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The role of planetary satellites in magnetospheric processes
,idv.
I, pp. 31—46. Printed in Great Britain.
SpaC~i 1?c~. Vol.
© COSPAR,
1981.
0273—1177/81/OlOl—0031$05.00/0
THE ROLE OF PLANETARY SATELLITES IN MAGNETOSPHERIC PROCESSES C. K. Goertz* Max-Planck-Institut für Aeronomie, D-341 I Kat!enburg-Lindau 3, FRG
ABSTRACT
A large satellite in a magnetosphere can disturb significantly the magnetic and electric fields in its vicinity. The nature of the disturbance depends on the conductivity of the body, its own magnetic field, the plasma parameters (density, temperature, flow velocity, composition) and the boundary conditions imposed by the planet’s ionosphere. Under certain conditions large field aligned electric fields can arise which cause particle acceleration and hence emission of plasma and radio waves. A number of observations relevant to the case of the Jovian moon lo will be briefly reviewed. The coupling of 10 with the magnetosphere is discussed in terms of pick—up and Alfv~nwaves. We argue that most of the ions making up the lo torus are created in b’s immediate vicinity where the electric field is reduced by a factor of about 4 from its full corotational value. INTRODUCTION Recent in situ observations of the satellites of Jupiter and Saturn have emphasized the importance of their interaction with the magnetosphere. For example, we now believe that lo provides most of the low energy thermal plasma in the Jovian magnetosphere and a significant fraction of high energy particles. Planetary satellites may absorb energetic particles and thus control the energetic particle environment, if they orbit within the planetary magnetosphere. The energetic particles in turn can effect the surface properties of the satellites, lead to sputtering of neutrals and impact ionization of neutral atmospheric particles. The resulting charged particle environment around a satellite can be drastically
*
On leave from the University of Iowa, Iowa City, Iowa 52240, USA
31
32
C. K. Goertz
different from other regions of the magnetosphere, as exemplified by the great bo plasma torus. Plasma wave propagation characteristics, growth and/or absorption rates are hence effected by the satellite. Satellites can cause auroral activity in the ionosphere of the parent planet and change the structure and chemistry of the ionosphere. The importance of the role of planetary satellites for magnetos— pheric processes can hardly be overestimated. We will consider only those satellites which orbit within the magnetosphere of the planet. For the earth’s moon this is only occasionally the case. The four Galileon satellites of Jupiter always stay within the Jovian magnetosphere. Many of Saturns satellite do so also, although some may exit at times from the magnetosphere like our own moon. Satellites, or moons, moving within the magnetosphere are subject to special conditions. Among these are: (i) They are surrounded by significant fluxes of trapped energetic charged particles. (ii) The environment also contains low energy plasma. (iii) The magnetic field near the satellite contains the planetary (dipole) field, i.e. the satellites are magnetically connected to the planet. (iv) Since the satellites move relative to the planet’s surface (ionosphere) there exist electric fields in the vicinity of the satellites. The satellites are effected by all four conditions and in turn change themselves the four conditions. The interaction is thus a complex, presumably non—linear, phenomenon, the exact nature of which depends on the properties of the moon itself, the conditions in its vicinity and the boundary conditions in the parent planet’s ionosphere. In what follows we will in turn deal with the disturbance of the electric and magnetic fields created by the satellite, and the effect of this on energetic particles and the thermal plasma. We will try to keep the discussion general, although we will occasionally refer to the special case of 10, for which many observations and theories are available. In most case we can only describe the basic ideas and must refer the reader to the original literature. ELECTRIC AND MAGNETIC FIELDS NEAR THE SATELLITE Nonmagnetic Satellite Let us consider a spherical nonmagnetic moon moving through a region of uniform magnetic field. Then, in a frame of re~eren~e mo’~ingvith÷thesatellite, there will be an induced electrostatic field E.L — VS x B 0 where V is the velocity of the moon measured in a frame of reference corotatLng with the p~anet’sionosphere. The situation is depicted in Fig. 1. We assume that parallel electric fields do not exist or have decayed to zero. If the satellite has a conductivity a~and the surrounding medium a conductivity aM which for simplicity we assuifie to be a scalar the electric fields in the moon’s frame are [1]:
v5
x~
(1— a:aM
(1)
(2) where the induced dipole moment p is 3 =
—
a52a,~4 (~ x ~) R
(3)
Planetary Satellites in Magnetospheric Processes
33
Ionosphere
Fig. I The geometry of~thesatellite—planet interaction. is the rotational axis and M the magnetic dipole axis of the planet. The dipole moment is due to the surface charges on the moon. Although this treatment neglects the anisotropy of the surrounding medium it shows a number of important effects. x
4~I~4 -.
I I
I
I
‘III’ I~ ~\
~
~
bC
Fig. 2 Electric field (solid) and stream (broken) lines. a) Perfectly insulting moon (a — o) b) intermediate case c) perfectly conducting case +
(aSa~aM)
Case i: a -‘~ o. In this case the electric field is not disturbed at all. No currents f~owanywhere. An insulating moon does not disturb the fields in its vicinity. This case is shown in Fig. 2a. Case ii:
~‘
a~4. In this case the electric and magnetic fields are both
disturbed as shown in Fig. 2b. Currents flow through it which connect to currents flowing within the medium surrounding the satellite. The closure of the currents will be discussed below. Case iii: a + ~, i.e. the satellite is a perfect conductor. In this case the electric fie’d inside the moon is reduced to zero by an accumulation of polarization charges on the surface of the satellite. The elecr~ Eield outside is
34
C. K. Goertz
distorted by the addition of a dipole field. The field lines and resulting stream lines are shown in Fig. 2c. There are no currents flowing through it and the distortion of the magnetic field is small because only polarization currents flow, which will be discussed below. In case i plasma has access to the moon. and in case iii it has no access at all.
In case ii plasma has a reduced access
Insulating Satellites with Intrinsic Magnetic Fields Recently it has been suggested by many authors (2], [3], (4] that 10 and some Saturnian moons have an intrinsic magnetic field. Many interesting effects can occur when a satellite has an intrinsic magnetic field. One may have magnetic reconnection, a satellite magnetopause or even a bow shock. However, the fields around the satellite may not be determined by these rather complex phenomena but by the simple fact that even a perfectly insulating satellite with an intrinsic magnetic field distorts the electric field in its vicinity just because it distorts the magnetic field. For simplicity we assume that no currents flow in the moos’s vicinity and that the intrinsic field of the moon is a dipole field of moment m. If no parallel electric fields exist the electrostatic potential ~ is constant on a field line. The magnetic field lives and equipotentials in the ~icinityof the moon are shown for the two cases of in parallel or antiparallel to B 0 in Fig. 3.
ml
B0 R~
ImIcB0 R~
ImI~.B~ R~
ImI~B0 R~
Fig. 3 The distortion of the magnetic field lines when the moon has an intrinsic magnetic dipole field. The direction of the moon’s dipole is indicated by the arrow. Note the field lines are equipotential s. If m is antiparallel to B the electric field in the vicinity of an insulating satellite is similar to teat of a pe~fec~ly conducting satellite without an intrinsic field m. In both cases the E x convection woulg carry low energy particles smoothly around the moon. If in is parallel to B0 particles may have excess to the moon along the open field lines. The cross—sectional area of the field lines that connect to the moon is larger than the moon itself. In terms of particles access the antiparallel case is equivalent to a perfect conductor and the parallel case to an insulator. It should be noted that whereas in the previous section the electric field distortion existed all along the essentially “straight” field lines and hence the convection in the planet’s ionosphere
Planetary Satellites in Magnetospheric Processes
35
was perturbed, for an insulating moon with an intrinsic magnetic field the distortion of the electric field is limited to the vicinity of the moon. The convection in the planet’s ionosphere is not significantly perturbed. When the satellite has both a finite conductivity and in intrinsic magnetic field the electric field in the moon frame is given by equations (1) and (2) except that now B is the total magnetic field, i.e. planetary plus moon fie’d; and v is the 3 v disturbed velocity. when m is ofantiparallel to Bi~immaterial and in B R !n S is zero inconvection 10’s vicinity and the Thus conductivity the sa~ell.j~te determining the convection pattern. When in < B 3 and B in < o the conductivity is important, because v 0R 5, although smaller than t~esatellites velocity, is nonzero. The other cases can be dealt with straight—forwardly. It should be noted, that in all cases we have neglected magnetic fields due to locally induced currents, i.e. currents driven by the induced electric fields. For a more formal derivation of these relations we refer the reader to the papers by Goertz and Deift [1] and Ip [4]. Parallel Electric Fields We will now drop the assumption of vanishing parallel electric fields. This allows for the possibility of particle acceleration and field aligned currents. Consequently many models of the interaction of lo with the Jovian magnetosphere have concentrated on this aspect. The first question that arises is the following: Why, if the induced electric field across 10 is only perpendicular to the magnetic field, should there exist a parallel field at all? Recall that when the satellite has a non—zero conductivity charges will accumulate on its surface. The electric field due to the surface charges (i.e. not the field due to magnetic field distortions), mapped down the field lines into the planet’s ionosphere, will drive a Pederson current which is fed by field aligned currents. This field aligned current is limited by the current carrying ability of the plasma between the satellite and the ionosphere (Fig. 4). Without acceleration a thermal plasma can only supply the thermal current density, ~th — ne /kTe/ii~ If this current density is not large enough to supply the ionospheric Pederson currents charge imbalances develop along the field line and parallel potential drops occur. In this way the electric field across the ionosphere is reduced until the plasma current matches the Pederson current. Whether the parallel electric field occurs in sheaths [5], double layers [6] or over a larger distance [7] depends on the particular properties of the system, such as plasma density and temperature, electric field and ionospheric conductivity.
Ionosphere
Fig. 4 The satellites flux tube near the ionosphere. tial drop • occurs near the edges of the flux tube.
The poten-
36
C. K. Goertz
The mathematical formalism for this model is suite simple. Let us denote the height integrated Pederson current as I • E E’ where E’ is the field in the ionosphere (as seen in the planet’s fratue)Y The parallel current density is and the parallel potential drop along a field line is $. The electric fiel~due to the induced surface charges, suitably mapped to the planet’s surface is E’. 3y — j where t~ecoordinat~ Then the current continuity equation reads 31 / system is defined in Fig. 4. The condition o~steady state V x E 0 reads ~(V x ~)y dz
—
—
-~
-~
—E~~ — 0
(5)
Combining these equations and noting that the field V is constant inside the flux tube connecting the satellite with the ionosphere we ~et
~z (y)
32$
y
=0
(6)
with the boundary conditions that —
—
E
(7)
at the edge of the flux tube. Once a constituting relation between formulated one can solve for $(y).
+
j
and $ is
+
We see, however, that if j 0 and ~ 0 a potential drop must occur. It should be emphasized that this pot~ntialoccuk only when the conductivity of the satellite is non—zero. It is not enough to perturb the perpendiculat electric field by a magnetic field perturbation. For that case E~ 0. Various different relations between $ and Lynden Bell [6] used
jz
have been used.
Goldreich and
sign $
—ne
(8)
Gurnett (5] used
j
—
j~sign
$
(9)
Smith and Goertz (6] give a similar but somewhat more complicated form. In all cases the parallel potential drop $ can be easily obtained as a function of y. Smith and Coertz [6] show that in all cases the maximum potential drop occurs at the edge of the flux tube and that under special, though perhaps unrealistic, condition the parallel potential drop on one side of the flux tube may approach the total potential across the satellite, which e.g. in the case of bo amounts to 400 kV. Such a potential could produce large number of 400 keV charged particles. These seem to have been observed (see e.g. Fillius [8]). ELECTRIC AND MAGNETIC FIELDS NEAR THE SATELLITE (NON—STEADY CASE) In the previous section we have implicitely assumed that the time constant of the circuit connecting the moon with the planet is zero. However that is not the case and the steady state case may not ~bereached at all. As viewed from the planet the moon represents a moving perturbation of the plasma velocity. Any chat~geof plasma convection leads eventually to the emergence of two oppositely travelling Alfv~nwaves (9]. This is true for all magnetohydrodynamic perturbations inde—
Planetary Satellites in Magnetospheric Processes
37
pendent of their amplitude. The Alfv~nwave communicates to the adjoining plasma the stresses exerted by the satellite. Or in other words: The satellite imparts momentum to the plasma via emission of Alfvén waves. Fig. 5 shows the perturbation created by a satellite with finite conductivity. Since into a medium movingthe withAlfv~nwave a velocitymoves V relative to
~~ /
B
Ii /1
/
/
the moon the perturbatioA propagates along a characteristic which is inclined with respect to the background magnetic field as seen in the ~ frame. In the planet’s frame the perturbation propagates along the field line. Behind the wave front the plasma velocity and magnetic field are perturbed. We can estimate these perturbations by noting that the Alfv~nwave carries a current along the characteristic given by [10]
/ / /
-_________________ V
\\
Iw
through the satellite I =E E
\~
1/
Y~~ -
(10)
This current has to be fed by the current
H
j
E(E—E);EA—-V-— A o s
Since Is s w E
-
—
I
(11)
we have
S
E
-
(12)
And the perturbation of the velocity is z
LW
Fig. 5 The Alfv~nwings near Io. The two lower figures show the distor— tion of the field lines at two differ— ent values of y. The left hand one is at y — o. The charact:ristic is inclined by the angle 0 tan’(v /v )— A s A tanl(MA).
/~E
(13)
_______
v”r s o
=
~
A
s
For an Alfv~nwave the velocity amplitude is related to the magnetic field amplitude as ~b ~—.
t~V
=+~—
o
A
zS
(14)
_____
—
S
EA plays a r6le similar to that of a in equations (1) and (2). For more details we refer the reader to Coertz [II]a~id Southwood et al. [12]. After a time tA~the wave reaches the planet’s ionosphere where it is reflected. The reflection coefficient is [13]
~ R-—
IA —1p A p
(15)
The reflected wave will move into a medium in which moves with a velocity V relative to the moon and in which the magnetic field is tilted by an angle S
I tan
B
=
MA
I A
I
—
s
MA
V
=
s
MA K
—
LW
(16)
C. K. Goertz
38
It is easy to see that the return wave will be displaced relative to the moon by N 1 ( A21c 11K] (2—MX K) (17) iS/R = ~— s ds 1—M A
)
where the integral is from the moon to the planet. The ~1.isplacement 6 depends on the conductivity of the satellite. When I + we have k + 1 and 6 ~. 0. The g~ometryof the situation is shown in Fig. 6. Clearly only when 6/R < 1 will S. •. ••. •. the resistive properties of the ionos— phere have any influence at all. 9O!0~,~ ~~4l1 It is also relatively easy to show that Ill I when 6/R 3 << 1 a steady state is reached /ll / in which I ~• 91. Ii E =E I = El’ ~ E i~ s oE +1 ‘ s 1 +E o (18)
/
‘fi, I_i iO* I
o~ ,~-Jr A
/
~
‘
/I I
p5
Ps
where I’ is the suitably mapped ionospheric PedersoR conductance. The mapping must include both the divergence of the magnetic field lines and the possible existence of parallel electric fields. A treatment of the mapping would be beyond the scope of this paper.
We can now distinguish two types of interaction. When 6/R5 << 1 a steady state — current flows between the moon and the planet. The current is exactly parallel to the (distorted) magnetic field. When Fig. 6 The geometry of the magnetic 6/R > 1 the interaction must be described field in the Alfv~nwing. The thick in !erins of Alfv~nwaves emitted from the arrows indicate the direction of pro— moon. The current is not exactly paral— pagation. 6 is the distance by lel to the (distorted) magnetic field. which the return wave is displaced. In the second case the change in the s is along the characteristic of the plasma velocity is related to the magnetic Alfvèn waves, field perturbation by the Alfv~nwave relation (equation 14) whereas this is not true in the first case. We emphasize that these distinctions apply independent of whether the moon has an intrinsic magnetic field or not. Before the discovery of the great plasma torus around lo, the bo interaction was generally thought to be of the first type (6/R10 << 1). Today it seems more likely that >> 1 because the Alfv~ntravel time through the dense torus is quite large. The coefficient of reflection by the Jovian ionosphere is nearly 1, the collisionless damping of the Alfv~nwaves emitted by lo is negligible (14]. Thus the Alfv~nwaves emitted by lo will bounce many times between the two hemispheres of Jupiter and lo will carry behind it a wake filled with Alfv~nwaves such as shown in Fig. 7. Gurnett and Goertz [14]relate this pattern to the Jovian de— cametric arcs. THE MOTION OF CHARGED PARTCILES IN THE VICINITY OF A SATELLITE The motion of chargedparticlesis effected by the electric and magnetic fields. Unless the particle’s energy is so large that it’s gyroradius becomes comparable
Planetary Satellites
in Magnetospheric Processes
39
FIELD-AUGNED CURRENTS DECAMETRIC RADIATION SOURCES JUPITER ,‘
illj
tO > PLASMA TORUS
I0 -
-
ALFVEN WAVES
Fig. 7 The wake of Alfv~nwaves dragged around by lo (from Gurnett and Goertz [14]). with the moon’s radius adiabatic theory can be used to determine the trajectories of charged particles near the moon. The trajectories are curves along which the total energy (kinetic plus potential) first and second adiabatic invariants are conserved. In the literature only equatorially mirroring particles for which the second adiabatic invariant is zero have been considered. The trajectories will be energy— and species—dependent. Given an electric field and magnetic field in the moon’s vicinity it is straightforward to caluclate the trajectories. This has been done for a perfectly conducting 10 by Schulz and Eviatar [15]. Some trajectories are shown in Fig. 8. Zero energy particles will not intersect the moon. The effective cross—sectional radius for absorbing zero energy particles is zero+in this case. For energetic protons the VB drift is in the same direction as the E B 4rift far away from the moon. Thus energetic protons will not smoothly E x B drift around the moon but impinge onto the moon’s surface. The effective cross—sectional radius for absorbtion increases with increasing energy until for infinite energy it approaches the geometrical radius. Electrons with *ner~iesbelow an energy, at which the VB drift velocity exactly cancels the E x B drift, do not impinge on the moon at all. Thus the effective cross—Sectional radius for electron energies below this value is zero. Above this critical energy the effective radius varies as shown in Fig. 8b. For a finite conductivity the electric field perturbation outside the moon is reduced (see equation 2) and the variation of effective radius varies with energy and species as shown schematically in Fig. 8b[16]. For a moon with an intrinsic magnetic field the trajectories have been calculated by 1p [4]. Some of the trajectories are shown in Fig. 9. Whereas in the previous case the effective radius was zero at zero energies and equal to the geometric radius at infinite energies for a magnetic satellite the effective radius goes to zero with increasing energy. Furthermore in the previous case particles impact, if at all, uniformly over the moon’s surface. In this case the impact occurs on one side of the moon. This could account for an apparent asymetry in the sputtering strength of neutral sodium atoms[17].
40
C. K. Goertz
~ I Th
-
•.~l•.•~
,1
II
~
~ ,
‘
‘
‘‘:
I
~
I
~~—---~.—
‘‘~~
$
I
$
~~-~‘‘
Fig. 8a Drift paths of representative particles in the vicinity of Io: (a) particles having N — 0; (b) protons, M = 1 GeV/G; (c) electrons, N = 40 GeV/G; (d) electrons, N — 80 GeV/C; (e) electrons, M = 200 GeV/G; (f) electrons, N 400 GeV/G. Dashed curves represent critical (grazing) trajectories and separatrices. Other trajectories are identified by values of x~/a 1 or of (from Schulz and Eviatar [IS]).
‘!“P~~V&IiC ~.7GDi~MtS wVXTh I, I0~UtZ v.$A?ae. IS??)
rr,oVV.~ ~ N~&R~~ECTL~ ~$rAXTe~ I. 50I(M&TC
~F1I
~WU
~
V
EFT(CVPJE ~S~EPI,IS S~UVI. F~I PCISICTLV mØXTING
3
-
~ING r03£F~CCT~ I~IS~T~V ~
R*0I~I.
(XIItUAXC)
3
——_~—.
7-
-
2
I
—
S
L Co.
-i d’
G~I(TSICIS.
-
~-~--
—
dI
CUCV,m.S
~
IWICIC EMISIM~I
o’
c
~----~--~
_________________________~___I (Nt~GV
Fig. 8b The electrostatic equipotentials around lo and variation of effective absorption radius of 10 as a function of energy (from Thomsen (16]).
f
Planetary Satellites in Magnetospheric Processes
I
I
laJS—-O.5 1~O~O
-
-
~_
~
I
—1~~———.—
I I~
I
Ib)S.-0511
•.
~I I~
-o°
/
I,
l8O0~_~
I I, I ii
-—
~°.
/ \
I I -
-
-
770°
-
test the various possibilities?
The
data for particles all but our moon come tion of is own generally energy and only species from a dependent. short crossing How of cantheone some Pioneer 11 data obtained by the moon’s magnetic L—shell. Fig. 10 shows University of Iowa instruments (Van Allen et al.[18]) near the inbound and outbound crossings of b’s L—shell. We see that only low energy electrons and protons show any significant
particle geometric flux concept we have of effective to relate absorp— the tion radius to an absorption time.
)
Id)S.cV1•0o~J ~qo°
The discussion above shows the absorp—
changes particle the flux near lo. of In order to ofinterpret variation
270°
1.10-01 I
IcIS.-aST
1.101
-~--
41
~
—~--o
____________
Fig. 9 Trajectories of energetic particles around 10 assuming an intrinsic dipole field. The induced electric dipole moment is p = S V V B . The particle energy is W L BS .8025 key where B is
moons do absorb all particles that impinge on the surface the even flux if will This not beis zero necessary at the because moon’s L—shell the because new particles are continuously transported across the moon’s L—shell. The observed profile is the result of transport and absorption (Thomsen (16]). In many cases the transport is diffusive and from the shape of the particle flux variation one can estimate a diffusion strength. For example, if the time it takes a particle to diffuse the L—shell range covered by the across moon (extending from L~to L 2) is much larger than the
the intrinsic surrace field of Io in tam— mas. The figure is from 1~ [4].
absorp ion or loss time the flux will go to zero inside the moon’s L—shell. In the other extreme (strong diffusion and/or weak losses) the flux will hardly change. By loss time we mean the time it would take the moon to wipe out all the particles in the L—shell range covered by the moon. This time depends on the effective radius, the relative drift of the particles with respect to the moon and the size of the L—shell range covered by the moon. We quote here the equation by Thomsen et al. [19]which is similar to the ones of Simpson et al. [20]and Mogro—Campero and Fillius[21]. •1=
2v
(14
— L~) 2mm r
(19) (III 6 L where w,~(W) is the energy and species dependent drift rate of the particles, w is the ~rift rate of the moon whose effective radius is r . The average L—she~l is determined by the product of the diffusion coefficientmD and t. Since D is energy and species dependent (Thomsen[16]) the analysis of the observed profiles is very difficult. It is sufficient to note that the profile of the ions as compared to that with electrons has cast some doubts on the simple geometric picture of absorption. It seems that near bo other effects, such as pitch angle scattering or charge exchange, are more important than absorption. Even for Iu~(W) +
42
C. K. Goertz
__________________________________
007002ND
10
£MA7~(A
10
—
U
RAND*41 -~
S
tZ~~
I
£,.b~0W
~-
-~ £20002 U
U
I
e~2J~~ -~
0’
~
OGIMW.Ep. 341020
~n~__ 0
I I I 0 20 30 40 30
I~I 0
3I~
0
20 70 ~0
50
40 50 0 0 10 2101 33?
_....L.... 20
30
0 50 0 ,I.
0
20 30
Fig. 10 The variation of count rates for the Pioneer 11 flyby of Jupiter. The data are from the University of Iowa instrument package (from Thomsen (16]). electrons the profiles observed near bo are not completely understood in terms of the absorption described above. PLASMA IN THE MOON’S VICINITY (bo TORUS)
We have briefly discussed the absorption and (through parallel electric fields) acceleration of energetic particles. We now concentrate on the low energy particles, i.e. those for which the magnetic field drift is negligible compared to the electric field drift. The drift, which was discussed above leads to absorption and a plasma cavity behind the satellite. Such a cavity also exists for energetic particles. We will not discuss this as similar topics have been extensively discussed in connection with the earth’s moon. We will here concentrate on moons as a source of plasma. In particular we will emphasize the r~leof lo for maintaining the great plasma torus and neutral cloud around it. From ground based and in situ observations it has been established that_~here exists a doughnut shaped ~olu~e c~tai~jng a+dense (ne ‘U 1.. 4 x 10~cm ), warm (T. ‘U 30 eV) heavy ion (0 , S , 0 , S , Na ) plasma as well as neutral sodium atoms. The maximum of the plasma density occurs roughly at b’s L—shell (L — 6). The density decreases slowly with increasing distance but drops rather abruptly inside of L — 5.6. Inside of L — 5.6 the ion temperature becomes very small. W’ereas the plasma torus extends completely around Jupiter, the neutral sodium cloud is incomplete. This is understandable because electron impact ionization limits the life time of neutrals to some i05 seconds a time shorter than the
Planetary Satellites in Magnetospheric Prccesses
43
orbital period of lo. Beyond any reasonable doubt both the plasma torus and the neutral cloud are fed and maintained by bo. It is now believed that the neutrals are released from the surface by sputtering from impacting energetic particles (Matson et al.(17]). It is not clear whether the majority of plasma ions are released from Io as neutrals (by e.g. sputtering) which subsequently become ionized or whetter ~hey are produced in b’s ionosphere and then transported as ions away by the E x B drift. To release neutrals a thin atmosphere is required, because a too dense one would firstly absorb the energetic particles required for sputtering and secondly slow down the neutral particles belo~the 3escape speed. The critical density for sputtering to be effective is some 10 cm . On the other hand the atmosphere must be dense enough to support an ionosphere which was obse~vedby 3. The fact that 10 10 and controls the decametric radiation strong6 electrodynamical Pioneers 11 (Kliore et al.[22],[23]) at aindicates maximum adensity x 10 cm coupling between bo and Jupiter. This requires, as we have discussed above, a good bo conductance. A very thin atmosphere would not be compatible with that requirement, if the conductance were due to collisions. On the other hand, the existence of an ionosphere on bo is quite puzzling because as Cloutier et al. [21]have shown the pressure of the corotating magnetospheric plasma is by far larger than the restraining gravitational force. This is true even when the plasma velocity in b’s vicinity is considerably reduced. Cloutier et al. [24] conclude: “A terrestrial—type ionosphere can be maintained around bo
only some does, that
if substantial losses of both ions and neutrals can be compensated far by potent source mechanism”. We now know, that some potent source mechanism indeed, exist on bo; namely volcanism. It has been shown by Kumar [25] the volcanoes on bo can supply some iO3l molecules (SO 2) per second, a value safely above the value required for maintaining the torus (see below). It is generally assumed that the volcanoes emit particles and neutral molecules at a velocity below the escape speed. If that is true, the neutrals must be ionized in b’s atmosphere. The most likely mechanism to produce the ionization is impact ionization by a flux of electrons with energy in excess of 10 eV. We know that such a flux does exist near bo. In order for this process to be active the elec— trnons must ~a~e access to 10. I.e. the perfect conductivity or intrinsic magnetic field with m.B0 > R~ models are not compatible with impact ionization. On the other hand once ionization occurs the electric field will be modified as if bo were a conductor even though the Pederson conductivity is zero (i.e. no ion—neutral collisions). This is so because a newly created ion will move in response to the corotational electric field and be displaced relative to the simultaneously created electron (Goertz[11]). This charge separation will cause an electric field opposite to the applied one. In other words the current associated with picking up ions by the corotation field tends to build up charges that cancel the corota— tion field. The resulting electric field is determined by the balance of pick—up current and plasma current flowing away from and into lo. For the case of In this current is not exactly field aligned but must be viewed as being carried by Alfv~nwaves. The electric field in b’s vicinity can then be calculated by balancing the pick—up current with the Alfv~ncurrent (Goertz[11]) similar to our discussion above.
~
Pick—up creates ions whose gyroenergy W
is equal to
(20) Wg = (~ x ~ )2 lB where is the electric field at the point where the ions are created, e.g. the electric field in b’s ionosphere. The gyroenergy devided by the magnetic field strength is+a c~nstantof the motion. Once the ions are created and picked up they will E x B drift away from bo conserving W lB. Thus far away from In the ion—temperature indicates ~he electric field at th~point of creation. Bridge et al. (26] show that the S temperature in the torus is of the order of 30 eV. 2
44
C. K. Goertz
If the electric field at the point of creation had the full—corotational value one would expect a gyroenergy of 500 eV. The lower ion—temperature indicates a considerable reduction of the corotational electric field at the point where the ions are created. Since in the torus the ions drift at very nearly the full corotational speed (Bridge et al. [26]) we conclude that the ions cannot have been created in the torus but must have been created in the vicinity of In, presumably in its ionosphere. If the ions are created in b’s vicinity the electric field is by necessity reduced there (see Goertz (11]). The observed temperature requires ES to be a quarter of the corotational electric field or according to equation 1A. For pick—up the equivalent conductance is given by Goertz (12) that E~— 3 (11] as Es(pickup)
—
)~1 / A B2
(21)
where 11 is the mass of ions created per second and A is the surface area of the region where the ions are created, i.e. the cross—sectional area of bo. Neubauer [10] estimates 1A — 2.2 mhos. Thus we need N — 9 x 1o29 atomic masses per second to account for the reduction of electric field without recourse to any collisional conductance. This is comfortably below the value which according to Kumar (25] the volcanoes could supply. It is also very similar to the estimates of In mass loading obtained by Hill (27]. Note that this estimate does not depend on the existence of an intrinsic magnetic field as long as some magnetic field lines intersect In’s surface. This is so because the electric field scales roughly as B along a field line and Wg/B is a constant of the motion. The thermal energy injected into the magnetosphere by these ions is of the order of 1012 W, comparable to but somewhat smaller than the total UV power radiated from the torus (Broadfoot et al. (28]) seems likely that the In torus contains an additional heat source. The power contained in the Alfv~nwaves may be that source. It can be shown by combining equations (11), (12), (20) and (21) that P I wave S particle
A
Some of the Alfv~nwave energy is presumably dissipated in the torus which could account for the 2 x io12 W DV emission from it. Although these numbers are encouraging considerable doubt is cast on the scenario whereby the ions are created in In’s vicinity by the fact that the UV radiation observed by Voyagers 1 and 2 does not increase with In in the field of view. Shemansky [29] claims that the additional radiation expected to occur when sulphur and oxygen are ionized in In’s atmosphere should amount to 100 R — 1000 R well above the observation limit of 50 R — 200 R. However, the chemistry may not be known well enough. Furthermore with In in the field of view the torus radiation itself would be absorbed. Recently Cheng (private communication) has argued that a considerable fraction of the volcanic gas can escape from In and that the ionization takes place in the torus itself where the electric field is not markedly reduced. (The pick—up conductivity would be considerably smaller because of the much large surface area of the torus.) Although this possibility cannot be ruled out the fact that the ion—temperature in the torus is so low supports a model in which the ionization takes place near bo. A further argument for a strong interaction of In itself with the magnetosphere is provided for by the observation of the magnetic field perturbation in the vicinity of the nominal bo flux tube (Ness et al. (30]). The total current is of the order of some io6 A which is comparable to the maximum current that can flow according to equation (11) and the estimate of 1A given by Neubauer [10]. It seems that the conductance of In is of the order of In that case a signifi—
Planetary Satellites in Magnetospheric Processes
45
cant electric field exists in b’s atmosphere. Without a continuous production of ionospheric ions the ionosphere would be blown away by the magnetospheric wind in a short time. SUMMARY
We have shown how the conductivity of a moon without an intrinsic magnetic field determines the electric field in its vicinity. Due to the motion of the moon relative to the magnetosphere charges are induced on the moon’s surface which partly cancel the motional electric field inside the moon and add a dipole electric field outside the moon. The magnitude of the induced dipole moment depends on the moon’s conductivity. We then discussed the case of a moon with an intrinsic magnetic field and showed that even an insulating moon with an intrinsic magnetic field will distort the electric field around it. Several cases of the intrinsic magnetic field model were discussed. When the boundary conditions in the planet’s ionosphere are taken into account where the electric field due to the surface charges drives a Pederson current, the existence of a field aligned electrostatic potential drop becomes possible. A simple mathematical model of the moon—ionosphere circuit was given. Whereas in a steady state the resistive properties of the planet’s ionosphere are important, that is not the case in the non—steady state. In the case of bo we argue that the current through In does not close by Pederson currents in Jupiter’s ionosphere but through currents flowing in two Alfvên wings which propagate along characteristics inclined with respect to the background magnetic field. Only when the travel time of an Alfv~nwave from the moon to the planet is very short compared to the time it takes the plasma to convect past the moon, will a steady state analysis be applicable. We then discussed the processes that lead to the emission of Alfvên waves, namely pick—up of newly created ions in In’s ionosphere. We argue that most of the inns maintaining the great bo torus must be produced near In and not in the torus, because in the torus they would be created with much larger gyroenergies than observed. Furthermore without ion—production in In’s ionosphere, an ionosphere could not be maintained against the ram pressure of the magnetospheric wind. References 1. Goertz, C.K. and P.A. Deift; Planet. Space Sci. 21, 1399, 1973 2.
Neubauer, F.M.; Geophys. Res. Lett., 5, 905, 1978
3.
Kivelson, M.C., et al.; Science, 205, 491, 1979
4.
Ip, W.H.; MPAE Rept.,
5.
Gurnett, D.A.; Astrophys. J., 175, 525, 1972
6.
Smith, R.A. and C.K. Goertz; J. Geophys. Res. 83, 2617, 1978
7.
Goldreich, P. and D. Lynden—Bell; Astrophys. J., 1S6, S9, 1969
8.
Fillius, W.;
9.
Parker, F.N.; Cosmical Magnetic Fields, Clarendon Press, Oxford, 1979
1980
Jupiter, ed. by T. Gehrels, Univ. of Arizona Press, Tucson, 1976
10.
Neubauer, F.M.; J. Geophys. Res., 85, 1171, 1980
11.
Goertz, C.K.;
12.
Southwood, D.J., et al.; J. Geophys. Res., 85 (in press), 1980
13.
Schnler, M.; Planet. Space Sci., 18, 977, 1970
J. Geophys. Res., 85 (in press), 1980
46
14.
C. K. Goertz
Gurnett, D.A. and C.K. Goertz; University of California, Los Angeles, Rept. PPG—472, 1980
15.
Schulz, N. and A. Eviatar; Astrophys. J. Lett., 211, L149, 1977
16.
Thomsen, M.F.;
17.
Matson, D.L., et al.; Astrophys. J., 192, L43, 1974
18.
Van Allen, J.A., et al.; Science, 188, 459, 1975
19.
Thomsen, M.F., et al.; J. Geophy~s. Res., 82, 5541, 1977
20.
Simpson, J.A., et al.; J. Geophys. Res., 79, 3522, 1974
21. 22.
Mogro—Campero, A. and W. Fillius; J. Geophys. Res., 81, 1289, 1976 Kliore, A., et al.; Science, 183, 323, 1974
23.
Kliore, A., et al.; Icarus, 24, 407, 1075
24.
Cloutier , P.A., et al.; Astrophys. Space Sci., 55, 93, 1978
25. 26.
Kumar, S.; Nature, 280, 758, 1979 Bridge, H.S., et al.; Science, 204, 987, 1979
27.
Hill, T.W.;
28.
Broadfnot, A.L., et al.; Science, 209, 979, 1979
29.
Shemansky, D.E.; Mass loading and the diffusion loss rate of the 10 plasma torus, preprint, 1980 Ness, N.F., et al.; Science, 204, 982, 1979
30.
Space Sc, 17, 369, 1979
J. Geophys. Res., 84, 6554, 1979
I, pp. 31—46. Printed in Great Britain.
SpaC~i 1?c~. Vol.
© COSPAR,
1981.
0273—1177/81/OlOl—0031$05.00/0
THE ROLE OF PLANETARY SATELLITES IN MAGNETOSPHERIC PROCESSES C. K. Goertz* Max-Planck-Institut für Aeronomie, D-341 I Kat!enburg-Lindau 3, FRG
ABSTRACT
A large satellite in a magnetosphere can disturb significantly the magnetic and electric fields in its vicinity. The nature of the disturbance depends on the conductivity of the body, its own magnetic field, the plasma parameters (density, temperature, flow velocity, composition) and the boundary conditions imposed by the planet’s ionosphere. Under certain conditions large field aligned electric fields can arise which cause particle acceleration and hence emission of plasma and radio waves. A number of observations relevant to the case of the Jovian moon lo will be briefly reviewed. The coupling of 10 with the magnetosphere is discussed in terms of pick—up and Alfv~nwaves. We argue that most of the ions making up the lo torus are created in b’s immediate vicinity where the electric field is reduced by a factor of about 4 from its full corotational value. INTRODUCTION Recent in situ observations of the satellites of Jupiter and Saturn have emphasized the importance of their interaction with the magnetosphere. For example, we now believe that lo provides most of the low energy thermal plasma in the Jovian magnetosphere and a significant fraction of high energy particles. Planetary satellites may absorb energetic particles and thus control the energetic particle environment, if they orbit within the planetary magnetosphere. The energetic particles in turn can effect the surface properties of the satellites, lead to sputtering of neutrals and impact ionization of neutral atmospheric particles. The resulting charged particle environment around a satellite can be drastically
*
On leave from the University of Iowa, Iowa City, Iowa 52240, USA
31
32
C. K. Goertz
different from other regions of the magnetosphere, as exemplified by the great bo plasma torus. Plasma wave propagation characteristics, growth and/or absorption rates are hence effected by the satellite. Satellites can cause auroral activity in the ionosphere of the parent planet and change the structure and chemistry of the ionosphere. The importance of the role of planetary satellites for magnetos— pheric processes can hardly be overestimated. We will consider only those satellites which orbit within the magnetosphere of the planet. For the earth’s moon this is only occasionally the case. The four Galileon satellites of Jupiter always stay within the Jovian magnetosphere. Many of Saturns satellite do so also, although some may exit at times from the magnetosphere like our own moon. Satellites, or moons, moving within the magnetosphere are subject to special conditions. Among these are: (i) They are surrounded by significant fluxes of trapped energetic charged particles. (ii) The environment also contains low energy plasma. (iii) The magnetic field near the satellite contains the planetary (dipole) field, i.e. the satellites are magnetically connected to the planet. (iv) Since the satellites move relative to the planet’s surface (ionosphere) there exist electric fields in the vicinity of the satellites. The satellites are effected by all four conditions and in turn change themselves the four conditions. The interaction is thus a complex, presumably non—linear, phenomenon, the exact nature of which depends on the properties of the moon itself, the conditions in its vicinity and the boundary conditions in the parent planet’s ionosphere. In what follows we will in turn deal with the disturbance of the electric and magnetic fields created by the satellite, and the effect of this on energetic particles and the thermal plasma. We will try to keep the discussion general, although we will occasionally refer to the special case of 10, for which many observations and theories are available. In most case we can only describe the basic ideas and must refer the reader to the original literature. ELECTRIC AND MAGNETIC FIELDS NEAR THE SATELLITE Nonmagnetic Satellite Let us consider a spherical nonmagnetic moon moving through a region of uniform magnetic field. Then, in a frame of re~eren~e mo’~ingvith÷thesatellite, there will be an induced electrostatic field E.L — VS x B 0 where V is the velocity of the moon measured in a frame of reference corotatLng with the p~anet’sionosphere. The situation is depicted in Fig. 1. We assume that parallel electric fields do not exist or have decayed to zero. If the satellite has a conductivity a~and the surrounding medium a conductivity aM which for simplicity we assuifie to be a scalar the electric fields in the moon’s frame are [1]:
v5
x~
(1— a:aM
(1)
(2) where the induced dipole moment p is 3 =
—
a52a,~4 (~ x ~) R
(3)
Planetary Satellites in Magnetospheric Processes
33
Ionosphere
Fig. I The geometry of~thesatellite—planet interaction. is the rotational axis and M the magnetic dipole axis of the planet. The dipole moment is due to the surface charges on the moon. Although this treatment neglects the anisotropy of the surrounding medium it shows a number of important effects. x
4~I~4 -.
I I
I
I
‘III’ I~ ~\
~
~
bC
Fig. 2 Electric field (solid) and stream (broken) lines. a) Perfectly insulting moon (a — o) b) intermediate case c) perfectly conducting case +
(aSa~aM)
Case i: a -‘~ o. In this case the electric field is not disturbed at all. No currents f~owanywhere. An insulating moon does not disturb the fields in its vicinity. This case is shown in Fig. 2a. Case ii:
~‘
a~4. In this case the electric and magnetic fields are both
disturbed as shown in Fig. 2b. Currents flow through it which connect to currents flowing within the medium surrounding the satellite. The closure of the currents will be discussed below. Case iii: a + ~, i.e. the satellite is a perfect conductor. In this case the electric fie’d inside the moon is reduced to zero by an accumulation of polarization charges on the surface of the satellite. The elecr~ Eield outside is
34
C. K. Goertz
distorted by the addition of a dipole field. The field lines and resulting stream lines are shown in Fig. 2c. There are no currents flowing through it and the distortion of the magnetic field is small because only polarization currents flow, which will be discussed below. In case i plasma has access to the moon. and in case iii it has no access at all.
In case ii plasma has a reduced access
Insulating Satellites with Intrinsic Magnetic Fields Recently it has been suggested by many authors (2], [3], (4] that 10 and some Saturnian moons have an intrinsic magnetic field. Many interesting effects can occur when a satellite has an intrinsic magnetic field. One may have magnetic reconnection, a satellite magnetopause or even a bow shock. However, the fields around the satellite may not be determined by these rather complex phenomena but by the simple fact that even a perfectly insulating satellite with an intrinsic magnetic field distorts the electric field in its vicinity just because it distorts the magnetic field. For simplicity we assume that no currents flow in the moos’s vicinity and that the intrinsic field of the moon is a dipole field of moment m. If no parallel electric fields exist the electrostatic potential ~ is constant on a field line. The magnetic field lives and equipotentials in the ~icinityof the moon are shown for the two cases of in parallel or antiparallel to B 0 in Fig. 3.
ml
B0 R~
ImIcB0 R~
ImI~.B~ R~
ImI~B0 R~
Fig. 3 The distortion of the magnetic field lines when the moon has an intrinsic magnetic dipole field. The direction of the moon’s dipole is indicated by the arrow. Note the field lines are equipotential s. If m is antiparallel to B the electric field in the vicinity of an insulating satellite is similar to teat of a pe~fec~ly conducting satellite without an intrinsic field m. In both cases the E x convection woulg carry low energy particles smoothly around the moon. If in is parallel to B0 particles may have excess to the moon along the open field lines. The cross—sectional area of the field lines that connect to the moon is larger than the moon itself. In terms of particles access the antiparallel case is equivalent to a perfect conductor and the parallel case to an insulator. It should be noted that whereas in the previous section the electric field distortion existed all along the essentially “straight” field lines and hence the convection in the planet’s ionosphere
Planetary Satellites in Magnetospheric Processes
35
was perturbed, for an insulating moon with an intrinsic magnetic field the distortion of the electric field is limited to the vicinity of the moon. The convection in the planet’s ionosphere is not significantly perturbed. When the satellite has both a finite conductivity and in intrinsic magnetic field the electric field in the moon frame is given by equations (1) and (2) except that now B is the total magnetic field, i.e. planetary plus moon fie’d; and v is the 3 v disturbed velocity. when m is ofantiparallel to Bi~immaterial and in B R !n S is zero inconvection 10’s vicinity and the Thus conductivity the sa~ell.j~te determining the convection pattern. When in < B 3 and B in < o the conductivity is important, because v 0R 5, although smaller than t~esatellites velocity, is nonzero. The other cases can be dealt with straight—forwardly. It should be noted, that in all cases we have neglected magnetic fields due to locally induced currents, i.e. currents driven by the induced electric fields. For a more formal derivation of these relations we refer the reader to the papers by Goertz and Deift [1] and Ip [4]. Parallel Electric Fields We will now drop the assumption of vanishing parallel electric fields. This allows for the possibility of particle acceleration and field aligned currents. Consequently many models of the interaction of lo with the Jovian magnetosphere have concentrated on this aspect. The first question that arises is the following: Why, if the induced electric field across 10 is only perpendicular to the magnetic field, should there exist a parallel field at all? Recall that when the satellite has a non—zero conductivity charges will accumulate on its surface. The electric field due to the surface charges (i.e. not the field due to magnetic field distortions), mapped down the field lines into the planet’s ionosphere, will drive a Pederson current which is fed by field aligned currents. This field aligned current is limited by the current carrying ability of the plasma between the satellite and the ionosphere (Fig. 4). Without acceleration a thermal plasma can only supply the thermal current density, ~th — ne /kTe/ii~ If this current density is not large enough to supply the ionospheric Pederson currents charge imbalances develop along the field line and parallel potential drops occur. In this way the electric field across the ionosphere is reduced until the plasma current matches the Pederson current. Whether the parallel electric field occurs in sheaths [5], double layers [6] or over a larger distance [7] depends on the particular properties of the system, such as plasma density and temperature, electric field and ionospheric conductivity.
Ionosphere
Fig. 4 The satellites flux tube near the ionosphere. tial drop • occurs near the edges of the flux tube.
The poten-
36
C. K. Goertz
The mathematical formalism for this model is suite simple. Let us denote the height integrated Pederson current as I • E E’ where E’ is the field in the ionosphere (as seen in the planet’s fratue)Y The parallel current density is and the parallel potential drop along a field line is $. The electric fiel~due to the induced surface charges, suitably mapped to the planet’s surface is E’. 3y — j where t~ecoordinat~ Then the current continuity equation reads 31 / system is defined in Fig. 4. The condition o~steady state V x E 0 reads ~(V x ~)y dz
—
—
-~
-~
—E~~ — 0
(5)
Combining these equations and noting that the field V is constant inside the flux tube connecting the satellite with the ionosphere we ~et
~z (y)
32$
y
=0
(6)
with the boundary conditions that —
—
E
(7)
at the edge of the flux tube. Once a constituting relation between formulated one can solve for $(y).
+
j
and $ is
+
We see, however, that if j 0 and ~ 0 a potential drop must occur. It should be emphasized that this pot~ntialoccuk only when the conductivity of the satellite is non—zero. It is not enough to perturb the perpendiculat electric field by a magnetic field perturbation. For that case E~ 0. Various different relations between $ and Lynden Bell [6] used
jz
have been used.
Goldreich and
sign $
—ne
(8)
Gurnett (5] used
j
—
j~sign
$
(9)
Smith and Goertz (6] give a similar but somewhat more complicated form. In all cases the parallel potential drop $ can be easily obtained as a function of y. Smith and Coertz [6] show that in all cases the maximum potential drop occurs at the edge of the flux tube and that under special, though perhaps unrealistic, condition the parallel potential drop on one side of the flux tube may approach the total potential across the satellite, which e.g. in the case of bo amounts to 400 kV. Such a potential could produce large number of 400 keV charged particles. These seem to have been observed (see e.g. Fillius [8]). ELECTRIC AND MAGNETIC FIELDS NEAR THE SATELLITE (NON—STEADY CASE) In the previous section we have implicitely assumed that the time constant of the circuit connecting the moon with the planet is zero. However that is not the case and the steady state case may not ~bereached at all. As viewed from the planet the moon represents a moving perturbation of the plasma velocity. Any chat~geof plasma convection leads eventually to the emergence of two oppositely travelling Alfv~nwaves (9]. This is true for all magnetohydrodynamic perturbations inde—
Planetary Satellites in Magnetospheric Processes
37
pendent of their amplitude. The Alfv~nwave communicates to the adjoining plasma the stresses exerted by the satellite. Or in other words: The satellite imparts momentum to the plasma via emission of Alfvén waves. Fig. 5 shows the perturbation created by a satellite with finite conductivity. Since into a medium movingthe withAlfv~nwave a velocitymoves V relative to
~~ /
B
Ii /1
/
/
the moon the perturbatioA propagates along a characteristic which is inclined with respect to the background magnetic field as seen in the ~ frame. In the planet’s frame the perturbation propagates along the field line. Behind the wave front the plasma velocity and magnetic field are perturbed. We can estimate these perturbations by noting that the Alfv~nwave carries a current along the characteristic given by [10]
/ / /
-_________________ V
\\
Iw
through the satellite I =E E
\~
1/
Y~~ -
(10)
This current has to be fed by the current
H
j
E(E—E);EA—-V-— A o s
Since Is s w E
-
—
I
(11)
we have
S
E
-
(12)
And the perturbation of the velocity is z
LW
Fig. 5 The Alfv~nwings near Io. The two lower figures show the distor— tion of the field lines at two differ— ent values of y. The left hand one is at y — o. The charact:ristic is inclined by the angle 0 tan’(v /v )— A s A tanl(MA).
/~E
(13)
_______
v”r s o
=
~
A
s
For an Alfv~nwave the velocity amplitude is related to the magnetic field amplitude as ~b ~—.
t~V
=+~—
o
A
zS
(14)
_____
—
S
EA plays a r6le similar to that of a in equations (1) and (2). For more details we refer the reader to Coertz [II]a~id Southwood et al. [12]. After a time tA~the wave reaches the planet’s ionosphere where it is reflected. The reflection coefficient is [13]
~ R-—
IA —1p A p
(15)
The reflected wave will move into a medium in which moves with a velocity V relative to the moon and in which the magnetic field is tilted by an angle S
I tan
B
=
MA
I A
I
—
s
MA
V
=
s
MA K
—
LW
(16)
C. K. Goertz
38
It is easy to see that the return wave will be displaced relative to the moon by N 1 ( A21c 11K] (2—MX K) (17) iS/R = ~— s ds 1—M A
)
where the integral is from the moon to the planet. The ~1.isplacement 6 depends on the conductivity of the satellite. When I + we have k + 1 and 6 ~. 0. The g~ometryof the situation is shown in Fig. 6. Clearly only when 6/R < 1 will S. •. ••. •. the resistive properties of the ionos— phere have any influence at all. 9O!0~,~ ~~4l1 It is also relatively easy to show that Ill I when 6/R 3 << 1 a steady state is reached /ll / in which I ~• 91. Ii E =E I = El’ ~ E i~ s oE +1 ‘ s 1 +E o (18)
/
‘fi, I_i iO* I
o~ ,~-Jr A
/
~
‘
/I I
p5
Ps
where I’ is the suitably mapped ionospheric PedersoR conductance. The mapping must include both the divergence of the magnetic field lines and the possible existence of parallel electric fields. A treatment of the mapping would be beyond the scope of this paper.
We can now distinguish two types of interaction. When 6/R5 << 1 a steady state — current flows between the moon and the planet. The current is exactly parallel to the (distorted) magnetic field. When Fig. 6 The geometry of the magnetic 6/R > 1 the interaction must be described field in the Alfv~nwing. The thick in !erins of Alfv~nwaves emitted from the arrows indicate the direction of pro— moon. The current is not exactly paral— pagation. 6 is the distance by lel to the (distorted) magnetic field. which the return wave is displaced. In the second case the change in the s is along the characteristic of the plasma velocity is related to the magnetic Alfvèn waves, field perturbation by the Alfv~nwave relation (equation 14) whereas this is not true in the first case. We emphasize that these distinctions apply independent of whether the moon has an intrinsic magnetic field or not. Before the discovery of the great plasma torus around lo, the bo interaction was generally thought to be of the first type (6/R10 << 1). Today it seems more likely that >> 1 because the Alfv~ntravel time through the dense torus is quite large. The coefficient of reflection by the Jovian ionosphere is nearly 1, the collisionless damping of the Alfv~nwaves emitted by lo is negligible (14]. Thus the Alfv~nwaves emitted by lo will bounce many times between the two hemispheres of Jupiter and lo will carry behind it a wake filled with Alfv~nwaves such as shown in Fig. 7. Gurnett and Goertz [14]relate this pattern to the Jovian de— cametric arcs. THE MOTION OF CHARGED PARTCILES IN THE VICINITY OF A SATELLITE The motion of chargedparticlesis effected by the electric and magnetic fields. Unless the particle’s energy is so large that it’s gyroradius becomes comparable
Planetary Satellites
in Magnetospheric Processes
39
FIELD-AUGNED CURRENTS DECAMETRIC RADIATION SOURCES JUPITER ,‘
illj
tO > PLASMA TORUS
I0 -
-
ALFVEN WAVES
Fig. 7 The wake of Alfv~nwaves dragged around by lo (from Gurnett and Goertz [14]). with the moon’s radius adiabatic theory can be used to determine the trajectories of charged particles near the moon. The trajectories are curves along which the total energy (kinetic plus potential) first and second adiabatic invariants are conserved. In the literature only equatorially mirroring particles for which the second adiabatic invariant is zero have been considered. The trajectories will be energy— and species—dependent. Given an electric field and magnetic field in the moon’s vicinity it is straightforward to caluclate the trajectories. This has been done for a perfectly conducting 10 by Schulz and Eviatar [15]. Some trajectories are shown in Fig. 8. Zero energy particles will not intersect the moon. The effective cross—sectional radius for absorbing zero energy particles is zero+in this case. For energetic protons the VB drift is in the same direction as the E B 4rift far away from the moon. Thus energetic protons will not smoothly E x B drift around the moon but impinge onto the moon’s surface. The effective cross—sectional radius for absorbtion increases with increasing energy until for infinite energy it approaches the geometrical radius. Electrons with *ner~iesbelow an energy, at which the VB drift velocity exactly cancels the E x B drift, do not impinge on the moon at all. Thus the effective cross—Sectional radius for electron energies below this value is zero. Above this critical energy the effective radius varies as shown in Fig. 8b. For a finite conductivity the electric field perturbation outside the moon is reduced (see equation 2) and the variation of effective radius varies with energy and species as shown schematically in Fig. 8b[16]. For a moon with an intrinsic magnetic field the trajectories have been calculated by 1p [4]. Some of the trajectories are shown in Fig. 9. Whereas in the previous case the effective radius was zero at zero energies and equal to the geometric radius at infinite energies for a magnetic satellite the effective radius goes to zero with increasing energy. Furthermore in the previous case particles impact, if at all, uniformly over the moon’s surface. In this case the impact occurs on one side of the moon. This could account for an apparent asymetry in the sputtering strength of neutral sodium atoms[17].
40
C. K. Goertz
~ I Th
-
•.~l•.•~
,1
II
~
~ ,
‘
‘
‘‘:
I
~
I
~~—---~.—
‘‘~~
$
I
$
~~-~‘‘
Fig. 8a Drift paths of representative particles in the vicinity of Io: (a) particles having N — 0; (b) protons, M = 1 GeV/G; (c) electrons, N = 40 GeV/G; (d) electrons, N — 80 GeV/C; (e) electrons, M = 200 GeV/G; (f) electrons, N 400 GeV/G. Dashed curves represent critical (grazing) trajectories and separatrices. Other trajectories are identified by values of x~/a 1 or of (from Schulz and Eviatar [IS]).
‘!“P~~V&IiC ~.7GDi~MtS wVXTh I, I0~UtZ v.$A?ae. IS??)
rr,oVV.~ ~ N~&R~~ECTL~ ~$rAXTe~ I. 50I(M&TC
~F1I
~WU
~
V
EFT(CVPJE ~S~EPI,IS S~UVI. F~I PCISICTLV mØXTING
3
-
~ING r03£F~CCT~ I~IS~T~V ~
R*0I~I.
(XIItUAXC)
3
——_~—.
7-
-
2
I
—
S
L Co.
-i d’
G~I(TSICIS.
-
~-~--
—
dI
CUCV,m.S
~
IWICIC EMISIM~I
o’
c
~----~--~
_________________________~___I (Nt~GV
Fig. 8b The electrostatic equipotentials around lo and variation of effective absorption radius of 10 as a function of energy (from Thomsen (16]).
f
Planetary Satellites in Magnetospheric Processes
I
I
laJS—-O.5 1~O~O
-
-
~_
~
I
—1~~———.—
I I~
I
Ib)S.-0511
•.
~I I~
-o°
/
I,
l8O0~_~
I I, I ii
-—
~°.
/ \
I I -
-
-
770°
-
test the various possibilities?
The
data for particles all but our moon come tion of is own generally energy and only species from a dependent. short crossing How of cantheone some Pioneer 11 data obtained by the moon’s magnetic L—shell. Fig. 10 shows University of Iowa instruments (Van Allen et al.[18]) near the inbound and outbound crossings of b’s L—shell. We see that only low energy electrons and protons show any significant
particle geometric flux concept we have of effective to relate absorp— the tion radius to an absorption time.
)
Id)S.cV1•0o~J ~qo°
The discussion above shows the absorp—
changes particle the flux near lo. of In order to ofinterpret variation
270°
1.10-01 I
IcIS.-aST
1.101
-~--
41
~
—~--o
____________
Fig. 9 Trajectories of energetic particles around 10 assuming an intrinsic dipole field. The induced electric dipole moment is p = S V V B . The particle energy is W L BS .8025 key where B is
moons do absorb all particles that impinge on the surface the even flux if will This not beis zero necessary at the because moon’s L—shell the because new particles are continuously transported across the moon’s L—shell. The observed profile is the result of transport and absorption (Thomsen (16]). In many cases the transport is diffusive and from the shape of the particle flux variation one can estimate a diffusion strength. For example, if the time it takes a particle to diffuse the L—shell range covered by the across moon (extending from L~to L 2) is much larger than the
the intrinsic surrace field of Io in tam— mas. The figure is from 1~ [4].
absorp ion or loss time the flux will go to zero inside the moon’s L—shell. In the other extreme (strong diffusion and/or weak losses) the flux will hardly change. By loss time we mean the time it would take the moon to wipe out all the particles in the L—shell range covered by the moon. This time depends on the effective radius, the relative drift of the particles with respect to the moon and the size of the L—shell range covered by the moon. We quote here the equation by Thomsen et al. [19]which is similar to the ones of Simpson et al. [20]and Mogro—Campero and Fillius[21]. •1=
2v
(14
— L~) 2mm r
(19) (III 6 L where w,~(W) is the energy and species dependent drift rate of the particles, w is the ~rift rate of the moon whose effective radius is r . The average L—she~l is determined by the product of the diffusion coefficientmD and t. Since D is energy and species dependent (Thomsen[16]) the analysis of the observed profiles is very difficult. It is sufficient to note that the profile of the ions as compared to that with electrons has cast some doubts on the simple geometric picture of absorption. It seems that near bo other effects, such as pitch angle scattering or charge exchange, are more important than absorption. Even for Iu~(W) +
42
C. K. Goertz
__________________________________
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~-
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U
I
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OGIMW.Ep. 341020
~n~__ 0
I I I 0 20 30 40 30
I~I 0
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0
20 70 ~0
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40 50 0 0 10 2101 33?
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Fig. 10 The variation of count rates for the Pioneer 11 flyby of Jupiter. The data are from the University of Iowa instrument package (from Thomsen (16]). electrons the profiles observed near bo are not completely understood in terms of the absorption described above. PLASMA IN THE MOON’S VICINITY (bo TORUS)
We have briefly discussed the absorption and (through parallel electric fields) acceleration of energetic particles. We now concentrate on the low energy particles, i.e. those for which the magnetic field drift is negligible compared to the electric field drift. The drift, which was discussed above leads to absorption and a plasma cavity behind the satellite. Such a cavity also exists for energetic particles. We will not discuss this as similar topics have been extensively discussed in connection with the earth’s moon. We will here concentrate on moons as a source of plasma. In particular we will emphasize the r~leof lo for maintaining the great plasma torus and neutral cloud around it. From ground based and in situ observations it has been established that_~here exists a doughnut shaped ~olu~e c~tai~jng a+dense (ne ‘U 1.. 4 x 10~cm ), warm (T. ‘U 30 eV) heavy ion (0 , S , 0 , S , Na ) plasma as well as neutral sodium atoms. The maximum of the plasma density occurs roughly at b’s L—shell (L — 6). The density decreases slowly with increasing distance but drops rather abruptly inside of L — 5.6. Inside of L — 5.6 the ion temperature becomes very small. W’ereas the plasma torus extends completely around Jupiter, the neutral sodium cloud is incomplete. This is understandable because electron impact ionization limits the life time of neutrals to some i05 seconds a time shorter than the
Planetary Satellites in Magnetospheric Prccesses
43
orbital period of lo. Beyond any reasonable doubt both the plasma torus and the neutral cloud are fed and maintained by bo. It is now believed that the neutrals are released from the surface by sputtering from impacting energetic particles (Matson et al.(17]). It is not clear whether the majority of plasma ions are released from Io as neutrals (by e.g. sputtering) which subsequently become ionized or whetter ~hey are produced in b’s ionosphere and then transported as ions away by the E x B drift. To release neutrals a thin atmosphere is required, because a too dense one would firstly absorb the energetic particles required for sputtering and secondly slow down the neutral particles belo~the 3escape speed. The critical density for sputtering to be effective is some 10 cm . On the other hand the atmosphere must be dense enough to support an ionosphere which was obse~vedby 3. The fact that 10 10 and controls the decametric radiation strong6 electrodynamical Pioneers 11 (Kliore et al.[22],[23]) at aindicates maximum adensity x 10 cm coupling between bo and Jupiter. This requires, as we have discussed above, a good bo conductance. A very thin atmosphere would not be compatible with that requirement, if the conductance were due to collisions. On the other hand, the existence of an ionosphere on bo is quite puzzling because as Cloutier et al. [21]have shown the pressure of the corotating magnetospheric plasma is by far larger than the restraining gravitational force. This is true even when the plasma velocity in b’s vicinity is considerably reduced. Cloutier et al. [24] conclude: “A terrestrial—type ionosphere can be maintained around bo
only some does, that
if substantial losses of both ions and neutrals can be compensated far by potent source mechanism”. We now know, that some potent source mechanism indeed, exist on bo; namely volcanism. It has been shown by Kumar [25] the volcanoes on bo can supply some iO3l molecules (SO 2) per second, a value safely above the value required for maintaining the torus (see below). It is generally assumed that the volcanoes emit particles and neutral molecules at a velocity below the escape speed. If that is true, the neutrals must be ionized in b’s atmosphere. The most likely mechanism to produce the ionization is impact ionization by a flux of electrons with energy in excess of 10 eV. We know that such a flux does exist near bo. In order for this process to be active the elec— trnons must ~a~e access to 10. I.e. the perfect conductivity or intrinsic magnetic field with m.B0 > R~ models are not compatible with impact ionization. On the other hand once ionization occurs the electric field will be modified as if bo were a conductor even though the Pederson conductivity is zero (i.e. no ion—neutral collisions). This is so because a newly created ion will move in response to the corotational electric field and be displaced relative to the simultaneously created electron (Goertz[11]). This charge separation will cause an electric field opposite to the applied one. In other words the current associated with picking up ions by the corotation field tends to build up charges that cancel the corota— tion field. The resulting electric field is determined by the balance of pick—up current and plasma current flowing away from and into lo. For the case of In this current is not exactly field aligned but must be viewed as being carried by Alfv~nwaves. The electric field in b’s vicinity can then be calculated by balancing the pick—up current with the Alfv~ncurrent (Goertz[11]) similar to our discussion above.
~
Pick—up creates ions whose gyroenergy W
is equal to
(20) Wg = (~ x ~ )2 lB where is the electric field at the point where the ions are created, e.g. the electric field in b’s ionosphere. The gyroenergy devided by the magnetic field strength is+a c~nstantof the motion. Once the ions are created and picked up they will E x B drift away from bo conserving W lB. Thus far away from In the ion—temperature indicates ~he electric field at th~point of creation. Bridge et al. (26] show that the S temperature in the torus is of the order of 30 eV. 2
44
C. K. Goertz
If the electric field at the point of creation had the full—corotational value one would expect a gyroenergy of 500 eV. The lower ion—temperature indicates a considerable reduction of the corotational electric field at the point where the ions are created. Since in the torus the ions drift at very nearly the full corotational speed (Bridge et al. [26]) we conclude that the ions cannot have been created in the torus but must have been created in the vicinity of In, presumably in its ionosphere. If the ions are created in b’s vicinity the electric field is by necessity reduced there (see Goertz (11]). The observed temperature requires ES to be a quarter of the corotational electric field or according to equation 1A. For pick—up the equivalent conductance is given by Goertz (12) that E~— 3 (11] as Es(pickup)
—
)~1 / A B2
(21)
where 11 is the mass of ions created per second and A is the surface area of the region where the ions are created, i.e. the cross—sectional area of bo. Neubauer [10] estimates 1A — 2.2 mhos. Thus we need N — 9 x 1o29 atomic masses per second to account for the reduction of electric field without recourse to any collisional conductance. This is comfortably below the value which according to Kumar (25] the volcanoes could supply. It is also very similar to the estimates of In mass loading obtained by Hill (27]. Note that this estimate does not depend on the existence of an intrinsic magnetic field as long as some magnetic field lines intersect In’s surface. This is so because the electric field scales roughly as B along a field line and Wg/B is a constant of the motion. The thermal energy injected into the magnetosphere by these ions is of the order of 1012 W, comparable to but somewhat smaller than the total UV power radiated from the torus (Broadfoot et al. (28]) seems likely that the In torus contains an additional heat source. The power contained in the Alfv~nwaves may be that source. It can be shown by combining equations (11), (12), (20) and (21) that P I wave S particle
A
Some of the Alfv~nwave energy is presumably dissipated in the torus which could account for the 2 x io12 W DV emission from it. Although these numbers are encouraging considerable doubt is cast on the scenario whereby the ions are created in In’s vicinity by the fact that the UV radiation observed by Voyagers 1 and 2 does not increase with In in the field of view. Shemansky [29] claims that the additional radiation expected to occur when sulphur and oxygen are ionized in In’s atmosphere should amount to 100 R — 1000 R well above the observation limit of 50 R — 200 R. However, the chemistry may not be known well enough. Furthermore with In in the field of view the torus radiation itself would be absorbed. Recently Cheng (private communication) has argued that a considerable fraction of the volcanic gas can escape from In and that the ionization takes place in the torus itself where the electric field is not markedly reduced. (The pick—up conductivity would be considerably smaller because of the much large surface area of the torus.) Although this possibility cannot be ruled out the fact that the ion—temperature in the torus is so low supports a model in which the ionization takes place near bo. A further argument for a strong interaction of In itself with the magnetosphere is provided for by the observation of the magnetic field perturbation in the vicinity of the nominal bo flux tube (Ness et al. (30]). The total current is of the order of some io6 A which is comparable to the maximum current that can flow according to equation (11) and the estimate of 1A given by Neubauer [10]. It seems that the conductance of In is of the order of In that case a signifi—
Planetary Satellites in Magnetospheric Processes
45
cant electric field exists in b’s atmosphere. Without a continuous production of ionospheric ions the ionosphere would be blown away by the magnetospheric wind in a short time. SUMMARY
We have shown how the conductivity of a moon without an intrinsic magnetic field determines the electric field in its vicinity. Due to the motion of the moon relative to the magnetosphere charges are induced on the moon’s surface which partly cancel the motional electric field inside the moon and add a dipole electric field outside the moon. The magnitude of the induced dipole moment depends on the moon’s conductivity. We then discussed the case of a moon with an intrinsic magnetic field and showed that even an insulating moon with an intrinsic magnetic field will distort the electric field around it. Several cases of the intrinsic magnetic field model were discussed. When the boundary conditions in the planet’s ionosphere are taken into account where the electric field due to the surface charges drives a Pederson current, the existence of a field aligned electrostatic potential drop becomes possible. A simple mathematical model of the moon—ionosphere circuit was given. Whereas in a steady state the resistive properties of the planet’s ionosphere are important, that is not the case in the non—steady state. In the case of bo we argue that the current through In does not close by Pederson currents in Jupiter’s ionosphere but through currents flowing in two Alfvên wings which propagate along characteristics inclined with respect to the background magnetic field. Only when the travel time of an Alfv~nwave from the moon to the planet is very short compared to the time it takes the plasma to convect past the moon, will a steady state analysis be applicable. We then discussed the processes that lead to the emission of Alfvên waves, namely pick—up of newly created ions in In’s ionosphere. We argue that most of the inns maintaining the great bo torus must be produced near In and not in the torus, because in the torus they would be created with much larger gyroenergies than observed. Furthermore without ion—production in In’s ionosphere, an ionosphere could not be maintained against the ram pressure of the magnetospheric wind. References 1. Goertz, C.K. and P.A. Deift; Planet. Space Sci. 21, 1399, 1973 2.
Neubauer, F.M.; Geophys. Res. Lett., 5, 905, 1978
3.
Kivelson, M.C., et al.; Science, 205, 491, 1979
4.
Ip, W.H.; MPAE Rept.,
5.
Gurnett, D.A.; Astrophys. J., 175, 525, 1972
6.
Smith, R.A. and C.K. Goertz; J. Geophys. Res. 83, 2617, 1978
7.
Goldreich, P. and D. Lynden—Bell; Astrophys. J., 1S6, S9, 1969
8.
Fillius, W.;
9.
Parker, F.N.; Cosmical Magnetic Fields, Clarendon Press, Oxford, 1979
1980
Jupiter, ed. by T. Gehrels, Univ. of Arizona Press, Tucson, 1976
10.
Neubauer, F.M.; J. Geophys. Res., 85, 1171, 1980
11.
Goertz, C.K.;
12.
Southwood, D.J., et al.; J. Geophys. Res., 85 (in press), 1980
13.
Schnler, M.; Planet. Space Sci., 18, 977, 1970
J. Geophys. Res., 85 (in press), 1980
46
14.
C. K. Goertz
Gurnett, D.A. and C.K. Goertz; University of California, Los Angeles, Rept. PPG—472, 1980
15.
Schulz, N. and A. Eviatar; Astrophys. J. Lett., 211, L149, 1977
16.
Thomsen, M.F.;
17.
Matson, D.L., et al.; Astrophys. J., 192, L43, 1974
18.
Van Allen, J.A., et al.; Science, 188, 459, 1975
19.
Thomsen, M.F., et al.; J. Geophy~s. Res., 82, 5541, 1977
20.
Simpson, J.A., et al.; J. Geophys. Res., 79, 3522, 1974
21. 22.
Mogro—Campero, A. and W. Fillius; J. Geophys. Res., 81, 1289, 1976 Kliore, A., et al.; Science, 183, 323, 1974
23.
Kliore, A., et al.; Icarus, 24, 407, 1075
24.
Cloutier , P.A., et al.; Astrophys. Space Sci., 55, 93, 1978
25. 26.
Kumar, S.; Nature, 280, 758, 1979 Bridge, H.S., et al.; Science, 204, 987, 1979
27.
Hill, T.W.;
28.
Broadfnot, A.L., et al.; Science, 209, 979, 1979
29.
Shemansky, D.E.; Mass loading and the diffusion loss rate of the 10 plasma torus, preprint, 1980 Ness, N.F., et al.; Science, 204, 982, 1979
30.
Space Sc, 17, 369, 1979
J. Geophys. Res., 84, 6554, 1979