Loki – A Lava Lake in Rarefied Circumplanetary Cross Flow Andrew Walker David Goldstein, Philip Varghese, Laurence Trafton, and Chris Moore University of Texas at Austin Department of Aerospace Engineering 27 th RGD Symposium July 14 th, 2010 Supported by grants through the NASA Planetary Atmosphere program and Outer Planets Research

Outline Background information –Io –Loki Overview of our DSMC code –Atmospheric model –Hot spot model Gas dynamic results –Flow features –Boundary layer separation –Convection of heat Conclusions

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, SO 2, was detected by the Voyager IR spectrometer in 1979 (Pearl et al., 1979) Background Information on Io Surface Temperature ~ 90 K – 115 K Length of Ionian Day ~ 42 hours Mean free path near the surface: noon ~ 5 m midnight ~ 100 km

Loki Loki is the most powerful volcano in the solar system (Rathbun et al., 2002) - A lava lake with periodic eruptions (540 day period) (Rathbun et al., 2002) Marchis et al. measured the emission intensity in 3 IR bands. From their observations they calculated Loki’s effective area and temperature - A HS = ×10 3 km 2 ; T HS = K (Marchis et al., 2005) Loki Figure courtesy of Marchis et al. (2005). Global IR intensity from IoFigure courtesy of Rathbun et al. (2004). High res. image of the lava lake Loki. Lava Lake Land “Island”

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-lifemillisecond-second Time step0.5 seconds Between Collisions0.1 seconds - hours Residence TimeSeconds - Hours Rotational Half-life~250 seconds Ballistic Time (atm)~265 seconds Ballistic Time (hs)~340 seconds Flow Evolution1-2 Hours Simulation Time~2.5 hours Io Day42 Hours

y x φ 3D –The domain is discretized by a spherical grid –Domain extends from Io surface to 400 km in altitude –Encompasses 90° of longitude and 10° ( ±5° from equator) of latitude Parallel –MPI –Tested up to 360 processors; ~1 million molecules per processor; ~4,000 comp. hrs Loki Sub-domain DSMC in 3D/Parallel Full Planet Domain Galileo observation of Loki in visible and IR

Atmospheric Model – Boundary Conditions Pt. 1 SO 2 residence time on rock (Sandford and Allamandola, 1994): –Molecules which impact the surface stick for a period of time dependent on the rock surface temperature, T ROCK :  H S (  H S /k B = 3460±40 K) : Surface binding energy of SO 2 on a SO 2 frost,  o (2.4×10 12 s -1 ) : Lattice vibrational frequency of SO 2 within surface matrix site. –Model assumes rock is coated with a thin monolayer of SO 2 Sublimation & condensation of SO 2 frost –Unit sticking coefficient –Sublimation rate given by: (Wagman, 1979) SO 2 surface frost fraction from Galileo NIMS data (Douté et al., 2001): –Within a computational cell, rock and frost are assumed segregated with the relative abundances determined by the frost fraction –The frost fraction also determines the probability that a molecules hits frost or rock

Dual frost/rock surface temperature: –Independent thermal inertias and albedos –Lateral heat conduction assumed negligible –T FROST varies between ~115 K and ~96 K –T FROST ~109 K near Loki Day-to-night pressure gradient –Pressure varies exponentially with T FROST –dP/dx peaks at x ≈ 600 km; Loki is located at x ≈ 1400 km –Pressure varies from ~0.7 nbar to less than a pbar Atmospheric Model – Boundary Conditions Pt. 2

Hot Spot Model Non-frost surface T NON-FROST ≈ 120 K No sublimation Temperature-dependent residence time Hot Spot: Loki Assumed circular disk T HS ≈ 332 K A HS ≈ 10.9×10 3 km 2 SO 2 surface frosts T FROST ≈ 110 K Sublimates SO 2 Unit sticking Molecules impacts hot spot and desorbs nearly instantaneously (~10 ms) Molecules sticks for residence time then desorbs Boundary Layer flow driven by day-to-night pressure gradient R d B-ATM d B-HS Collision

Three-dimensionality of wind pattern Winds are driven by a day-to-night pressure gradient As the boundary layer flow reaches the adverse pressure gradient formed by Loki, the flow separates and a vortex forms Winds diverts around the high pressure region formed by Loki

Cross Flow / Hot Spot Interaction Case 1 – Uniform 50:50 frost/rock; Unit sticking on “rock”; No plasma heating Case 2 – Inhomogeneous Surface Frosts; Temp. Dep. Res. Time ; No plasma heating Case 3 – Inhomo. Surf. Frosts; Temp. Dep. Res. Time; Plasma heating (1.3 ergs/cm 2 s)

Translational temperature profiles at several distances from the peak pressure region –1450 km is ~10 km downstream of the center of the hot spot; 1500 km is ~10 km downstream of the hot spot edge T TRANS cools rapidly at low altitudes because: –the wind speeds are lower –the gas is sufficiently collisional (energy is transferred from translational to rotational and vibrational energy modes and then radiated) At higher altitudes, T TRANS cools less rapidly because of the higher wind speeds and lower collision rate Effects of Plasma Heating C2 (Case 2) does not include plasma heating. C3 (Case 3) includes plasma heating (1.3erg/cm 2 s) Data are extracted at 20 km altitude

Conclusions Rarefied atmospheric winds interact with the hot spot Loki –The rarefied atmosphere varies from Kn HS to 0.5 at low altitudes –Near Loki, Kn HS ≈ near the surface and 5×10 -3 at 20 km Rarefied boundary layer flow develops due a day-to-night pressure gradient –In Case 1 and 2, the BL separates because of the adverse pressure gradient created by the hot spot –In Case 3, the BL remains attached because the plasma heating increases the favorable pressure gradient and decreases the relative size of the adverse pressure gradient created by the hot spot Heat convection is largely controlled by  = t RAD U/R where  ≤ 1 for all cases –In Cases 1 and 2,  ≈ 0.5 at ~20 km –In Case 3,  ≈ 1.0 at ~40 km; therefore heat is convected further with plasma heating

Important Parameters Non-dimensional Parameters Convection of Heat: Boundary layer separation: Equilibration of pressure:

Number Density drop ~exponentially with altitude for both Case 2 and 3 –In Case 3, plasma heating inflates the upper atmosphere leading to a denser atmosphere at high altitudes Wind speed shows a boundary layer profile –Case 2 B.L. thickness ~20 km; Case 3 B.L. thickness ~40 km –Much higher wind speeds at all altitudes in Case 3 compared to Case 2 Momentum flux above ~10 km is higher in Case 3 because of the higher wind speeds –At 20 km, Case 3 x-direction momentum flux is ~6x higher Upstream Boundary Layer Properties C2 (Case 2) does not include plasma heating. C3 (Case 3) includes plasma heating (1.3erg/cm 2 s) Note: x-axis is altitude not x

Knudsen Number The atmospheric rarefaction characterized by Kn HS and Kn ATM –Kn HS = /R where is the mean free path and R is Loki’s effective radius –Kn ATM = /H where H=kT/mg is the scale height, k is Boltzmann’s constant, T is the translational temperature, m is the molecular mass of SO 2, and g is the gravitational acceleration Generally, Kn ATM > Kn HS because H < R as shown on the previous slide. At high altitudes (>30 km), Kn HS & Kn ATM > 1. Near the surface: –Kn HS varies between ~10 -4 and 0.5 –Kn ATM varies between ~2×10 -3 and 5 Above Loki, Kn HS and Kn ATM fall off more slowly because of the increased scale height