• 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]• Found no signal in all cases, suggesting a

greater jet width (smaller rvel); simulated flyby misses plume in all cases.

• Ran cases with imposed spreading half-angle θsp at the vent (Cases 6 and 7)

• 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.

1. Density contribution from each individual source, n, along the trajectory is determined via simulation.

2. The total density, ntotal, along the trajectory is obtained as follows:

3. L-S fitting of ntotal to INMS data is performed to obtain optimized set of si.

FM model uses the DSMC velocity distributions to

assign its particles velocities at each

point source.

Velocities of gas molecules and

grains are sampled to form

velocity distributions.

Modeling the Gas-Grain Plume of EnceladusS. 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

Parametric Study Using Model

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.

IntroductionIn 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.

The ModelWe 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.

• Modeled channel as converging-diverging nozzle• Assumed isentropic water vapor expansion from

its triple point in the reservoir to the vent

Subsurface Model

Direct Simulation Monte Carlo (DSMC) Model for Collisional Near-Field• 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

Free-molecular (FM) Model for Collisionless Far-Field • 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

Reservoir

Throat

Vent

Property Value

Diameter 3.0 mMach number 5Temperature 50 KDensity 0.00004 kg/m3

Pressure 0.9 PaSpeed 900 m/sVent-to-throat area ratio 36

Table 1. Vent Conditions (Gas-only)

Triple point of Water:Temperature = 273.16 K Pressure = 612 Pa

Flow becomes collisionless.

Collisional flow in the near-field

DSMC domain

Vent conditions are used as input to DSMC model for gas; grains

are initialized independently.

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).

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.

Case rmass rvel θsp ()1 0.1 1.0 02 1.0 1.0 03 1.0 0.5 04 1.0 0.4 05 1.0 0.3 06 1.0 1.0 157 1.0 1.0 30

Table 2. Parameter Values

Source Tiger Stripe

Strengths (kg/s)

E3 E5 E7

I Baghdad 0 0 26.0II Damascus 33.7 0 0III Damascus 0 0 0IV Alexandria 21.6 0 82.1V Cairo 0 63.1 104.0VI Baghdad 23.0 62.6 0VII Baghdad 0 0 0VIII Cairo 0 0 56.8

Total Strength 78.3 125.7 268.9

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.

Gas-only Case Case 1 Case 2 Case 3

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.

Credit: NASA/JPL

Figure 1. Gas number density contours. Black lines are outlines of grain columns.

Far-field Results vs. Cassini INMS Data

Definitions of Parameters:rmass Vent mass flow rate ratio of grains

to gas

rvel Vent velocity ratio of grains to gas

θsp Spreading half-angle of gas/grain jet imposed at the vent (see figure)

Constraining Width of Grain Jets

Figure 2. Least-Squares-Fitted Simulated Water Number Density Distributions along the Cassini E3, E5 and E7 trajectories compared to INMS data [5] [6].

Table 3. Optimized Source Strengths (pure gas, θsp = 0)

• Simulated Cassini flyby water density distributions• Performed least squares (L-S) fitting to INMS results to analyze the temporal

variability of the plume

si: Strength of source ini: Density contribution of

source i along trajectory

L-S Fitting Procedure:

Figure 4. FWHM of the grain jets, normalized by the DSMC domain height (10 km), vs. velocity ratio, rvel.

Vent

θsp

0.2 0.4 0.6 0.8 1.00.0

0.1

0.2

0.3

0.4

0.5

0.6

rvel

FWH

M/1

0 km

Case 5Case 4

Case 3Case 2

Case 7

Case 6

Non-zero spreading angle

Case Signal?6 (θsp = 15) No7 (θsp = 30) Yes

Credit: NASA/JPL