Explosive volcanism and the compositions of cores of differentiated asteroids

Earth and Planetary Science Letters, 117 (1993) 111 - 124 Elsevier Science Publishers B.V., Amsterdam

111

[CL]

Explosive volcanism and the compositions of cores of differentiated asteroids Klaus Keil a,1 and Lionel Wilson a,b,1 a Planetary Geosciences, Department of Geology and Geophysics, School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, Honolulu, HI 96822, USA b Environmental Science Division, Institute of Environmental and Biological Sciences, Lancaster University, Lancaster LA1 4YQ, UK

Received November 3, 1992; revision accepted March 8, 1993

ABSTRACT Eleven iron meteorite groups show correlations between Ni and siderophile trace elements that are predictable by distribution coefficients between liquid and solid metal in fractionally crystallizing metal magmas. These meteorites are interpreted to be fragments of the fractionally crystallized cores of eleven differentiated asteroids. Many of these groups crystallized from S-depleted magmas which we propose resulted from removal of the first partial melt (the Fe,Ni-FeS cotectic melt) by explosive pyroclastic volcanism of the type envisaged by Wilson and Keil [8]. We show that these dense, negatively buoyant melts can be driven to asteroidal surfaces due to the presence of excess pressure in the melt and the presence of buoyant bubbles of gas which decrease the density of the melt. We also show that, in typical asteroidal materials, veins will form which grow into dikes and serve as pathways for migration of melt and gas to asteroidal surfaces. Since cotectic Fe,Ni-FeS melt consists of about 85 wt% FeS and 15 wt% Fe,Ni, removal of small volumes of eutectic melts results in major loss of S but only minor loss of Fe,Ni, thus leaving sufficient Fe,Ni to form sizeable asteroidal cores.

1. Introduction Eleven of the thirteen known iron meteorite groups show correlations between Ni and siderop h i l e t r a c e e l e m e n t s t h a t c a n b e p r e d i c t e d by d i s t r i b u t i o n c o e f f i c i e n t s b e t w e e n l i q u i d a n d solid m e t a l (e.g. [1], a n d r e f e r e n c e s t h e r e i n ) . T h e s e e l e v e n g r o u p s a r e r e f e r r e d to as t h e m a g m a t i c i r o n m e t e o r i t e g r o u p s a n d a r e t h o u g h t to b e fragments of fractionally crystallized cores of eleven differentiated asteroidal parent bodies [e.g., 2 - 4 ] . B a s e d o n t h e a b u n d a n c e p a t t e r n s o f siderophile trace elements and the effects that S has o n t h e d i s t r i b u t i o n c o e f f i c i e n t s o f t h e s e e l e m e n t s b e t w e e n l i q u i d a n d solid m e t a l , s e v e r a l a u t h o r s h a v e e s t i m a t e d t h e initial S c o n t e n t s o f the magmas from which the magmatic iron meteo r i t e g r o u p s c r y s t a l l i z e d [e.g., 2 - 5 ] . T h e y f o u n d that many of these groups must have crystallized

1 Also associated with the Hawaii Center for Volcanology.

f r o m m a g m a s t h a t w e r e d e p l e t e d in initial S c o n t e n t s by f a c t o r s o f u p to a b o u t 6 f r o m t h o s e o f r e a s o n a b l e p r e c u r s o r m a t e r i a l s , s u c h as o r d i n a r y c h o n d r i t e s . I n T a b l e 1, w e list t h e m a g m a t i c i r o n m e t e o r i t e g r o u p s f o r w h i c h e s t i m a t e s o f initial S c o n t e n t s a r e a v a i l a b l e [3-5]. W e also list r a n g e s of their metallographic cooling rates and parent b o d y r a d i i c a l c u l a t e d f r o m t h o s e r a t e s [6], a n d

TABLE 1 Estimated initial S contents of magmas of magmatic iron meteorite groups, their metallographic cooling rates (MCR), parent body radii (R), and percentage required loss of cotectic Fe,Ni-FeS liquid (LCL) Group

S (%)

MCR R (km) (K Ma- 1)

II AB 10 -17 6-12 III AB 4 -5 3-75 IV A 1.0-1.8 11-500 IV B 0.6-1.2 30-260 H chondrites * 8.6

100-73; 138-31; 75-13; 47-17;

LCL (%)

avg. 87 avg. 85 avg. 44 avg. 32

0 41 82 88

* This is the S content of the metallic Fe,Ni-FeS portion of H chondrites

0012-821X/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved

K. K E I L A N D L. W I L S O N

112

give the best estimates of the specific radii, using the most plausible cooling rates and parent body models [H. Haack, pers. commun.; 6]. This table indicates that, with decreasing S content, meteorite cooling rates increase and, hence, parent body radii decrease. A number of hypotheses have been proposed to explain the initial S content depletions of magmas in the magmatic iron meteorite groups, including loss by volatilization, by continuous removal as an immiscible liquid, and by removal of metastable liquid layers produced by episodic melting [7]. Here we propose a new model to account for the S depletions of a number of the magmatic iron meteorite groups, involving explosive volcanism as postulated by Wilson and Keil [8]. These authors showed that a few hundred ppm of expanding volatiles present in early partial (basaltic) melts on the aubrite parent body (or other differentiated asteroids less than about 100 km in radius) would, upon ascent of the magma to the surface of the body, cause disruption into a spray of droplets moving with velocities in excess of the local escape velocities of small asteroidalsized bodies. The droplets would thus escape and be lost into space, mostly by spiralling into the sun, 4.55 Ga ago. As a result, no such basaltic rocks exist, neither as individual meteorites nor as clasts in brecciated aubrites. This concept of pyroclastic volcanism has also been applied to explain the lack of basaltic rocks complementary to the ureilites [9-11], and Muenow et al. [12] have shown how pressure rises in asteroids of at least tens of MPa due to partial melting cause the growth of pathways (fractures, connecting into dikes) which can deliver these early partial melts to the surfaces of asteroids. We now suggest that the depletion in initial S contents of the magmas of some of the magmatic iron meteorites is the result of cotectic Fe,Ni-FeS melts being removed from the parent bodies by explosive pyroclastic volcanism and lost into space. This process is expected to be more effective on smaller bodies and, thus, could explain the decrease in initial S contents of Fe,Ni magmas with decreasing parent body radii (Table 1) [13]. If the precursor material of the magmatic iron meteorite groups was roughly similar in composition to ordinary chondrites such as those of the H group, as seems reasonable, then it contained 16.8 wt% Fe,Ni and

5.1 wt% FeS [14], and an unfractionated F e , N i FeS magma derived from such material should have 76.7 wt% Fe,Ni and 23.3 wt% FeS. However, upon heating of an asteroid of H group composition, the first partial melt would form at the Fe,Ni-FeS cotectic temperature of about 980°C and consist of about 85 wt% FeS and 15 wt% Fe,Ni [15,16]. When all of the FeS in the asteroid has been incorporated into such a melt, the latter would represent 6.0 wt% of the asteroid; because of its high density (5000 kg m-3), the melt occupies about 4.2 % of the volume of the asteroid. We will show that the negative buoyancy of this dense melt can be compensated by the presence of volatiles concentrations of a few hundred to a few thousand ppm, the subsequent expansion of which then drives pyroclastic volcanism of the type envisaged by Wilson and Keil [8]. For example, removal of about 88% of the Fe,Ni-FeS cotectic liquid from an average H group precursor material would deplete the residue in S content to approximately that of the IVB iron meteorite group, which is the group most highly depleted in S (Table 1). These percentages are even lower for the magmatic iron meteorite groups with higher initial S contents (Table 1). However, because the cotectic melt is relatively poor in Fe,Ni (15 wt%) and rich in sulfide (85 wt%), removal of even 88% of this melt would result in removal of only about 3.5 wt% metallic Fe,Ni and leave about 96% of the original Fe,Ni to form a sizeable core. Thus, it appears that loss of cotectic melt through pyroclastic volcanism can account for the puzzling depletions of certain magmatic iron meteorite magmas in initial S contents. 2. Theoretical considerations

2.1. Pressures in fluids produced by partial melting The vertical principal stress Pm in the solid matrix of an asteroid can be well approximated as a lithostatic pressure, and varies with radial distance R from the center according to Pro(R)

=

( 2 / 3 ) r r G p 2 ( R 2 - R 2)

(1)

where G is the gravitational constant (6.67 × 10 ll m 3 s 2 kg 1), Ps is the mean density of the asteroid (assumed to be uniform; i.e., the asteroid is not differentiated at this point and the pressure

EXPLOSIVE VOLCANISM AND THE COMPOSITIONS OF CORES OF DIFFERENTIATED ASTEROIDS

at the center of the asteroid is not so high that compressibility effects are important), and R 0 is the asteroid's radius. The range of central pressures for bodies with radii in the range 10-100 km is therefore about 0.17-17 MPa before any heating and subsequent melting occurs. At pressures up to at least tens of MPa, the density p~ of a eutectic F e , N i - F e S melt is approximately independent of pressure [17] and can be calculated from the relative proportions of the metal and sulfide components using known densities [18]. The value of Pl, which is very close to 5000 kg m -3, is significantly greater than the bulk density of the asteroid, &, about 3500 kg m -3 for an H group chondrite precursor body [19]. It is no trivial matter to drive significant amounts of such a negatively buoyant melt to the surface of the parent body. However, there are two factors which can aid the eruption of a negatively buoyant melt: the presence of an excess pressure in the melt, and the presence of (buoyant) bubbles of gas. We show below that both these factors play important roles in melting episodes in asteroids. Before any melting begins, the asteroid consists of an assemblage of mineral grains with small pockets of gas present in spaces between some of the grains. The initial pressure in the gas will reflect a combination of the ambient conditions in the Solar Nebula when the asteroid accreted and the process of accretion itself, and may be quite low. However, if there has been enough time between the formation of the asteroid and the onset of melting for significant plastic creep of the matrix, allowing compaction of part of the original void space, the pressure in 'the gas pockets may be as high as the matrix pressure. We shall find it convenient to work in terms of

113

the mass fraction, n, of the asteroid which consists of volatiles. Let the voids occupy a volume fraction f of the asteroid (after any compaction has taken place but before any heating begins) and contain gas with density pg. The partial volume Vg occupied by the gas is equal to (n/pg), and the partial volume vs of the solid material is [(1 - n)/ps]. Since by definition f = [Vg/(Vg + Vs)], we have, after minor substitution and rearrangement pg = & [ n ( 1 - f ) ] / [

f ( 1 - n)]

(2)

Let us assume that n is 1000 ppm, which appears to be a reasonable value for the contents of volatile elements of unequilibrated ordinary chondrites [20-23] (i.e., of the typical primitive precursor rocks which, upon melting and fractionation, formed the magmatic iron meteorite groups). The gas densities implied by void fractions of 5, 10 and 20% in a parent body with bulk density Ps = 3500 kg m -3 are then 66.6, 31,3 and 14.0 kg m -3 respectively. If the initial temperature of the asteroid is T i, the pressures Pi implied by these densities can be found using the perfect gas law (an imperfect but adequate approximation):

Pi = pgTi( C / m )

(3)

Here C is the universal gas constant (8.314 J mol - t K - t ) and m is the mean molecular weight of the gas (we use rn = 30 to represent a mixture of likely volatiles such as nitrogen and carbon monoxide). If we take a likely value of T i = 200 K, the above densities imply pressures of Pi = 3.69, 1.75 and 0.78 MPa, respectively. As a heating episode in an asteroid progresses, the pressure in the trapped gas pockets rises as

TABLE 2 T h e initial gas pressures, Pi, and pressure increases, APh, in gases trapped in the void spaces of asteroids after heating from 200 to 1253 K, the temperature of a F e , N i - F e S cotectic liquid, f , the void space, is given as a volume fraction and n, the gas mass fraction, is given in ppm. T h e pressures are given in MPa n

100 300 1000 3000 10000

f = 0.05

f = 0.10

f = 0.15

f = 0.20

f = 0.25

Pi

A Ph

Pi

A Ph

Pi

A Ph

Pi

A Ph

Pi

h Ph

0.37 1.11 3.69 11.1 37.2

1.94 5.82 19,38 58,0 191,6

0.18 0.52 1.75 5,25 17,64

0.92 2.76 9.19 27.6 91.8

0.11 0.33 1,10 3.31 11,1

0.58 1.74 5.79 17.4 58.1

0.078 0.23 0.78 2.34 7.84

0.41 1.23 4.09 12.3 41.1

0.058 0.18 0.58 1.75 5.88

0.31 0.92 3.07 9.21 30.84

114

K. KE1L A N D L. W I L S O N

the temperature rises from the initial value Ti to a final value Tf. The pressure rise A P h is partly accommodated by compression of the solid matrix, and is given by [12] as In[1 +

(APh/Pi) ] + (APh//Z)

=

ln(Te/Ti)

(4)

where /z is the shear modulus of the largely silicate matrix ( ~ 10 GPa) [24]. This treatment disregards the ~ 3% thermal expansion of the volume of the asteroid matrix during the ~ 1000 K temperature increase as being small compared with the gas volume increase (the second term on the left-hand side could also be disregarded for the same reason). Equation (4) must be solved iteratively for A Ph starting from some initial estimate. If the temperature rises from Ti = 200 K to the melt eutectic of Tf = 980°C = 1253 K, then for the above values of Pi = 3.69, 1.75 and 0.78 MPa, the corresponding values of AP h are 19.38, 9.19 and 4.09 MPa. Table 2 summarizes the above numerical examples and also shows the initial pressures and pressure increments generated by the heating process for void fractions up to f = 0.25 and gas mass fractions of n = 100, 300, 1000, 3000 and 10,000 ppm. As melting begins (progressively from the center of the asteroid outwards), small veins of melt will form along grain boundaries. The increase in volume of the melting phases will be accommodated partly by invasion of the gas-filled pockets (assuming some are present) and partly by elastic compression of both the liquid and the solid matrix. Muenow et al. [12] showed that the pressure rise A P m in the system when no gas pockets are present is given by: AP m = [((r/p,)

-

1]/31n[1

+

{(4qlz)/(3/3)}] (5)

where /3, the bulk modulus of the metal-sulfide melt, will be in the range 50-60 GPa at low pressures [17]; /.~ is again the shear modulus of the solid matrix; (o'/pj) is the ratio of the densities of the solids undergoing melting (which do not have the same density as the bulk of the asteroid) and the resulting liquid, and has a value of ~ 1.1; and q is the volume fraction of melting that has occurred. The values of A P m due to 1%,

3% and 10% by volume melting are found to be ~ 13 MPa, 39 MPa and 128 MPa in this case. We now consider the more general case of melting when gas pockets are present. The pockets, initially occupying a volume fraction f of the asteroid, as before, contain gas at temperature Tf and pressure (Pi + APh), as defined by eq. (4), at the end of the initial heating phase. When melting has progressed to the point where a solid volume fraction q has melted, the liquid volume created in excess of the volume of solid melted is [(o'/pl)q]. We assume that all of this liquid enters the space occupied by gas, compressing the gas as it does so. Since gases are more compressible than solids or liquids, this assumption leads to lower values of the pressure rise caused by the increase in volume due to melting than would occur if no gas pockets were present. If the fraction of solid melted increases from q to (q + dq), the liquid volume increases by [(o-/pj)dq]; the remaining solid, the existing liquid and the gas are all compressed by varying amounts to accommodate the new liquid, causing a pressure increase dP. The solid volume decrease is ( 1 q)(dP/lz) and the liquid volume decrease is [(o'/pj)q(dP//3)]. The gas volume decrease is found from the equation of state, which implies that (Pi + A P ) f = PUg, where P and Ug are the general values of the pressure and the fractional gas volume, respectively. From the earlier definitions, Zg = [ f - (o'/pl)q]. Differentiating the equation of state and substituting for ug we find that the decrease in gas volume due to the pressure rise d P is dug=

{[f-(o'/pOq]2dp}/[(Pi + A P h ) f ]

(6)

Equating the volume increase due to melting to the sum of the volume decreases due to the compressions of the three phases present, we have

[((r/p,)dq]

q)(dP/lz)] + [(o'/pl)q(dP//3)]

= [(1 -

+ {[I- ((r/p,)ql2de} /[(5

+ APh)f]

(7)

If we define the following quantities for convenience: A = ((r/pl), B = [/x -1 +f/(Pi + APh)], C = {(or/pl)//3} - - /[.~-1 _ [2(o./pL)/(ei + Aeh) ]

EXPLOSIVE VOLCANISM AND THE COMPOSITIONS OF CORES OF DIFFERENTIATED ASTEROIDS

a n d D = [(o/pl)2/{(Pi gral becomes

+ APh)f}],

fQ[B+Cq+DqZ]-IAdq=[

Q and n, calculated using the pressure Pf to determine the gas density and taking the sulfide l i q u i d d e n s i t y t o b e Pl = 5 0 0 0 k g m -3. A s o n e would expect, both the final pressure and the bulk density of the gas/liquid mixture increase with the amount of melting, and the values are l a r g e s t w h e n t h e v o i d s p a c e a v a i l a b l e is l e a s t (Figs. 1 a n d 2). A s i m i l a r p a t t e r n is f o u n d f o r o t h e r g a s m a s s f r a c t i o n s , n , in t h e p a r e n t a s t e r oid, the pressure increasing and the density dec r e a s i n g as n i n c r e a s e s . H o w e v e r , t h e d e p e n d e n c e o n n is n o t l i n e a r : if n i n c r e a s e s b y a f a c t o r o f 3, P f i n c r e a s e s t y p i c a l l y b y a f a c t o r o f 1.5, w h i l e Pb d e c r e a s e s b y o n l y 5 % . I t s h o u l d b e noted that in calculating the pressure rises in T a b l e 3, w e h a v e i g n o r e d t h e p o s s i b i l i t y t h a t s o m e of the gas phase (assumed to be predominantly n i t r o g e n a n d c a r b o n m o n o x i d e ) m a y d i s s o l v e in the Fe,Ni-FeS melt. The solubility of nitrogen in S - r i c h F e , N i m e l t s is k n o w n t o b e less t h a n 1 p p m at pressures of the order of 1 MPa and tempera-

then the inte-

Pf

dP

(8)

" ( Pi + APh)

w h e r e Pf is t h e f i n a l p r e s s u r e r e a c h e d w h e n t h e t o t a l v o l u m e f r a c t i o n o f s o l i d m e l t e d is Q. T h e integration can be carried out analytically. Writi n g f o r c o n v e n i e n c e E = [4BD - C 2 ] I/2, t h e f i n a l r e s u l t is Pf = (Pi + APh) +

2(A/E)

X {arctan[(ZDQ

+

115

C)/E] - arctan[C/E]}

(9) Table 3 shows final pressures Pf resulting from various degrees of partial melting, Q, for a range of values of the void fraction, f, in an asteroid c o n t a i n i n g a t o t a l g a s m a s s f r a c t i o n o f n = 1000 p p m . A l s o g i v e n is t h e b u l k d e n s i t y , Pb, o f t h e mixture of liquid and gas for each combination of TABLE 3

The final pressure, Pf, in the gas trapped in the void spaces of an asteroid containing n = 1000 ppm by mass gas after various degrees of partial melting, Q, to form a Fe,Ni-FeS cotectic liquid, f, the void space, is given as a volume fraction and Pf is given in MPa. The bulk density, Pb, of the mixture of liquid and gas bubbles, given in kg m -3, is also shown for each combination of Q and f Q 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24

f = 0.05

f = 0.10

f = 0.15

f = 0.20

f = 0.25

Pf

Pb

Pf

Pb

Pf

Pb

Pf

Pb

Pf

Pb

29.21 39.70 60.97 115.28 220.31 . . . . . . . . . . . . .

1099 2092 2991 3631 3892 -

12.28 13.98 16.24 19.36 23.94 31.29 44.80 75.70 159.48 255.36 . . . . . . . . . . . . .

526 1019 1510 1997 2479 2950 3399 3785 3991 4143 -

7.43 8.07 8.82 9.73 10.85 12.26 14.08 16.54 20.03 25.35 34.39 52.67 101.04 211.38 276.96

331 643 953 1265 1575 1884 2193 2500 2805 3106 3400 3674 3886 3974 4138

5.15 5.46 5.82 6.23 6.70 7.25 7.90 8.67 9.61 10.77 12.26 14.22 16.92 20.87 27.17 38.69 65.13 144.17 250.51

234 454 674 894 1113 1333 1552 1771 1991 2209 2427 2645 2862 3077 3288 3493 3677 3793 3871

3.82 4.00 4.20 4.43 4.68 4.96 5.27 5.63 6.04 6.51 7.06 7.72 8.51 9.48 10.69 12.27 14.38 17.37 21.91 29.58 44.99 86.77 200.78 273.23

176 340 505 670 835 1000 1165 1330 1495 1659 1824 1988 2153 2317 2481 2645 2808 2970 3131 3289 3440 3567 3630 3727

. . . . .

. . . . . . . .

. . . . . . . .

. . . . .

. . . .

. . . . . . . .

. . . . .

. . . . .

. . . . .

116

K. KEIL A N D L. WILSON

300t 1=0.0 7

t=0.1/

f=O,1/

1=02 /

f=02/

100

~_ 30

0

0.05

0.10

0.15 0.20 0.25 Q Fig. 1. Values of the final pressure, Pf, in the gas trapped in the void spaces of an asteroid containing n = 1000 ppm by mass gas after various degrees of partial melting, Q. The curves are labelled by f, the total void space in the asteroid expressed as a volume fraction of the whole body.

tures of the o r d e r of 1200 K [25], so only a negligible fraction o f an initial gas c o n t e n t o f 1000 p p m weight fraction of the a s t e r o i d w o u l d b e t a k e n up by several weight p e r c e n t of melt. W h e r e a s t h e r e a p p e a r to b e few d a t a on the

2.2. Growth of veins and migration of melt and gas into dikes

5000 /

f=0.10 .

f=0.15. 1-0 20

f

y;-

~" 3000 _E a_~ 2000 1000 1 0

solubility of C O in sulfide melts, its solubility in silicate melts is of t h e o r d e r of 20 p p m u n d e r t h e above p r e s s u r e a n d t e m p e r a t u r e conditions; t h e solubility is n o t likely to b e o r d e r s of m a g n i t u d e g r e a t e r t h a n this in sulfide melts, so that the s a m e a r g u m e n t applies. W e n o t e that t h e m e t a l a n d sulfide c o m p o s i tions we have q u o t e d e a r l i e r for the a s t e r o i d s c o n s i d e r e d in this p a p e r imply t h a t the m a x i m u m v o l u m e fraction o f m e l t i n g which occurs to p r o d u c e a m e t a l - s u l f i d e liquid is a b o u t 0.042. T a b l e 3 a n d Fig. 2 t h e n show t h a t for all void s p a c e values g r e a t e r t h a n a b o u t f = 0.052, a n d at even s m a l l e r values of f while m e l t i n g is not comp l e t e d , t h e b u l k density of t h e g a s / l i q u i d mixture g e n e r a t e d by the m e l t i n g p r o c e s s is less t h a n the density of the a s t e r o i d matrix. Thus, p r o v i d e d t h e gas, which will be p r e s e n t as b u b b l e s with initial sizes c o m p a r a b l e to those of t h e i n t e r g r a n u l a r voids in which it is p r e s e n t , stays d i s p e r s e d t h r o u g h o u t the liquid (this issue is a n a l y z e d b e low), the fluid p h a s e p r o d u c e d will b e b u o y a n t , d e s p i t e the fact t h a t the liquid a l o n e is m u c h d e n s e r t h a n the matrix.

I 0.05

I 0.10

I 0.15

I 0.20

0,25

Q Fig. 2. Values of the bulk density, Pb, in the mixture of gas bubbles and Fe,Ni-FeS liquid trapped in the void spaces of an asteroid containing n = 1000 ppm by mass gas after various degrees of partial melting, Q. The curves are labelled by f, the total void space in the asteroid expressed as a volume fraction of the whole body. The horizontal line marks the bulk density of the asteroid, 3500 kg m-3; gas/liquid mixtures with densities less than this value will rise buoyantly. The vertical line marks the volume fraction of melting ( ~ 0.042) expected on the basis of the initial bulk composition of the asteroid. Hence, all void spaces in excess of about f = 0.052 will lead to buoyant gas/liquid mixtures.

T h e r a n g e o f initial sizes of the m e l t veins p r o d u c e d in an a s t e r o i d should b e similar to t h e r a n g e of grain sizes f o u n d in m e t e o r i t e s j u d g e d to have h a d a similar p a r e n t b o d y ( ~ 1 /.Lm to ~ 1 m m in this case) [26]. A s m e l t i n g p r o g r e s s e s a n d liquid m i g r a t e s into void spaces, the effective initial vein size is m o r e n e a r l y e q u a l to the size o f a typical void, which is m o r e difficult to e s t i m a t e . H o w e v e r , s o m e c o n s t r a i n t s on likely void sizes, t o g e t h e r with the c o n s e q u e n c e s of t h e p r e s s u r e rise d u e to melting, can b e e x p l o r e d by c o n s i d e r ing the stresses g e n e r a t e d at the tips o f e l o n g a t e , p r e s s u r i z e d cavities. T h e i n t e r n a l p r e s s u r e in an e l o n g a t e cavity will cause cracking of t h e cavity tips, a n d c o n s e q u e n t g r o w t h of t h e cavity, if t h e stress intensity, K , at t h e tips is equal to t h e f r a c t u r e toughness, Kcrit , o f the m a t r i x [27]. F o r l a b o r a t o r y - s c a l e m e a s u r e m e n t s on s i l i c a t e - d o m i n a t e d rocks, Kcrit is o f t h e o r d e r o f 1 M P a m 1/2. A value ~ 100 times l a r g e r t h a n this is i n f e r r e d from studies o f t h e e m p l a c e m e n t o f k i l o m e t e r - s c a l e mafic dikes in t e r r e s t r i a l

EXPLOSIVE VOLCANISM AND THE COMPOSITIONS OF CORES OF DIFFERENTIATED ASTEROIDS

volcanoes [28], but the discrepancy is related to inelastic processes occurring near the dike tip and to the inability of the cooling melt to completely fill the dike tip [27]. In the case of millimeter-scale veins containing melt in the process of forming and at the temperatures in question, the lower, laboratory-scale value is much more likely to be applicable. The stress intensity K is given [27] by (10)

K = Pd al/2

where a is the vertical cavity half-length and Pd is the driving pressure, defined as the difference between the absolute internal fluid pressure Pf and the least principal stress in the surrounding matrix Pro" (It should be noted that in the above and all following equations we use a two-dimensional model of the cavities and veins; i.e., we disregard the influence of the longest horizontal dimension, which has a much smaller effect on the stress intensity than the intermediate length, the vertical dimension a [29]). For the pressure increases implied by eq. (9), the fluid pressure Pf is in some cases very much greater than the matrix pressure, Pm, even at the centers of asteroids as large as 100 km in radius, and so in the interiors of these bodies Pd is essentially equal to Pf. However, in other cases Pf is comparable to, or even less than, Pm" In Table 4 we give some values of the driving pressure Pd calculated for cavities situated at 20%, 50% and 80% of the radial distance from the center of asteroids with radii 10, 30 and 100 km, in each case for an asteroid gas content of

117

n = 1000 ppm and the same range of void space fractions, f , used in the previous section. It can be seen that Pd decreases with increasing asteroid size and with increasing void space fraction, and that in some cases the value calculated for Pd is negative. These negative values of Pd are not in themselves physically impossible, since they are simply the consequence of Pm being larger than Pf. However, such cases would lead to negative values of the stress intensity K in eq. (10), and the properties of elastic media are such that, under stress conditions where K is non-positive at either end of an elongate cavity, that end progressively pinches shut, decreasing the cavity length and increasing the internal pressure until K becomes exactly zero. Thus, none of the void fractions producing negative values of K should in fact have survived the pre-heating phase of the asteroid's history during which it was assembled from smaller bodies. Hence, for a fixed total gas content, a large asteroid must end its assembly phase with a relatively low total void space, and the gas in the voids must have a relatively high pressure, compared with conditions in a smaller asteroid. The largest driving pressure in Table 4 is Pd= 115.22 MPa, corresponding to a location near the surface of a small (10 km radius) body. The stress intensity produced by this pressure would be equal to a fracture toughness of 1 MPa m 1/2 for a half-length of 75 ~m. So any vein or cavity larger than this size and subject to this stress would grow spontaneously, increasing its length and decreasing its internal pressure until the stress in-

TABLE 4 The driving pressure, Pd, in the gas and liquid trapped in void spaces at three radial distances (in km) from the centers of asteroids with radii 10, 30 and 100 km, each containing n = 1000 ppm by mass gas, after melting to form a F e , N i - F e S cotectic liquid is complete. The matrix pressure, Pm, is given for each radial distance, f, the void space, is given as a volume fraction and the corresponding value of Pf, the final pressure after melting is complete, is given in MPa Radius = 10 km Radial distance: Pm:

f

ef

0.05 0.10 0.15 0.20 0.25

115.28 19.36 9.73 6.23 4.43

Radius = 30 km

Radius = 100 skm

2 0.16

5 0.13

8 0.06

6 1.48

15 1.16

24 0.55

20 16.43

50 12.84

80 6.16

115.11 19.19 9.57 6.07 4.26

115.15 19.23 9.60 6.10 4.30

115.22 19.28 9.67 6.17 4.37

113.80 17.88 8.25 4.75 2.96

114.12 18.20 8.58 5.08 3.27

114.72 18.80 9.18 5.68 3.87

98.85 2.93 -6.70 - 10.20 - 12.00

102.44 6.52 -3.10 - 6.60 - 8.41

109.12 13.19 3.57 0.07 - 1.73

118

K. K E I L A N D L. W I L S O N

tensity became equal to the fracture toughness. The corresponding cavity size at a location near the middle of a 100 km radius asteroid, where P~ = ~ 98 MPa, is 102 /J.m. For a vein equal in size to the largest likely grain size of 1 mm, the driving pressure required to cause vein growth would be about 30 MPa, and Table 4 shows that all of the veins with this size in asteroids where the void fraction f is initially less than about 0.08 will grow in this way, increasing the void space and decreasing the gas pressure. Thus, the onset of vein or cavity growth during the heating phase occurs earlier for the larger cavities and later for the smaller ones, and in all cases acts to decrease the final, maximum values of Pf, and hence Pd, at the expense of increasing the void space. The important net effect of this process that concerns us here is that the higher values given in Table 3 for the pressure in, and hence the density of, the fluids in veins are overestimates, and an even wider range of conditions than those mentioned earlier will lead to a net buoyancy of the trapped fluid. The general increase in the volume occupied by liquid as melting proceeds, and as some enlargement of individual cavities and melt veins occurs by cracking at their tips, will mean that eventually some coalescence events between initially nearby veins and cavities will occur. The joining of adjacent veins in this way in general leads to a reduction of the internal driving pressure. This can be seen by combining eq. (10) with an expression for the mean width, x, of a two-dimensional vein of vertical length 2a and uniform driving pressure Pd [e.g., 28,30]: x ~ 0.8Pda(1 - ~')/1~

(11)

where v is Poisson's ratio of the matrix and/~ its shear modulus. If two such veins, each oriented vertically and on the point of fracturing at their tips, coalesce into a single vein, the new vein length will be twice the initial length of the old veins and the new volume will also be doubled, and so the mean width will not change. Eq. (11) then implies that the driving pressure will decrease by a factor of 2. The new stress intensity at the enlarged crack tip will be K = (0.5P,0(2a) 1/2 = 0.707Pal al/2, i.e., ~ 70% of the initial value. Because the driving pressure decreases, there is no reason to expect further cracking of the vein

edges (in any direction--disregarding the dimension at right-angles to a and t is not important), and the above argument is self-consistent. This pressure reduction in the fluid inside the newly enlarged vein becomes significant when much smaller veins subsequently become connected to the large vein, because it causes viscous flow of fluid and previously trapped pockets of gas out of the small veins into the large one. Exactly this process was described by Sleep [31] for the tapping of partial melts by growing veins in ascending mantle material under mid-ocean ridges on Earth. The movement of melt out of a small vein into a larger one causes an increase in pressure and thickness in the large vein as long as its tips do not crack further. This can be seen by considering the case of a large vein with driving pressure Pl, half-length a I and thickness x I receiving melt from a smaller vein with driving pressure Ps, half-length a s and thickness x S to form a new vein with driving pressure Pn, half-length a . and thickness" x,. Equation (11) shows that the crosssectional area of a two-dimensional vein can be written as A = ( a x ) = ~ 0.8Pda:(1 - u)/I.~ = APd a 2, where the constant A is introduced for convenience. So we can write A l = AP~a 2 and A S = APsa 2. The smaller vein is assumed to join the larger one in such a way that the larger vein length does not change, so that a n = a~. Melt will flow from the smaller vein to the larger until the pressures within them are equal. Let some fraction y of the area (the equivalent, for a two-dimensional vein, of the volume) of the smaller vein be absorbed by the time this condition is reached, so that A n = A l + y A s. If we define y A s = a A l , where of necessity 0 < a < 1, we have A n = A l + 7As = A l + a A l = APna2n = APn a2 = (1 + a ) A P , a 2 So Pn = (1 + a ) P l and x n = Xl(1 -[- O/). Thus, the pressure in large veins will rise by a factor (1 + a), which must lie between 1 and 2, when melt flows into them and will decrease by a factor likely to be close to 2 whenever they grow by cracking, as we saw above. An equilibrium between these two growth modes will be reached at an internal pressure somewhere between the melt pressure in the

119

EXPLOSIVE VOLCANISM AND THE COMPOSITIONS OF CORES OF DIFFERENTIATED ASTEROIDS

smallest veins and the least principal stress in the matrix [31]. If we take the spread of driving pressure values in Table 4 and allow for the vein pressure reductions in the smaller void space cases due to vein growth during the heating and melting phases, as discussed above, the highest driving pressures expected, in cases where a few large veins are fed by many smaller veins joining them from the sides so that minimal vein lengthening occurs, are of the order of at least a few MPa. The lowest driving pressures, resulting from large numbers of vertical vein coalescence events, could be several orders of magnitude smaller. An elaborate Monte-Carlo type calculation of the pressure histories of many growing veins, allowing for a plausible range of initial vein sizes and stress conditions, would be needed to discover the most common final driving pressures. Such an analysis is beyond the scope of the present paper, but some preliminary calculations [L. Wilson and K. Keil, in prep.] suggest that final driving pressures of a few tens of kPa in cavities with half heights of at least many hundreds of meters (which therefore qualify to be called dikes) should be common in asteroids with radii in the 10-100 km range.

2.3. Migration of growing dikes In the Earth's interior, dikes growing to sufficiently great lengths can migrate under gravitational forces [32]. Dike migration takes place [33] when cracking occurs at one end of a dike (requiring that K >/Kcrit a t that end) and closure occurs at the other (requiring that at the tip K ~< 0). If a dike of length 2a contains a fluid of density Pb and is embedded in a matrix of density ps, Parfit [28] and Secor and Pollard [33] show that, if account is taken of the stress gradients implied by the differing densities of the matrix and the dike fluid, the stress intensities at the two ends of the dike are given by

K=Pa al/2 +- (a3/Z/Z)glPb - P s I

(12)

where g is the local acceleration due to gravity and the positive sign applies at whichever end of the dike is m i g r a t i n g - - t h e upper end if Pb < Ps and the lower end if Pb > Ps" Imposing K = 0 at the closing end of the dike, we find

Pa = ( a / Z ) g l p b - - P s I

(13)

and setting K

=

Kcrit at the opening end

gcrit=Pdal/2w(a3/2/2)glpb--Ps[

(14)

Solving these two equations we have

a = [Kcrit/(glpb --Ps I)] 2/3 V2

(15) ~1/3

Pd = ( 1 / 2 ) ( g l pb --Ps I " ~ c r i t /

(16)

Table 3 shows that, after completion of melting (Q = ~ 0.04) in an asteroid with n = 1000 p p m gas, the bulk density Pb of the gas/liquid mixture in the resulting veins may lie anywhere in the range 3600 to less than 1000 kg m 3, the exact value depending on the initial asteroid void space as modified by all of the processes discussed above. So with a matrix density ps = 3500 kg m -3, I Pb -- P s ] may lie anywhere in the range from slightly negatively buoyant through zero to 2500 kg m - 3 positively buoyant, with a high probability of the value being close to 1000 kg m -3 positively buoyant. The value of g at a distance R from the center of a spherical body of uniform density Ps is given by

g( R) = ( 4/3)rrGpsR

(17)

So at a distance of 5 km from the center of an asteroid of radius 10 km, g = ~ 0.005 m / s 2 and at a distance of 50 km from the center of an asteroid of radius 100 kin, g = ~ 0.05 m / s 2. Equations (15) and (16) then show that, in the smaller body, dike migration under gravitational stresses will occur when the dike half-height a = 3420 m and the driving pressure Pa = 8.6 kPa, whereas in the larger asteroid the required conditions are a = 737 m and Pd = 18.4 kPa. The exact values of these parameters will vary with radial position in an asteroid of a given size and will also depend (weakly) on the total asteroid gas content. Our preliminary calculations of the consequences of vein coalescence mentioned above suggest that these conditions can commonly be met, and so imply that dike migration should eventually occur in asteroids after enough coalescence events have taken place. Migration should have the effect of increasing the efficiency of coalescence, since a rising dike will have access to a population of smaller veins with which it would otherwise never have come into contact. A net positive buoyancy will only be maintained in veins or dikes containing a mixture of a

120

K. KEIL AND L. WILSON

dense F e , N i - F e S liquid and gas bubbles as long as the bubbles are disseminated throughout the liquid. The tendency of the bubbles will always be to rise to the top of the liquid. When segregation is complete, the stress distribution imposed on the walls of the crack will be significantly different from that present when the bubbles are uniformly distributed, and the first-order effect will be to encourage upward growth of the upper crack tip [29]. However, a situation can be envisaged in which the crack eventually pinches shut at some point along its length and two separate cracks are formed, the positively buoyant one tending to rise and the negatively buoyant one tending to migrate downwards. The picture is more complicated when veins are growing by mutual coalescence, for if gas has segregated to the top of a vein which then joins another vein from below, the gas pocket at the top of the original vein is now located in the middle of the composite vein and begins a new episode of migration. We explore the fate of rising gas bubbles by finding the rise speed u of a bubble with radius r containing gas with density pg through a liquid with density Pl and viscosity ~7 at a radial distance R from the center of an asteroid, where the acceleration due to gravity is g ( R ) given by eq. (17). Equating the viscous drag force to the upward buoyancy force

( 4 / 3 )7rr3( p, - pg) g = 67rrlru'

(18)

the terminal velocity reached after an initial acceleration period is u = [2rZ(p,-pg)g]/(9rt)

(19)

Table 5 shows some examples of u as a function of R for bubbles with radii of 10 ~zm to 1 mm, the likely initial range expected on the basis of the grain size distribution in the asteroid. Due to the low gravity values, these speeds can be very small, even though the viscosity of the F e , N i - F e S melt is also small ( ~ 10 -2 Pa s, [34]). However, two factors cause these calculated values to be upper limits on bubble rise speeds. First, although initial gas pocket sizes will be of the same order as the grain sizes, the consequence of the overall pressure rise (from Pi to Pf) in the gas

TA B LE 5 The equilibrium rise speeds u of gas bubbles with a range of radii r as a function of their radial distance R from the center of an asteroid. The corresponding values of g, the acceleration due to gravity, are shown for each value of R, and the time constant ~- given by eq. (21) is shown for each value of r Bubble radius, r = Time constant, ~- =

10/xm 2600 yrs

100 p~m 26 yrs

R (km)

g ( m m / s 2)

Bubble rise speed ( p , m / s )

3 10 30 100

2.9 9.8 29.3 97.8

0.032 0.11 0.33 1.09

3.2 10.9 32.6 108.7

1 mm 0.26 yrs

320 1090 3260 10870

will be to decrease the linear dimensions of bubbles by the cube root of the ratio Pf/Pi. Using values of Pi from Table 2 and P~ from Table 3 it is found that, for a wide range of values of partial melt fraction Q and total void space fraction f , this size reduction is by a factor close to 2 (rising to larger values only as f becomes much less than 5%). Second, at relatively large values of f or small values of Q, the volume fraction of gas in veins and pore spaces can be l a r g e - - u p to 50%. The resulting interactions between closely spaced bubbles cause the bulk fluid to have a higher viscosity than that of the liquid alone as regards the motion of any one bubble. The consequent factor by which the bubble rise speed decreases can be calculated from various theoretical treatments [35] by evaluating the gas and liquid volume proportions from Table 3 (with due allowance for the gas compression mentioned above) and is typically 2 - 5 for f ~ 0.1, rising to 10-20 for f ~ 0.25. This reduction depends only on f and Q, being independent of asteroid size, and implies that values of the rise speed u found from eq. (19) are overestimates by a factor which can range from 2 to 20. Because g varies with R, u will also vary with R in a given asteroid and, since we are concerned with gas bubbles migrating through possibly quite long (hundreds to thousands of meters) dikes, it is relevant to find the time required for a bubble to migrate a given distance. If we put u = d R / d t , where t is the time, and insert eq. (17) explicitly

E X P L O S IVE VOLCANISM AND T H E C O M P O S I T I O N S O F CORES O F D I F F E R E N T I A T E D A S T E R O I D S

for g(R) in eq. (19), we find

Ri

(20) where t' is the time required for the bubble to rise between radial distances R i and Rf. Integration of (20) gives

t'= ~" ln(Rf/Ri)

(21)

where ~- is a characteristic time scale given by

T=[(27rl)/[8rrr2(pl-Pg)OsG]]

(22)

and is the time required for a bubble to reach a radial distance e ~ 2.718 times its initial radial distance from the center of the asteroid. Table 5 includes the values of ~- corresponding to bubble radii in the range 10 /zm to 1 mm, which range from 2600 yrs to 3 months. We saw above that the larger dikes expected to form in 10 km radius asteroids may have lengths of several kilometers. Equation (22) shows that the time taken for a bubble to travel from, say a depth of 5 km to a point near the surface of a 10 km radius asteroid in a dike 5 km long is then 2 months for a 1 m m radius bubble and 1800 yrs for a 10 /xm radius bubble. In a 100 km radius asteroid the likely sizes of the larger dikes will range up to 1 km; the time taken for a bubble to move from, say a depth of 50 km to a depth of 49 km in such a body is then 2 days for a 1 m m radius bubble and 52 yrs for a 10/xm radius bubble. These time scales must be judged against two other factors. One is the time scale for significant melting to occur in asteroids of various sizes. Comparison of ages of chondrites and achondrites suggests that, although heating, melting, fractionation and cooling of differentiated asteroids may have taken place in less than about 10 )< 10 7 yrs, melt probably existed for only a few million years [36]. Therefore, it is very likely that volatiles will locally migrate to the tops of individual veins as they form and, thus, it will be the last stages of v e i n / s m a l l dike connections that will control the bubble distribution. The other important factor is the speed with which a migrating dike can move through the asteroid matrix. Treatments of the coupled problem of melt movement in a propagating dike [37]

121

show that the dike propagation speed is limited by the speed, u m, with which the fluid within the dike can move, given in the case of laminar motion (which is appropriate for all of the speeds found here) by

blm

=

[ g(Ps -- Pb)X2] /(12rl)

(23)

where x is the mean dike width. Equation (11) shows that the m e a n widths of the dikes used in the above example are 3.4 m m in the case of the 10 km radius asteroid and 1.6 m m in the case of the 100 km radius body. These widths are likely to be underestimates, since the approximate methods used to arrive at the lengths of these dikes take minimal account of small veins joining larger veins from the side, and so underestimate the internal driving pressure for a given dike length and, thus, also underestimate the width. Hence, the dike rise speeds deduced from eq. (23) for these examples (1.0 and 2.7 m m / s , respectively) are probably lower limits. The implication is that the times required by these dikes to travel vertical distances equal to their own lengths are at most 48 days and 3.2 days, respectively. Since these times are very close to the times required by the largest (1 m m radius) bubbles to rise completely through the liquid in these dikes, found above to be 60 days and 2 days, and since, as we saw earlier, these travel times are lower limits because of bubble crowding, it seems clear that the majority of the gas bubbles in a dike will not migrate far through the liquid on the time scale needed for the final stages of interconnection of small dikes into the final generation of dikes that rise to the asteroid surface. Thus, under most circumstances, the deductions we have made about the net positive buoyancy of dikes containing metal-sulfide liquids and gas bubbles are self-consistent. However, we also note that, in the larger of the above asteroids, the 1 m m bubble rise time (2 days) is less than the dike rise time (3.2 days), whereas in the smaller asteroid it is a little longer (60 and 48 days, respectively). Furthermore, this bubble rise time was calculated for movement from the 50 km depth to the 49 km depth in the large asteroid; if we carry out the calculation for a zone very near the surface, say from the 1 km depth to the surface itself, the rise time is halved to ~ 1 day, now only one third of the dike rise

122

time. Since these relatively faster gas bubble rise speeds will also encourage coalescence of smaller bubbles with larger ones overtaking them, thus increasing their rise speeds even further, it seems very likely that we have identified the reason why larger asteroids suffered less S loss than smaller ones (Table 1): Gas segregation at the tops of near-surface dikes occurred much more commonly in the larger bodies, and this resulted in elimination of net buoyancy more commonly in larger than in smaller asteroids. Table 1 suggests that a rapid change in average buoyancy occurred at an asteroid radius near 80 km. We cannot yet show in detail that our mechanism is consistent with this, but expect to be able to do so when the results of the Monte Carlo simulations of dike sizes, internal pressures and growth rates mentioned earlier have been completed.

2.4. Discharge of melt at the surface Whenever the upper tip of a growing or migrating dike intersects the surface of an asteroid, some discharge of melt must occur. Initially, the melt will accelerate upwards at all levels in the dike at a rate determined by the local pressure gradient. The pressure gradient will evolve with time in a way controlled by the passage of an expansion wave downwards from the surface. As the expansion wave engulfs each volume element of fluid in the dike, the expansion of the gas in the bubbles will cause upwardacceleration of the liquid. Eventually the fractional volume of gas will exceed some critical value ( ~ 75% [38]) beyond which the liquid disrupts into droplets with sizes similar to those of the gas bubbles, leading to a pyroclastic eruption at the surface in the manner described by Wilson and Keil [8]. The relaxation of the stresses holding the dike open will reinforce this process and, unless a significant tensile stress exists in the near-surface layers of the asteroid, the dike will close progressively from the bottom upwards as the fluid escapes [32], so that all of the liquid is eventually discharged. The issue of how much of the erupted liquid emerges through the surface vent with a velocity greater than the escape velocity from the asteroid hinges entirely on the size of the asteroid, which determines the escape velocity, and the gas con-

K. K E I L A N D L. W I L S O N

tent of the melt, which determines the eruption speed. The calculations of Wilson and Keil [8] show that a gas content of 300-500 p p m in the liquid would lead to eruption velocities exceeding the escape speed on 30 km radius asteroids but not on 100 km radius bodies. This gas content in the liquid would require a total asteroid gas content of only about 20-30 ppm, assuming that all of the gas was transferred into the growing veins and dikes and that none of it was effectively lost by migrating to the top of the final generation of dikes reaching the surface. 3. Depletion of magmatic iron meteorite groups in trace elements A number of authors have noted the progressive depletion in relatively volatile and siderophile trace elements such as Co, P, Au, As, Cu, Ga, Sb, Ge and Zn from, for example, magmatic iron meteorite groups IIAB to I I I A B to I V A to IVB (for a summary, see [39]). Although these meteorite groups show an analogous progressive depletion in initial magma sulfur contents (Table 1), it appears that the trace element depletions have not resulted from the removal of F e , N i - F e S cotectic liquid during pyroclastic volcanism, which we propose is responsible for the depletion in sulfur. Most of these trace elements are strongly siderophile and, for S-rich liquids, have solid m e t a l / l i q u i d metal distribution coefficients greater than 1 and, thus, would be expected to be retained in the remaining solid metal and not be removed with the F e , N i - F e S liquid [40]. Rather, the trace element contents of the magmatic iron meteorites appear to have been established during condensation from the solar nebula, because the depletions are correlated with condensation temperature [39,41]. However, the depletion of the magmatic iron meteorite magmas in initial sulfur appears not to be a nebular effect. Sulfur has the lowest condensation temperature of all the elements considered by Scott [39], but is less depleted by factors of about 10-1000 than some of the trace elements that have higher condensation temperatures, such as Ga, Sb, Ge and Zn. We therefore conclude that trace element and sulfur depletions in magmatic iron meteorite groups are largely decoupled from one another, and that the depletion in sulfur is due to removal

E X P L O S I V E V OL C AN IS M A N D T H E C O M P O S I T I O N S O F CORES OF D I F F E R E N T I A T E D A S T E R O I D S

of F e , N i - F e S partial melt by pyroclastic volcanism, w h e r e a s the trace e l e m e n t d e p l e t i o n s a n d t r e n d s seem to have b e e n established d u r i n g n e b ular c o n d e n s a t i o n .

4. Summary W e have discussed the S d e p l e t i o n of m e m b e r s of the eleven groups of iron m e t e o r i t e s which a p p e a r to be derived from the fractionally crystallized m e t a l cores of d i f f e r e n t i a t e d asteroids. W e have shown that a p p r o p r i a t e l y S - d e p l e t e d magmas could have b e e n p r o d u c e d if some small fraction of the first partial melt in these asteroids, a S-rich F e , N i - F e S cotectic liquid, was r e m o v e d by explosive pyroclastic volcanism. A l t h o u g h the initial cotectic melts w o u l d have b e e n negatively b u o y a n t relative to their p a r e n t bodies, we have shown that the p r e s e n c e of a small a m o u n t of gas t r a p p e d in t h e m w o u l d have c o m m o n l y led to a n e t positive b u o y a n c y of the b u l k fluid. T h e pressure rise in the g a s - l i q u i d mixture o n m e l t i n g would have led to the f o r m a t i o n of growing veins a n d cracks which would e v e n t u a l l y i n t e r c o n n e c t to form dikes r e a c h i n g the surface, allowing partial loss of the b u o y a n t fluids with a n efficiency which decreases with i n c r e a s i n g asteroid size, thus m i m i c k i n g the t r e n d of S d e p l e t i o n seen in the meteorites.

Acknowledgements W e t h a n k H. Haack, E . R . D . Scott, D. M u e n o w a n d E.A. Parfitt for v a l u a b l e discussion. W e are also grateful for the c o m m e n t s of an a n o n y m o u s reviewer a n d for those of J o h n W o o d , who drew o u r a t t e n t i o n to gas solubility, a n d of J o h n I_onghi, who drew o u r a t t e n t i o n to the significance of gas b u b b l e crowding a n d siderophile trace e l e m e n t d i s t r i b u t i o n coefficients. This work was s u p p o r t e d in part by the N a t i o n a l A e r o n a u t i c s a n d Space A d m i n i s t r a t i o n , grants N A G 9-454 a n d N A G W 3281 (K. Keil, P.I.). This is P l a n e t a r y G e o s c i e n c e s P u b l i c a t i o n 724 a n d School of O c e a n a n d E a r t h Science a n d T e c h n o l o g y P u b l i c a t i o n 3162.

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