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.