Dust in jupiter's magnetosphere: Origin of the ring

Dust in jupiter's magnetosphere: Origin of the ring

Planet. Space Sci. Vol. 28, pp. 1101-1110 Pergmon Press Ltd., 1980. F’rinted in Northern Ireland DUST 00324633/80/1201-1101$02.00/0 IN JUPITER’S MA...

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Planet. Space Sci. Vol. 28, pp. 1101-1110 Pergmon Press Ltd., 1980. F’rinted in Northern Ireland

DUST

00324633/80/1201-1101$02.00/0

IN JUPITER’S MAGNETOSPHERE: ORIGIN OF THE RING G. E. MORFILL and E. GRtJN

Max-Planck-Institut

fiir Kernphysik,

Postfach

10 39 80, 6900 Heidelberg,

W. Germany

and T. V. JOHNSON

Jet Propulsion

Laboratory,

California

Institute

of Technology,

4800 Oak Grove

Drive, Pasadena,

CA 91103,

U.S.A.

(Received in final form 20 August 1980)

model for the production of the Jovian ring is proposed. The ‘visible’ ring particles are micron-sized and produced by erosive collisions between an assumed population of km-sized parent bodies and sub-micron sized magnetospheric dust particles. These small dust particles are ejected by volcanoes from IO. The observed topology of the ring is described quite well with the theory, and

Abstract-A

properties

of the parent

bodies

are deduced.

INTRODUCTION

Voyager I and II observations have shown that Jupiter is the third planet in our solar system which is now known to possess a dust ring (Owen et al., 1979, Smith et al., 1979). The relevant parameters which have been inferred from the measurements are: The ring is located approximately at a distance of 1.8 RJ (I$ = Jupiter radius) from the Jovicentre and lies in the Jovian equatorial plane. Its thickness perpendicular to this plane is not known; observations lead to an upper limit of 530 km. The extent of the ring in the equatorial plane is -7000 km. The ‘visible’ particles are micron-sized, and the slant optical depth is -10m4. The outer edge of the ring appears more abrupt than the inner edge. Assuming the ‘visible’ particles have a radius of 4 pm, we can estimate the particle density as 3 X lo-’ cmm3. the mass density as 8 x 10-l’ g cmm3 and the total mass of p-sized material as 1.3 x 1O’Og. The ‘visible’ particles are those showing up in forward scattered light. There could also be a population of larger size particles which would be seen mainly in backscattered light, although it has been demonstrated (Griin et al., 1980) that both forward and backscatter measurements can be described very well with the same particle size distribution n, - s;‘.~, where 2 x 10m5s s, 5 2.5 x 10m4cm. However, due to the large uncertainties in the measurements, a second (larger size) particle population may exist, provided the number densities are much smaller than the number densities of the micron-sized component (see Griin et al., 1980). For the sake of completeness, we must mention that direct dust observations were performed by the

meteoroid penetration detectors on board the Pioneer 11 spacecraft while it was traversing the ring region. Humes (1976) reported one impact of a dust particle of mass m 2 2 x lo-’ g in the vicinity of the ring. The actual mass depends on the impact velocity. A possible second count close to perijove was discarded due to possible radiation interferences. The traversal of the 30 km thick ring by Pioneer 11 took place within a few seconds. There is an uncertainty in the time when the penetration occurred of approx. 83 min. Therefore it is not possible to identify an impact as due to a ring particle or a sporadic background particle. There is even the possibility that multiple penetrations occurred within a time interval of 83 min after the first impact. These penetrations will not be registered by the experiment because the counter is locked out for a period of approx. 83 min after the first penetration. This characteristic does not allow the identification of multiple penetrations of ring particles. Even the number of impacts of possible ring particles is unknown because of the long deadtime of the instrument. Nevertheless we assume that not more than two impacts were recorded during close fly-by of Jupiter. This assumption may be verified later, if the total number of recorded penetrations reaches 108, which is the number of penetration cells of the instrument and therefore equals the maximum possible number of recorded counts. For further discussion of these measurements see Humes (1980). The fact that the size of the ‘visible’ particles is estimated to be so small implies that these particles must have been produced fairly recently (in geological time scales). Radiation pressure drag from the

1101

1102

G. E. MORFTLL, E. GRCJNand T. V. JOHNSON

sun alone yields a life time for these particles (total time required to spiral from 1.8R, into the Jovian atmosphere of
Johnson et al. (1980) showed that there is a strong possibility that small dust particles in the volcanic plumes of the Jovian satellite IO can become electrically charged and can then be removed from the gravitational field of 10 through the influence of the Jovian electromagnetic field. The particle radii must be smaller than -lo-’ cm, and their injection velocity into the Jovian magneto-

sphere is -57 km/set (difference between the corotation speed and 10 orbital speed). Morfill et al. (1980) showed further that for such small particles, and a typical particle surface potential of -10 V, the subsequent motion in the magnetosphere is dominated by electromagnetic forces. For a discussion of the equilibrium grain potential see Morfill et al. (1980) and Griin et al. (1980). The particle motion is practically adiabatic, i.e. the particles gyrate about their field line, corotate and execute bounce motions between their mirror points. The maximum mirror latitude Ed= 10” is the inclination of the Jovian magnetic equatorial plane with respect to the orbital plane of 10. Morfill et al. (1980) also showed that sputtering by heavy ions in the 10 plasma torus may destroy very small dust particles (radii smaller than - 1O-6 cm) so that the grain size distribution of those dust particles which escape from 10 and then disperse throughout the inner Jovian magnetosphere is narrow and peaked around a value s - 10m5cm. The main transport process in the magnetosphere is diffusive; the stochastic element in the particle motion is due to random charge fluctuations. Beyond a distance of - 12R,, the dipole field is distorted by an equatorial current sheet (Smith et al., 1974) and at that distance the dust particles can escape freely from the Jovian system. Finally, another factor which affects the motion of the dust grains is friction with the ambient plasma, which reduces the particle velocity below the injection speed of -57 km/set. Morfill et al. (1980) have calculated all these transport effects quantitatively, and this makes it possible for us to estimate ‘most likely’ values for the 10 grain velocities, D, (once the particles have diffused to L = r/R, = 1.8, the location of the proposed ring parent bodies), the mean grain density (n) in the inner magnetosphere and the diffusive radial transport speed, v~, where vd is defined from 1 an vd=K--=C. n ar

RI,

Here K is the diffusion coefficient due to charge fluctuations, and, in a steady state, we have assumed that the scale length of the ,dust density gradient is typically the orbital radius of 10. Figure 1 shows the radial diffusive drift velocity as a function of dust particle radius for different particle speeds (with respect to the magnetic field), v. The diffusion coefficient calculated by Morfill et al. (1980) was used at L = 1.8, the location of the dust ring. Also shown in Fig. 1 is the limit where the adiabatic treatment of the dust particles breaks

Origin

1103

of the ring

With these adopted values it becomes possible to investigate the interaction of the 10 produced grains with the proposed parent particles in the Jovian ring quantitatively and to calculate ring topology, time variations, intensity and to speculate on the effects of other small moons like Amalthea. Clearly, the values selected above are only approximate, but they follow from a transport theory (Morfill et al., 1980) and should not be in error by more than a factor 2 or 3. PRODUCTION

10-e

FIG. 1. RADIAL FUNCTION

10-h

10-S PARTICLE

RADIUS (cm)

DIFFUSIVE

DRIFT

OF DUST PARTICLE

VELOCITY

RADIUS

THE EQUATORIAL

PLOTTED

AT 1.8&

AS A

DISTANCE

IN

PLANE

Results are taken from the transport theory and plasmasphere model of Morfill et al. (1980) and are plotted for different particle velocities with respect to the magnetic field. Also shown is the adiabatic limit of applicability of the transport theory, and, for comparison, the radial drift due to radiation pressure effects, which is obtained if electromagnetic forces were absent.

down. With our assumption that the plasma electron energy E, =const = 10 eV, and the plasma density n, = 522L-’ cmm3 (see Morfill et al., 1980) the adiabatic limit is independent of dust particle radius, s, and L = r/R,. For comparison purposes we have also plotted the radiation pressure induced drift in Fig. 1. This is the radial drift velocity imparted on the dust particles by the solar radiation pressure if electromagnetic forces were negligible. Based on Fig. 1 and the dust-gas friction calculations shown in Morfill et al. (1980) we adopt the following ‘most likely’ values for the 10 grains at the location of the ring: (these numbers are rounded up or down and therefore do not correspond exactly to a single point in Fig. 1) particle

radius

s = 10e5 cm

particlevelocity ditisivedriftvelocity

21= lo6 cm/set vd = 10 cm/set

meanparticledensity(n) where which range these area escape

(2)

= &f,,/mA,u,

hj,, is the amount of matter (in particulates) escapes 10 per second (in the required radius around 10m5 cm), m is the mean mass of escaping dust particles and A, is the surface at r = R, = 12R, where dust particles may freely. A1 is given by A, = 4rrR,‘sin

eO.

(3)

OF MICRON-SIZED

GRAINS

From impact studies we obtain the following empirical relationships (see e.g. Dohnanyi, 1969; Gault and Wedekind, 1969): When a small particle of mass m and velocity 21 collides with another body, we can get ‘erosive collisions’ if the target is sufficiently large with respect to the projectile size, or we can get ‘catastrophic disruption’ if the target is too small. In erosive collisions the ejected mass is given by m,=ym

(4)

where y - 5 x lo-‘” t? (v in cm/set). fragment ejected has a mass

The

largest

m,-O.lym and the size distribution

(5)

of the ejected

grains is

g(m) = Cm-@ dm where

p = 1.8 and C is determined ym=

(6) from

ml. I1

mg(m)

dm.

(7)

Catastrophic disruption occurs when the target mass is less than -1OOym. In the case of 10 produced particles interacting with the proposed ring parent bodies we obtain largest ejected fragments with radii in the micron The ejected range, as well as smaller particles. fragments themselves can, of course, also collide with 10 produced particles and with each other. The largest ejected fragments (which are the visible ring particle component) have a low ejection velocity, of the order metres/sec., which is still above the escape velocity for e.g. kilometre sized parent bodies. However the velocity is too low for destructive collisions among these ejecta to play a role. On the other hand, the relative velocity between these large ejecta and IO produced particles is of the order of tens of kilometres/sec. Collisions then result in catastrophic disruption. Thus the process which creates p-sized particles will also lead to

1104

G. E. MORFILL,E. GROAN and T. V.

their destruction, and therefore p-sized particles should have a unique spatial distribution which depends on the distribution in space of the parents, on the density and motion of the 10 produced grains and on the dynamic behaviour of p-sized grains in the Jovian magnetosphere. It can be shown (see e.g. Morfill et al., 1980) that whilst gravity is unimportant for particles with radii t10e5 cm (A Frn) when compared to electromagnetic forces, it is the dominant force for p-sized grains. Consequently the evolution of the p-sized particle orbit is governed by e.g. radiation pressure effects which leads to a slow spiralling towards the planet. This description of the evolution of the visible ring (p-sized particles), which will be formulated mathematically in the next chapters, with a discussion of the consequences and inferred properties of the parent bodies, is simplified. Processes which have so far been ignored, and which may play a role are long term effects of electromagnetic scattering by the offset and inclination of the dipole field (Consolmagno, 1980) and other loss processes (e.g. reabsorption of F-sized grains by the parent bodies). Sputtering losses and electrostatic fragmentation are not expected to play a role in the ring regime (for a quantitative evaluation see Morfill et al. 1980, Griin et al. 1980). SPATIAL

STRUCXURE

OF MICRON-SIZED

dt

3

N = n2rrr drh’.

(8)

and with n, = no at time t = 0 this yields (9)

The particles spiral towards Jupiter under the influence of radiation pressure, and this gives a relation between distance r from the Jovicentre and time. Taking only solar radiation pressure forces to be important (this underestimates the drag forces somewhat) we obtain (see Allan 1962, 1967)

(10)

=2N

R

(13)

78

and the flux is F=--

R

2nh’

s-/a’;

.

(11)

(14)

2rr dr-y

The loss rate of p-sized particles is simply 1 I

TS,‘F.

Substituting for rB = 2~&

(1%

r/3v (Jackson,

1963) we

get L = 3& T

s,%v sin Ed.

From (11) we put .$ = s~,/~T,so that with (16) we obtain 5=

9J?

m,nv sin Ed 4Tpa

(17)

m, =$~ps,~ IS ’ the mass of the F-sized particles. We can express the average density of 10 emitted dust grains, (n), in terms of the mass flux fi10 (see expressions 2) and insert this for n in equation (17). Utilizing relation (5), i.e. m,/m =O.lr we then obtain finally V”A2

where at t = 0 we fix r = R,, s, is the radius of the dust particle (in cm) and for Jupiter a = 1.32 10-16. From (9) and (10) we get

(12)

In half a bounce period, $rB, all particles have crossed the equator once, i.e. the rate of 10 particle traversal through the monolayer is

- =

T

n, = noe-t'T.

The loss time 7 is calculated in the following way: The ejecta velocities for the p-sized fragments is small, so that the inclination spread of those particles must be small also. The observed thickness h 530 km is in good agreement with this. On the other hand, the 10 produced dust grains execute bounce motions in the Jovian dipolar magnetic field, with a maximum mirror latitude Ed-- lo”, i.e. they populate a region of much greater thickness h’ = 2r sin eO. We can therefore approximate the p-sized particles as occupying a monolayer by comparison. The number of 10 particles in a radius interval dr is

EJECTA

Micron sized particles are destroyed by collisions with 10 produced particles at a rate l/7. The temporal evolution in particle density is

da,=

JOHNSON

5 = 8.32 x 1O-18d

Vd

(18)

and using the ‘most likely’ values for u and ud (see 2) we get

.$= 0.823&.

(19)

1105

Origin of the ring Substituting this in expression (11) we obtain the spatial variation in the p-sized particle density, assuming that the source is a S-function. As can be seen from the expression (ll), the relative dust density n,/n, decreases faster with decreasing distance, r, if &f10 is larger. This is due to the fact that the destruction rate of p-sized ejecta is then higher. In Fig. 2 we have plotted the relative intensity (Owen et al. 1979) in the form of a radial ring profile. Measurements from the near side ring portion and the far side portion (both normalized to unity at their respective maxima) are shown, the difference between the two measurements is shaded. As can be seen, both profiles yield almost the same radial distribution. Assuming that the relative intensity I/I, is linearly proportional to the relative dust particle density of p-sized grains, n,/n,, we have shown some theoretical curves assuming a S-function source located at a distance of 1.74R,. Three conclusions can be drawn from Fig. 2: (1) A single s-function type source (i.e. parent bodies circling Jupiter in a narrowly restricted radius range) is not compatible with the measurements. If the spread around the &function source was due to orbit eccentricities of the p-sized ejecta, then a ring thickness h 530 km would not be understood. (2) The fall-off in relative intensity towards smaller distances is compatible with our creation and subsequent destruction mechanism if the satellite 10 ejects dust grains in the size range 10~6-10-5 cm with a rate of -13 g/set.

DISTANCE

FIG.

2.

(3) Towards smaller distances, p-sized grains do not contribute a major portion of the scattered light intensity. The multitude of even smaller grains, produced by destructive collisions, becomes important. In order to investigate the radial extent, l,, of parent bodies, we have produced Fig. 3. Here we have assumed that parent bodies of sufficient mass occupy a monolayer in the Jovian equatorial plane, with a homogeneous distribution over a radial distance 1,. As can be seen, the density of F-sized particles builds up to a maximum at the inner edge of the parent body region, and then decays towards smaller distances with the same law as that obtained for a a-function source. The best fit is obtained for &fro = 13 g/set, 1, = 0.08RJ.

(20)

Pioneer 11 charged particle data has indicated a for the width of those ring partivalue of -O.lR, cles, which are effective in absorbing the energetic particles (Fillius 1976, W. H. 1979). If the absorption is mainly caused by the parent bodies, then the agreement between our fit of l, = 0.08Rr and the measured value of O.lRr is satisfactory. On the other hand, if we include the absorption (energy loss during penetration) by the p-sized ejecta, the width of the ring (to half maximum intensity is -O.l5R,, which is also reasonably close to the width derived from the energetic particle measurements. The higher level of light intensity beyond 1.82R, is again caused by submicron particles, ejecta from the parent bodies with high escape velocities and

(I=?~)

RADIALPROFILEOFTHERELATIVERINGOFTICALINTENS~TYDER~VEDFROMTHEMEASUREMEMS OFOWENETAL. (1979).

The near side and far side profile have both been arbitrarily

normalized to 1 at their maximum and the region between them is shaded. Three theoretical curves are shown, assuming a d-function production of ‘visible’ particles at 1.74R,. The fall-off in intensity towards Jupiter (smaller distances) is best fitted with a mass loss k,, (in particulates) of 12.8 g/set. The broad shape of the main portion of the ring is not compatible with a single d-function type source.

G. E. MORFILL,E.GRCJN

1106

DISTANCE

andT.V.

JOHNSON

(RJ)

FIG. 3. SAME ASFIG. 2, EXCEPTTHATTHESOURCEISASSLJMEDTOBEUNIFORMOVERAREGION 1.74 AND 1.82R,. The agreement

between measurements (shaded region) and theory (heavy solid line) is very good. The deviations below lSR, and beyond 1.82R, are explained in the text.

correspondingly larger eccentricities and inclinations. According to our model, the Jovian ring then consists of three components: (1) a group of parent particles, more of less homogeneously distributed between 1.74 and 1.82R,, in an equatorial monolayer, (2) a population of p-sized particles ejected from this parent distribution by collisions with 10 particles. The scale height perpendicular to the equatorial plane is observed to be of the order -10 km (Smith et al. 1979), i.e. the p-sized grains envelope their parents. A scale height of -10 km corresponds to a velocity dispersion of -2 mlsec at 1.8R,. This is in good agreement with the low escape velocities of the largest ejected fragments predicted by our mechanism. According to the calculations, the density of p-sized grains has a maximum at the inner edge of the parent distribution (-1.74&) and decreases gradually towards Jupiter. (3) a population of sub-micron particles, partially source particles from 10, partially fragments produced by collisions. These particles populate a disc extending beyond the outer edge of the ring and filling the space inside the ring. These particles are not so easily ‘visible’ optically because of their small size, but there is some indication in the observations for a disc and halo component, which supports our model. PROPERTIES

BETWEEN

OF THE PARRNT

BODIES

We can obtain some information about the parent bodies from our model of the ring. Inherent in our model is the assumption that the ring is a quasipermanent feature of the Jovian system, i.e. existed over geological times (--10”sec). The

mass loss rate due to radiation pressure effects from the sun can be calculated, and gives a clue to the minimum total mass of the parent bodies. Also, from the measured optical depth of the ring, and the creation and destruction rates of p-sized particles, we obtain a measure of the exposed surface area of the parent ring particles. Finally radiation pressure drag calculations yield an estimate of the minimum size of the parent bodies. (1) Mass loss rate and minimum total mass Themasslossratedue toradiationpressureeffectson p-sized grains (i.e. excluding destructive collisions) is given by the total flux of particles crossing the inner boundary of the ring (which has an area 27rR,h): iI& = 2rrRohn,m,vR

(21)

where vR is given for Jupiter by (see Allan, 1967)

(22) For an optical depth D, we obtain the mean density of p-sized particles

w=+. I‘

From Fig. 2 we obtain for 1, = O.l7R,, and D has been measured to be lo-“. Substituting (22) and (23) in (21) gives R,‘hD hi, = 1.1 x 1ol5 p1,

.

(24)

Substituting R, = 1.8R,, the maximum value for the

1107

Origin of the ring thickness allowed from the observations, 30 km, p = 1 g/cm3, gives finally hi, = 4.5 X lo-’ g/set

h=

$=(I-P,)7 0

(25)

over geological times (- 1Ol7 set) this implies that the total mass of parent particles must exceed a critical value && = 4.5 x 1o15 g

After the second bounce (or time TV) we have

(26)

by a considerable margin, otherwise the supply of p-sized grains will be near exhaustion. The mass ‘loss’ rate due to destructive collisions by the 10 particles, using the values of equation (20), is about 10 times as high as the ‘loss’ rate due to radiation pressure effects given in (25).

and after a time j&rB we get +(1-P,)‘. 0

(32)

NO The number of half-bounces, j=-.

j, is simply given by

2t,

(33)

78

The minimum parent size is determined by the condition that radiation pressure forces from the sun should not cause the parent bodies to spiral into the planet in geological times, tc - 10” sec. The condition is simply (27)

Thus the flux of 10 particles drifting in at the outer edge of the parent regime is (particles/set) F1 = (n)A,v,

sp >>13 cm. There may be other constraints become apparent later.

(28) for sp, as will

We assume that the parent bodies occupy a monolayer at the equator, located at a mean distance R, with radial extent 4,. The total area A occupied by parent bodies is then A = 2rrR& and the total surface area presented is A,. The probability of collision during one traversal of this monolayer is PL = A,/A. It has already been mentioned that the motion of the 10 produced particles is governed by electromagnetic forces, in particular that these particles execute bounce motion (period 7B - 3.8 x lo4 set) in the dipolar field and that there is a diffusive radial drift with velocity vd. The rate of equator crossings is R = 2/rB, and the time taken by the 10 particles to traverse the region occupied by the parent bodies is tp = lJvd - 5.6 x 1O’sec. The fraction of particles ‘lost’ by collisions after the first bounce is P,, and the fraction left is I-P,.

F2 = (it)A3vd where A3 = 4a(R, - kd)’ sin Q,. For &c
(3) Surface area of parent bodies

(29)

(34)

where A, = 4rR,‘sin E,,, and the flux, after absorption by the parent bodies has been taken into account, is

which yields for the radius sp of the parent bodies

0

(31)

For P, K 1 we can write

(2) Minimum parent size

;=

(30)

N,

-_(ztJT,)PL

NO

(35) Q. We

(36)

Substituting for 7B and $, and making use of the fact that PL<
(l-g)(n)A,vdq

(37)

where r) - 1 is the efficiency with which a F-sized particle is produced in a given collision. The rate of destruction or loss of p-sized grains is assumed to be dominated not by radiation pressure drift, but by destructive collisions with 10 grains. We get IR,J = (n,)2mROZWh1 7 where (n,) is the mean density of p-sized grains (equation 23) and l/7 the loss rate (equation 16).

1108

G. E. MORRLL E. G~ij~andT.V. JOHNSON

In the steady state, gains equal losses, so that from (36), (37) and (38) we obtain in the (realistic) Iimit for small PL

wi

-{(n)A,u,n ‘rt3

=(~~)2~R~~~~~. 7

(39)

Substituting for 4, mu.AZ, (n,) (equation 23) and T (equation 16) we finally obtain P,=&

f,11

(40)

The optical depth in the plane of the parent particles is Pii= P1 ~~~, where h, is the scale height of the parent body distribution. If the parents are distributed in a monolayer, and if the mean radius of the parent bodies is sp, we get

Substituting numbers, h - 106 cm, t, - O.OSR, = 5.7 x 10’ cm (Fig. 3) D = 10e4 and n - 1, we obtain P1-

Choosing, obtain

1.75 x 10-7.

as an example,

(4la)

s, = 1 km (see later) we

P,, = 5D = 5 x lo-“.

(4lb)

Thus we see that the optical depth PIIof the parent bodies in the plane of the ring exceeds that of the p-sized particles. However, if the parent bodies occupy a monolayer, and the ring is viewed from a latitude OL> O.l”, the optical depth P, CD, with the above parameters. The exposed surface area of the parent bodies, A, = AP is then only dependent on the location of the ring, Ro, its vertical thickness h, the measured opticai depth, D, and the efficiency for producing ~-sized visible grains, n. A, = 2rrR0hD/n, A, = 8.1 x 10” cm’.

(42)

This number is not very large. It corresponds to a single spherical body with diameter 32 km, however it is unlikely that only a single body is responsible. One reason is the shape of the resolved ring (see Figs. 2 and 3) which argues against a single Sfunction-type source, a second reason may be the possibility that the escape velocity of heavy secondaries from their parent body exceeds the velocity which they can obtain in the impact, i.e. ‘visible’ secondaries may not be able to escape from very large parent bodies.

(4) ~~i~um

size of parent bodies

The vertical thickness of the ring of M-sized particles gives us a measure of their velocity dispersion after leaving the parent body. Measurements yield an upper limit to this thickness of about 30 km. If we adopt a value of 10 km as an example, we find that this corresponds to a velocity dispersion of u, 2 mlsec. This velocity dispersion may be due to the kinetic energy dispersion of the ejecta, or it may result from gravitational perturbations with parent bodies and from electromagnetic perturbations (Consolmagno, 1980). Thus if we know the ejection speed v,, of a p-sized fragment produced in an erosive collision, and set this equal to the escape velocity, we can calculate the upper size limit for the parent body. Since the velocity of p-sized fragments produced in an erosive collision with 10 particles is of the order 2 mlsec (see Griin et al. 1980), we may define the size of the largest body which may be regarded as a source of visible, p-sized, particles from iv,

,_GM -s,

(43)

i.e. the gravitational potential at the surface of the parent body (mass M, radius So) equals the kinetic energy with a velocity 21, = 2 m/set. G is the gravitational constant. Substituting numbers, we find that the critical size for parent bodies is s, - 2.7 km.

(44)

The escape velocity is proportional to the radius of the parent body, so we see that signi~cantly larger parents with radii of the order tens of kilometres can be ruled out practically as a source of visible p-sized particles produced in erosive collisions with IO particies. This is important in the context of Amalthea (length -265 km, thickness - 140 km, Smith et al. 1979), which cannot, therefore, be regarded as a possible source for p-sized ‘visible’ dust particles, but may be a source of sub-micron ejecta (these have higher ejection velocities.) The same argument applies to the moons 1979 Jl and 1980 Jl, which have diameters of the order 50 km. With the estimate for the area presented by the (target) parent bodies (equation 42) and the lower and upper size limits (equations 28 and 44 respectively) we can now estimate the mean number of parent bodies in the ring and their total mass. The number of parent bodies is given simply by n, = A,/~.s~=

(45)

Origin

and their total mass is M, = A,$pq.

(46)

From the condition that M, >>MC (see equation 26) we obtain q(min) - 100 m. Also we had s, (max) 1 km (see equation 44). This yields 2.6 x lo4 parent bodies of radius 100m or 260 parent bodies of radius 1 km. The corresponding masses are 1.1 x 10” g or 1.1 X 1O1’ g respectively. Long term effects of orbit perturbations by the Galilean satellites would tend to favour a size distribution for the parent bodies closer to the upper limit of s, - 1 km. On the other hand, if the parent bodies of the p-sized particles are ‘herded’ into a ring by a small satellite (e.g. 1979 Jl), Dermott et al. (1980), then a parent body distribution with smaller masses is probably more reasonable. In this discussion we have not considered reabsorption of the p-sized ejecta by the parent bodies, although this may in principle be quite important. We can make one qualitative comment at this stage. If the parent ring (which must exist to explain the p-sized) is produced by the gravitational herding of two satellites (Goldreich and Tremaine, 1979) at the outer and inner edge, absorption of p-sized ejecta by the inner satellite would probably be very important and lead to a sharp inner edge

FIG. 4.

1109

of the ring

for the visible ring. However, it would require a more detailed calculation than is possible here, in order to arrive at a quantitative model.

SUMMARY

AND DISCUSSION

Figure 4 summarizes the topology of the dust particle populations in the vicinity of the Jovian ring. The solid points on the equatorial plane show the extent of the parent bodies. The contour lines (not to scale in the direction perpendicular to the equatorial plane) show the 0.75, 0.5 and 0.25 relative intensity level of ~-sized particles, which envelope their parent bodies. The parent bodies occupy a monolayer, whereas the vertical extent of the p-sized particles is -10 km. The ‘wedge’ shaped region is occupied by the submicron (~10~~ cm) particles ejected by the volcanic activity on 10. According to our model, the topology of the observed particle ring and its properties (p-sized particles) is explained by the same process: Particles ejected during volcanic activity from 10 (narrow size range at -10d5 cm) populate the inner magnetosphere by a process of radial diffusion caused by statistical surface charge fluctuations. These particles have velocities of the order tens of

SCHEMATICDIAGRAMOF~ETHREEPARTICLEPOPULATIONSINTHEVICIN~OFTHERING.

(1) parent bodies (solid points, km-sized), (2) micron-sized ‘visible’ particles (three contour lines are shown representing 0.75, 0.5 and 0.25 peak density, not to scale in the vertical direction), (3) 10 particles (these occupy a ‘wedge’ with half angle c0 = 10” and are submicron, radii - 1OF cm).

1110

G. E. MORFILL, E. GR&

km/set and produce erosive collisions with any sizeable material debris in orbit around Jupiter. If the debris, or parent body, is sufficiently small (radius -km) these collisions lead to the ejection of micron-sized ‘visible’ particles. These secondary particles spiral towards Jupiter under the influence of radiation pressure forces. Subsequent collisions between the micron-sized ejecta particles and the original 10 particles are destructive, and it is this process which is responsible for the formation of a ring rather than a disc of p-sized particles. The requirements for this process to work, expressed in numbers, are: (1) The mass loss in particulates from 10 is -13 glsec. This must be compared with an estimated loss rate of 10” particles (sulphur or oxygen)/cm’sec which corresponds to a mass loss of 10’ g/set in gaseous form (Broadfoot et al. 1979) and appears quite reasonable. (2) The mass loss from 10 of - 13 g/set must also be seen in the light of the estimated mass in particulates thrown up in a single large volcano. This number is estimated (Johnson et al. 1979) at -lo7 g/set. The required loss from 10 is therefore only a minute fraction of the (in principle) available SUPPlY. (3) There exists a parent population with a total

exposed area of - 8 X 1O1* cm2 in the form of microsatellites between 1.82 and 1.74&, possibly fragments of a tidally disrupted body. The sizes of these parent bodies range from - 100 m to - 1 km, although larger bodies should exist also. The total mass of the parent bodies is of the order 1017lOlag, sufficiently greater than the critical mass required to replenish losses over geological times. (4) The ring is a quasipermanent feature of the Jovian system, as permanent as the volcanic activity on 10. We make no speculations about the origin of the parent bodies in this paper. One possibility has already been discussed by Prentice and ter Haar (1979). however we wish to point out that the ‘visible’ particles mechanism.

cannot

be

explained

by

their

and T. V.

JOHNSON

REFERENCES

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