Modeling the Gas-Grain Plume of Enceladus
S. K. Yeoh, T. A. Chapman, D. B. Goldstein, P. L. Varghese, L. M. Trafton
The University of Texas at Austin; E-mail: skyeoh@utexas.edu
Credit: NASA/JPL
Credit: NASA/JPL
Introduction
Far-field Results vs. Cassini INMS Data
In 2005, Cassini first detected a gas-grain plume over Enceladus’ south pole
originating from the tiger-stripe fractures. The discovery not only helped unlock some
mysteries, such as the source of Saturn’s E-ring grains [1] and the origin of the very
bright expanses in Enceladus’ south polar region [2], but also opened doors to new
possibilities, including the existence of extra-terrestrial life [3]. Consequently, it has
been a very active area of research. Here, we model both the gas and the grain
components of Enceladus’ plume to constrain the conditions at the sources.
• Simulated Cassini flyby water density distributions
• Performed least squares (L-S) fitting to INMS results to analyze the temporal
variability of the plume
The Model
We simulate the different regimes of the plume using models of different scales that
are linked together to obtain the entire plume. Then, simulated flybys are performed
and the results are compared with available in-situ data.
L-S Fitting Procedure:
Source
1. Density contribution from each
individual source, n, along the
I
trajectory is determined via simulation.
II
2. The total density, ntotal, along the
III
trajectory is obtained as follows:
IV
V
VI
VII
VIII
Free-molecular (FM) Model
for Collisionless Far-Field
Flow becomes collisionless.
Collisional flow
in the near-field
Velocities of gas
molecules and
grains are sampled
to form velocity
distributions.
DSMC domain
Vent conditions are
used as input to DSMC
model for gas; grains
are initialized
independently.
Subsurface Model
si: Strength of source i
ni: Density contribution of
source i along trajectory
Diameter
Mach number
Temperature
Density
Pressure
Speed
Vent-to-throat area ratio
3.0 m
5
50 K
0.00004 kg/m3
0.9 Pa
900 m/s
36
Vent
Throat
Reservoir
• Modeled channel as converging-diverging nozzle
• Assumed isentropic water vapor expansion from
its triple point in the reservoir to the vent
Triple point of Water:
Temperature = 273.16 K
Pressure = 612 Pa
Parametric Study Using Model
We vary the parameters one at a time and study their
effects on the plume near-field and far-field. Grains
are 1-µm in size.
Definitions of Parameters:
θsp
Spreading half-angle of gas/grain
jet imposed at the vent (see figure)
θsp
Vent
Case
1
2
3
4
5
6
7
rmass
0.1
1.0
1.0
1.0
1.0
1.0
1.0
rvel
1.0
1.0
0.5
0.4
0.3
1.0
1.0
θsp ()
0
0
0
0
0
15
30
Table 2. Parameter Values
Near-Field Gas Number Density Contours
• Gas contours are hardly affected by grains in Case 1 (rmass = 0.1, rvel = 1.0).
• Grains change the gas contours in Cases 2 (rmass = 1.0, rvel = 1.0) and 3 (rmass = 1.0,
rvel = 0.5), especially near the plume center.
• Grain columns are straight in Cases 1 and 2 and spreads out slightly in Case 3.
Gas-only Case
Case 1
E7
26.0
0
0
82.1
104.0
0
0
56.8
78.3
125.7
268.9
Table 3. Optimized Source Strengths
(pure gas, θsp = 0)
Figure 2. Least-Squares-Fitted Simulated Water Number Density Distributions
along the Cassini E3, E5 and E7 trajectories compared to INMS data [5] [6].
Constraining Width of Grain Jets
Table 1. Vent Conditions
(Gas-only)
Vent velocity ratio of grains to gas
E5
0
0
0
0
63.1
62.6
0
0
3. L-S fitting of ntotal to INMS data is
performed to obtain optimized set of si.
• Uses a representative set of
computational particles to
statistically approximate the
motions of real gas molecules
and grains
• Implements two-way coupling
between gas and grains
Value
rvel
Total Strength
E3
0
33.7
0
21.6
0
23.0
0
0
Direct Simulation Monte
Carlo (DSMC) Model for
Collisional Near-Field
Property
rmass Vent mass flow rate ratio of grains
to gas
Baghdad
Damascus
Damascus
Alexandria
Cairo
Baghdad
Baghdad
Cairo
Strengths (kg/s)
Case 2
Case 3
• Determined effect of vent velocity ratio, rvel, on grain jet width (Cases 2, 3, 4 and 5)
• Jet width measured using Full Width at Half Maximum (FWHM)
• Jet width increases as rvel decreases; smaller rvel (larger velocity slip) results in
greater drag, thus grains are more entrained and spread out by gas flow.
• Simulated E2 flyby to compare with E2
CDA data [7]
Case 7
0.6
Non-zero
• Found no signal in all cases, suggesting a
spreading
0.5
greater jet width (smaller rvel); simulated
angle
Case 6
flyby misses plume in all cases.
0.4
• Ran cases with imposed spreading halfCase 4
0.3
angle θsp at the vent (Cases 6 and 7)
Case 5
Case 3
0.2
Case
Signal?
Case 2
6 (θsp = 15)
No
0.1
7 (θsp = 30)
Yes
FWHM/10 km
• Simulates ballistic particle
motion under the influence of
gravity
• Places 8 point sources on the
planet surface, according to
locations and jet orientations
determined by Spitale and
Porco [4]
• Includes analytic global and
background sources
FM model uses the
DSMC velocity
distributions to
assign its particles
velocities at each
point source.
Tiger
Stripe
• Minimum spreading half-angle to obtain
a signal: 15 < θsp < 30
• Through extrapolation (see Figure 4), even
with rvel = 0, the FWHM is still smaller
than that of Case 6, implying no signal for
this case as well.
0.0
0.0
0.2
0.4
0.6
0.8
1.0
rvel
Figure 4. FWHM of the grain jets,
normalized by the DSMC domain
height (10 km), vs. velocity ratio, rvel.
Conclusions
• A low mass flow rate of grains, compared to that of gas, and a small velocity
difference at the vent barely affect the gas flow for micron-sized grains.
• Plumes are variable over period between flybys (months), varying by nearly 4×
between E2 and E7; plumes may be variable on even shorter time scales.
• Constraint on grain jet width suggests other mechanisms may be responsible for
grain formation, perhaps condensation above as opposed to below the vent [8]. It
is also possible that the grains may not be coming out radially but may already
have a spreading angle at the vent.
References: [1] Baum, W.A., et al., 1981. Saturn’s E Ring: I. CCD Observations of March 1980. Icarus 47, 84–96. [2] Porco, C.C., et al., 2006.
Cassini Observes the Active South Pole of Enceladus. Science 311, 1393–1401. [3] McKay, C.P., et al., 2008. The Possible Origin and Persistence of
Life on Enceladus and Detection of Biomarkers in the Plume. Astrobiology 8, 909–919. [4] Spitale, J.N., Porco, C.C., 2007. Association of the jets of
Enceladus with the warmest regions on its south-polar fractures. Nature 449, 695–697. [5] Smith, H.T., et al., 2010. Enceladus plume variability and
the neutral gas densities in Saturn’s magnetosphere. J. Geophys. Res. 115, A10252. [6] Dong, Y., et al., 2011. The water vapor plumes of Enceladus. J.
Geophys. Res. 116, A10204. [7] Waite, J.H., et al., 2006. Cassini Ion and Neutral Mass Spectrometer: Enceladus Plume Composition and Structure.
Science 311, 1419–1422. [8] Schmidt, J., et al., 2008. Slow dust in Enceladus’ plume from condensation and wall collisions in tiger stripe fractures.
Nature 451, 685–688.
Figure 1. Gas number density contours. Black lines are outlines of grain columns.
Acknowledgements: Work is supported by NASA Cassini Data Analysis Program (CDAP) grants
NNX08AP77G and NNH09ZDA001N-CDAP. Computations were performed at the Texas
Advanced Computing Center (TACC).