Modeling the Plumes of Enceladus Seng K. Yeoh, Todd A. Chapman Advisors: David B. Goldstein, Philip L. Varghese, Laurence M. Trafton Support is provided

Modeling the Plumes of Enceladus

Seng K. Yeoh, Todd A. Chapman

Advisors: David B. Goldstein, Philip L. Varghese, Laurence M. Trafton

Support is provided by the NASA CDAP and TACC.

02/23/2012

Enceladus: A Mysterious Moon of Saturn

Credit: NASA/JPL-Caltech

Some Facts About Enceladus• Diameter ~310 miles• Orbital period of ~1.4 Earth days (~33 hours)• Distance from Saturn center ~4 Saturn radii (~150,000 miles )• 14th satellite from Saturn• Mean density ~1600 kg/m3

• Gravitational acceleration ~0.113 m/s2

• Bond albedo ~0.99 (value for moon ~ 0.12)


Diverse Surface Morphology


•

• Northern hemisphere dotted with craters

• Almost crater-less south polar region• South polar region also marked by

long, parallel fractures known as “tiger stripes”

Unusual Structure of Saturn’s E Ring• Wide, tenuous, diffuse• Consists mostly of ice grains• Densest at Enceladus orbit• Narrow E-ring grain distribution

(micron-sized) suggests a liquid or vapor source in contrast to broad range by impacts

• Enceladus possible major source?


Quick Facts on Cassini-Huygens• Collaboration between NASA , ESA and ASI• Cassini spacecraft and Huygens probe• Launched October 1997• Arrived at Saturnian system July 2004• Extended mission to September 2017

6.7 m

4 m


Three Closest Enceladus Flybys in 2005• 1st encounter (17 February ) - Closest approach: 1295 km - Found tenuous atmosphere

• 2nd encounter (9 March) - Closest approach: 497 km - Detected southerly water-ion source

• 3rd encounter (14 July) - Closest approach: 168 km - Discovered active south polar region - Provided unequivocal evidence of plume over south pole!

Some Plume Images


The plume you see is actually the dust particle plume as they scatter sun light, not the gas plume!

CIRS, ISS: Temperature Maps

Composite Infrared Spectrometer (CIRS)Imaging Sub-System (ISS)

South polar hot spot

Combination of CIRS and ISS found areas with high brightness temperature coincide with tiger stripe fractures.

CIRS detected prominent south polar hot spot (>85 K in brightness or blackbody-fit temperature).


Ingress

Egress

South pole

UVIS: Stellar Occultation Observations

Ultraviolet Imaging Spectrograph (UVIS)Far Ultraviolet Spectrograph (FUV)

Signal of star disappears because star is behind Enceladus

Attenuation of signal of star due to absorption by faint atmosphere during ingress

Ingress Egress


INMS, CDA: Plume Composition and Structure• Gas plume composition inferred: ~90% water, ~3% CO2, ~4% CO or N2, ~2%

methane and <~1% of acetylene, propane, hydrogen cyanide, and ammonia• Noticeable asymmetry in both water vapor and dust densities • Consistent with a plume source in the south polar region

Ion and Neutral Mass Spectrometer (INMS)Cosmic Dust Analyzer (CDA) Credit: NASA/JPL-Caltech

Tiger Stripe fractures may be source of plume!• Strong spatial coincidence with infrared hot spot locations (from CIRS) and

locations along tiger stripes• Determined locations and jet orientations of eight strongest sources• Strongest sources being Baghdad and Damascus sulci

Yellow Roman numerals: triangulated jet sources (eight sources)

Red boxes: hot spots detected by CIRS

Composite Infrared Spectrometer (CIRS) Credit: NASA/JPL-Caltech

Vent

Overview of Our Plume Model

Axisymmetric Direct Simulation Monte Carlo (DSMC) model

Free-molecular model

Sub-surface channel

Velocities of Escaping DSMC molecules

Velocity Distribution

Point sources

Collisional flow

stagnation conditions

T0 = 273.16 K

p0 = 612 Pa

vent exitMaE

Sub-surfacereservoir

Our Sub-surface Flow Assumptions

Terrestrial Glacial Crevasse

• Circular hole as vent • Water vapor as gas• Channel simply modeled as converging-diverging nozzle• Short channel (~O(10 m))• Negligible heat transfer and frictional effects• Isentropic flow

Conditions at Vent Exit taken as DSMC input

Vent Conditions:Diameter ~3 mngas~1021 molecules/m3 Tgas~50 KVgas ~900 m/s (MaE = 5)Mass flow rate ~0.2 kg/s

0.5 m

Credit: Wikipedia, NASA/JPL-CaltechEnceladus “crevasse” perhaps?

The Basics of DSMC

• Spatial domain is decomposed into cells.

• Representative particles move and collide in cells.

• Key idea is move and collide steps can be decoupled at timescales much smaller than mean collision time.

• Macroscopic quantities (temperature, density, etc.) are obtained by averaging over molecular properties in given cell.

• Cells can have a variety of boundary conditions: vacuum, specular/diffuse reflection, or periodic.

DSMC Simulation and Parameters• Local Knudsen number, Kn = λ/L where

λ is mean free path and L is gradient-based length scale, i.e. L = ρ/ .

• DSMC domain extends from vent (Kn ~0.001) to 10 km from vent (Kn ~100).

• DSMC calculates is multi-staged (8 stages) :

- Using a single timestep and a single grid size for entire domain may not be a good idea as properties drop rapidly.

- In each stage, timestep is chosen to resolve mean collision time and grid size to resolve mean free path.

• Multi-staging works because flow is supersonic (downstream flow does not affect upstream flow).

2 m

vent

10 km

Vent Conditions:ngas~1021 molecules/m3 Tgas~50 KVgas ~900 m/s (MaE = 5)

1st stage:Timestep = 1 x 10-6 sGrid size = 0.004 m

8th stage:Timestep = 0.005 sGrid size = 20 m

Velocities of Escaping DSMC Particles serve as input to free-molecular model

Free-molecular Model

• Water particles launched from eight point sources

• Locations and jet orientations of sources as determined from Spitale and Porco

• Total mass flow rate ~100 kg/s• Each source can have a different mass

flow rate (or source rate)• Particles move in ballistic manner

under gravitational field• Plasma, radiation, and electromagnetic

effects not accounted for (future work)

Particle velocities assigned randomly from velocity distribution constructed from escaping DSMC particles

DSMC Results of Near-field: Number density

First 3 stages: vent to 10 m Last 2 stages: 0.5 km to 10 km

DSMC Results of Near-field: Translational Temperature


Translational temperature, Ttr is defined as:

DSMC Results of Near-field: Rotational Temperature


Rotational temperature, Trot is defined as:

DSMC Results of Near-field: Equilibrium flow


• Collisions cause translational and rotational energy modes to exchange energy and equilibrate.• Temperature difference, |Ttr-Trot|, provides a measure of how equilibrium the flow is.

Velocity Components of Escaping DSMC Molecules

Planet surface

Tangential Velocity (tangential to planet surface)

Normal Velocity (normal to planet surface)

Molecule Velocity

Planet center

North Pole

Velocity Distributions for Different Mass Flow Rates0.001 x ṁnom 0.01 x ṁnom

0.1 x ṁnomnominal (ṁnom ~0.2 kg/s)

where γ is the ratio of specific heats (4/3), R is the gas constant (462 J/kg-K) and T0 is the stagnation temperature (273 K)

= 1005 m/s

Flow gets more collisional in near-vent region.

Ultimate speed:

Comparing Simulation Results with In-Situ Data

• Modeled two Cassini flybys:i) E3 Flyby:- 12 March 2008- Closest Approach: 50 km (~31 miles)ii) E5 flyby:- 9 October 2008- Closest Approach: 21 km (~13 miles)

• Water density data was collected to compare to INMS in-situ data

• Global sputtering source and E-ring background added to simulation results

• Also modeled Gamma Orionis Stellar Occultation on 14 July 2005

• Compare results to UVIS occultation data

Ion and Neutral Mass Spectrometer (INMS)Ultraviolet Imaging Spectrograph (UVIS) http://www.youtube.com/watch?v=qZKM8MfUpUs

Gas Column Density Contours

Units: molecules/cm2

-500 -400 -300 -200 -100 0 100 200 300 400-4

-2

0

2

4

6

8

10

12

14

16x 10

15

Time (s)

Sla

nt C

olum

n D

ensi

ty (#

H2O

/cm

2)

Gamma Orionis Occultation

UVISSimulation

Simulation Data vs. In-Situ Data

Closest Approachbefore after

Note: All eight sources are of equal strengths. (flyby on 14 July 2005, different from E3 and E5!)

-30 -20 -10 0 10 20 3010

3

104

105

106

107

108

E3 INMS

Distance from Enceladus (Re)

#H2O

/cm

3

simulationINMS



(closest approach: 50 km)Note: All eight sources are of equal strengths.

-30 -20 -10 0 10 20 30 4010

3

104

105

106

107

108

109

E5 INMS

Distance from Enceladus (Re)

#H2O

/cm

3

simulationINMS



(closest approach: 21 km)Note: All eight sources are of equal strengths.

Examining Time-Variability of Plume• Source strength may vary over time, thus different for each flyby!

Our approach to analyzing time-variability of plume:• First, we determine contribution from each source by turn on only a source

one by one.• Determine number density by superposition of all source contributions:

where Dsimulated(x) is total simulated number density, pn(x) is density contribution from nth source and sn is weight for nth source

• Can do superposition of contributions because flow is free-molecular• Smooth and curve-fit INMS data to produce a curve• To find source strengths at each flyby, perform least-squares fitting for

Dsimulated(x) to curve• Minimize square of residual:

where yi is observations.

Results from Time-Variability Analysis

SourceTiger Stripe Strengths (kg/s)

E3 E5I Baghdad 0 0II Damascus 33.7 0III Damascus 0 0IV Alexandria 21.6 0V Cairo 0 63.1VI Baghdad 23.0 62.6VII Baghdad 0 0VIII Cairo 0 0

Total strength (kg/s) ~78 ~126

-30 -20 -10 0 10 20 3010

3

104

105

106

107

108

E3 INMS with Least Squares Fit

Radius from Enceladus (Re)

#H

2O

/cm

3

simulationINMS



-30 -20 -10 0 10 20 30 4010

3

104

105

106

107

108

109

Radius from Enceladus (Re)

#H

2O

/cm

3

E5 INMS with Least Squares Fit

simulationINMS



Dust Particle Plume Simulations• Particles launched at gas speed (900 m/s)• Low mass loading (<10%) so gas affects dust but not the other way

around• Particles are pure ice (density =920 kg/m3)• Particles are moved by gas according to free-molecular drag

(diameter-based Knudsen number, KnD ~ O(1000)).


10-nm dust column density

[km]

[km]



[km]

[km]



[km]

[km]



[km]

[km]


1-micron dust column density

[km]

[km]


Conclusions so far• Jet flow out of the vent is very likely

to be supersonic.• Enceladus plume varies with time.

Documents

Modeling the Plumes of Enceladus Seng K. Yeoh, Todd A. Chapman Advisors: David B. Goldstein, Philip L. Varghese, Laurence M. Trafton Support is provided