply that
atmospherichydrogenhad escapedand that
which a fraction,l/e, of a group of escaping regenerativeprocesseshave ceased.
particleswill experienceno further collisionsas
they go to infinitely greater heights [Spitzer,
1957]. Conditionsin the hydrogen exosphere
are determinedby propertiesof the atmosphere
at the critical level. Conversely,measurement
of the hydrogen coronal distribution is a meas-
AstheMariner6 and7 spacecraft
approached
Mars, the hydrogencoronawas first detected
whentheclosest
pointof thespectrometer
optic
axisto Mars was at a planetocentric
distance
of about30,000km [Barth et al., 1971].The
anglebetweenthe optic axis and the sun sub-
ure of conditions
at the criticallevel.The prop- tended at the spacecraftwas 117ø for Mariner
ertiesof primary importanceare the exospheric 6 and135ø for Mariner7. In thisgeometry
the
temperature,or effectiveMaxwellian tempera- signalis dominatedby the hydrogendistributure, that will give the observedhydrogendis- tion at a pointalongthe opticaxisthat passes
tribution, and the number density at the criticlosest
to the planet.The solarzenithangleof
cal level.
this point was 27ø and 44ø for the first limb
A sensitivemethodof determiningthe distributionof hydrogenis the detectionand analysis
of Lyman-a radiation that is produced from
resonantscatteringof the 1216-A solar Lyman-a
line by atmospherichydrogen.These Lyman-a
airglow measurements,
togetherwith appropriate radiative transfer and densitymodels,yield
crossings
of Mariner 6 and 7, respectively.
The
distanceof the closest
point alongthe opticaxis
to Mars is the effectivesamplealtitude.As the
spacecraftcontinuedto approachMars, the
Lyman-a intensity increasedto a maximum
when the field of view crossed the illuminated
limb. Observationswere then made of the illumi-
nated discof Mars, acrossthe eveningtermiCopyright ¸
1971by the American Geophysical Union.
6666
nator and darkside, and finally off the dark
HYDROGEN LYMaN-a
limb. In this discussion Mariner
6 and 7 data
obtained above the bright limb at sample
altitudesranging from 24,000 down to 200 km
are analyzed.This treatment includesthe determination of the appropriate hydrogendistribution model and the exospherictemperature
with proper consideration
of the effectof multiple scatteringon the Lyman-a intensity.
The Lyman-• intensity,•, expressed
hereas an
apparent column emissionrate, 4•r•, can be
written
as
DaTa
6667
per atom [Chamberlain, 1961]. In this discussion, 9 = 1.0 X 10-• sec-•, using the solar flux
measurement of Brunet and Rense [1969].
Observations of the Lyman-a corona surrounding Mars were made with a 250-mm
focal length Ebert-Fastie scanningspectrometer
[Pearce et al., 1971]. A 250-mm focal length
telescopewas used,which gave an angularfield
of view 0023' X 203' and provided an altitude
resolution of 26 km on Mariner
4•rlt-
Fv/•
(1)
where F is the effective solar flux seen by a
hydrogenatom, • is the atmosphericoptical
depth at line center, and •9 includesradiative
transfer effects.The effectivesolarflux, F, is defined as
F = WS:,
Av•r•/2
(2)
where•r•Y,is the solar flux assumedto be constant
over the wavelength interval where atmospheric
resonancereradiation is important, and Av is
the Doppler width in frequencyunits. Emission
is assumedto occurat a wavelengthindependent
of absorptionsothat the assumptionof complete
redistribution of frequency is used to model
multiple scattering effects.Both 4•rg and F are
given in units of rayleighs.An apparentcolumn
emissionrate 4•rlt = i rayleigh is equivalent to
6 and 34 km on
Mariner 7 at the bright limb. Two photomultiplier tube detectors,or channels,were used
to cover the spectral range 1100-4300 A. Lyman a was measured in second and third orders
with the short-wavelengthchannel that was
sensitive from
1100 to 2000 A. The two chan-
nels were simultaneouslyscannedevery 3 sec.
This analysis used the second-orderdata obtained at 10-A resolution.A samplingrate of 1
sample per channel per 5 msec gives 9 measurements
across the line for each scan. The
spectral information obtained from these observations is shown in Figure 1, which is an
averageof 10 Mariner 6 Lyman-a spectra.
The sets of bright limb data from Mariner
6 and from Mariner
7 each consist of more than
1500 individual Lyman-a spectrataken at altitude intervals of approximately 20 km. To
display this large number of measurements
an intensity It = 106/4•r photonscm-• sec-1
conveniently, the spectra were averaged in
ster-1. If the optical depth, •, is small compared
groupsof 25 near the planet and 50 beyond
with unity alongall optical paths in the medium,
14,000 km. These groups were chosento be
singlescatteringappliesand the factor • is equal
small enough so that the altitude variation of
to unity. In general• can be greateror lessthan
unity dependingon whether multiple scattering
buildup or attenuation is the dominant radiative
transfer effect. The optical depth at line center is
givenby
• =
aN
...o•
200-
z•o
Ioo
(s)
where(r -- 5.96 ß 10-• T-•/•'cm•' is the cross
section
at temperature,
T, at the centerof the
Lyman-a line. The columndensity,N, is the
number
ofhydrogen
atoms
cm
-•'along
theline
of sight. When singlescatteringis applicable,
equationI is oftenwrittenin the form
4•r•t= gN
o
(4)
whereg - F(ris the emission
ratefactordefined Fig. 1.
as the number of photonsscatteredper second
1200
1225
1250
WAVEL•'N6TH
Average of 10 Mariner 6 Lyman-a
spectra near the bright limb.
ANDERSON AND I-IORD
6668
age.Mean valuesfor the signaland background
were recalculatedwithout noisespikes.
8.0-
6.0
4.0
2.0-
o.s
0.•0.4,-
0.•-
0.1
,
6
12
18
24
R (103 KM)
Fig. 2. Best fit to the Mariner 6 data including
radiative transfer effects. Solid curve represents
the intensity predicted by theoretical model with
To -- 350øK and no • 3.0 X 10'4 cm-•.
Each Lyman-a measurementconsistsof two
components,
an exosphericsignaland a Lyman-q
sky background [Barth, 1970]. To determine
the sky background,1300 spectraobtainedat
sample distancesgreater than 60,000 km were
averaged.The martian hydrogencorona was
detectedwhenthe sampledistancewaslessthan
30,000 km. The sky backgroundfor Mariner
6 and 7 was 290 --+4 and 316 _+ 4 rayleighs,respectively. Galactic coordinates were 81.14ø
longitude, --50.18 ø latitude, and 89.54ø longitude, --13.54ø latitude, respectively.The errors
indicated are associated with calculation of the
mean intensity by averaging1300 spectrafrom
each instrument; the errors do. not reflect uncertainties in the instrument
calibration. Each
spacecraft was pointed in a fixed direction in
the intensity is not affected.At large distances inertial spaceuntil the bright limb was crossed,
from the planet the hydrogen density decreases sothe sky backgroundintensitysubtractionwas
constant for both Mariner 6 and 7.
more slowly with altitude, so more spectramay
Figures 2 and 3 are graphs of the Mars
be includedin the averagewithout losingaltitude information.
Lyman-q intensity with sky backgroundsubTo determinethe true signal,a constantnoise tracted [Barth et al., 1971]. The vertical scale
level, obtained by averaging several samples is fixed by the absolutecalibrationof the specadjacent to the Lyman-a line, was subtracted. trometer. An estimate of the error in absolute
In addition obvious noise spikes were removed calibrationis --+70% [Pearce et al., 1971]. The
by comparingindividualsampleswith the aver- abscissascale shows the distance from the closest
I0.0
8.0
6.0
4.0
1.0
0.8
0.6
0.4
0.2
0.1
5.65
I
I
I
!
6
12
18
24
R (103 km)
Fig. 3. Best fit to the Mariner 7 data including radiative transfer effects. Solid curve
representsthe intensity predicted by theoretical model with To -- 350øK and no -- 2.5 X
104 cm -•.
HYDROGEN L¾•AN-a
point alongthe optic axisto the centerof Mars.
Error bars shownin Figures2 and 3 indicate
DATA
6669
the exospherictemperature T•, the escapeor
critical level radius Re, and the number density
the standard .deviations of the individual meas-
Hydrogen atoms are assumedto be in ballistic, satellite,and escapeorbits.The contribution
to the density is determined for these components by consideringthe energy constraints
HYDROGEN DISTRIBUTION
and angular dependencefor each type of orbit.
Satellite orbits are populated by infrequent
A detailedhydrogendistributionis considered
only above the escapelevel. Trial calculations collisions that occur within the corona and are
indicate the exosphericLyman-a intensity is lost by rare destructive processessuch as
insensitiveto the distributionof hydrogenbelow photoionizationand charge transfer collisions
[Chamberlain, 1963]. The extent to which satelthe escapelevel and relatively insensitiveto the
total amount. Analysis of the Lyman-a inten- lite orbits are populated is not known, but
Chamberlain indicates that a level does exist
sity when Mariner observedthe disc of Mars
shouldbe sensitiveto the amount of hydrogen above which satellite orbits become depleted.
The degreeto which escapeorbits are popubetweenthe escapelevel and the altitudewhere
COs becomesopaque. Hunten and McElroy lated is also in doubt. Chamberlain and Smith
[1970] have discussedthe hydrogen densities [1971] show that depletionof the high-velocity
in this region of the Mars atmosphere.Owing tail of the Maxwellian distribution function may
to the relative insensitivity of the measured retard the escape of hydrogen atoms from a
exosphericintensity considered
in this work, a CO•. atmosphereby 50% of the classicalJeans
nominalvalue of 250 km is chosenfor the escape value. The approach used here has been to
level with an amount of hydrogenequivalentto
neglect atoms in satellite orbits and to assume
a full complementof escapingatoms. Addition
oneopticaldepth belowthis level.
Above 250 km the density distribution is of satellite orbits to the model reduces the
determined from considerationof orbit theory exospherictemperaturederivedfrom thesedata.
and solution of the collisionlessBoltzman equa- Depletionof escapingparticlesleadsto a higher
tion [Chamberlain,1963]. The densitydistribu- temperature.
tion determined in this manner is a function of
Figures4 and 5 showsinglescatteringcolumn
urements in each group of intensity measurements. Relative weights are assignedon this
basisfor comparisonwith theoreticalmodels.
10.0
1.0
R$C :7. RC
5. RC ---•
O.I
5.R c
I-R c
5
6
15
50
R(10 $ KM)
Fig. 4. Theoretical single scatteringslant intensitiesfor T• -- 350øK and values of the satellite critical level equal to 1, 3, 5, and 7 times R•. All curveshave the samevalue oœn•.
6670
ANDEeSON AN•) Hoed
I0.0
1.0 -
700
,-,.
500
•
4oc
350øK---//•
,01
3
6
15
30
R(103 KM)
Fig. 5. Theoreticalsinglescatteringslantintensitiesfor the satellitecritical]eve]equal
to R, and for temperaturesT, = 250, 300, 350, 400, 500, and 700øK. All curveshave the
same value of
emission
rates calculated
for the Mariner 6
boundaryexistswhereC02 absorption
becomes
Mars encountergeometry.Figure 4 indicates important.In thisdiscussion
theupperboundary
the effectof addingsatelliteorbits.In Figure is taken at a radial distance 10 times the lower
5 the exospherictemperatureis varied.
boundary.Hydrogenbeyondthisdistancemakes
a negligiblecontributionto the observed
planeTRANSFER EQUATZONS
tary intensity.The right-handsideof equation
Radiative transfer effects on the observed in5 is an average of the product of the source
tensityweretaken into accountby a factorfi functionS(R') and transmission
functionTIt(R,
in equation1. The factorfi is foundby solving R ') ] alongthe line of sight.Opticaldepthfrom
the basicequationsof radiativetransfer [Chan- the observationpositionR to a point R • along
drasekhar,1960]. In this analysisthe assump- the line of sight is t(R, R'). The transmission
tion of complete frequency redistribution is functionis given by
made with absorptionand emissionprofilesassumed to be Doppler. Thomas [1963] discussesthese assumptionsin detail. By solving
=
exr
the transferequations,the correctionfactormay
be written
where a(x) is the Doppler broadeningfunction
exp (--x •) and x -- (v -- Vo)/A•, is the fre-
27o
fo
t(R'Rb)
where t(R, Rb) is the optical depth from the
observationpositionR along the line of sight
to an effective boundary Rb. The vector R,
will lie on one of two spheresthat bound the
Lyman-e• scattering region. An effective lower
quency shift from line center •o measured in
Doppler widths.
In this formulation, solution of a transcendental equation for the sourcefunction is the
heart of the problem. Thomas [1963] and
Meier and Mange [1970] have obtained solutions for the Lyman-a planetary geometry.
Methods used here will be described in a later
publication. The source function satisfies the
integral equation
HYDROGEN LYMAN-e• DATA
ß
6671
(7)
fi
13
The driving term, or single scattering source
function, is the result of direct solar illumination and is givenby
(8)
wheret(R, R•,,) is the opticaldepth from position R to the boundary of the exospherein the
directionof the sun.Definingthe pr•ary source
function in this way causesSo(R) and therefore
S(R) to reduce to unity for an optically thin
medium.The integral over optical path in equation 7 is identical to the integral in equation 5
except for the kernel function
io
200
•(t)=• •• exp[-.(x)t]a(x)
dx
In equation 7 an average of the optical path
integral is taken over all directions,or a solid
angle .• = 4• ster, about the point R.
In units of effective solar flux, the predicted
3oo
400
HYDROGEN
500
600
EXOSPHERIC
TEMPERATURE
(OK)
Fig. 6. Distribution of the root mean square
(rms) errors when the best models at each temperature are fitted to the data.
column emission rate is
Combination of the definition of /3 (equation
5) with the formal solution (equation 10) gives
the predictedintensity expressedin equation1.
Rssvr•s
In the processof choosingthe exosphefic
model that best explainsthe observedintensifies, two key parameters,along with their associated uncertainties, are determined. These
parameters are the total vertical optical depth,
or equivalentlythe number densityat the critical level, and the exospherictemperature.The
follo•ng procedurewas usedto determinethese
parameters.
First, a vertical optical depth was chosenfor
each of the selectedtemperatures, 250•, 300•,
350•, 400•, 500•, and 700OK basedon the observed intensity beyond 14,000 •.
In this
region of the exospherethe ratarive transfer
correctionis small, so the predictedsinglescat-
tering intensityis adequateto give a first estimate of the verticalopticaldepth.
The secondpart of the procedureis to vary
the optical depth to find the optimumvalue for
each of the selectedtemperaturesby using
radiative transfer theory and the completeset
of data shownin Figures 2 and 3. In selecting
these optimum optical depths,the root mean
square (rms) error was minimized. Two results
were obtained from this analysis. First, the
initial estimatesof vertical optical depth were
very closeto the optimum values for each temperature. This result indicatesthat the absolute
intensities measured in the outer part of the
exosphereare consistentwith the best relative
intensity shape for each temperature, provided
by an optimum choice of optical thickness.
Second,among the selectedtemperatures with
the proper optical thickness, the best fit is
providedby choosing
the exospheric
temperature
to be 350øK.
The
rms error
as a function
of
temperature for Mariner 6 is shownin Figure 6.
An optimum fit found by usingthis two-parameter model corresponds
to a minimum rms error
of 10% and gives nominal values of 3 X 10'
6672
ANDERSON AND •{ORD
10.0
=2.0xlO
4CM
-3
=3.0xlO4CM
-3
=4.0
xlO4CM
-3
1.0
0.1
$
I
6
I
15
30
R (103 KM)
Fig. 7. Radiativetransfercorrected
intensitiesfor T• -- 350øKand n• -- 2, 3, and 4 X
10' cm-a modelscalculatedfor the Mariner 6 trajectory. Intensitieshave been normalizedto
the n• -- 3 >< 10' cm-a model at large distances.
cm3 for the numberdensityat the criticallevel
and 350øKfor the exospheric
temperature.
The third step in this procedureis to deter-
Figures2 and 3, compared
with the slopesimplied by the varioustemperaturemodels,an
upperlimit of 450øKis placedonthe exospheric
mine the uncertainties associated with these
temperature or a standarddeviation of -F 100øK.
parameters,particularlythe exospheric
temperaIn summary,least-squares
analysisgivesan
ture. In Figure 6 the steepincreasein rms error exospherictemperatureof 350ø _+ 100øK and
as the temperature decreasesbelow the best-fit • criticallevel volumedensityof 3 +---I X 10'
value reflectsthe rapid changein the shapeof cm-8independent
of instrument
calibration.
Figthe theoreticalcurveas onegoesto lower-tem- ures 5 and 6 are graphsof the 350øK model
perature models. On the basis of the low-tem-
togetherwith the data. In Figure7 graphsof
peraturepart of the curveshownin Figure6, it
the 350øK model for critical level volume densi-
is estimated that the lower limit on the ex-
tiesof 2, 3, and4 X 10' cm-8are given.Table
ospherictemperatureis 250øK, or a standard I givesthe volumedensityas a functionof altideviationof --100øK. As the temperaturein- tude above the critical level for the 350øK
creasesabove350øK, the shapeof the theoreti- model with n• = 3 X 10' cm-•.
cal curvedoesnot changeits basicshapebut does
SUM MARY
changeslope.When the optimum700øK model
is fitted to the data for example,virtually all
A modeldensitydistributiontogetherwith a
data points close to the planet lie above the
theoretical curve, while all those far from the
spherical radiative transfer formulation have
planet lie below.In other words,the rms error
beenusedto analyzeMars Lyman-a data obtained from ultraviolet spectrometers
on Mari-
in Figure 6 assumes• random distribution of
ner 6 and 7. Values were obtained for the tem-
errors and doesnot properly reflect how badly
the slope of the 700øK model disagreeswith
the data. To specify an upper limit on the
exospherictemperaturea differentanalysismust
be used.If one considers
the slopeuncertainty
of the data on the logarithmic scale'shownin
atomichydrogenat the baseof the exosphere.
A measureof the stability of the Mars atmosphere againstlossof atomichydrogencan be
obtainedfrom the escapetime of a hydrogen
perature, 350øK, and density,3 X 10' cm-• of
atom from the exosphere.
The exospherictern-
HYDROGEN LYMAN-a
TABLE
1.
6673
REFERENCES
Volume Density Distribution
Altitude, km
Density, 104 cm-3
250
500
75O
1000
2500
5O00
750O
10000
12500
15000
17500
20000
22500
3.0
2.1
1.7
1.4
0.61
0.24
0.12
O.O72
0.048
0.034
0.026
0.020
0.016
perature and density determinedhere give an
escapeflux of 1.8 X 108 cm-• sec-• and an escape
time of 10' see, which is less than 1 Martian
day. A primary sourceof hydrogenmust therefore exist in the lower atmosphere of Mars.
The source of atomic hydrogen on Mars is
probably the dissociation of water vapor.
Hunten and McElroy [1970] estimatethat the
integratedphotodissociation
rate of water vapor
is between 10• and 10TMcm-• sec-•. Therefore,
this source is more than adequate to account
for the flux of atomic hydrogenthat is currently
escapingfrom the planet.
Acknowledgments. We thank Charles A. Barth
for his advice and creative suggestions,and Lloyd
Wallace for his many useful comments.
This work was supported by NASA contract
NGL
I)ATA
06-003-052.
Barth, C. A., Mariner 6 measurements of the
Lyman-alpha sky background, Astrophys. J.
Left., 161, L181, 1970.
Barth, C. A., C. W. Hord, J. B. Pearce, K. K.
Kelly, G. P. Anderson, and A. I. Stewart,
Mariner 6 and 7 ultraviolet spectrometer experiment: Upper atmosphere data, J. Geophys.
Res., 76, 2213, 1971.
Brunet, E. C., and W. A. Rense, Rocket observations of solar ultraviolet emission lines, Astrophys. J., 157, 417, 1969.
Chamberlain, J. W., Physics o] the Aurora and
Airglow, Academic, New York, 1961.
Chamberlain, J. W., Planetaw coronae and atmospheric evaporation, Planet. Space Sci., 11,
901, 1963.
ChamberlMn, J. W., and G. R. Smith, Comme,,ts
on the rate of evaporation from a non-Maxwellian atmosphere,Planet. Space Sci., in press,
1971.
Chandrasekhar, S., Radiative
Transfer, Dover,
New York, 1960.
Hunten, D. M., and M. B. McElroy, Production
and escape of hydrogen on Mars, J. Geophys.
Res., 75, 5989, 1970.
Meier, R. R., and P. Mange, Geocoronal hydrogen: An analysis of the Lyman-alpha airglow
observedfrom Ogo 4, Planet. Space Sci., 13, 803,
1970.
Pearce, J. B., K. A. Gause, E. F. Mackey, K. K.
Kelly, W. G. Fastie, and C. A. Barth, The
Mariner 6 and 7 ultraviolet spectrometers,Appl.
Opt., 10, 805, 1971.
Spitzer, L., The terrestrial atmosphere above 300
km, in The Atmosphere o] the Earth and
Planets, edited by G. P. Kuiper, University of
Chicago Press, Chicago, Ill., 1957.
Thomas, G. E., Lyman-alpha scattering in the
earth's hydrogen geocorona, 1, J. Geophys. Res.,
68, 2639, 1963.
The Editor thanks M. B. McElroy and another
referee for their assistance in evaluating this
paper.
(Received March 22, 1971;
accepted June 29, 1971.)