www.sciencemag.org/cgi/content/full/science.1198366/DC1
Supporting Online Material for
Cassini Finds an Oxygen–Carbon Dioxide Atmosphere at Saturn’s Icy
Moon Rhea
B. D. Teolis,* G. H. Jones, P. F. Miles, R. L. Tokar, B. A. Magee, J. H. Waite, E. Roussos,
D. T. Young, F. J. Crary, A. J. Coates, R. E. Johnson, W.-L. Tseng, R. A. Baragiola
*To whom correspondence should be addressed. E-mail: [email protected]
Published 25 November 2010 on Science Express
DOI: 10.1126/science.1198366
This PDF file includes:
Materials and Methods
SOM Text
Figs. S1 to S10
References and Notes
Supporting Online Material
Cassini Finds an Oxygen–Carbon Dioxide Atmosphere at Saturn’s Icy Moon Rhea
B. D. Teolis, G. H. Jones, P. F. Miles, R. L. Tokar, B. A. Magee, J. H. Waite, E. Roussos,
D. T. Young, F. J. Crary, A. J. Coates, R. E. Johnson, W.-L. Tseng, R. A. Baragiola
Methods
1. Estimating Rhea surface irradiation and sputtering
1.1 Ion Irradiation
The Saturnian magnetosphere roughly co-rotates with Saturn, sweeping past
Rhea and preferentially bombarding the trailing hemisphere [Fig. 2]. Here we
r
have assumed a bulk plasma speed of v0 = vcorot − vRhea ≈ 49.1 km/s relative to
Rhea, with vRhea = 8.5 km/s the Rhea orbital speed, and vcorot ≈ 57.6 km/s the
plasma speed estimated by Wilson et al. (S1) in Saturn’s reference frame. We
have treated the Saturn ion population by assuming two dominant populations
(S2): (i) protons and (ii) water group ions consisting of O+, OH+, H2O+ and H3O+
which we have denoted as W+ and approximate for the calculations as having
mass 16 amu and charge +1. Using densities of 0.4 H+ and 5 W+ per cm3 (S1),
r
r
we have approximated the 3-dimensional velocity distributions f H + (v ) and fW + (v )
of each population in the plasma rest frame based on (i) Wilson et al.’s (S1) bidirectional Maxwellian fits for H+ and W+ from the 26 November, 2005 CAPS data
near Rhea and (ii) a power law fit to the higher energy MIMI Charge Energy
Mass Spectrometer [CHEMS] energy spectra from the 2 March, 2010 encounter
(S3). The Maxwellian fits under-estimate the CAPS data above several hundred
eV (S1), and thus we applied an interpolation of the CAPS and MIMI fits in the
0.18 - 32 keV range for H+, and 0.7 - 8 keV for W+. To obtain the distributions as
seen on Rhea’s surface we translated f H + and fW + in velocity space to the Rhea
r
r
r r r
coordinate frame: f (v ) → f (v ') , where v ' = v + v0 . Using a computer algorithm to
backtrack the H+ and W+ trajectories from the point of impact on the surface, we
r
have also estimated the surface access function g (v ') , which is zero if the
trajectory is obstructed (S4) by Rhea’s surface at any other point due to the ion
gyromotion, and unity otherwise [though due to the large ion gyroradii [Fig. S1]
~95 % of the ambient H+ and W+ flux has access to Rhea’s surface]. We
estimated the H+ and W+ surface bombardment flux FH + (θ ,ϕ , ε ) and FW + (θ ,ϕ , ε )
versus particle energy ε at 20×30 points of latitude θ and longitude ϕ by
r
numerically integrating g H + f H + and gW + fW + times v '•nˆ [with n̂ the unit surface
1
normal] over velocity space within the 2π steradians of sky visible from each
point [here we ignore local topographical restrictions on the field of view]. As an
example we show in Fig. S1 the energy distributions for H+ and W+ calculated at
the apexes of the leading and trailing hemisphere. As expected the intensity is
greater on the trailing than the leading hemisphere, with the difference being
greatest near the peak of the energy distribution, and less at higher energies
r
corresponding to ion speeds much greater than the bulk flow speed v0 ≈ 49.1
km/s. Approximations inherent in the calculation procedure are that (i) ion
trajectory perturbations due to the plasma wake over the leading hemisphere and
(ii) surface charging, do not drastically alter the distribution striking the surface.
Figure S1. The energy distribution of the H+ and W+ flux bombarding the apexes of the leading
and trailing hemispheres estimated according to the method described in the text. The
distributions are for ions arriving from all directions over 2π steradians of visible sky. The H+ and
W+ gyroradii in a 26 nT (S5) magnetic field are given on the top axis.
Finally, we calculated the O2 production S H + (θ , ϕ ) and SW + (θ , ϕ ) versus position
[Figs. S2 and S3] by integrating the irradiation flux and the yields YH + (ε ) and
YW + (ε ) over energy ε :
S (θ , ϕ ) = ∫ F (θ , ϕ , ε )Y (ε ) dε ,
(S1)
where the Y (ε ) were estimated from the O2 radiolysis model described in section
2.
2
Figure S2. Estimated O2 production versus position from equation S1 over Rhea’s trailing
hemisphere. Includes H+ and W+ from equation S1, electrons from equation S4, and UV photons
[section 1.3]. Arrow: co-rotation direction.
Figure S3. Same as Fig. S2 over the leading hemisphere.
1.2. Electron Irradiation
Although the electron plasma densities and moments throughout the Saturn
system inside 20RS have been surveyed recently by Schippers et al. (S6), the
Cassini observations during the 26 November, 2005 Rhea flyby showed an
electron depletion in Rhea’s vicinity, the cause of which is still uncertain (S7, S8).
We therefore used the CAPS ELS and MIMI Low Energy Magnetospheric
Measurement System [LEMMS] data (S3) obtained directly from the 2 March,
2010 flyby to characterize the electron plasma bombarding Rhea. Since for
r
r
electrons v0 << vthermal we neglected plasma co-rotation and assumed an
r
isotropic flux distribution Φ e (ε ) = v f e (v ) with helical field line-bound trajectories [ B
points south at ~26 nT (S5) near Rhea]. The gyroradii are much smaller than
Rhea for all but a negligible fraction [~0.1 %] of high energy electrons faster than
~105 eV [Fig. S4]. Therefore the electron density striking Rhea can be
3
characterized as having a nearly north-south field-aligned bulk flow, with a
surface bombardment flux decreasing toward the equator according to a sin θ
surface access function:
g e (θ ) ≈ Bˆ • nˆ = sin θ ,
with the surface flux versus energy given by
r
Fe (θ , ε ) = g e (θ ) ∫ f e (v ) v • nˆ dvˆ = g e (θ ) Φ e (ε )
2π str
and the O2 production Se (θ ) by
(S2)
∫
vˆ • nˆ dvˆ ≈ π Φ e (ε ) sin θ , (S3)
2π str
S e (θ ) = ∫ Fe (θ , ε )Ye (ε ) dε ≈ π sin θ ∫ Φ e (ε )Ye (ε ) dε ,
(S4)
r
where we have estimated Ye (ε ) in section 2. Since the v0 transit time across
Rhea’s diameter of ~(1528 km) / (49.1 km/s) = ~31 seconds is much shorter than
the electron magnetospheric north-south bounce period below ~105 eV (S5), we
do not include in equation S3 any longitudinal dependence as seen at Europa
[where flux tube depletion due to shorter bounce periods causes (S9) preferential
trailing side irradiation].
Figure S4. Solid black line: Φ e electron spectrum used in the calculations, reconstructed from
the 2 March, 2010 CAPS ELS spectrum [~10 deg pitch angle, all anodes averaged, 20 min before
Rhea closest approach] merged [above 30 keV] with a power law fit to the MIMI LEMMS (S3)
electron spectrum [averaged 20-100 deg pitch angle scans 40-25 min before, and 50-65 min after
closest approach]. Dashed black line: For comparison, distribution predicted at Rhea’s orbit from
the plasma moments of Schippers et al. (S6). Red line: Electron gyroradius in a 26 nT (S5)
magnetic field.
4
1.3. Solar Ultraviolet Photons
Scaling the solar UV irradiance spectrum at 1 AU (S10) to Saturn’s orbital
distance [9.49 AU on 2 March, 2010] we estimated an irradiance of I 0 = 4.4×1014
eV/m2/s for photon energies above the experimentally measured O2 synthesis
threshold of 10 eV (S11, S12). The irradiance I at Rhea’s surface is I 0 cos γ ,
with γ the solar zenith angle, and we estimated O2 photodesorption from the
surface as φ I = φ I 0 cos γ , with φ = 5.2×10-5 O2 per eV the photodesorption yield
measured from Lyman-alpha [10.2 eV] irradiated 100 K ice (S13). Total O2
photoproduction is computed from Rhea’s π R 2 cross section as π R 2φ I 0 =
4.2×1022 s-1, where Rhea’s radius R = 764.3 km.
1.4. Energy and atmospheric contribution of the initially sputtered O2
To account for the porous regolith morphology of Rhea’s surface ice, we treated
the energy distribution of the initially sputtered O2 molecules as a sum of two
contributions: (i) a fraction α of sputtered O2 molecules which first re-impact and
thermally accommodate with other regolith grains before escaping the surface,
and (ii) the remaining 1 − α ejected from the regolith unobstructed. We used
α ≈ 70% based on Monte Carlo regolith sputtering simulations for a cosine
sputter ejection distribution (S14), and assumed for this thermally accommodated
O2 fraction a Maxwell-Boltzmann energy distribution at the local surface
temperature. For the remaining directly sputtered 30% we used the laboratory
O2 energy distribution measured from 1.5 MeV Ar+ irradiated ice (S15). Since
this is the only such published measurement for O2 from ice, we apply the
distribution for all irradiation sources [photons, electrons, ions] and energies. We
estimate that ~33 % of the directly sputtered O2 has energy above the required
0.067 eV for gravitational escape, while for the thermally accommodated O2 the
escape fraction is much smaller: 1.8 % at the maximum 100 K (S16) Rhea
temperature. Hence the fraction of initially sputtered O2 which escapes Rhea
immediately is small: ~(1 – 0.7) × 0.33 = ~10 %. We estimate that the directly
sputtered population has an average lifetime of ~8000 seconds within the Hill
sphere [7.6 Rhea radii] before either (i) escaping or (ii) re-impacting Rhea
[whereupon it is thermally accommodated with the surface]. By contrast, the
estimated average lifetime for oxygen in the atmosphere is ~105 sec, and
therefore nearly all atmospheric O2 molecules are thermally accommodated: 1 (1 – 0.7)×(~8000 sec) / (~105 sec) = ~97.6 % within 7.6 Rhea radii. O2 molecules
have on average ~57 surface collisions before escape [not counting possible
multiple collisions in the surface regolith], which is also sufficient to decorrelate
the spatial distribution of O2 from the positional distribution of production S (θ , ϕ ) .
5
1.5. Sputtered H2O and H2
O2 and H2 are the dominant radiolysis products sputtered from ice, and therefore
these species will be sputtered from Rhea in an ~2:1 stoichiometric ratio as seen
in laboratory experiments (S17-S20), corresponding to 4.9×1024 H2/sec [i.e.,
twice the value for O2, see Table 1]. There are no published measurements of
the sputtered H2 energy distribution from ice, but assuming the same distribution
as for O2 and repeating the calculations in part 4 above for H2, one obtains an H2
fraction of 95.3 % above the 0.004 eV gravitational escape threshold. For the
remaining 4.7 % Jeans escape will dominate the loss due to the low mass, and
the estimated atmospheric lifetime of ~1.4×104 seconds for the bound H2
corresponds to an average H2 / O2 ratio of 2×0.047×(~1.4×104) / (~105 sec) =
~1.3 %, with the factor of 2 the ratio of H2 to O2 production. This relatively low
atmospheric abundance explains the lack of H2 detection by INMS, although H2+
formed by ionization is present in the ambient plasma (S2).
We estimated the sputtering of water molecules from Rhea by replacing the
yield functions YH + (E ) and YW + (E ) for O2 sputtering with the analogous functions
for H2O, which are now well characterized (S21). We used equation S12 in
section 2 to account for the distribution of ion incidence angles onto the
differently oriented regolith grain surfaces, and reduced the result by a factor
1 − α = 0.3 since, unlike the more volatile O2, sputtered H2O molecules reimpacting neighboring grains are adsorbed and cannot escape the regolith.
Therefore the escaping molecules do not have a thermally accommodated
energy distribution component. The calculations give 0.054 and 5.37×1024 H2O /
sec sputtered by H+ and W+ from Rhea [consistent with other (S22) estimates], of
which ~83 % are expected to have energies above the 0.038 eV Rhea escape
threshold if one uses the experimentally measured sputtered H2O energy
distribution (S15). The remaining ~17 % of the water molecules will fall back to
the surface where, in contrast to H2 and O2, they re-adsorb. We estimate an
average H2O [escaping and non-escaping] lifetime of ~4200 seconds within the
Hill sphere, yielding an estimated average H2O / O2 ratio of 2.2×(4200 sec / ~105
sec) = 9.2 % inside 7.6 Rhea radii [i.e. undetectable by INMS], with the factor 2.2
the estimated ratio of H2O to O2 sputtering from Rhea.
1.6. Secondary Sputtering
The pickup ion gyroradii [314, 630 and 866 km for cold O, O2 and CO2 ions with
r
E = 1.28 V/km: the field for v0 = 49.1 km/s] are of the order of Rhea’s 764 km
radius, and therefore positive and negative pickup ions are accelerated toward
Rhea by the co-rotation electric field over the Saturn and anti-Saturn Rhea
hemispheres, respectively. Taking the altitude of ionization as the estimated
average molecule height of ~60 - 120 km over the day-night hemispheres, we
6
r
obtain E × h = ~77 – 153 eV for the average day-night surface impact energies.
However the situation is much more complex, since the pickup ions also
transport charge to the surface, thereby affecting the surface potential and
energies of the impacting ions. At the steady state surface potential the sum of
the currents from all sources [i.e. positive and negative pickup ions, primary ions,
magnetospheric electrons, secondary electrons and photoelectrons] will be zero.
An accurate estimate of the pickup ion flux and energy distribution will therefore
require the modification of current Rhea charging models (S23) to include pickup
ions the in current balance condition.
2. Model for O2 Radiolysis from ice by ions and electrons
Using previously available laboratory data and understanding, atmospheric
models of Europa and Ganymede have either set the O2 surface production rate
as an assumed fixed fraction of the H2O sputtering (S24), or left the source as a
flexible fitting parameter (S25-S28). However for Rhea we have applied the
knowledge gained from recent experimental work for electrons (S29, S30) and
ions (S17) to model and quantitatively predict the O2 sputtering rate from ice for
any projectile and energy. A key experimental finding is that O2 production takes
place near the ice surface, i.e., it’s formation in ice is a decreasing function of the
depth x below the surface of the solid where ions or electrons deposit their
energy. Suggested explanations for the surface effect are H or H2 outdiffusion
(S17), which favors oxygen synthesis by changing the stoichiometry near the
surface, and/or an interaction of mobile electronic excitations with the surface
(S29, S30).
The number of O2 molecules synthesized per unit of deposited energy is
characterized by a radiolysis yield G (x ) which is a decreasing function of depth,
but experiments so far (S17) have not measured G ( x ) directly [only the trapped
O2 distribution, which is broadened compared to G (x ) by radiation-induced
diffusion]. However one can approximate G ( x ) by using a reasonable analytic
function. We have chosen an exponential form
G (x ) = G0 exp(− x / x0 ) ,
(S5)
with G0 and x0 as fitting parameters. The experiments also show an increase of
O2 synthesis with ice temperature (S31), and hence G0 is temperaturedependent. However we have not attempted to include the explicit temperature
dependence in equation S5 since, from the limited number of available
measurements, the exact dependence appears to be a function of projectile
7
properties (S17-S21, S29, S32). Rather, we have aimed here to estimate an
average G0 that is applicable over Rhea’s temperature range (S16).
The O2 yield [i.e. the number of oxygen molecules produced per incident ion]
is given by
∞
Y = ∫ δ ( x ) G ( x ) dx ,
(S6)
0
where δ ( x ) denotes the energy deposition [i.e. the stopping power] into the solid
versus depth, which we have evaluated for ions with the TRIM Monte Carlo code
(S33). Using TRIM we excluded from δ ( x ) the energy going directly to lattice
phonons, since phonons do not contribute to radiolysis [though the correction is
typically negligible for ion energies > ~1 keV].
Figure S5. Comparison of the measured O2 sputtering yield from ice to the prediction of equation
S6 with x0 = 30 Ǻ and G0 = 4.48×10-3 eV-1. We use data for ice temperatures as close as
possible to the maximum [~100 K], mean [~66 K] and minimum [taken here to be 35 K] Rhea
surface temperatures (S16), although some experiments were only done outside of this range.
Measurements performed versus temperature are adjoined by vertical lines, with the measured Y
always increasing with temperature. Bar-Nun et al. (S19): ■: 0.5-5 keV H+; Bahr et al. (S34): ▼:
200 keV H+; Brown et al. (S18): ∆: 1500 keV He+; Bar-Nun et al. (S19):
: 1-5 keV Ne+;
+
Baragiola et al. (S32), Teolis et al. (S17): □: 100 keV Ar ; Teolis & Baragiola (S35): ○: 0.2-3.5 keV
Ar+; Teolis et al. (S17): □: 4.5 keV Ar+; Chrisey et al. (S20): : 30 keV Kr+.
In Fig. S5 we compare
measurements, plotting
temperature range (S16).
[with the G0 uncertainty
the prediction of equation S6 to the laboratory ion
[where possible] measurements within Rhea’s
Using x0 = 30 (±5) Ǻ and G0 = 4.48×10-3 (±0.2) eV-1
resulting mainly from the experimental temperature
8
range], we have obtained agreement with the measurements to an order of
magnitude or better.
We also compute the average radiolysis yield Gavg , equal to Y / ε :
∞
Gavg =
Y
ε
=
∫ δ (x )G(x ) dx
0
∞
∫ δ (x ) dx
,
(S7)
0
where ε is the total deposited energy which does not contribute to lattice
phonons [approximately equal to the ion energy > ~1 keV]:
∞
ε = ∫ δ ( x ) dx .
(S8)
0
A longstanding source of confusion has been the very different Gavg values,
ranging over four orders of magnitude, implied by the laboratory measurements
[as seen in Fig. S5 where, e.g., 1500 and 0.5 keV ions produce similar amounts
of O2]. However, as shown in Fig. S6, the drastic variation of Gavg is in fact
predictable, and consistent with the result of equation S7.
Figure S6. From the same data as Fig. S5: comparison of the measured Gavg of O2 from ice to
the prediction of equation S7 with x0 = 30 Ǻ and G0 = 4.48×10-3 eV-1. As shown, the model
correctly predicts the previously unexplained variation of measured Gavg.
9
In Figs. S7 and S8 we show that this variation is a consequence of the ion range.
Ions stopped close to the surface, where O2 synthesis tends to occur, are
efficient oxygen producers [high Gavg ], while highly penetrating ions that deposit
most of their energy at depth are inefficient [low Gavg ]. As an approximation one
can substitute into equation S7 a step function energy deposition distribution
δ ( x ) = ε / xmax extending down to the ion range xmax , yielding:
Gavg ≈
1
xmax
xmax
∫ G(x ) dx = G x
0 0
0
1 − exp(− xmax / x0 )
,
xmax
(S9)
This expression [with x0 = 30 Ǻ and G0 = 4.48×10-3 eV-1] is a good fit to the ion
range dependence of Gavg , as shown in Figs. S7 and S8. In the limit of large ion
ranges xmax >> x0 equation S9 yields an inverse dependence of Gavg on ion
range:
Gavg ≈
G0 x0
xmax
for
xmax >> 30 Ǻ,
(S10)
while Gavg ≈ G0 for xmax << x0 .
Figure S7. From the same data as Figs. S5 and S6: the measured Gavg plotted versus ion range
[taking into account the incident angle of the ions in the experiments]. Solid line: equation S9 with
x0 = 30 Ǻ and G0 = 4.48×10-3 eV-1. Dashed Line: equation S10 with the same values.
10
Figure S8. Same as Fig. S7 plotted in log-log scale.
In contrast to ions, published calibrated measurements for O2 yields from
electron irradiated ice are scarce, and so far such measurements have been
limited to energies no greater than 100 eV (S11, S12). Here we have used the
known ranges of electrons in ice (S36, S37) to estimate the yield as
Ye = α ε eGavg ,
(S11)
with ε e the electron energy and Gavg computed from equation S9. We include
the scaling factor α = 0.29 based on a comparison with the most recent available
(S3) electron measurements below 30 eV [Fig. S9]. As an exception to equation
S11 we have set Ye = 0 for ε e < 10 eV: the approximate energy threshold for O2
production seen in laboratory experiments (S11, S12).
11
Figure S9. Circles: laboratory measurements of Gavg for electron stimulated desorption of O2
versus energy [5 – 30 eV] and electron range, from an amorphous nonporous 30 monolayer ice
film vapor deposited onto Pt(111) at 100 K, for electrons incident at 45 deg (S3). The
measurements have ±50% uncertainty. Solid Line: the prediction of equation S9 used to model
O2 from ions. Dashed line: Equation S11, used to model electrons. Dotted Line: 10 eV
approximate threshold for O2 radiolysis (S11,S12).
We estimated the O2 yield per incident ion for an ice regolith, as exists on
Rhea’s surface, by averaging Y over incidence angle β to approximate an
ensemble of randomly oriented grain surfaces:
π /2
Yregoltih =
∫ Y (β ) cos β sin β dβ
0
π /2
∫ cos β sin β dθ
π /2
= 2 ∫ Y (β ) cos β sin β dβ ,
(S12)
0
0
where we have included the cos β dependence of the surface flux. To compute
Y (β ) for ions we used the energy deposition distribution at non-normal incidence
δ ( x, β ) = δ (x' , 0 ) / cos β , with x' = x / cos β , in equation S6. For electrons we
corrected Gavg in equation S11 for non-normal incidence by using
xmax = xmax, θ =0 cos β in equation S9. We show the results of equation S12 for H+,
W+ and electrons in Fig. S10, which we have used in equations S1 and S4 to
estimate the production of O2 from Rhea’s surface by ions and electrons.
12
Figure S10. Prediction of equation S12 for the O2 yield Yregolith per incident projectile from an ice
regolith for protons, water group ions, and electrons. We used these results in equations S1 and
S4 to estimate the O2 sputtering from Rhea’s surface.
Other parameters which we did not consider in the model are the crystalline
phase (S38) and impurities (S39, S40) in Rhea’s ice: conditions that suppress
(S12, S41) the laboratory O2 yields compared to the pure amorphous ices used
in most of the experiments (S3, S17-S20, S30, S32, S35). However, based on
the limited available measurements (S12, S41), we consider these effects to be
within the uncertainty due to the temperature range and dispersion of the
laboratory data [Figs. S5 - S8]. In addition, while ice microporosity enhances
laboratory O2 yields from electrons due to the large pore surface area (S29),
recent experiments show microporosity to be unstable against ion bombardment
(S42, S43). Therefore the electron data (S3) reported in Fig. S9 measured from
nonporous ice samples are an appropriate analog to Rhea’s ion-irradiated ice.
13
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S16.
S17.
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S21.
S22.
S23.
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