1. The Potential Hazard to Cassini from Small Dust in Enceladus Plumes
Larry W. Esposito
23 August 2007

2. Cassini clipped edge of plume: INMS, CDA in situ Results
~1 minute before closest approach the Cosmic Dust Analyzer detected a peak in the number of small particles (blue diamonds), 460 km altitude
35 seconds before closest approach the Ion Neutral Mass Spectrometer measured a large peak in water vapor (yellow diamonds), 270 km altitude
Gas and dust plumes are decoupled at these altitudes
Cassini actually flew through the outer edge of Enceladus’ plume
Red line is closest approach to hot spot
Green line is c/a to Enceladus
Coma observed by INMS out to 4000 km. Densities in this extended region may be indicative of flux that varies on time scales of < 1 hr
Hill sphere radius = 948 km

3. CDA Peak
INMS Peak
Outline of hot spot

4. Composition of Plume is Water Vapour
I=I0 exp (-n*)
I0 computed from 25 unocculted samples
n = column density
 = absorption cross-section, function of wavelength
Water spectrum from Chan et al, Data taken at 298 K.
The absorption spectrum of water (pink line) is shown compared to Enceladus’ plume spectrum (I/I0) for a column density of n = 1.5 x 1016 cm-2

5. Structure of the Plume
The increase in water abundance is best fit by an exponential curve – a comet-like evaporating atmosphere (1/R2) does not fit the data well, nor do global hydrostatic cases
The best fit scale length is 80 km

6. UVIS Plume Model (Tian 2007)
A new model has been developed for Enceladus’ plumes by Tian, Toon, Larsen, Stewart and Esposito, paper in Icarus
Monte Carlo simulation of test particles given vertical + thermal velocity, particle trajectories tracked under influence of gravity and collisions
Assumes source of multiple plumes added together along each tiger stripe
UVIS ray path across tiger stripes

7. Monte Carlo model results - Predicted Plume Shape
Simulations by Teddy Tian. Paper submitted to Icarus
10,000 test particles given a vertical velocity and a thermal velocity. Thermal velocity direction is chosen randomly and speed satisfies a Boltzmann distribution for Tthermal. Tthermal of 140 to 180K not much affect on results (these temps from Spencer). If T=273 then crack must be very narrow.
Inferred surface density is 1010 to 1011 cm-3
Trajectories of particles tracked under the influence of gravity and collisions. Mean free path is calculated, increases with altitude. Number density near surface is high enough for collisions. Model which takes into account viewing geometry of tiger stripes suggest 10 to 100 % of stripes are venting
Level 1.0 => 1017 cm2; Level 0.1 => 1016 cm2

8. Monte Carlo Model - Fit to Data
Zero Vz => sublimation -> column density declines more rapidly than observed
Mass deposition is 2 orders of magnitude < escape rate, still adequate to resurface and account for high albedo
Density distribution in plume as f(z): n(z) = nsurf * (1 + (z/(1+Vz/Vth))-2
Number density of plume consistent w/ column density = 1.5 x 1016 cm-2 is cm-3, depending on assumed line of sight altitude range. If vertical velocity is same order of magnitude as thermal velocity the surface density is cm-3
Best fit to UVIS column density as a function of altitude requires a vertical velocity of 300 to 500 m/sec
Water flux is x 1027 molecules/sec = kg/sec
(consistent with initial estimate)

9. Detecting Temporal Variability
The water budget derived from the water vapor abundance shows Enceladus supplies most if not all of the OH detected by HST, atomic oxygen in the Saturn system detected by UVIS
Implies activity for > 15 years, since HST observed OH in 1992 (Shemansky et al)
The water source has not changed by any large factor.
Since the oxygen in the system comes from Enceladus UVIS may be able to remotely monitor Enceladus’ activity levels by monitoring the system oxygen level

10. O1304 trend shows factor of 2x changes on weekly, monthly, yearly scales

11. Enceladus Summary
UVIS measures water source large enough to create neutral oxygen cloud and to re-supply E ring
UVIS column density equal to about a single 1/2 mm ice grain per square meter

12. Plume physical explanations
Models
Fumarole model. Misty vapor cools as it expands; ice particles condense. T ~ 170K.
Geyser model. Local heating gives boiling water at depth, vent geometry gives vertical velocity, collimation; bubbles form and liquid freezes, effectively lofting larger particles to high speeds. T ~ 270K.
Comet model. Sublimating vapor lifts ice grains from vent interface and carries them away. T ~ 200K.

13. Comparable mass
In all these models, there is a close coupling between the ice and vapor
Growth, lofting and/or evaporation involve an interchange between water molecules and solid ice particles
For any significant interchange of mass or momentum, the column of water vapor incident on an ice grain’s surface area must have a comparable mass to the grain mass

14. Mass Balance N0 *  * a2 * H * mH20 =  * 4/3 *  * a3
For H ~ 40km,  ~ 1, we solve for a (in microns) a ~ N0/ (1012 cm-3)
Thus, high pressure vents could loft or grow big particles, potentially dangerous to Cassini

15. Observational constraints
The shape of the observed plumes shows
V0 > Vth
Tian etal can match the UVIS results with V0 ~ 400 m/s and N0 ~ 1010 – 1012 cm-3
This gives typical grain sizes a ~ 0.01–1, roughly consistent with photometry and CDA measurements: these particles are not dangerous, by orders of magnitude

16. Hazard calculation: Approach and assumptions
Plume has cylindrical symmetry about pole
Plume density is estimated along Cassini path from water column measured by UVIS star occultation
See following figures (from Spencer and Hansen): UVIS had a measurement at predicted highest density location for rev 61

18. Rev 61 plume max----->

19. Calculation
If all water vapor along this line of sight to star (Ncol = 2E15/cm2) were swept up by Cassini’s sensitive area (0.8 m2), this would form a solid ice sphere of radius 500 microns
Assume measured solid particle size distribution can be extended as a power law in radius to sizes dangerous to Cassini
CDA: q = 4
RPWS: q = 6.4 (radius power law)

20. Number of dangerous particles
Calculate the predicted number of hits by dangerous particles (r > 900 microns, Dave Seal) if Cassini flew a path with same minimum altitude:
ND = fI* (4-q)/(q-1) *
a03/(amax4-q - amin4-q) *
(a*1-q - amax1-q)

21. Key parameters a*: dangerous particle radius, 900 microns
a0: equivalent ice radius, 500 microns
amin, amax: size range, radius microns
fI: ratio of solid ice mass to water vapor
q: power law size index

22. Results
ND = 3E-9 fI for q = 6.4 (RPWS)
ND = 2E-3 fI for q = 4 (CDA)

23. Values for fI, mass ratio solid/gas
Simple physical arguments of mass balance, force balance, growth of solids from vapor give fI < 1
Comparing mass loss of solids published by ISS, CDA to vapor by UVIS gives fI ~ 0.01
Recent ISS analysis gives fI ~ 1
Schmidt physical model gives fI ~0.6
Comparing UVIS and VIMS: fI > 0.01

24. H2O absorption at 2.7 microns

25. H2O absorption at VIMS resolution

26. But, what about small, high pressure vents
But, what about small, high pressure vents? They could loft dangerous particles. Signal more variable within plume …
Outside
Within plume

27. Same number of high and low outliers

28. Conclusions from 2 independent searches
Sensitive to events as small as 50m; opacity as small as 10%
We see no significant deviations from smooth variation
Outlier events have width less than 1km and opacity less than twice mean

29. Why this is conservative
Physical models show it is much harder to loft larger particles: power law extrapolation is conservative
No evidence of big temporal variations, or of high pressure vents
This idealized model makes no specific claims about the exact plume mechanism: these are all included in the factor fI

30. Conclusions
Extrapolating Cassini plume measurements to rev 61 and to radius dangerous to Cassini, using the most optimistic size range, provides a conservative estimate of the number of hits expected of 0.2fI% or less
A physical model by Schmidt gives 10-5
Better measurements of the size distribution and its opacity would improve the model