APPENDIX D
CALCULATION OF ION SPUTTERING RATES
Table VIII. Estimation of Sputtering Rates due to
Low-Energy Plasma (Voyager PLS)
|
Europa
|
Ganymede
|
Callisto
|
Ion Species
|
H
|
O
|
S
|
H
|
O
|
S
|
H
|
O
|
S
|
Mass density, amu cm-3,1
|
1500
|
150
|
15
|
Composition, 2 |
Typically 20% H, 40% O, 40% S where measurable
|
Number density ions cm-3
|
15.5
|
30.9
|
30.9
|
1.55
|
3.09
|
3.09
|
0.155
|
0.309
|
0.309
|
Co-rotational energy, eV ion-1,3
|
39.5
|
632
|
1260
|
160
|
2560
|
5120
|
192
|
3080
|
6160
|
Thermal kT, eV, 1
|
Generally approx. 100eV, with a few colder regions
|
Co-rotational flux (trailing hemisphere),106 ion cm-2
s-1
|
130
|
270
|
270
|
27
|
54
|
54
|
3.0
|
5.9
|
5.9
|
Thermal flux (isotropic), 106 ions cm-2 s
-1
|
61
|
30
|
21
|
6.1
|
3.0
|
2.1
|
0.61
|
0.30
|
0.21
|
Yield, H2O molecules per ion at co-rotational energy,
4
|
0.3*
|
8
|
16
|
0.4
|
8
|
16
|
0.5
|
8
|
16
|
H2O yield due to ion corotational flux, 106 molec.
cm-2 s-1
|
39*
|
2200
|
4300
|
11
|
430
|
860
|
1.5
|
47
|
94
|
H2O yield due to corotational flux from all species
106 molec. cm-2 s-1
|
6500
|
1300
|
140
|
H2O ice erosion rate, 10-6 mm yr-1
|
66 |
13 |
1.4 |
Notes
1McNutt et al, 1981. 2Bagenal and Sullivan,
1981. 3Wolff and Mendis, 1983. 4Johnson et al,
1984, assuming yield for S ions is twice that for O ions with same velocity
(Johnson, pers. comm.).
*Yield for thermal energy used (as higher than corotational energy
in this case).
Table IX. Estimation of Sputtering Rates due to
High-Energy Plasma (Voyager LECP)
|
Europa
|
Ganymede
|
Callisto
|
Assumed Composition
|
H
|
O
|
S
|
H
|
O
|
S
|
H
|
O
|
S
|
Number density, ions cm-3,2
|
3.0
|
20
|
40
|
0.15
|
0.7
|
1.4
|
0.02
|
0.1
|
0.2
|
Co-rotational energy, eV ion-1,1
|
39.5
|
632
|
1260
|
160
|
2560
|
5120
|
192
|
3080
|
6160
|
Minimum energy detectable by Voyager 2 (E1),
keV,2
|
28
|
66
|
100
|
28
|
66
|
100
|
28
|
66
|
100
|
Co-rotational flux (traliling hem.), 106 ions cm-2,s-1
|
27
|
180
|
350
|
2.6
|
12
|
24
|
0.39
|
1.9
|
3.9
|
'Thermal' flux (isotropic),kT=E1,106
ions cm-2 s-1
|
200
|
500
|
880
|
9.8
|
18
|
31
|
1.3
|
2.5
|
4.4
|
Yield, H2O molecules per ion with E=E1,3
|
2
|
30
|
40
|
2
|
30
|
40
|
2
|
30
|
40
|
H2O yield due to 'thermal' flux, 106molecules
cm-2 s-1
|
400
|
15000
|
35000
|
20
|
540
|
1200
|
2.6
|
75
|
180
|
H2O ice erosion rate,10-6 mm yr-1
|
4.0
|
150
|
360
|
0.21
|
5.5
|
12
|
0.027
|
0.77
|
1.8
|
Notes
1 Wolff and Mendis, 1983.
2 Krimigis et al, 1981. E1 is used
as the energy for all detected ions because of the observed steepness of
the energy distribution. An unknown number of ions lie below the detection
threshold of the instrument.
3 Johnson et al, 1984, assuming yield for S ions
is twice that for O ions with same velocity (Johnson, pers. comm.).
The Galilean satellites are immersed in Jupiter's large and dynamic
magnetosphere, which contains ions derived variously from the solar wind,
the Jovian atmosphere, and the surfaces of the satellites themselves. The
major heavy ions (Z > 2) are oxygen and sulfur ions derived from
the surface of Io. Outside the Io torus, the plasma contains a thermalized
population with a kT of 100's of eV, detected by the Voyager PLS
experiment (Bagenal and Sullivan, 1981), and a much hotter component with
comparable number density and an equivalent kT of 10's of keV, measured
by the LECP instrument (McNutt et al, 1981, Krimigis et al,
1981). There is also a high-energy tail with energies in the MeV range.
The hot and cold populations differ in composition, satellite impact
geometry, and sputtering mechanism, and must be considered separately.
Tables VIII and IX summarize current knowledge of the important characteristics
of each component, and estimate the ice erosion rates on the surfaces of
the icy Galilean satellites due to each. An ice density of 0.92 is assumed,
to allow comparison with the sublimation rate calculations in Chapter 8
that make the same assumption. There are numerous uncertainties inherent
in these estimates, including the following:
1) The spatial and temporal variability of the plasma
is poorly known, as Voyager only provided localized `snapshots'. The tabulated
densities and fluxes refer to the `plasma sheet' near the Jovian equatorial
plane, and densities outside this sheet are reduced by about an order of
magnitude (e.g. McNutt et al, 1981). Callisto, and possibly Ganymede,
spend some of their time outside the sheet.
2) The energy range between a few keV and several
10's of keV per ion was not measured by Voyager and ion densities and compositions
in this range are not known. The sputtering from ions in this range is
not included in the numbers given. Even the width of the unmeasured energy
range is not known, as the lower energy limit of the LECP instrument depends
on the (unknown) ion composition (see point 3 below).
3) The composition of the ions in the 100
keV range, which may be the most important sputterers, is essentially unknown.
Table IX therefore sets limits by calculating rates assuming the plasma
is composed entirely of H, O, or S ions. The analysis is complicated by
the fact that the Voyager LECP instrument, which measures the ions of this
energy, responds differently to ions of different composition (Krimigis
et
al, 1981), so that both number densities and energies are a function
of assumed composition. It can be seen from Table IX that the sputtering
rate depends drastically on the assumed plasma composition.
For both the high and low energy ions, fluxes due to both the thermal
motions of the ions and their bulk co-rotation with Jupiter are tabulated,
in order to indicate the anisotropy of the flux on the satellite surfaces.
For the low energy ions the corotational flux is much greater than the
thermal flux, indicating that bulk motion dominates and almost all the
plasma impacts the trailing hemispheres of the satellites. The tabulated
sputtering rates thus refer to the center of the trailing hemisphere.
In the case of the high energy ions the co-rotational flux, though
always less than the `thermal' flux, is comparable if the plasma is composed
mostly of heavy ions, indicating considerable concentration of the flux
of even the energetic ions on the trailing hemispheres. Calculation of
net fluxes as a function of position on satellite surfaces under these
conditions is complex, and is not attempted here. The tabulated sputtering
rate is that due to the `thermal' flux only, and actual rates will be greater
in the center of the trailing hemisphere and less in the center of the
leading hemisphere.
It appears from comparison of Tables VIII and IX that the sputtering
rates due to the two plasma components are comparable, depending on the
composition of the high energy component. The values for Europa are in
broad agreement with those given in Seiveka and Johnson (1982).
APPENDIX E
ICE ABSORPTION BAND DEPTHS
IN SEGREGATED SURFACE SPECTRA
The calculation of the depth of an absorption band in the spectrum of a
surface composed of an areal mix of ice and a spectrally neutral material
is straightforward, given a knowledge of the spectral properties of the
two components. Clark et al (1986) define absorption band depth
D
as
where $R_B$ is the reflectance in the band center and RC
is the reflectance of the continuum at the same wavelength (i.e. the reflectance
of a cubic spline fit through the peaks between absorption features). If
the surface is composed of two components, an ice component with band and
continuum reflectances RBI and RCI,
band depth DI, and fractional areal coverage fI,
and a spectrally neutral component with reflectance RN
and fractional areal coverage fN ( fN
= 1-fI ), then
and
so
i.e. band depth is diluted by the fraction of the total continuum light
that comes from the ice component. Similarly, given the band depth in the
integrated spectrum and an assumed fractional coverage and reflectance
of the neutral component, the band depth in the ice component is given
by
and its continuum reflectance by
These equations are used in Figs. 38 and 39
of Chapter 10 to determine the ice component band depths at 1.04, 1.25,
1.52, and 2.02 microns for Callisto, assuming a spectrally neutral component
with a reflectance of 0.15 and varying fractional areal coverage. The values
of RC for the Callisto spectrum for the four absorptions
(0.23, 0.22, 0.212, and 0.187 respectively) were estimated by eye from
Fig. 3 of Clark (1980), assuming equivalence of reflectance and geometric
albedo. The resulting accuracy should be sufficient for present purposes.