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 ) 14 th satellite from Saturn Mean density ~1600 kg/m 3 Gravitational acceleration ~0.113 m/s 2 Bond albedo ~0.99 (value for moon ~ 0.12) Credit: NASA/JPL-Caltech

Diverse Surface Morphology Credit: NASA/JPL-Caltech 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? Credit: NASA/JPL-Caltech

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 m 4 m Credit: NASA/JPL-Caltech Three Closest Enceladus Flybys in st encounter (17 February ) - Closest approach: 1295 km - Found tenuous atmosphere 2 nd encounter (9 March) - Closest approach: 497 km - Detected southerly water-ion source 3 rd encounter (14 July) - Closest approach: 168 km - Discovered active south polar region - Provided unequivocal evidence of plume over south pole!

Some Plume Images Credit: NASA/JPL-Caltech 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). Credit: NASA/JPL-Caltech

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 IngressEgress Credit: NASA/JPL-Caltech

INMS, CDA: Plume Composition and Structure Gas plume composition inferred: ~90% water, ~3% CO 2, ~4% CO or N 2, ~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 T 0 = K p 0 = 612 Pa vent exit Ma E Sub-surface reservoir 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 m n gas ~10 21 molecules/m 3 T gas ~50 K V gas ~900 m/s (Ma E = 5) Mass flow rate ~0.2 kg/s 0.5 m Credit: Wikipedia, NASA/JPL-Caltech Enceladus “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: n gas ~10 21 molecules/m 3 T gas ~50 K V gas ~900 m/s (Ma E = 5) 1 st stage: Timestep = 1 x s Grid size = m 8 th stage: Timestep = s Grid 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 First 3 stages: vent to 10 m Last 2 stages: 0.5 km to 10 km Translational temperature, T tr is defined as:

DSMC Results of Near-field: Rotational Temperature First 3 stages: vent to 10 m Last 2 stages: 0.5 km to 10 km Rotational temperature, T rot is defined as:

DSMC Results of Near-field: Equilibrium flow First 3 stages: vent to 10 mLast 2 stages: 0.5 km to 10 km Collisions cause translational and rotational energy modes to exchange energy and equilibrate. Temperature difference, |T tr -T rot |, 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 Rates x ṁ nom 0.01 x ṁ nom 0.1 x ṁ nom nominal (ṁ nom ~0.2 kg/s) where γ is the ratio of specific heats (4/3), R is the gas constant (462 J/kg-K) and T 0 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 Closest Approach: 50 km (~31 miles) ii) E5 flyby: - 9 October 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)

Gas Column Density Contours Units: molecules/cm 2

Simulation Data vs. In-Situ Data Closest Approachbeforeafter Note: All eight sources are of equal strengths.(flyby on 14 July 2005, different from E3 and E5!)

Simulation Data vs. In-Situ Data Closest Approachbeforeafter (closest approach: 50 km) Note: All eight sources are of equal strengths.

Simulation Data vs. In-Situ Data Closest Approachbeforeafter (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 D simulated (x) is total simulated number density, p n (x) is density contribution from n th source and s n is weight for n th 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 D simulated (x) to curve Minimize square of residual: where y i is observations.

Results from Time-Variability Analysis Source Tiger StripeStrengths (kg/s) E3E5 IBaghdad00 IIDamascus33.70 IIIDamascus00 IVAlexandria21.60 VCairo063.1 VIBaghdad VIIBaghdad00 VIIICairo00 Total strength (kg/s) ~78 ~126

Closest Approachbeforeafter Simulation Data vs. In-Situ Data

Closest Approachbeforeafter Simulation Data vs. In-Situ Data

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/m 3 ) Particles are moved by gas according to free-molecular drag (diameter-based Knudsen number, Kn D ~ O(1000)).

Units: molecules/cm 2 10-nm dust column density [km]

Units: molecules/cm 2 50-nm dust column density [km]

Units: molecules/cm nm dust column density [km]

Units: molecules/cm nm dust column density [km]

Units: molecules/cm 2 1-micron dust column density [km]

Credit: NASA/JPL-Caltech

Conclusions so far Jet flow out of the vent is very likely to be supersonic. Enceladus plume varies with time.