Moon/Plasma Interactions

Moon/plasma interactions

Krishan K. Khurana Institute of Geophysics and Planetary Physics University of California at Los Angeles Email: [email protected] Io Europa Ganymede Callisto 1818 km 1560 km 2634 km 2400 km radius 3530 kg m-3 2990 kg m-3 1940 kg m-3 1851 kg m-3 density 0.377 0.348 0.311 0.358 C/MR2 42.46 hr 85.22 hr 171.71 hr 400.54 hr period

Meet the Galilean moons , worlds of fire and ice.

The moons are phase locked with Jupiter. 2 Record of impact craters reveals the surface ages of solar system bodies

3 Plasma corotates with Jupiter

4 Figure courtesy: R. E. Johnson, Univ. of Virginia Plasma properties near Jupiter’s satellites

Io Europa Ganymede Callisto 57 104 177 323 V (km/s)

150-340 145-700 130-1700 30-6500 VA (km/s)

27-53 76-330 190-1400 230-4400 CS (km/s) 0.2-0.4 0.1-0.6 0.1-1.1 0.02-8.5 MA 1.0-2.1 0.2-1.1 0.1-0.8 0.03-1.2 Ms

0.2-0.4 0.1-0.5 0.04-0.7 0.02-1.2 Mf

200 30 2 1000 P (Mho) No shock forms upstream of the moons 5 6 Field and Plasma Properties near Saturn’s Icy moons

From Khurana et al. 2008, Icarus 7 Moon/Plasma Interaction Types

The interactions can be broadly classified into four different types.

1. Inert moon 1. Supersonic medium (The Earth’s moon, Phoebe) 2. Subsonic medium (Tethys, Rhea) 2. External conductivity 1. Ionospheric (Pedersen and Hall) (Io, Europa) 2. Plasma pick-up (Enceladus, Dione?) 3. Internal conductivity (Europa, Callisto) 4. Magnetized moon (Ganymede)

In ggpeneral most moons present a combination of interaction types. 8 The moon is an inert object Mass absorbing super-magnetosonic interaction

Phdhase space density in a supersonic pl lasma || and  refer to directions w.r.t. field Assume vflow  B

10 Mass absorbing super-magnetosonic interaction

11 Expansion of plasma into a vacuum

Z = s/t

Samir et al. Rev. Geophysics, [1983] Self-similar solution of isothermal expansion into a Halekas et al., J.G.R. [2005] vacuum. 12 Supersonic interaction with the Earth’s Moon

HlkHalekas, BlBale, Mitchell and Lin, JGR, 2005

13 Moon/Plasma Interaction Types

The interactions can be broadly classified into four different types.

In ggpeneral most moons present a combination of interaction types. 14 Phase space density in a subsonic plasma || and  refer to directions w.r.t. field Assume vflow  B

15 Mass absorbing sub-magnetosonic interaction

Khurana et al 2008, Icarus

The wake signature in the Z direction gets extended considerably. A Particle with a particular field-aligned velocity is absorbed if located in its shadow wing. Tethys

17 Tethys Tethys 15 data (Background subtracted) 2 S II 1 0 -1 BX_TE -2 2 1

TEIS 0 __ -1 BY -2 1 0 -1 BZ_TEIS -2 200 180 160 |B| [nT] |B| 140 DOY: 267 02:25 02:30 02:35 02:40 02:45 02:50 02:55 03:00 2005-S ep- 24 X_TEIS 0.61 1.45 2.16 2.76 3.23 3.59 3.83 3.95 Y_TEIS 17.88 12.80 7.71 2.61 -2.51 -7.63 -12.77 -17.91 Z_TEIS -2.58 -2.52 -2.47 -2.41 -2.35 -2.28 -2.22 -2.15 R_TEIS 18.07 13.13 8.38 4.49 4.72 8.74 13.51 18.47

• Cassini trajectory from right to left. • Both Y and Z signatures are consistent with an absorbing moon model. • Field enhances in the wake to maintain pressure balance. Rhea appears geological ly inactive.

19 Rhea

Rhea flyby (Orbit 18) Background subtracted 1.0 0.5 0.0 -0.5 BX_RHIS -1.0 1.6 0.8

_RHIS 0.0 YY B -0.8 4.0 2.0 0.0 -2.0 BZ_RHIS -4.0 30.0

T] 28.0 nn 26.0

|B| [ 24.0 22.0 DOY: 330 22:30 22:35 22:40 22:45 22:50 2005-Nov-26 X_RHIS 1.74 1.66 1.60 1.56 1.55 Y_RHIS -4.34 -1.49 1.37 4.23 7.08 Z_RHIS -0330.33 -0320.32 -0300.30 -0290.29 -0270.27 R_RHIS 4.69 2.25 2.13 4.52 7.25

• SfttjtflfttihtSpacecraft trajectory from left to right. • Field enhances in the wake to maintain pressure balance. • Both Y and Z signatures are consistent with an absorbing moon model. • X signature may be due to subsonic regime interaction. 20 Rhea Hybrid Simulation Roussos et al. (Ann. Geophys. 2007)

21 Moon/Plasma Interaction Types

The interactions can be broadly classified into four different types.

In ggpeneral most moons present a combination of interaction types. 22 MHD interaction of a conducting moon with flowing plasma. External conductivity: Alfven wings

After, Drell et al. 1963, Neubaeur, 1980,

Southwood et al. 1980, Hill et al. 1983 23 Alfvén Wings The Alfvén winggps are parallel to the characteristics given b y:   VA  V0  B0 / 0 If the moon’ s Pedersen conductance or its “plasma pick -up conductance” is large, the current strength is limited by the medium’s Alfvén conductance: A 1/(0VA) and is given by:

1/ 2 I  2ΣA  4V0(Rm  H ) / 0 

Rm is the radius of the moon and H is its ionospheric thickness. In general sat  A I  4B0v0(Rm  H ) sat  2 A After Neubauer (J.G.R., 1980) , Southwood et al. (1980, J.G.R.), Hill et al. (1983, Dessler book) Plasma pick-up current (Goertz, 1980)

j + B - E=E=--uuxB u Start with a newly-ionized neutral at rest. Initial motion is “up” for ions and “down” for electrons. This gggpives a charge separation over a distance of rL,I, the Larmor radius of ions

– A pickup current: jpu=q(dn/dt) rL,i results. – Following initial acceleration , the particles start to gyrate and drift to left at speed u. – The energy is drawn from background plasma, slowing it down. m S j  i E   E where S is the plasma pick-up25 rate pickup B2 pickup Global image of Io

Io derives its heat fofrom tidstides generated byyp Jupiter.

26 Io’ volcanic atmosphere

27 I32 data with background from KK97 C/A 800 400 Bx 0 -400 400 0 By -400 -800 -1200 -1600 Bz -2000 -2400 Io Polar flyby 2400 2000 |B| I = 3 MA 1600 1200 DOY: 01:05289 01:10 01:15 01:20 01:25 01:30 01:35 01:40 01:45 2001-Oct-16 Spacecraft Event Time (UT) X -4.20 -3.06 -1.98 -0.89 0.22 1.33 2.43 3.52 4.60 Y 2.15 1.54 0.96 0.38 -0.21 -0.80 -1.37 -1.95 -2.52 Z -0.37 -0.59 -0.79 -0.98 -1.14 -1.24 -1.32 -1.40 -1.48 R 4744.74 3483.48 2342.34 1381.38 1181.18 1991.99 3093.09 4264.26 5455.45

28 MHD modeling of I32 data

I32 Data, background, MHD, MHD with Induction 800

400 Bx (nT) 0

-400 200

-200

By (nT) -400

-600

-800 -1400

-1600

-1800 Bz (nT)

-2000

-2200 DOY: 289 01:15 01:30 01:45 02:00 02:15 2001-Oct-16 X -1.99 1.33 4.60 7.83 11.06 Y 0850.85 -0950.95 -2692.69 -4424.42 -6166.16 Z -0.91 -1.12 -1.13 -1.13 -1.13 range 2.35 1.98 5.45 9.06 12.71 Europa’s surface is young, indicating internal activity. However no vents are present.

30 Generation of Europa’s atmosphere

31 Figure courtesy: R. E. Johnson, Univ. of Virginia Plasma and photo bombardments generate atmospheres

Johnson RE et al. [2004, Jupiter 32 Book, Edited by Bagenal et al.] Atmospheres of the icy Galilean satellites McGrath et al. [2004]

At these temperatures, 1015 cm-2  10-12 bar 33 Modeling of Alfven wing current system

34 Alfven wing Modeling for E25, I =105 Amps E25 30.0 0.0 Bx (nT)-30.0 -60.0 -90. 00 60.0 30.0 By(nT) 0.0 -30.0 -360.0-60.0 -390.0 Bz(nT)-420.0 -450.0 -480.0 540. 00 510.0 |B| nT 480.0 450.0 420.0 DOY: 329 16:20 16:25 16:30 16:35 16:40 16:45 16:50 1999-Nov-25 x2.79 2.92 3.08 3.26 3.47 3.69 3.96 y-6.59 -4.73 -2.87 -1.01 0.85 2.63 4.56 z2.753.895.026.167.288.369.53 range7.67 6.79 6.55 7.04 8.11 9.51 11.28

35 Enceladus

36 A close-up of the Tiger Stripes Enceladus

37 Temporal variations of the plume of Enceladus

38 Enceladus’s plume interacts with plasma

39 Shifted mass-loading region

Enceladus 4, R = 3.0 R X = 1.5 R , Z = -4.0 R Enceladus 3, Rcloud = 4.0 RE X = 4.0 RE, Z = -4.0 RE cloud E  E  E 10 2.000 0.000 5 alf alf

xx -2. 000 xx B B -4.000 Bx, Bx, 0 -6.000 -5 -8.000 12 14.000

8 12.000 Byalf Byalf 4 10.000 By, By, 0 8.000

6. 000 -280-4 -300.000 -310.000 -300 -320.000 Bzalf Bzalf -320 -330.000 Bz, Bz, -340 -340.000 -360 -350.000 DOY: 48 03:15:00 03:20:00 03:25:00 03:30:00 03:35:00 03:40:00 03:45:00 03:50:00 DOY: 68 09:00 09:05 09:10 09:15 09:20 2005-Feb-17 2005-Mar-9 X -22.14 -17.44 -12.68 -8.13 -3.79 0.33 4.23 7.92 11.37 X -10.83 -6.75 -2.46 2.05 6.77 Y 25. 51 19. 51 13. 05 6466.46 -0280.28 -7147.14 -14. 14 -21. 27 -28. 53 Y -10. 26 -3. 38 3363.36 9969.96 16. 43 Z 4.11 4.23 4.36 4.49 4.62 4.74 4.86 4.98 5.10 Z 2.37 2.45 2.52 2.60 2.68 R 34.03 26.51 18.71 11.31 5.98 8.58 15.54 23.24 31.13 R 15.11 7.94 4.87 10.50 17.97

Enceladus 11, Rcloud = 4.0RE X = 4.0 RE, Z = -4.0 RE 5

0 xalf

BB -5 Imaggging Observations have shown

Bx, Bx, -10

-15 that a plume near the south pole 30 20 10 spouts dust and gas into space. Thus Byalf 0 By, By, -10 -20 the mass-loadinggg region would be -310 -320 expected to be shifted below Bzalf

Bz, Bz, -330

-340 Enceladus. Here we model the flyby DOY: 195 19:50 19:55 20:00 20:05 2005-Jul-14 X -6.89 -4.10 -1.11 2.06 5.41 signatures with a mass-loading region Y-10.96 -5.00 0.85 6.6112..727 Z -15.90 -8.56 -1.21 6.14 13.48 R 20.50 10.73 1.85 9.25 19.02 located 4 RE below Enceladus. 40 Rate of Mass loading J y  qnL  nmv / B

Mv I y    J ydXdZ  Jy Bly Z where M  nm dX dY dZ

X BlyI y or M   v The rate of mass-loading can be  related to the current passing 320x109 x2000x103 x1.0x105 through the mass-loadinggg region. 26x103 Surprisingly, the total amount of mass loading implied is quite low. M  2.5kg/s After Chris Goertz 41 [1980], JGR Moon/Plasma Interaction Types

The interactions can be broadly classified into four different types.

In ggpeneral most moons present a combination of interaction types. 42 The principle behind electromagnetic induction

Eddy currents BInduced(t)

BPrimary(()t)

The primary and secondary The total field fields shown separately

–Eddy currents generate a secondary or induced field which reduces the primary field inside the conductor. –The induced field can be detected with a sensor. Jupiter provides the primary field

• The Galilean satellites are located in the inner and middle magnetosphere of Jupiter. • Because the dipole and rotation axes of Jupiter are not aligned, the moons experience a varying fie ld in the ir frame. Electrodynamic equation

• Generalized Ohm’s law: J   (E  u B) Take curl of above equation   J   ( E   (uB))

• Use Ampere’s Law   B  0J

 ( B)   0 ( E   (uB))

• Use Faraday’s Law EB/t

  2   B   B   0   (u  B)    t  Induced field from a plane half-space

• The electrodynamic equation describes the convection and diffusion of the magnetic field in a conductor:

  2   B   B      (u  B )    t  • In the absence of convection in the conductor, the equation reduces to the well known diffusion equation:  B  2B    t • The solution for a conducting half-space plane(z >0) in the presence of a uniform oscillating field is:

B  B e z / S ei(tz/S ) 0 1/2 where S ( /2) is the skin dhdepth . which shows that the field decays in the conductor by an e folding within a skin depth S. The diffusion time for the field is: T   S 2  The Likely Material

TblTable 1. CdtiitiConductivities of common matilterialsand their skin depths for a ten-hour wave. Material Conductivity Skin depth for a (at 0 C) ten hour wave (S/m) (km) Water (pure) 10-8 106 Ocean Water 2752.75 60 Ice 10-8 106 Ionosphere 210-4 7103 (E layer) Granite 10-1210-10 108107 Basalt 10-1210-9 1083106 Magnetite 104 1 Hematite 10-2 103 Graphite 7104 0.4 Cu 5.9107 .01 Fe 1107 .03

Three layer model

48 Induction from a finite-conductivity shell

Because the primary field is uniform and the conductivity distribution has spherical symmetry, the induced field outside the conductor (rr 0 ) is a dipole field  B  0 3r M r  r 2M r 5 (1) sec 4 whose moment M oscillates at the same frequency  and along the same direction e0 as the primary field. The moment can therefore be written: 4 M   Aei B r 3 2, prim m 0 so that Eq. 1 becomes:  i t  2 3 5 Bsec  Ae Bprim 3r  e0 r  r e0 rm 2r  (2) The parameters A and  are real numbers, which after Parkinson (1983, Introduction to geomagnetism) are gibhiven by the compl ex equati ons: 3  r  RJ52() r 0 k J 52 () r 0 k Aei   0   r  RJ() r k J () r k (3) m 12 0 12 0 rkJ1521 () rk R  (4) 3()J32r 1k  r 1kJ 12 ()r 1k ki()12 J where 0 has the dimension of a (complex) wave vector, m is the Bessel function of first kind and order m . Galileo Observations at Europa

• E4 and E14 passes showed signatures consistent with induced dipolar fields from currents flowing near the surface. The direction of the dipole moment was directed towards Europa in both cases (as expected). • A subsequent pass (E26) confirmed that the dipole moment flipped in response to the different orientation of E14 Jupiter’s field as expected from theory. Galileo Observations at Callisto

•Dur ing the C3 fl y by, the magnetic field of Jupiter was directed radially outward. •Dur ing the C9 fl y by, the magnetic field of Jupiter was directed radially inwards. •The ob served i nd ucti on signature also showed opposite polarities. •This con firms tha t electromagnetic induction and not a permanent dipole is the source of the observed signature.

51 And what about Callisto’s surface?

Callisto appears inactive on every length scale. 52 The inductive response for Ganymede

Myo = 49 nT

82% response 100% response

Induced moment in a metallic sphere

Kivelson et al. Icarus, 2002 The Likely Material

Detailed modeling shows that:

• “Near” surface conductors are required to fit Europa, Ganymede & Callisto measurements • Source of field cannot be far below the surface because the field 3 strength falls like (r/Rsurf) and signature would become too weak to detect.

• We know that Europa’s H2O layer is ~ 150 km thick, Ganymede and Callisto’s > 400 km. • Glo ba l su b-surfftltfkthikdface oceans of at least a few km thicknesses and located at a depth of a few to tens of km for Europa and ~ 150 km for Ganymede and Callisto are required to explain the observed signatures. Io’s Interior Motivation

High lava temperatures hint of a mushy magma ocean in Io

Keszthelyi, McEwen, and Taylor, 1999, Icarus How can induction studies help? Electrical conductivity is a strong function of temperature and melt fraction.

Oman Gabbro Karelia Olivinite Maumus et al. 2005 Three layer model • Assume crust thickness d = 50 km ∞ eltillilectrically insu ltilating

•rm = 1820 km

• r0 = 1770 km.

• Core radius r1 = 600 – 900 w ith ∞ conductivity. • Mantle thickness h =

r0 -r1 = 870 – 1170 km with a range of •T = 12.953 hrs, B = 850 nT conductivities. syn syn • Torb= 42.46 hrs Borb ~ 50 nT Induction from core + mantle

A and for =1000 S/m  core

2 4 900 0

0 1 0 0 2

0 0

0 0 0 5 5

3 2

5 900 0 0 3 0 3 4

0 0 0

2 5 5

1 0 0 0

4 3 4

950

0 5

1000 0 2 40 0

5 100 2 (km) 0 0

0 0 0 55

1 0 0 5 5

2 3 5 5

0 3 3 4 0 0 ntle 0 0 2 0

0 aa 0 0

4 4 3 m

h 1050

5 1100

5 100 0 0 0

0 0

0 5

0 0 5 5 4

2 3

5 5 50

3 0 4 3 0 0

1150 0 2 0 5

0 0 0

1 6

4 4 3 600 -4 -3 -2 -1 10 10 10 10  (S/m) mantle conductivitymantle (S/m) MHD simulation: I24

I24 Data, background, MHD 400 300

(nT) 200

Bx 100 0 800 )

TT 600 400 By (n 200 -1600 -1800 -2000

Bz (nT) Bz -2200 -2400 DOY: 284 03:45 04: 00 04: 15 04: 30 04: 45 1999-Oct-11 X -9.57 -6.91 -4.23 -1.51 1.40 Y 8.08 5.26 2.44 -0.38 -3.11 Z 0.03 0.05 0.08 0.10 0.11 range 12.53 8.68 4.88 1.56 3.41 I24 (MHD with Induction)

I24 Data, background, MHD, MHD with Induction 400 300

(nT) 200 xx

B 100 0 800

T) 600 400 By (n 200 -1600 -1800 -2000

Bz (nT) Bz -2200 -2400 DOY: 284 03:45 04:00 04:15 04:30 04:45 1999-Oct-11 X -9.57 -6.91 -4.23 -1.51 1.40 Y 8.08 5.26 2.44 -0.38 -3.11 Z 0.03 0.05 0.08 0.10 0.11 range 12.53 8.68 4.88 1.56 3.41 Moon/Plasma Interaction Types

The interactions can be broadly classified into four different types.

In ggpeneral most moons present a combination of interaction types. 63 Ganymede is a magnetic moon

64 Ganymede: A Moon with Magnetism (with th k an tJ hT ks to Torrence Johnson)

65 Multiple passes shdhhowed that Ganymede is surrounded by a mini- magnetosphere that rocks with the ~10 hour period of Jupiter’s rotation.

66 Convection in Ganymede’s magnetosphere

67 MHD model

• SlSolve three-dimensi onal resi s tive MHD equa tions in sp her ica l coordinates. ( Linker et al., 1998)

    (v )  0 t  v      v  v    P  J  B  t  P    (Pv )  (  1) P(  v )  J 2  t  A    v  (  A)  -  (  A) t     B    A , J    B Jia et al. 2008, JGR Jia et al. 2009, PhD thesis Simulation domain and numerical mesh

• Non-uniform spherical mesh covering a

calculation domain 0.5RG

2D cut of the simulation grid

Jia et al. 2008 Boundary conditions

3 40RG 1. Core boundary -Fixed mag net ic flu x co rr espon din g

to Ganymede’s internal field 2 1.05RG

3. Outer boundary 1 0.5RG - Upstream: fixed values for B, v, p and rho v  0 - Downstream: oppyen boundary conditions 2. Inner boundary - Fixed plasma density and pressure - Velocity: (()a) v  0 (ppp(appropriate for hi gh ionos pheric conductance )    (b) vperp continuous, i. e., vperp,1  vperp,2 Jia et al. 2008  vpar,1  0 G1, G2, G7, G8, G28, G29 90

• Trajectory distribution of 60 Galileo’s six close encounters 30 to Ganymede in a Ganymede- 0 itude (deg)itude centered spherical coordinates. tt La -30

-60 Upstream Downstream -90 0 60 120 180 240 300 360 Longitude (deg)

Induction efficiency is modeled as a fit parameter when fitting the residuals (data – MHD model) to an induced field model. Magnetosphere of Ganymede and its current systems

Flow

x Flow

•Maggpnetopause current • Tail current Jia et al. 2008 • Field-aligned current V Alfvén characteristics:   tan 1( flow ) VA GdGanymede EhEarth

(From NASA-GSFC ISTP picture archives) 6RG Plasma flow

XZ plane XY plane

Flow Flow

Streamlines Comparisons between simulation results and the Galileo MAG data G2 flyby in the GphiO coordinates G2 (Polar) 400

Bx [nT] -400

400

0 By [nT] -400

0 Flow -400 z [nT]

BB -800

-1200 1200

800 ag [nT]

mm 400 B 0 DOY: 250 18:40 18:50 19:00 19:10 19:20 19:30 1996-Sep-6 X -0.58 -0.19 0.19 0.56 0.92 1.21 Y -3.45 -1.75 -0.00 1.75 3.46 4.86 Z 0.73Galileo 0.93 data 1.09 1.14 1.16 1.17 range 3.57 1.99 1.10 2.16 3.76 5.15 Superposition model (Kivelson et al., 2002) MHD simulation Comparisons between simulation results and the Galileo MAG data G8 (Upstream, Low-latitude)

Flow

Galileo data Superposition model (Kivelson et al., 2002) “V=0” boundary condition

“Vperp continuous” boundary condition Conclusions

• WhWe have discovere dhd that: – The large moons of Jupiter and Saturn display all four types of moon/plasma interactions. – Tethys and Rhea do not have atmospheres or internal magnetic fields. – The Io and Europa plasma interactions are caused by their atmospheres supported by plasma bombardment. – Enceladus and Dione also have tenuous atmospheres maintained by vent activity. – Europa, Ganymede and Callisto possess subsurface oceans. – Ganymede has its own magnetosphere and plasma convects into it through field line reconnection. Exercise 1

For G anymed e 2 fly by, Assume tha t the o bserve d fie ld resu lts from two sources: An internal dipole and an external uniform field. From the observations near Ganymede, calculate the vector dipole moment in units of nT field generated in the equatorial plane.

Bobserved =B= Bext +[D].M (1) where the matrix [D] depends only on the coordinates of the observation platform and is given by 3x2  r2 3xy 3xz  5  2 2  (2) D  r  3xy 3y  r 3yz   2 2   3xz 3yz 3z  r 

and M is the vector dipole moment (in units of magnetic field observed at the surface at the magnetic equator.) 79 Exercise 2

• AthtAssume that E’Europa’s ocean iftldtihllis a perfectly conducting shell. Calculate the magnetic field along the trajectory of Galileo for the E14 flyby when the inducing field was (40, -160, 0) nT.

• Hint M = (-20, 80, 0) 80