A Comprehensive Numerical Model of Io

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A Comprehensive Numerical Model of Ios
Sublimation-Driven AtmosphereAndrew
WalkerDavid Goldstein, Chris Moore, Philip
Varghese, and Laurence TraftonUniversity of
Texas at AustinDepartment of Aerospace
EngineeringSanta Fe DSMC Workshop September
16th, 2009Supported by the NASA Planetary
Atmosphere ProgramIn collaboration with Deborah
Levin and Sergey Gratiy at Pennsylvania State
University
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Outline

• Background information on Io
• Overview of our DSMC code
• Gas dynamic results
• Conclusions
• Validation Comparison to Observations (Time
  permitting)

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Background Information on Io
Io
Plasma Torus
Jupiter

• Io is the closest satellite
• of Jupiter
• Io radius 1820 km
• It is the most volcanically
• active body in the solar
• system
• The primary dayside species, SO2, was detected by
  the Voyager IR spectrometer in 1979
• Pearl et al. (1979)
• Since then many observations have failed to
  determine whether Ios atmosphere is
  pre-dominantly volcanically or sublimation-driven.
  

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Background Information on Io
Frost patch of condensed SO2
Volcanic plume with ring deposition

• Surface Temperature 90 K 115 K
• Length of Ionian Day 42 hours
• Mean free path near the surface

lnoon 10 m lmidnight 100 km
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Overview of our DSMC code

• Three-dimensional
• Parallel
• Important physical models
• Dual rock/frost surface model
• Temperature-dependent residence time
• Rotating temperature distribution
• Variable weighting functions
• Quantized vibrational continuous rotational
  energy states
• Photo-emission
• Plasma heating

Time scales Vibrational Half-life millisecond-seco
nd Time step 0.5 seconds Between Collisions 0.1
seconds - hours Residence Time Seconds -
Hours Ballistic Time 2-3 Minutes Flow
Evolution 1-2 Hours Simulation Time 2
hours Eclipse 2 hours Io Day 42 Hours
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DSMC in 3D/Parallel

• 3D
• The domain is discretized by a spherical grid
• Domain extends from Io surface to 200 km in
  altitude
• Encompasses all latitudes and longitudes
• Parallel
• MPI
• Tested up to 360 processors
• Parameters
• 180 million molecules in domain
• 1 degree resolution in latitude and longitude
• Exponential vertical grid that resolves mean free
  path

?
y
f
x
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Boundary Conditions Frost Fraction

• SO2 surface frost fraction from Galileo NIMS data
  (Doute et al., 2001)
• Area fraction of SO2 frost of a 1o by 1o element
• High latitudes and longitudes from 0o to 60o
  interpolated
• Within a computational cell, the rock and frost
  are assumed segregated with the relative
  abundances determined by the frost fraction
• The frost fraction provides the probability for a
  molecule to hit frost or rock and the fractional
  area of each cell that sublimates

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Boundary Conditions Residence Time

• SO2 Sublimation Condensation on SO2 frost
• Sublimation Rate /m2-s
• Unit Sticking Coefficient

• SO2 residence time on rock
• When a molecule hits the rock surface, it sticks
  for a period of time dependent on the rock
  surface temperature
• 
  s (Eq. 1)

• -DHS (DHS/kB 346040 K) Surface binding
  energy of SO2 on a SO2 frost,
• - TS Rock surface temperature
• - no (2.41012 s-1) Lattice vibrational
  frequency of SO2 within surface matrix site.
• Model assumes rock is coated with a thin
  monolayer of SO2

• Two residence time models tested
• The short residence time model uses Eq. 1.
• The long residence time model uses Eq. 1 x
  1000.
• The long residence time model may be
  appropriate
• for a highly porous rock.

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Boundary Conditions Surface Temperature
Trock

• Dual frost/rock surface temperature
• Independent thermal inertias and albedos
• Lateral heat conduction assumed negligible
• Same peak temperature (115 K)
• Model based on Saur and Strobel (2004)
• Temperature Dist. validated by Rathbun et al.
  (2004)
• Rathbun et al. measured brightness temperature
  with Galileo PPR
• Matched cooling rate during night

Tfrost
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Vertical Column Density

• Column density predominantly (exponentially)
  controlled by surface frost temperature
• Due to exponential dependence of SO2 vapor
  pressure on surface frost temperature
• Frost fraction has small (proportional) effect on
  column
• Leads to slightly irregular column densities on
  dayside
• Large irregularities on the nightside where the
  surface temperature is nearly constant
• Winds have negligible effect on the column

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Mach Number at 30 km Altitude

• Streamlines in white Sonic line in dashed white
  Surface temperature contours in thick black (104
  K and 108 K)
• Dusk vs. dawn asymmetry ( Horseshoe-shaped Shock)
• Due to extended dawn atmospheric enhancement
  which blocks west-moving flow
• Along the equator, Mach numbers peak at
• M1.40 for eastward flow M0.84 for westward flow

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Translational Temperature at 3 km Altitude

• Coldest (100 K) near peak surface temperature
• Plasma energy coming down column of gas is
  completely absorbed above this altitude
• Very warm (360 K) near the M1.4 shock at the
  dusk terminator
• Compressive shock heating

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Thermal Non-Equilibrium
Trot
Ttrans

• Translational temperature
• In equilibrium with the surface frost temperature
  at very low altitudes on dayside only
  (temperatures elevated near surface on nightside
  due to plasma heating)
• Temperature rapidly increases due to plasma
  heating
• Rotational temperature
• In thermal equilibrium with translation at
  altitudes below 10 km on the nightside
• Thermal equilibrium is maintained to higher
  altitudes on the dayside because of the higher
  collision rate
• Cold pocket of gas (60 K) at 3 km altitude on
  the dayside

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Conclusions

• Column density is predominantly controlled by the
  frost surface temperature
• Small effects from the surface frost fraction and
  negligible effects from flow
• The pressure-driven supersonic flow diverges from
  near the region of peak surface frost
  temperature toward the nightside
• The extended dawn enhancement
• blocks the westward flow
• Supersonic to east, north,
• and south of peak pressure
• Horseshoe-shaped shock
• Rotational temperatures are
• not in equilibrium with
• translational temperatures
• Above 10 km on the nightside
• Above 50 km on the dayside

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Types of Available Observations
Plume Images
Auroral Glows
IR Map of Hot Spots
IR Map of Passive Background
Lyman-a inferred column densities
Disk-Averaged Spectra
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Composite Atmosphere Sublimation Volcanic

• A nightside Pele-type plume computed with our 2D
  DSMC code (Zhang et al., 2004)
• The axi-symmetric plume calculation is rotated in
  1 degree increments to form a full
  three-dimensional plume
• The plumes (large Pele-type and smaller
  Prometheus type) are superimposed on the
  sublimation atmosphere by mass-averaging all of
  the properties

• Composite atmosphere showing density 100 m above
  surface with two near limb slices showing density
  with altitude
• Streamlines in white show flow away from peak
  frost temperature as well as deflection around
  plumes
• 10 persistently active volcanic plumes (Geissler
  et al., 2004 Pele and 9 prometheus-type) were
  superimposed

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Comparison to Observations

• Comparison of our atmospheric simulations with
  inferred column densities from Lyman-a
  observations
• 115 K cases both show reasonable agreement with
  the peak of Feagas data (Feaga et al., 2009)
  however, the peak in Feagas data may be from
  additional volcanic column.
• There are morphological differences at mid- to
  high latitudes between the simulations and
  observations

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Comparison to Observations

• Comparison of band depth vs. central longitude
  for several atmospheric cases (Gratiy et al.,
  2009)
• The upper curve is a cos1/4(q) variation with a
  90 K nightside temperature
• The lower curves are the temperatures needed to
  create a column densities inferred by Lyman-a
  observations. The empirical fit is also a
  cos1/4(q) variation but with a 0 K nightside
  temperature.