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The accumulation of chondritic material
EARTH AND P L A N E T A R Y
SCIENCE LETTERS 1 (1966) 93-96. NORTH-HOLLAND PUBL. COMP., AMSTERDAM
ACCUMULATION
OF CHONDRITIC
MATERIAL
A . G. W . CAMERON Institute for Space Studies, Goddard Space Flight Center, NASA, New York, N. Y., USA and Belfe~" Graduate School of Science, Yeshiva University, New York, N . Y . , USA
Received 12 April 1966
Whipple's suggestion that chondrules are melted in lightning flashes is examined in the context of models of the primordial solar nebula previously proposed by the writer. It is shown that solid bodies in the chondrule size range can be melted, but much larger bodies cannot be melted and much smaller bodies will be vaporized. Accumulation mechanisms involving electrostatic acceleration and gas motions are discussed.
Whipple [1] has r e c e n t l y s u g g e s t e d that lightning d i s c h a r g e s may play a r o l e in the f o r m a t i o n of c h o n d r u l e s in the p r i m o r d i a l s o l a r nebula. It i s the p u r p o s e of this note to develop this i d e a s e m i q u a n t i t a t i v e l y within the f r a m e w o r k of the p r e v i o u s d i s c u s s i o n by the w r i t e r of the f o r m a tion of the s o l a r nebula [2, 3]. In the p r e v i o u s d i s c u s s i o n it was noted that c o n s e r v a t i o n of an g u la r m o m e n t u m in the c o l l a p s e and f r a g m e n t a t i o n of an i n t e r s t e l l a r gas cloud should r e s u l t in the f o r m a t i o n of a p u r e n e b u l a r disk without a c e n t r a l s t e l l a r body in hyd r o s t a t i c e q u i l i b r i u m [3]. It now a p p e a r s that the m a g n e t i c fi el d t r a p p e d in this nebula will be weak [4]. The w r i t e r p r e s e n t l y b e l i e v e s that the init i al d i s s i p a t i o n of the disk will r e s u l t f r o m the v i s c o s i t y a s s o c i a t e d with t u r b u l e n c e as s u g g e s t ed by Von W e i z s ~ c k e r [5]. In this d i s s i p a t i o n the i n n e r p a r t s of the nebula m o v e i n w a r d s to f o r m the sun and the o u t e r p a r t s m o v e outwards to c o n s e r v e an g u l ar m o m e n t u m . To allow f o r m a s s l o s s f r o m the sun in the T T a u r i s ta g e and f o r the m a s s in the o u t e r p a r t s of the nebula e v e n t u ally d i s s i p a t e d by the s o l a r wind, we s h a ll a s s u m e that the n e b u l a r disk contains two s o l a r
eddies which a r e set up by the d y n a m i c a l i r r e g u l a r i t i e s of the co l l ap se. In this note we s h a l l be i n t e r e s t e d in p r o b a b l e conditions in the p r i m o r d i a l nebula in the r e g i o n in which the m e t e o r i t e p a r e n t b o d i e s probably f o r m e d : let us say in the v i c i n i t y of 2 a s t r o n o m i c a l units. In [3] it w as pointed out that n e a r l y the s a m e i n i t i a l d en si t y d i s t r i b u t i o n s in the c o l l a p s ing i n t e r s t e l l a r cloud could give r i s e to two quite d i f f e r e n t density d i s t r i b u t i o n s in the n e b u l a r disk: a u n i f o r m l y r o t a t i n g d i s t r i b u t i o n and an ax i al l y condensed distribution. F o r the conditions a s s u m e d h e r e , the c o r r e s p o n d i n g r a n g e of s u r f a c e d e n s i t i e s in the n e b u l a r disk is (1-4) x 10 4 g / c m 2, and the r o t a t i o n a l v e l o c i t i e s lie in the r a n g e of 10 5 to 10 6 c m / s e c . Both of t h e s e r a n g e s of n u m b e r s would be s o m e w h a t l o w e r e d in the i n i t i a l disk due to the p r e s e n c e of the high t h e r m a l and turbulent e n e r g i e s d i s c u s s e d above. The ax i al l y condensed disk has the h i g h e r s u r f a c e density and r o t a t i o n a l v c : c c i t y , r ' r o m ref. [2] we note that the p r e s s u r e in the plane of the disk is approximately
masses.
w h e r e a is the s u r f a c e density in g / c m 2. Hence o u r i n t e r e s t i n g r an g e of p r e s s u r e s is 10 -5 to 10 -4 a t m o s p h e r e s , independent of t e m p e r a t u r e . The d en si t y of the gas i s a p p r o x i m a t e l y
The c o l l a p s e of the i n t e r s t e l l a r cloud t a k e s p l a c e n e a r l y in f r e e fall, so that the f o r m a tion of the p r i m o r d i a l n e b u l a r disk is a d y n a m i c a ll y v i o l en t p r o c e s s . A r g u m e n t s s i m i l a r to those given p r e v i o u s l y [2] then i n d i c a t e that the hydrogen content of the disk will i n i t i a l l y be ioni z e d to a d i s t a n c e of the o r d e r of 5 a s t r o n o m i c a l units. A c o m p a r a b l e amount of e n e r g y may be e x p e c t e d to be s t o r e d i n i t i a l l y in l a r g e t u r b u l e n t
P = 1 . 3 x 10 -13 a2 a t m o s p h e r e s ,
p = 4 x 10 -15 ~ 2 / T g / c m 3 , o r within an o r d e r of magnitude of 10 -6 g / c m 3 f o r t y p i c a l cooling t e m p e r a t u r e s in the following discussion. If we a s s u m e that the n eb u l ar disk e m i t s en -
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e r g y like a b l a c k body, then the t i m e t r e q u i r e d to c o o l to a t e m p e r a t u r e T (effectively f r o m a r bitrarily large initial temperature) is t-
knott - - 25err T3
7 . 3 x 1011 ~ s e c ~T 3
'
w h e r e k, N o and ~r a r e the Boltzmann, A v o g a d r o and Stefan r a d i a t i o n c o n s t a n t s , and /~ i s the m e a n m o l e c u l a r weight. F o r the conditions d e s c r i b e d above, the t i m e r e q u i r e d to cool into the r a n g e (1-2) × 103 OK i s 106 to 107 s e c (a few months). In t h i s r a n g e of t e m p e r a t u r e the f i r s t c h e m i c a l c o n d e n s a t i o n s ( m o s t l y i r o n and m a g n e s i u m s i l i c a t e ) will o c c u r , and it i s the r e s u l t i n g d u s t cloud which w i l l e n s u r e that an a p p r o x i m a t e b l a c k body r a d i a t i o n p r o c e s s w i l l t a k e p l a c e . The m e c h a n i s m of c o n d e n s a t i o n w i l l r e s e m b l e d r o p l e t f o r m a t i o n in a cloud c h a m b e r . If a cloud c h a m b e r i s expanded v e r y slowly, a few l a r g e d r o p l e t s a r e f o r m e d . Rapid e x p a n s i o n p r o d u c e s finely d i v i d e d d r o p l e t s . If the n e b u l a r d i s k i s opaque to photons with e n e r g y of o r d e r kT, a s will be the c a s e when dust i s p r e s e n t , then t h e r e w i l l b e a t e m p e r a t u r e g r a d i e n t between the c e n t r a l p l a n e and the e m i t t i n g s u r f a c e , and with t u r b u l e n c e p r e s e n t the gas w i l l be c y c l e d through a r a n g e of t e m p e r a t u r e s . Hence a c o n d e n s a t i o n of m o d e r a t e l y finely divided s o l i d p a r t i c l e s (of s o m e t h i n g like m i c r o n size) m a y b e e x p e c t e d when the motion of the gas c a u s e s it to cool upon expansion. The c o n d e n s a t i o n s w i l l take p l a c e upon the ions p r o d u c e d by the d i s i n t e g r a t i o n of r a d i o a c t i v e s u b s t a n c e s that m a y b e p r e s e n t , such a s 40K and 26A1. When the gas i s r e c o m p r e s s e d , the m o r e v o l a t i l e s u b s t a n c e s in the p a r t i c l e s a r e l i k e l y to be e v a p o r a t e d . Hence a v e r y c o m p l e x h i s t o r y of the f o r m a t i o n of s o l i d p a r t i c l e s i s to b e expected. L e t u s c o n s i d e r the s i t u a t i o n when the n e b u l a r t e m p e r a t u r e h a s f a l l e n low enough so that the solid particles are stable against evaporation. R a d i o a c t i v i t y will continue to f o r m ion p a i r s in the gas. B e c a u s e of t h e i r low m a s s , the e l e c t r o n s have a g r e a t e r m o b i l i t y in the gas, and they will c o l l e c t on the c o n d e n s e d p a r t i c l e s m o r e r a p i d l y than w i l l the ions. At t h i s point we invoke a g e n e r a l p r i n c i p l e d i s c u s s e d in t e r m s of cloud p h y s i c s by Colgate [6]. T u r b u l e n c e in the gas w i l l tend to p r o d u c e s e p a r a t i o n of the c h a r g e , so that t h e r e i s a tendency to a p p r o a c h an e q u a l i t y between the t u r b u l e n t e n e r g y d e n s i t y ½ ~ t (where v t i s a m e a n t u r b u l e n t velocity) and the e n e r g y d e n s i t y E2/8~ of the e l e c t r i c f i e l d r e s u l t i n g f r o m the c h a r g e s e p a r a t i o n . H o w e v e r , the e l e c t r o s t a t ic e n e r g y d e n s i t y will be l i m i t e d by the e l e c t r i c
b r e a k d o w n of the gas, which w i l l p r o d u c e l i g h t ning f l a s h e s . In a lightning d i s c h a r g e a p l a s m a column i s c r e a t e d having a r a d i u s of o r d e r of m a g n i t u d e one c e n t i m e t e r . Since the p r i n c i p a l i o n i z e d c o n s t i t u e n t i s hydrogen, the p l a s m a t e m p e r a t u r e w i l l be of o r d e r 104 OK o r m o r e . If lightning d i s c h a r g e s r e p r e s e n t one p r i n c i p a l m e c h a n i s m for the d i s s i p a t i o n of t u r b u l e n t e n e r g y , then we have s e e n that the e n e r g y r e l e a s e by t h i s m e c h a n i s m should be sufficient to enable any given e l e m e n t of the gas to p a r t i c i p a t e in about one lightning d i s c h a r g e , for the r e g i o n of i n t e r e s t . Colgate [6] h a s a l s o pointed out that s m a l l e l e c t r i f i e d p a r t i c l e s (or d r o p l e t s ) in clouds w i l l b e a c c e l e r a t e d by the e l e c t r o s t a t i c f i e l d s much m o r e s t r o n g l y than by g r a v i t y , and hence the e l e c t r i c f i e l d s w i l l v e r y g r e a t l y enhance the r a t e of d r o p c o a l e s c e n c e . T h i s i s b e c a u s e the d i f f e r ent c h a r g e to m a s s r a t i o s of the d r o p l e t s w i l l p r o d u c e d i f f e r e n t v e l o c i t i e s in a given e l e c t r i c field, and the d r o p l e t s w i l l have an enhanced r a t e of c o l l i s i o n with one another. T h i s c o a l e s c e n c e p r o c e s s w i l l be of much g r e a t e r r e l a t i v e i m p o r t a n c e in the p r i m o r d i a l n e b u l a owing to the s m a l l g r a d i e n t s of g r a v i t a t i o n a l f i e l d s t h e r e . H o w e v e r , it should be noted that p a r t i c l e s of l a r g e r m a s s (~ 1 m m in size) will r e c e i v e only s m a l l a c c e l e r a t i o n s ; hence they will r a r e l y c o l l i d e with one another. They w i l l m a i n l y grow by a c c r e t i o n of much s m a l l e r p a r t i c l e s . The p o s s i b i l i t y of an e l e c t r o s t a t i c a c c u m u l a t i o n p r o c e s s has p r e v i o u s l y b e e n pointed out by Wood [7]. We c o n s i d e r next what w i l l happen when one of t h e s e c o m p o s i t e a c c u m u l a t e d p a r t i c l e s i s caught in a lightning d i s c h a r g e . Whipple [1] h a s s u g g e s t e d that the p l a s m a pinch p r o d u c e d by the d i s c h a r g e w i l l c o m p r e s s and liquify t h e s e p a r t i c l e s . H o w e v e r , the c h a r g e to m a s s r a t i o of the p a r t i c l e s i s much s m a l l e r than f o r p l a s m a ions; hence the pinch a c c e l e r a t i o n w i l l a c t only m i l d l y on the c o n d e n s e d p a r t i c l e s . Whipple f u r t h e r s u g g e s t e d that the c o n d e n s e d p a r t i c l e s which would b e a c t e d upon by the lightning c o n s i s t e d of low d e n s i t y d u s t b a l l s , p r e s u m a b l y like t h o s e of the small meteors produced as cometary debris. H o w e v e r , I would e x p e c t that the t e m p e r a t u r e c y c l i n g a c c o m p a n y i n g t u r b u l e n c e would l e a d to fairly compact structures. In the lightning d i s c h a r g e a p l a s m a m u s t b e c r e a t e d . If half the h y d r o g e n i s i o n i z e d u n d e r o u r t y p i c a l d e n s i t y conditions (10 -6 g / c m 3 ) , then p l a s m a k i n e t i c t e m p e r a t u r e s in the v i c i n i t y of 1.5 × 104 OK w i l l b e p r o d u c e d , a c c o r d i n g to the Saha i o n i z a t i o n equation. We a r e i n t e r e s t e d in the t r a n s p o r t of e n e r g y to the c o n d e n s e d p a r t i -
THE ACCUMULATION OF CHONDRITIC MATERIALS c l e s by the i m p a c t of e l e c t r o n s and ions in the p l a s m a . The electrons have the greater mobility
because of their small mass, and hence they will i m p a c t m o s t r a p i d l y on a c o n d e n s e d p a r t i c l e . T h i s w i l l build up a s t r o n g n e g a t i v e c h a r g e on the p a r t i c l e , which will inhibit the i m p a c t of f u r t h e r e l e c t r o n s but a c c e l e r a t e the i m p a c t of ions. Hence the heating r a t e i s d e t e r m i n e d by the m o bility of the ions. We s h a ll s e e below that the he a ti n g is independent of the p l a s m a density, so that we s h al l i g n o r e the c h a n g e s in this density r e s u l t i n g f r o m the i n i t i a l pinch and l a t e r expansion p h a s e s of the p l a s m a column. We s h a ll a l s o i g n o r e heating by the hot n e u t r a l gas a f t e r r e combination has o c c u r r e d , s i n c e m i c r o t u r b u l e nce is likely to c o n v e c t this gas away f r o m the condensed p a r t i c l e s . We take as a c h a r a c t e r i s t i c r e c o m b i n a t i o n t i m e that in which the n u m b e r of ions d e c r e a s e s by a f a c t o r e. Hence this t i m e is 1
T-- - - , Oln e
w h e r e a is the r e c o m b i n a t i o n c o e f f i c i e n t f o r hyd r o g e n and n e is the e l e c t r o n n u m b e r density. T he n u m b e r of p a r t i c l e s ( e l e c t r o n s plus ions) s t r i k i n g unit c r o s s s e c t i o n a l a r e a in t i m e ~ is o n e - t h i r d of the flux of e l e c t r o n - i o n p a i r s , o r ~neVT. The a v e r a g e e n e r g y p e r p a r t i c l e is ~kT, and we t a k e l t h e c o r r e s p o n d i n g a v e r a g e v e l o c i t y v = (3kT/m)~. R e c o m b i n a t i o n will take p l a c e on the p a r t i c l e s u r f a c e , and we n e g l e c t the e n e r g y r e m o v e d by e v a p o r a t i o n of the r e s u l t i n g h y d r o gen atoms. We take the r e c o m b i n a t i o n c o e f f i c i e n t f o r hydrogen as [8]: a ~ 4.7 × 10 -11 T -½ c m 3 / s e c . F o r the condensed p a r t i c l e b e i n g heated we take density Pc, heat c a p a c i t y C, and r a d i u s r . Hence the h eat i n g of the p a r t i c l e will be
(~ hey T)(~ kT)(4~r 2) AT
(~ ~ocr3)C
Following K r i n o v [ 9 ] , we take the heat c a p a c i t y C = 7.5 × 106 e r g / g OK. H e n c e the t e m p e r a t u r e r i s e is AT = 1.8 × 10 -6
T2/pc r .
We v e r i f y that the heating is independent of the p l a s m a density, although not of the t e m p e r a t u r e . The heating is i n v e r s e l y p r o p o r t i o n a l to the d i m e n s i o n s of the condensed p a r t i c l e . Let us find the d i m e n s i o n s of a p a r t i c l e which
95
can be raised to the meltin~ ~irLt. Chondrules melt at about 1800OK or somewhat more. Solid c o n d e n s a t i o n of i r o n and m a g n e s i u m s i l i c a t e will occur n e a r 1300°K [10]; hence we wish Z~T ~ 1000OK, allowing f o r cooling of the nebula b e tween the t i m e s of p a r t i c l e condensation and e x p o s u r e to the lightning stroke. We take Pc = 3.4 g / c m 3, t y p i cal of c h o n d r i t i c m a t e r i a l . Hence r ~ 0.12 cm. T h i s is a t y p i cal chondrule si ze. P a r t i c l e s much l a r g e r than this will not be m e l t e d , and p a r t i c l e s much s m a l l e r a r e likely to be v a p o r ized. T h i s p i c t u r e a p p e a r s capable of explaining many g e n e r a l p r o p e r t i e s of chondritic m a t e r i a l . F o l l o w i n g melting, a chondrule will cool rapidly, a condition n e c e s s a r y f o r the production of g l a s s which o c c u r s in s o m e c h o n d r u l e s [10]. Following cooling, f u r t h e r a c c u m u l a t i o n o f s m a l l p a r t i c l e s on the e x t e r i o r of c h o n d r u l e s will r e s u l t f r o m the e l e c t r o s t a t i c a c c e l e r a t i o n p r o c e s s d i s c u s s e d p r e v i o u s l y ; the r e s u l t i n g a c c u m u l a t e d p a r t i c l e s a r e likely to be m o r e v o l a t i l e , to contain m o s t of the e l e m e n t s in the p e r i o d i c table, and to f o r m the m a t r i x p a r t of the u l t i m a t e chondritic m a t e r i a l . T h i s is c o n s i s t e n t with the hypothesis of A n d e r s [11] that c h o n d r i t i c m a t e r i a l is a m i x t u r e of v a r i a b l e p r o p o r t i o n s of m a t e r i a l condensed at high t e m p e r a t u r e and m a t e r i a l condensed at low t e m p e r a t u r e . A c c u m u l a t i o n of the c h o n d r u l e s plus m a t r i x m a t e r i a l into l a r g e r bodies probably depends m o s t l y on the e f f e c t s of t u r b u l e n c e in the gas. V a r i a t i o n s in abundances will r e s u l t both f r o m s e l e c t i v e v o l a t i l i z a t i o n in the lightning f l a s h e s and f r o m e l e c t r o s t a t i c a c c e l e r a t i o n of co n d en sed m a t e r i a l away f r o m the point of condensation. M i n e r a l s c h a r a c t e r i s t i c of widely diff e r e n t f o r m a t i o n conditions will e x i s t adjacent to one another. T h i s d i s c u s s i o n has f o c u s s e d on conditions i n the p r i m o r d i a l s o l a r nebula in the v i c i n i t y of the a s t e r o i d belt. At s m a l l e r r a d i a l d i s t a n c e s s o m e c h a r a c t e r i s t i c d i f f e r e n c e s will o c c u r . The s u r f a c e density of the nebula is l a r g e r ; the r a t e of co o l i n g is s m a l l e r ; the t u r b u l en t e n e r g y density is g r e a t e r ; and the p l a s m a t e m p e r a t u r e p r o d u c e d in lightning f l a s h e s will be g r e a t e r . Hence chond r u l e s will be l a r g e r and can be r e p e a t e d l y melted. It would be d e s i r a b l e to s e e if s e l e c t i v e e v a p o r a t i o n of s i l i c a t e s f r o m c h o n d r u l e s can o c c u r in lightning f l a s h e s . The s l o w e r gas cooling and f a s t e r gas m o t i o n s will lead to m o r e r ap i d a c c u m u l a t i o n of l a r g e r bodies; h en ce the l a r g e r b o d i e s will contain s m a l l e r amounts of the m o r e v o l a t i l e m a t e r i a l s . The l a r g e r m a s s f r a c t i o n of i r o n and s m a l l e r m a s s f r a c t i o n of p o t a s s i u m in
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t h e e a r t h r e l a t i v e to c h o n d r i t e s a p p e a r s c o n s i s tent with this picture. I w i s h to t h a n k F. L. W h i p p l e , J . A . Wood, E. Anders, S.A. Colgate, and P. Thaddeus for valua b l e d i s c u s s i o n s c o n c e r n i n g s o m e of t h e p h y s i c a l and chemical processes discussed in this paper.
REFERENCES [1] F.L. Whipple, A suggestion as to the origin of chondrules, p r e p r i n t (1966). [2] A . G . W . Cameron, The formation of the sun and planets, I c a r u s 1 (1962) 13.
[3] A. G. W. Cameron, F o r m a t i o n of the s o l a r nebula, I c a r u s 1 (1963) 339. [4] G.W. Pneuman and T. P. Mitchell, Evolution of the s o l a r magnetic fie!d~ I c a r u s 4 (1965) 494. [5] C. F. Von Weizs~cker, Ueber die Entstehung des P l a n e t e n s y s t e m s , Z. Astrophysik 22 (1944) 319. [6] S. A. Colgate, Enhanced drop c o a l e s c e n c e by e l e c t r i c fields in equilibrium with turbulence, p r e p r i n t (1965). [7] J.A.Wood, Chondrutes and the origin of t e r r e s t r i a l planets, Nature 194 (1962) 127. [8] C. W. Allen, Astrophysical quantities (The Athlone P r e s s , University of London, 1963). [9] E. L. Krinov, P r i n c i p l e s of m e t e o r i t i c s ( P e r g a m o n P r e s s , Oxford, 1960). [10] J . A . Wood, On the origin of chondrules and chondrites, I c a r u s 2 (1963) 152. [11] E. Anders, Origin, age, and composition of m e t e orites, Space Sci. Rev. 3 (1964) 583.
SCIENCE LETTERS 1 (1966) 93-96. NORTH-HOLLAND PUBL. COMP., AMSTERDAM
ACCUMULATION
OF CHONDRITIC
MATERIAL
A . G. W . CAMERON Institute for Space Studies, Goddard Space Flight Center, NASA, New York, N. Y., USA and Belfe~" Graduate School of Science, Yeshiva University, New York, N . Y . , USA
Received 12 April 1966
Whipple's suggestion that chondrules are melted in lightning flashes is examined in the context of models of the primordial solar nebula previously proposed by the writer. It is shown that solid bodies in the chondrule size range can be melted, but much larger bodies cannot be melted and much smaller bodies will be vaporized. Accumulation mechanisms involving electrostatic acceleration and gas motions are discussed.
Whipple [1] has r e c e n t l y s u g g e s t e d that lightning d i s c h a r g e s may play a r o l e in the f o r m a t i o n of c h o n d r u l e s in the p r i m o r d i a l s o l a r nebula. It i s the p u r p o s e of this note to develop this i d e a s e m i q u a n t i t a t i v e l y within the f r a m e w o r k of the p r e v i o u s d i s c u s s i o n by the w r i t e r of the f o r m a tion of the s o l a r nebula [2, 3]. In the p r e v i o u s d i s c u s s i o n it was noted that c o n s e r v a t i o n of an g u la r m o m e n t u m in the c o l l a p s e and f r a g m e n t a t i o n of an i n t e r s t e l l a r gas cloud should r e s u l t in the f o r m a t i o n of a p u r e n e b u l a r disk without a c e n t r a l s t e l l a r body in hyd r o s t a t i c e q u i l i b r i u m [3]. It now a p p e a r s that the m a g n e t i c fi el d t r a p p e d in this nebula will be weak [4]. The w r i t e r p r e s e n t l y b e l i e v e s that the init i al d i s s i p a t i o n of the disk will r e s u l t f r o m the v i s c o s i t y a s s o c i a t e d with t u r b u l e n c e as s u g g e s t ed by Von W e i z s ~ c k e r [5]. In this d i s s i p a t i o n the i n n e r p a r t s of the nebula m o v e i n w a r d s to f o r m the sun and the o u t e r p a r t s m o v e outwards to c o n s e r v e an g u l ar m o m e n t u m . To allow f o r m a s s l o s s f r o m the sun in the T T a u r i s ta g e and f o r the m a s s in the o u t e r p a r t s of the nebula e v e n t u ally d i s s i p a t e d by the s o l a r wind, we s h a ll a s s u m e that the n e b u l a r disk contains two s o l a r
eddies which a r e set up by the d y n a m i c a l i r r e g u l a r i t i e s of the co l l ap se. In this note we s h a l l be i n t e r e s t e d in p r o b a b l e conditions in the p r i m o r d i a l nebula in the r e g i o n in which the m e t e o r i t e p a r e n t b o d i e s probably f o r m e d : let us say in the v i c i n i t y of 2 a s t r o n o m i c a l units. In [3] it w as pointed out that n e a r l y the s a m e i n i t i a l d en si t y d i s t r i b u t i o n s in the c o l l a p s ing i n t e r s t e l l a r cloud could give r i s e to two quite d i f f e r e n t density d i s t r i b u t i o n s in the n e b u l a r disk: a u n i f o r m l y r o t a t i n g d i s t r i b u t i o n and an ax i al l y condensed distribution. F o r the conditions a s s u m e d h e r e , the c o r r e s p o n d i n g r a n g e of s u r f a c e d e n s i t i e s in the n e b u l a r disk is (1-4) x 10 4 g / c m 2, and the r o t a t i o n a l v e l o c i t i e s lie in the r a n g e of 10 5 to 10 6 c m / s e c . Both of t h e s e r a n g e s of n u m b e r s would be s o m e w h a t l o w e r e d in the i n i t i a l disk due to the p r e s e n c e of the high t h e r m a l and turbulent e n e r g i e s d i s c u s s e d above. The ax i al l y condensed disk has the h i g h e r s u r f a c e density and r o t a t i o n a l v c : c c i t y , r ' r o m ref. [2] we note that the p r e s s u r e in the plane of the disk is approximately
masses.
w h e r e a is the s u r f a c e density in g / c m 2. Hence o u r i n t e r e s t i n g r an g e of p r e s s u r e s is 10 -5 to 10 -4 a t m o s p h e r e s , independent of t e m p e r a t u r e . The d en si t y of the gas i s a p p r o x i m a t e l y
The c o l l a p s e of the i n t e r s t e l l a r cloud t a k e s p l a c e n e a r l y in f r e e fall, so that the f o r m a tion of the p r i m o r d i a l n e b u l a r disk is a d y n a m i c a ll y v i o l en t p r o c e s s . A r g u m e n t s s i m i l a r to those given p r e v i o u s l y [2] then i n d i c a t e that the hydrogen content of the disk will i n i t i a l l y be ioni z e d to a d i s t a n c e of the o r d e r of 5 a s t r o n o m i c a l units. A c o m p a r a b l e amount of e n e r g y may be e x p e c t e d to be s t o r e d i n i t i a l l y in l a r g e t u r b u l e n t
P = 1 . 3 x 10 -13 a2 a t m o s p h e r e s ,
p = 4 x 10 -15 ~ 2 / T g / c m 3 , o r within an o r d e r of magnitude of 10 -6 g / c m 3 f o r t y p i c a l cooling t e m p e r a t u r e s in the following discussion. If we a s s u m e that the n eb u l ar disk e m i t s en -
94
A.G.W. CAMERON
e r g y like a b l a c k body, then the t i m e t r e q u i r e d to c o o l to a t e m p e r a t u r e T (effectively f r o m a r bitrarily large initial temperature) is t-
knott - - 25err T3
7 . 3 x 1011 ~ s e c ~T 3
'
w h e r e k, N o and ~r a r e the Boltzmann, A v o g a d r o and Stefan r a d i a t i o n c o n s t a n t s , and /~ i s the m e a n m o l e c u l a r weight. F o r the conditions d e s c r i b e d above, the t i m e r e q u i r e d to cool into the r a n g e (1-2) × 103 OK i s 106 to 107 s e c (a few months). In t h i s r a n g e of t e m p e r a t u r e the f i r s t c h e m i c a l c o n d e n s a t i o n s ( m o s t l y i r o n and m a g n e s i u m s i l i c a t e ) will o c c u r , and it i s the r e s u l t i n g d u s t cloud which w i l l e n s u r e that an a p p r o x i m a t e b l a c k body r a d i a t i o n p r o c e s s w i l l t a k e p l a c e . The m e c h a n i s m of c o n d e n s a t i o n w i l l r e s e m b l e d r o p l e t f o r m a t i o n in a cloud c h a m b e r . If a cloud c h a m b e r i s expanded v e r y slowly, a few l a r g e d r o p l e t s a r e f o r m e d . Rapid e x p a n s i o n p r o d u c e s finely d i v i d e d d r o p l e t s . If the n e b u l a r d i s k i s opaque to photons with e n e r g y of o r d e r kT, a s will be the c a s e when dust i s p r e s e n t , then t h e r e w i l l b e a t e m p e r a t u r e g r a d i e n t between the c e n t r a l p l a n e and the e m i t t i n g s u r f a c e , and with t u r b u l e n c e p r e s e n t the gas w i l l be c y c l e d through a r a n g e of t e m p e r a t u r e s . Hence a c o n d e n s a t i o n of m o d e r a t e l y finely divided s o l i d p a r t i c l e s (of s o m e t h i n g like m i c r o n size) m a y b e e x p e c t e d when the motion of the gas c a u s e s it to cool upon expansion. The c o n d e n s a t i o n s w i l l take p l a c e upon the ions p r o d u c e d by the d i s i n t e g r a t i o n of r a d i o a c t i v e s u b s t a n c e s that m a y b e p r e s e n t , such a s 40K and 26A1. When the gas i s r e c o m p r e s s e d , the m o r e v o l a t i l e s u b s t a n c e s in the p a r t i c l e s a r e l i k e l y to be e v a p o r a t e d . Hence a v e r y c o m p l e x h i s t o r y of the f o r m a t i o n of s o l i d p a r t i c l e s i s to b e expected. L e t u s c o n s i d e r the s i t u a t i o n when the n e b u l a r t e m p e r a t u r e h a s f a l l e n low enough so that the solid particles are stable against evaporation. R a d i o a c t i v i t y will continue to f o r m ion p a i r s in the gas. B e c a u s e of t h e i r low m a s s , the e l e c t r o n s have a g r e a t e r m o b i l i t y in the gas, and they will c o l l e c t on the c o n d e n s e d p a r t i c l e s m o r e r a p i d l y than w i l l the ions. At t h i s point we invoke a g e n e r a l p r i n c i p l e d i s c u s s e d in t e r m s of cloud p h y s i c s by Colgate [6]. T u r b u l e n c e in the gas w i l l tend to p r o d u c e s e p a r a t i o n of the c h a r g e , so that t h e r e i s a tendency to a p p r o a c h an e q u a l i t y between the t u r b u l e n t e n e r g y d e n s i t y ½ ~ t (where v t i s a m e a n t u r b u l e n t velocity) and the e n e r g y d e n s i t y E2/8~ of the e l e c t r i c f i e l d r e s u l t i n g f r o m the c h a r g e s e p a r a t i o n . H o w e v e r , the e l e c t r o s t a t ic e n e r g y d e n s i t y will be l i m i t e d by the e l e c t r i c
b r e a k d o w n of the gas, which w i l l p r o d u c e l i g h t ning f l a s h e s . In a lightning d i s c h a r g e a p l a s m a column i s c r e a t e d having a r a d i u s of o r d e r of m a g n i t u d e one c e n t i m e t e r . Since the p r i n c i p a l i o n i z e d c o n s t i t u e n t i s hydrogen, the p l a s m a t e m p e r a t u r e w i l l be of o r d e r 104 OK o r m o r e . If lightning d i s c h a r g e s r e p r e s e n t one p r i n c i p a l m e c h a n i s m for the d i s s i p a t i o n of t u r b u l e n t e n e r g y , then we have s e e n that the e n e r g y r e l e a s e by t h i s m e c h a n i s m should be sufficient to enable any given e l e m e n t of the gas to p a r t i c i p a t e in about one lightning d i s c h a r g e , for the r e g i o n of i n t e r e s t . Colgate [6] h a s a l s o pointed out that s m a l l e l e c t r i f i e d p a r t i c l e s (or d r o p l e t s ) in clouds w i l l b e a c c e l e r a t e d by the e l e c t r o s t a t i c f i e l d s much m o r e s t r o n g l y than by g r a v i t y , and hence the e l e c t r i c f i e l d s w i l l v e r y g r e a t l y enhance the r a t e of d r o p c o a l e s c e n c e . T h i s i s b e c a u s e the d i f f e r ent c h a r g e to m a s s r a t i o s of the d r o p l e t s w i l l p r o d u c e d i f f e r e n t v e l o c i t i e s in a given e l e c t r i c field, and the d r o p l e t s w i l l have an enhanced r a t e of c o l l i s i o n with one another. T h i s c o a l e s c e n c e p r o c e s s w i l l be of much g r e a t e r r e l a t i v e i m p o r t a n c e in the p r i m o r d i a l n e b u l a owing to the s m a l l g r a d i e n t s of g r a v i t a t i o n a l f i e l d s t h e r e . H o w e v e r , it should be noted that p a r t i c l e s of l a r g e r m a s s (~ 1 m m in size) will r e c e i v e only s m a l l a c c e l e r a t i o n s ; hence they will r a r e l y c o l l i d e with one another. They w i l l m a i n l y grow by a c c r e t i o n of much s m a l l e r p a r t i c l e s . The p o s s i b i l i t y of an e l e c t r o s t a t i c a c c u m u l a t i o n p r o c e s s has p r e v i o u s l y b e e n pointed out by Wood [7]. We c o n s i d e r next what w i l l happen when one of t h e s e c o m p o s i t e a c c u m u l a t e d p a r t i c l e s i s caught in a lightning d i s c h a r g e . Whipple [1] h a s s u g g e s t e d that the p l a s m a pinch p r o d u c e d by the d i s c h a r g e w i l l c o m p r e s s and liquify t h e s e p a r t i c l e s . H o w e v e r , the c h a r g e to m a s s r a t i o of the p a r t i c l e s i s much s m a l l e r than f o r p l a s m a ions; hence the pinch a c c e l e r a t i o n w i l l a c t only m i l d l y on the c o n d e n s e d p a r t i c l e s . Whipple f u r t h e r s u g g e s t e d that the c o n d e n s e d p a r t i c l e s which would b e a c t e d upon by the lightning c o n s i s t e d of low d e n s i t y d u s t b a l l s , p r e s u m a b l y like t h o s e of the small meteors produced as cometary debris. H o w e v e r , I would e x p e c t that the t e m p e r a t u r e c y c l i n g a c c o m p a n y i n g t u r b u l e n c e would l e a d to fairly compact structures. In the lightning d i s c h a r g e a p l a s m a m u s t b e c r e a t e d . If half the h y d r o g e n i s i o n i z e d u n d e r o u r t y p i c a l d e n s i t y conditions (10 -6 g / c m 3 ) , then p l a s m a k i n e t i c t e m p e r a t u r e s in the v i c i n i t y of 1.5 × 104 OK w i l l b e p r o d u c e d , a c c o r d i n g to the Saha i o n i z a t i o n equation. We a r e i n t e r e s t e d in the t r a n s p o r t of e n e r g y to the c o n d e n s e d p a r t i -
THE ACCUMULATION OF CHONDRITIC MATERIALS c l e s by the i m p a c t of e l e c t r o n s and ions in the p l a s m a . The electrons have the greater mobility
because of their small mass, and hence they will i m p a c t m o s t r a p i d l y on a c o n d e n s e d p a r t i c l e . T h i s w i l l build up a s t r o n g n e g a t i v e c h a r g e on the p a r t i c l e , which will inhibit the i m p a c t of f u r t h e r e l e c t r o n s but a c c e l e r a t e the i m p a c t of ions. Hence the heating r a t e i s d e t e r m i n e d by the m o bility of the ions. We s h a ll s e e below that the he a ti n g is independent of the p l a s m a density, so that we s h al l i g n o r e the c h a n g e s in this density r e s u l t i n g f r o m the i n i t i a l pinch and l a t e r expansion p h a s e s of the p l a s m a column. We s h a ll a l s o i g n o r e heating by the hot n e u t r a l gas a f t e r r e combination has o c c u r r e d , s i n c e m i c r o t u r b u l e nce is likely to c o n v e c t this gas away f r o m the condensed p a r t i c l e s . We take as a c h a r a c t e r i s t i c r e c o m b i n a t i o n t i m e that in which the n u m b e r of ions d e c r e a s e s by a f a c t o r e. Hence this t i m e is 1
T-- - - , Oln e
w h e r e a is the r e c o m b i n a t i o n c o e f f i c i e n t f o r hyd r o g e n and n e is the e l e c t r o n n u m b e r density. T he n u m b e r of p a r t i c l e s ( e l e c t r o n s plus ions) s t r i k i n g unit c r o s s s e c t i o n a l a r e a in t i m e ~ is o n e - t h i r d of the flux of e l e c t r o n - i o n p a i r s , o r ~neVT. The a v e r a g e e n e r g y p e r p a r t i c l e is ~kT, and we t a k e l t h e c o r r e s p o n d i n g a v e r a g e v e l o c i t y v = (3kT/m)~. R e c o m b i n a t i o n will take p l a c e on the p a r t i c l e s u r f a c e , and we n e g l e c t the e n e r g y r e m o v e d by e v a p o r a t i o n of the r e s u l t i n g h y d r o gen atoms. We take the r e c o m b i n a t i o n c o e f f i c i e n t f o r hydrogen as [8]: a ~ 4.7 × 10 -11 T -½ c m 3 / s e c . F o r the condensed p a r t i c l e b e i n g heated we take density Pc, heat c a p a c i t y C, and r a d i u s r . Hence the h eat i n g of the p a r t i c l e will be
(~ hey T)(~ kT)(4~r 2) AT
(~ ~ocr3)C
Following K r i n o v [ 9 ] , we take the heat c a p a c i t y C = 7.5 × 106 e r g / g OK. H e n c e the t e m p e r a t u r e r i s e is AT = 1.8 × 10 -6
T2/pc r .
We v e r i f y that the heating is independent of the p l a s m a density, although not of the t e m p e r a t u r e . The heating is i n v e r s e l y p r o p o r t i o n a l to the d i m e n s i o n s of the condensed p a r t i c l e . Let us find the d i m e n s i o n s of a p a r t i c l e which
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can be raised to the meltin~ ~irLt. Chondrules melt at about 1800OK or somewhat more. Solid c o n d e n s a t i o n of i r o n and m a g n e s i u m s i l i c a t e will occur n e a r 1300°K [10]; hence we wish Z~T ~ 1000OK, allowing f o r cooling of the nebula b e tween the t i m e s of p a r t i c l e condensation and e x p o s u r e to the lightning stroke. We take Pc = 3.4 g / c m 3, t y p i cal of c h o n d r i t i c m a t e r i a l . Hence r ~ 0.12 cm. T h i s is a t y p i cal chondrule si ze. P a r t i c l e s much l a r g e r than this will not be m e l t e d , and p a r t i c l e s much s m a l l e r a r e likely to be v a p o r ized. T h i s p i c t u r e a p p e a r s capable of explaining many g e n e r a l p r o p e r t i e s of chondritic m a t e r i a l . F o l l o w i n g melting, a chondrule will cool rapidly, a condition n e c e s s a r y f o r the production of g l a s s which o c c u r s in s o m e c h o n d r u l e s [10]. Following cooling, f u r t h e r a c c u m u l a t i o n o f s m a l l p a r t i c l e s on the e x t e r i o r of c h o n d r u l e s will r e s u l t f r o m the e l e c t r o s t a t i c a c c e l e r a t i o n p r o c e s s d i s c u s s e d p r e v i o u s l y ; the r e s u l t i n g a c c u m u l a t e d p a r t i c l e s a r e likely to be m o r e v o l a t i l e , to contain m o s t of the e l e m e n t s in the p e r i o d i c table, and to f o r m the m a t r i x p a r t of the u l t i m a t e chondritic m a t e r i a l . T h i s is c o n s i s t e n t with the hypothesis of A n d e r s [11] that c h o n d r i t i c m a t e r i a l is a m i x t u r e of v a r i a b l e p r o p o r t i o n s of m a t e r i a l condensed at high t e m p e r a t u r e and m a t e r i a l condensed at low t e m p e r a t u r e . A c c u m u l a t i o n of the c h o n d r u l e s plus m a t r i x m a t e r i a l into l a r g e r bodies probably depends m o s t l y on the e f f e c t s of t u r b u l e n c e in the gas. V a r i a t i o n s in abundances will r e s u l t both f r o m s e l e c t i v e v o l a t i l i z a t i o n in the lightning f l a s h e s and f r o m e l e c t r o s t a t i c a c c e l e r a t i o n of co n d en sed m a t e r i a l away f r o m the point of condensation. M i n e r a l s c h a r a c t e r i s t i c of widely diff e r e n t f o r m a t i o n conditions will e x i s t adjacent to one another. T h i s d i s c u s s i o n has f o c u s s e d on conditions i n the p r i m o r d i a l s o l a r nebula in the v i c i n i t y of the a s t e r o i d belt. At s m a l l e r r a d i a l d i s t a n c e s s o m e c h a r a c t e r i s t i c d i f f e r e n c e s will o c c u r . The s u r f a c e density of the nebula is l a r g e r ; the r a t e of co o l i n g is s m a l l e r ; the t u r b u l en t e n e r g y density is g r e a t e r ; and the p l a s m a t e m p e r a t u r e p r o d u c e d in lightning f l a s h e s will be g r e a t e r . Hence chond r u l e s will be l a r g e r and can be r e p e a t e d l y melted. It would be d e s i r a b l e to s e e if s e l e c t i v e e v a p o r a t i o n of s i l i c a t e s f r o m c h o n d r u l e s can o c c u r in lightning f l a s h e s . The s l o w e r gas cooling and f a s t e r gas m o t i o n s will lead to m o r e r ap i d a c c u m u l a t i o n of l a r g e r bodies; h en ce the l a r g e r b o d i e s will contain s m a l l e r amounts of the m o r e v o l a t i l e m a t e r i a l s . The l a r g e r m a s s f r a c t i o n of i r o n and s m a l l e r m a s s f r a c t i o n of p o t a s s i u m in
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A.G.W. CAMERON
t h e e a r t h r e l a t i v e to c h o n d r i t e s a p p e a r s c o n s i s tent with this picture. I w i s h to t h a n k F. L. W h i p p l e , J . A . Wood, E. Anders, S.A. Colgate, and P. Thaddeus for valua b l e d i s c u s s i o n s c o n c e r n i n g s o m e of t h e p h y s i c a l and chemical processes discussed in this paper.
REFERENCES [1] F.L. Whipple, A suggestion as to the origin of chondrules, p r e p r i n t (1966). [2] A . G . W . Cameron, The formation of the sun and planets, I c a r u s 1 (1962) 13.
[3] A. G. W. Cameron, F o r m a t i o n of the s o l a r nebula, I c a r u s 1 (1963) 339. [4] G.W. Pneuman and T. P. Mitchell, Evolution of the s o l a r magnetic fie!d~ I c a r u s 4 (1965) 494. [5] C. F. Von Weizs~cker, Ueber die Entstehung des P l a n e t e n s y s t e m s , Z. Astrophysik 22 (1944) 319. [6] S. A. Colgate, Enhanced drop c o a l e s c e n c e by e l e c t r i c fields in equilibrium with turbulence, p r e p r i n t (1965). [7] J.A.Wood, Chondrutes and the origin of t e r r e s t r i a l planets, Nature 194 (1962) 127. [8] C. W. Allen, Astrophysical quantities (The Athlone P r e s s , University of London, 1963). [9] E. L. Krinov, P r i n c i p l e s of m e t e o r i t i c s ( P e r g a m o n P r e s s , Oxford, 1960). [10] J . A . Wood, On the origin of chondrules and chondrites, I c a r u s 2 (1963) 152. [11] E. Anders, Origin, age, and composition of m e t e orites, Space Sci. Rev. 3 (1964) 583.