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Interstellar potassium and argon
Earth and Planetary Science Letters, 36 (1977) 3 8 1 - 3 9 0
381
© Elsevier Scientific Publishing C o m p a n y , A m s t e r d a m - Printed in The Netherlands
I21
INTERSTELLAR POTASSIUM AND ARGON DONALD D. CLAYTON 1 Max-Planck-Institut far Kernphysik, Heidelberg (Federal Republic of Germany)
Received June 30, 1977
Isotopic anomalies are calculated in K and Ar that will be expected to be carried in interstellar grains. Special attention is given to the supernova condensates (SUNOCONS) that precipitate during the expansion of the explosive oxygen-burning zone of the interior, because that is where 39,41K and 36,38Ar find their natural origins. Expectations are given for: (1) K-Ar ages in excess of the solar age in accumulations of presolar grains, and (2) K anomalies in Ca-rich minerals within Allende inclusions, because experiments searching for such effects are currently underway. Considerable attention is also given to predictions of excess 36Ar owing to extinct 36C1 within presolar grains, and to descriptions of new correlations that can confirm its existence.
1. Introduction In preparation for new K-Ar studies o f primitive objects, especially inclusions of the carbonaceous chondrite Allende, I present herein a detailed theoretical description of isotopic anomalies in these elements that can be expected from presolar grains. While reinterpreting extinct radioactivities as being daughter excesses trapped in grains during the expansion and cooling o f supernova interiors, I have predicted [1 ] excess or unsupported 4°Ar due to prior 4°K decay within the interstellar grains and also excess 41K due to 41Ca decay there. Unsupported 4°Ar is that in excess o f what the 4°K concentration could yield in 4.6 Gyr. The present study gives details of those predictions and also presents the astrophysical basis for contemplating other isotopic anomalies in those same two elements. The context is the same as that I have advanced for reinterpreting apparent ages based on 129Xe, 244pu xenon, and carbonaceous-chondrite fission xenon [2], and on 26Mg/ 24Mg, 87 Sr/ 86 Sr, and 206 ' 207 Pb/ 204 Pb variations within Allende inclusions [3]. These alternate interpretations are of importance if the solids in the pre1 O n leave from Rice University, Houston, Texas, as H u m b o l d t Awardee, J a n u a r y - A u g u s t , 1977.
solar nebula were never vaporized and if the formation of meteorites and planets occurred more rapidly than can be accommodated by the conventional picture of live radioactivities at the time the solar system formed. To make matters clear from the outset, I wish to repeat the basic physical assumptions o f my model [3] of the formation of primitive unequilibrated inclusions. Regard the interstellar grains as having within their cores a collection of refractory thermal condensates, some of which precipitated during the expansion of the supernova interior and some of which condensed as mass was being lost from other types of stars. The supernova condensates (SUNOCONS) provide an especially important refractory component in the initial cold presolar nebula, and can, in principle, replace "the initial high-temperature condensation in the early solar system" as the parents [3] of the Ca-Al-rich inclusions. Before, during and after the collapse o f the solar nebula to a disk, the remainder of the condensibles will attach themselves by sticking cold to pre-existing grains. The resulting presolar condensates (PRESOLCONS) will then have volatile-containing mantles surrounding refractory cores (SUNOCONS and STARDUST from other types of stellar mass loss). In a large mechanical collection o f small (10 -4 cm) PRESOLCONS all con-
382 densibles will have roughly normal solar abundance, but local variations in the ratio of SUNOCONS to other matter will be expected, both as dust/gas fluctuations and as gradients in space and time in the accumulation process [3]. The Ca-Al-rich inclusions are then regarded [3] as being suddenly heated centimeter-sized samples that lose many volatiles while fusing the refractory cores in a partial melt so brief that equilibration cannot occur. The presolar grains themselves do not survice entirely, but the isotopic anomalies that they have carried are not homogenized in the inclusions, Within this framework we can first enumerate the K and Ar anomalies expected before discussing each. In K we expect the following anomalies: (1) 41K/39K variations owing to preferential residence of 41K in Ca-rich SUNOCONS, where it was preferentially incorporated as 1.3 X l0 s yr 41Ca, which is the nucleosynthetic progenitor of 41K in explosive oxygen burning [1 ]. This preferential incorporation of 41Ca depends on the capability of the element Ca to condense more readily than the element K. (2) 4°K/39K variations resulting from the fact that 4°K has a wider spectrum of nucleosynthetic origins than have the two stable isotopes of K, both of which are primarily products of explosive oxygen burning. (3) 4°K/39K varations owing to difference in average age between the gas atoms and the grains in the presolar nebula. In Ar we expect the following sources of anomalies: (4) 4°Ar/38Ar variations in the initial solar system resulting from excess 4°Ar from radiogenic 4°K decay in the interstellar dust [1 ]. Excess 4°Ar is by definition the 4°Ar that cannot be accounted for by subsequent decay of 4°K over the age of the solar system; i.e., samples with excess 4°Ar have apparent K-Ar ages greater than the age of the solar system. (5) 36Ar/aaAr ratios greater than normal owing to the decay of extinct 3 X 10 s yr 36C1in interstellar grains. (6) 4°Ar/38Ar ratios smaller than normal in any K-free SUNOCONS that may condense in explosive oxygen-burning ejecta, where 36Ar and 38Ar are normal but 4°Ar is absent. (7) 36Ar excesses in Ar trapped in SUNOCONS formed in ejecta of explosive silicon burning. These are not the only sources of variations in
these isotopes in meteorites, of course, for which other in situ processes (e.g., gas loss, cosmic rays) are well known. However, it is my purpose to emphasize those variations deriving from my picture. With this list as guide, we turn to a brief exposition of nucleosynthetic arguments pertaining to them.
2. Average fraction of ';OK remaining live at solar formation Relevant to all points above is a calculation of how much of all 4°K ever produced remained live at the time the solar system was formed. At that time, roughly 4.6 Gyr ago, the average isotopic composition of K will be taken to be 39K = 3910, 4°K = 5.76, and 41K = 289 on a scale Si = 106 [4]. The abundance that 4°K would have had had it been stable involves the age distribution of 4°K nuclei. The presolar galactic nucleosynthesis rate p(t) for 4°K cannot be known with certainty, but sufficient accuracy is obtainable by assuming that its time dependence was the same as for uranium. Instead of considering arbitrary histories of nucleosynthesis, moreover, it will suffice to characterize its rate by the well-studied exponential models of nucleosynthesis [5]:
Pi(t) = Pi exp ( - A t ) ,
t = 0 to to --- T
(1)
Here Pi is the relative production rate of the different nuclear species i, each of which for simplification is assumed to have the same time dependence. That assumption should be good enough for our purposes, although it may not be strictly correct. It will be noted that equation (1) does not consider a late spike that may have been associated with the formation of the solar system [6]. I am supposing for this paper that such a late spike injecting radioactive anomalies did not occur, so that the elements as we know them reflect their abundances in the interstellar cloud that gave birth to the sun. In particular, I take it that 4°K and 23SU were residuals of continuous exponential galactic nucleosynthesis (CONEXP). For this problem one can ignore the small free-decay interval, so that A and T in equation (1) must satisfy the relation:
2350 ~
-- 238Xl exp(-ZaSXT) - e x p ( - A T
(2)
383
were 0.32 is taken to be the U isotope ratio when the solar system began about 4.6 Gyr ago, and ru = p(235U)/p(238U) is taken to be the production ratio for these isotopes and has been estimated to lie in the range 1.4 < ru < 1.8 [5]. In Fig. 1 the values o f A ( G y r ) - l yielding this U ratio for each T are noted as points along three separate curves belonging to r = 1.4, 1.6, and 1.8. For those concordant solutions the ratio o f solar4°K to the total amount ever produced, 4°K, can be calculated from:
4°K
[
exp(-4°hT)- exp(-AT)
A
(3)
1 - exp(-AT)
=
These ratios provide the ordinate o f Fig. 1. F o r an astrophysically plausible case, T = 6 Gyr and r = 1.6
I --
\\~nl \hi 9
I
I
~
I
I
I
235U
.15
-
r
•~ 0.9
16 A-0
~
_
ru = 1.8/
~ 0.8 IP07
o.1
I
I 2
I
I 4
I
I 6
I 8 T (Gyr)
Fig. l. The ratio of the abundance of 4OK remaining at the origin of the solar system to the total production 4pOKis displayed for those cosmochronological models that also result in the isotopic abundance ratio 235U/238U = 0.32 at that time. The upper set of three curves are for three different values of the production ratio r U = P(235/P(238), and .Ploints along these curves are labeled by the value of A (Gyr)- that satisfy the U ratio for that galactic age T, plotted as abscissa. The lower three curves, with an inserted ordinate, measure the ratio of the average age T at solar birth to the age T of the Galaxy at that time. Numerical values are in Table 1. A best model is r U = 1.6, T = 6 Gyr at solar birth, and A = 0.154 (Gyr) - I , for which 4°K/4°K = 0.24 and~-/T = 0.576.
(for which A = 0.154 G y r - ] ) , we see that 24% o f all 4°K remained live at the beginning o f the solar system. For other choices of T and r the results are not much different. They are included in Table 1. For the same CONEXP models the average age ~-of the stable nuclei is given by: ~/T = [1 - e x p ( - A T ) ] - l - (AT) -1
(4)
and that ratio is both listed in Table 1 and included in Fig. 1. It has the value 0.576 for the T = 6 example above, meaning that the average age o f such nuclei at formation o f the solar system was ~ = 3.46 Gyr. Equality o f p ( t ) for 4°K and U may not be a correct assumption, but it would have to be a very bad one to invalidate the basic magnitudes. I f a late spike made 12% o f 23Su b u t no 4°K, for example, equation (2) shows that the proper A, T relationship is obtained formally by imagining ru to be increased by 12%, say from r u = 1.6 to ru = 1.8. Fig. 1 then shows that for each galactic age T the remaining 4°K is reduced by about 9%. This is not a big change in the total 4p°K that must be produced or in the amount o f cosmoradiogenic decay preceding the solar system. On the other hand, i f a late spike injected 4°K but no 23Su, the required galactic production o f 4°K is proportionately reduced. Only if a neighboring supernova injected most [6] o f 4°K will a large error be made in the cosmoradiogenic estimates. On that picture [6], however, fluctuations in 4°K/39K at least as large as the 160 variations [11 ] will be expected. With that clarification, I will return to the simpler models without the late spike that are m y concern. These models allow one to calculate quantities o f cosmochemical interest. Taking for a standard o f expectation the case r u = 1.6 and T = 6 Gyr, we see that if 24% o f 4°K remains, then 76% had already decayed before the sun formed. The fraction o f 4°K decays leading to 4°Ar will be taken to be 10.5%. A simple calculation independent of the 4°K branching ratio shows that the total cosmoradiogenic 4°Arcosmo is 3.5 times greater than the total amount o f 4°ArT® that can accumulate over the age T~ = 4.6 Gyr of the solar system. This result means that there exists a potentially great reservoir o f cosmoradiogenic 4°At, and the chemically interesting question is: How much o f it is in presolar grains making it capable o f being trapped in the formation o f solid bodies? If no 4°Ar is degassed from the interstellar grains containing
384 TABLE 1 4$!K in CONEXP models yielding 235U/238U = 0.32 T(Gyr)
i-u = 1.4
q~ = 1.6
A(Gyr)- ’
7/T
40
h(Gyr)-
ru = 1.8
’
;;/T
6F PK
8 6 5 4 3
0.045 0.154 0.274 0.522 1.20
0.530 0.576 0.611 0.663 0.750
40 gK
A(Gyr)-*
ru = 1.6, AG = 0.5 A IIT
40PK
0.207 0.238 0.259 0.287 0.321
0 0.078 0.182 0.394 0.959
0.500 0.539 0.575 0.602 0.712
0.230 0.267 0.287 0.313 0.345
40
>
40PK
0.092 0.216 0.350 0.634 1.45
0.561 0.605 0.639 0.692 0.783
0.185 0.216 0.239 0.266 0.301
0.515 0.538 0.557 0.585 0.642
0.218 0.269 0.301 0.343 0.392
Notes: T is time before solar system when nucleosynthesis began; exponential decline A is chosen to give U ratio for each ru; ru is production ratio P(235)/P(238);7 is average nuclear age at solar formation; 4zK/4iK is fraction of all 4oK produced remaining at solar formation; subscript G refers to a grain component younger than the gas.
some fraction f(K) of presolar K, the 40Ar/40K ratio today will be:
today = 11 + 35f(K)l
(z),,
(5) 0
where (40Ar/40K)T, is the ratio that would result from decay only over the age of the solar system, and has the value (40Ar/40K)~, = 1.137 if To = 4.6 Gyr and 4oX = 0.5373 (Gyr)-’ ; however, the real point of equation (5) is the enrichment factor 1 + 3.5 f(K), which leads to an excess in the apparent age given by: Anapparent)
in this model example is 40Arcosmo = 1.9 per lo6 Si atoms, but the corresponding amount and the corresponding analog to equation (5) is easily calculated for other choices of the galactic age T and of U production ratio Q. However, examination of Table 1 shows that no large differences can be expected within the set of models listed there, so that I can recommend the example I have given as a standard astrophysical expectation. Only if one considers models with greatly different physical assumptions will the numerical expectations be significantly different.
= 1.86 In [ 1 t 3.2 f(K)] Gyr
It seems not unreasonable to presume that 20% of 40K resided in presolar grains, in which case a mechanical assembly of PRESOLCONS would carry ab initio a quantity of 40Ar that is 70% of all that can have been generated by subsequent decay. Its apparent age would be greater than the true age of the solar system by AT = 0.92 Gyr, or T(K-Ar) = 5.5 Gyr. It is therefore of very great interest that such measurements on coarse-grained white inclusions of Allende [7] have indicated T(K-Ar) = 4.9 Gyr. This is a quantitatively plausible result of my model. It will also be evident that heating of this initial assembly could trap Ar gas with high 40Ar even in K-free phases, which would otherwise be regarded as later-generation minerals. The total amount of cosmoradiogenic 40Ar
3. 40K age difference between gas and dust As a physical assumption one could imagine that the K isotopic composition entering interstellar dust is exactly the same as the isotopic composition being injected into the interstellar gas. Even then a 40K anomaly could be expected owing to a different average residence time for gas and dust in the interstellar medium. I have previously suggested that the interstellar grains may have been substantially younger than the gas in the presolar nebula because of the greater ease with which gas can escape being incorporated into new star formation [3]. In that case there would be less 40K in the older gas than in the younger presolar grains at the time of formation of
385 the solar system. I have included the last columns of Table 1 to illustrate a sensible astrophysical parameterization of this effect. A younger presolar grain fraction could be easily and logically characterized by a value of A, say A G, that is smaller than the value of A characterizing the gas. The maximum age T would be equal for the two components. I have illustrated this by the choice AG = 0.5 A, so that the average grain age rG is from equation (4) less than the average for all nuclei. For the standard example T = 6 the value YG/T = 0.538 instead of 0.576, and the fraction of 4°K remaining live is increased to 0.269 instead of 0.238, corresponding to a fractional excess of 4°K in grains equal to 4°8 G = 13%. If 20% of K were trapped in grains, the gas would have a negative "ghost" [3] equal to 408 (ghost) = -3.2%. Variations in dust/gas ratio during accumulation could in this way result in variations in the primitive 4°K/39K ratio. Unfortunately, this model is probably too simple, and we must now turn to the likelihood that the isotopic composition of dust and gas differ for other reasons that are likely to have a greater magnitude.
4. Isotopic composition of K in SUNOCONS The tentative assumption of the last section, that the K composition in initial SUNOCONS is equal to that initially injected into the gas, is not likely to be correct. The largest effect has been predicted to be [1 ] a 41K excess in SUNOCONS from the decay of 41Ca. Our calculations [8,9] show that in explosive oxygen and silicon burning the 41K is synthesized almost entirely as this 1.3 × l0 s yr radioactive isotope of Ca, which is likely to be one of the first elements to condense during the expansion of the supernova interior. This condensation will fractionate 41Ca from 39K, which are otherwise synthesized in the proper abundance ratio. Following the subsequent decay in the interstellar medium, the Ca-rich SUNOCONS will have very large 41K/39K ratios when compared with normal mixes. To quantitatively examine this effect, consider that the explosive ejecta have the normal 41/39 ratio, but that a fraction.t(Ca) of Ca and f(K) of K condence in the SUNOCONS. I will later take f(Ca) = 0.5 and f(K) = 0.2 as examples of such chemical fractionation. Preferential condensation of Ca during quick expansion is expected for
thermal condensation. It follows that the SUNOCON 41K/a9K ratio will later be increased by the ratio f(Ca)/f(K), whereas the gas will be correspondingly depleted in 41K. The mixture of both reservoirs produces by definition normal (41K/a9K)o. Now during accumulation in the solar system, let the local mechanical mixture be enriched in the SUNOCON/ volatile ratio by a factor (1 + e) in comparison with the average normal ratio. The 41/39 ratio is thereby altered to: 4 ' K e/(Ca)+ 1 (~IK ] 39K - el(K) + 1 \39K ]o
(6)
which corresponds to a normal ratio for e = 0, the SUNOCON ratio for e = o% and the volatile ratio for e = - 1 . Taking the estimates f ( C a ) = 0.5 and f(K) = 0.2, and taking the SUNOCON/volatile enrichment to be e = 0.1, one finds a 41/39 ratio increased by 2.9%. This may be typical of what to expect for variations in Ca-Al-rich inclusions in Allende. Unfortunately for these predictions, preliminary searches [10] have not yet revealed such large effects. Perhaps I have overestimated the degree of separation of Ca and K in SUNOCONS or the degree of fluctuation that can be preserved in the subsequent chemistry that has fused the inclusions from the mechanical mixture [3], or even in the correctness of that picture itself. If the inclusions really were high-temperature condensates, no such effects would be expected, but then neither would oxygen anomalies [11 ]. The example of chemical fractionation is conservative, however, because the apparently old coarse-grained inclusion [7] has a K/Ca ratio 12 times smaller than AUende matrix, suggesting f(Ca)/f(K)/> 12 for SUNOCONS or that K was lost when they fused to make the inclusion itself. Of course, not all refractory interstellar cores are SUNOCONS, because other types of stars (e.g., red giants) lose hot gas in large amounts in which thermal condensation can also occur. Oxides of Ca, for example, that condense in red-giant mass loss should be isotopicaUy normal, at least in contrast to SUNOCONS. Arguments involving SUNOCONS must therefore be reduced by a factor measuring the dilution of SUNOCONS by other refractory STARDUST. Astronomical observations of interstellar Ca [ 12] show, however, that more than 99% of Ca is condensed in cold clouds, and more than 90% is condensed even
386 in the hot interstellar component. Since the Ca is born in a supernova from which it is first ejected, and since it can be expected to condense there [1,13], I regard the large depletions of interstellar Ca to signify that the Ca was condensed from the time of its very first appearance in the interstellar medium. To reach some other conclusion it would be necessary for Ca to be ejected in condensed forms from other types of stars at a rate that is 102 times greater than the rate of injection of Ca from supernovae. I calculate the latter rate to be 3 X 10-4Ms per year of Ca from supernovae, but it is presently difficult to know whether this rate is greater or less than that from other types of stars. I have tentatively taken them to be comparable in choosing for SUNOCONS the condensation f(Ca) = 0.5, but future work in astrophysics can clarify this choice. I must add, however, that such considerations also impact the presolar 16Ocomponent [11 ], and may play a role in limiting J 66 ~< 5% if the Ca-Al-rich inclusions are primarily fused interstellar grains as I have advocated [3]. Turning now to the origin of 4°K, I immediately find that the SUNOCONS may be deficient in it because the explosive burning of oxygen, which is the major origin of 39K and 41 K, is apparently not the major origin of 4°K. From the previous section we have that the primordial solar abundance 4~K = 5.76, corresponding as it does to only about 24% of all ever synthesized, indicates a nucleosynthesis requirement 4°K = 24. It is of interest to compare that abundance as a nucleosynthesis requirement with the yield expected from explosive oxygen burning, which is the origin of 39'41K. This calculation is readily carried out with satisfactory accuracy. The neutron density nn at the nuclear freeze-out [9] temperature T9f, in units of 109 K, of the oxygen-burning matter can be, on the average, obtained by the requirement that the 36Ar/ 38Ar isotopic ratio be well reproduced [9]. This results in: aSAr C(38Ar; Tgf) nn2 36Ar = 0.19 - C(36Ar; Tgf)
(7)
where the coefficients C(AZ;T) are defined and evaluated by Bodansky et al. [8]. This simple criterion has been shown to be astrophysically correct by Woosley et al. [9]. Solving it for the neutron density n n for any reasonable freeze-out temperature, which were also shown to lie in the range 3.0 < T9f
< 3.8 Gyr [9], allows the calculation of other key abundance ratios. In particular the freeze-out abundance of 4°K, and of 36C1, which will also be of interest, depends linearly on nn: 4°K = C(4°K; T9f) 39K C(39K, Tgf)nn ,
(8) 36C1 C(36C1;T9f) 3Sc-~= 'C(3sC1; 7-9t.)"g/" When these equations (8) are combined with equation (7) by elimination of nn, the self-consistent set of abundances that result are numerically: 36C1/3Sc1 = 1.282 X 10 -a'757/T9f, 4°K/39K = 1.913 × 10 -12"668/T9f
(9)
These are realistic estimates of the isotopic yields from explosive oxygen burning, and they are accompanied by normal ratios for 35C1/37C1 and 39K/41K, although 37C1 and 41K are, as we have emphasized, ejected as radioactive isotopes of Ar and Ca respectively. The yields in equation 9 are evaluated in Table 2, which also includes an absolute yield on the scale Si = 106. From there it is immediately obvious that for all reasonable freeze-out temperatures the total yield of 4°K is much less than the required 24 atoms• 106Si. Thus, explosive oxygen burning is not the primary source of 4°K. Taking T9f = 3.6 as most probable [9], I estimate that 2.3•24 = 9.6% of 4°K was synthesized in the explosive nucleosynthesis responsible for the bulk of the K isotopes. The immediate result is that 4°K/39K in SUNOCONS should be multiplied by the same factor. This deficiency of 4°K is seen to be larger than the age-difference effects discussed in the preceding section. The limit to ';OK deficiencies in the only study of K in Allende inclusions [10] is therefore just as strong as the limit from the normalcy of the 39/41 ratio there. There are several processes that tend to normalize the isotopic ratios, and I do not want to speculate about their relative importance at a time when so little data are available. I do predict the detectability of K variations and call for further studies of mineral separates of Allende inclusions. The actual origins of 4°K have been uncertain for a long time, and have been much discussed by astro-
387 TABLI~ 2 36C1 and 40K yields from explosive burning Yield *
36C1/3Sc1 40K/39K 36C1 ** 40K **
Freeze-out temperature T9f (109 K) 3.0
3.2
3.4
3.6
3.8
1.5 X 10-3 1.1 X 10-4 6.5 0.43
2.4 X 10-3 2.1 X 10-4 10 0.82
3.4 X 10-3 3.6 X 10-4 15 1.4
4.7 X 10-3 5.8 × 10-4 20 2.3
6.4 X 10-3 8.9 X 10-4 28 3.5
* Assuming 38Ar/36Ar = 0.19 in explosive oxygen burning. ** Per 106 Si atoms assuming chondritic 35C1, 39K result from the explosive burning of oxygen.
physics theorists. A quantitative study [14] of its origin in weak s-process irradiations has shown that it can be produced there if SaFe, another problem nucleus, is produced there. If their assumption that only 10% of 4°K remained live at solar formation is replaced by the present estimate of 24%, the combined overabundance factors for 4°K from Peters et al. [14] in their table 1 sum to about 100, comparable to that for SaFe, for weak fluences between r (1024n/cm 2) = 0.04 and 0.25. The problems with this origin lie in doubts [14] that this is the proper origin of SaFe and in the large associated overabundances of 37C1 and 41Ca, which, as 1 have described earlier, are almost surely due to the explosive oxygen burning. Larger neutron fluences, like those responsible for large Ba overabundances in red-giant atmospheres, may also produce significant amounts of 4°K, but no good calculation exists. For the interim I hold it likely that about half of 4°K owes its existence to the s-process irradiations. If that be the case, refractory condensates during mass loss from red giants (STARDUST) will be increased in the 4°K/a9K ratio. During solar accumulation processes, the PRESOLCONS will contain in their refractory component both STARDUST and SUNOCONS. In the subsequent partial melt [3] leading to the Ca-Al-rich inclusions, the STARDUST and SUNOCONS and matrix K may conceivably fuse to normal 4°K/a9K, considering that they are normal in bulk, but I think it more likely that inhomogeneities will persist. The 41K excesses in Ca-rich SUNOCONS still seem to me the best bet. The natural 4°K abundance has also been shown to be a possible product of neutron reactions on seed
nuclei during explosive carbon burning [15]. In this case the 4°K overabundance yields are comparable to those of the major products, Ne, Na, Mg and A1. The difficulty is that they are seen to be very temperature.sensitive from table 2 of Howard et al. [15] so that accurate statements are not possible. Nonetheless, I regard these results as having established the plausibility that a significant part of 4°K is due to such events. This raises the unanswered question of the mixing of explosive carbon products with those from explosive oxygen before the thermal condensation a few years later in the expanding gasses. This very question will impact not only the 4°K concentration in SUNOCONS, but also the very important question of the identity of the major host minerals. In summing up the cosmochemical implications, I estimate that the origins of 4°K = 24 are: 4°K = 2.3(explosive oxygen) + 10 (explosive carbon neutrons) + 12 (s-process). The question of its variability with respect to explosive-oxygen-produced 39K is then a question of the cosmochemical fate and mixing of these ejecta. The first source, explosive oxygen, has produced most of 39K and 41Ca [9]; the second source, explosive carbon is also believed to occur in a different shell of the same massive supernova; however, the third source, the s-process of slow neutron capture, which is not a major source of 39K and 41K, probably occurs primarily in red-giant stars of moderate mass. Although my emphasis has been on the SUNOCONS, I also urge close study of K isotopes in the carbonaceous-chondrite matrix. If matrix originated as a cold accumulation, the K isotopes will occupy
388 different physical sites. In that case preheating or some other physical treatment might drive off more 39K than 41K.
5. Excess 36Ar owing to extinct 36C1 There is another radiogenic Ar isotope that can be expected in STARDUST and SUNOCONS; 36Ar from decay of 3 X l0 s yr 36C1 in the grains. If it is possible to find excess 4°Ar due to presolar decay, it may be possible to find in the same samples excess 36Ar. Because the 36C1 would have been extinct at solar formation, unlike 4°K, no excess 36Ar will be expected in objects degassed in the solar system. One must search instead for 36Ar/38Ar ratios in excess of the normal ratio in primitive undegassed objects. Table 2 showed that the production of a6C1 in explosive oxygen burning is an order of magnitude greater than that of 4°K, being 36C1 = 20 per 106 Si for T9f = 3.6. SUNOCONS from this zone can therefore contain correspondingly more excess 36C1. In the other physical origins of 4°K, one also finds comparable production of 36C1. In the weak s-process 36C1 is made from 35C1 and 34S seed [14] with yields about equal to those of 4°K from 39K and 38Ar seeds. Thus I estimate 36Cls = 4°K s = 12. For the rapid neutron interactions in explosive carbon burning, the production of 36C1 is similar to that of 4°K, and although we [ 15 ] did not actually calculate 36C1 yields, I can see that it is plausible from those calculations to take 36Clr = 4°K r = 10. Thus the total nucleosynthesis yield of 36C1 is estimated by me to be a~C1 = 42 per 106 Si, in contrast to 4°K = 24. It follows that if the fraction trapped in grains is equal to that for K, the excess presolar 36Ar exceeds that of 4°Ar. Since 98% decays to 36Ar, as opposed to the 10.5% of 4°K that decays to 4°Ar, the average ratio of cosmoradiogenic abundances generated prior to the solar system is: [36Ar~ = 4 2 X 0.98 ~4---0~Ar]cosmo 24 ~ × 0.761"0= 21.5 whereas the ratio in grains must be modified still by the additional factor f(C1)/f(K). Nonetheless it is clear that large trapped 36Ar/38Ar ratios are possible in interstellar grains, and the question becomes that
of recognizing it unambiguously in meteoritic accumulates. What one wants is a Reynolds-type experiment that associates excess 36Ar* with Cl.bearing sites, in analogy to the 129Xe*-I correlation. This is commonly believed to be impossible owing to the absence of another reference isotope in Ar, but I have devised a way to demonstrate an analogous straight-line correlattion with the use of only two isotopes. Assume that the sample can be divided into accurate aliquots, labeled 1 and 2. Let aliquot 2 be irradiated with neutrons, converting some 37C1 into 38Ar*. Let 36Ar* designate that derived from the presolar decay of extinct 36C1. Assume that the total Ar is a mixture between a trapped component designated by subscript zero and the Cl-derived 36Ar* and 38Ar*. Then measure in temperature steps the 38Ar/36Ar ratio in both aliquots. Define for each temperature fraction the quantity: A(T)= ~-~ 2
l
36o+36"
and the ratio ~,(T) = (38/36)2/(38/36)1 = 1 + (38"! 380). Under the usual two-component mixing assumptions, there exists a straight-line correlation between the quantity 1/A(T) and the quantity [7(T) - 1] - I with intercept measuring the Cl-correlated ratio (36"/38")o and the slope measuring the isotopic composition of the ambient trapped gas; viz.: 1 /36"] --,--, A(T) \38"1 o
(36o/38o) "y(T)- 1
(,1)
where the subscript zero denotes the trapped component. This straight line could unambiguously associate excess 36Ar* with CI sites. Unfortunately it could not distinguish extinct 36C1 from excess 36Ar produced from in-situ neutron capture in the meteorite, which preferentially makes 36Ar from 3SC1(n,T) reactions. Very large 36Ar/38Ar ratios have in fact been found in inclusions of Allende [ 16], although those authors ascribed it to such in-situ neutron captures. The correct Cl-correlated cause can however, be identified by other noble-gas measurements on the same two aliquots. For example, the Kr isotopic composition in the irradiated and unirradiated aliquots will reveal how much in-situ neutron irradiation had previously occurred. I suggests such a program to identify extinct 36C1.
389 Another good program of the same type that I wish to here advocate irradiates the second aliquot with fast neutrons as are used in the schemes of K-Ar dating. The 36/38 ratio in the unirradiated aliquot can then be compared with the 4°Ar/39Ar ratio in the irradiated aliquot. A correlation could associate "carried" 36Ar with "carried" 4°Ar. It seems likely that the exploitation of such techniques can produce unique information for this problem, which has the potential to greatly clarify the presolar carrier phenomenon. It is perhaps worth emphasizing that the ratio (4°Ar/36Ar)0 in the ambient gas of the early solar system is expected on nucleosynthesis arguments to be very small, perhaps [4] about 2 X 10 -4. That the primordial gaseous value was in fact so small seems now confirmed by published measurements as low as 1.4 X 10 -3 in diamonds from Haver6 [17], and a value 2.8 × 10 -4 in Dyalpur is in press [18] by the same research group. I f these diamonds formed in the solar system, they must have trapped nearly primordial Ar gas. Larger 4°Ar/36Ar ratios are radiogenic, as commonly assumed, but I here re-emphasize that the decay need not have been in the solar-system body we study today. 4°Ar-rich internal atmospheres can exist even initially in an accumulation rich with presolar carriers, even if the carriers themselves are destroyed.
of the explosive silicon-burning zones. These 36Ar excesses would not be associated with C1, because the C1 yield also vanishes along with the 38Ar yield. Such 36Ar excess would instead be associated with sulfides [19] of Ca, Ti, and Cr-Fe-Ni. These sulfides would in this burning stage be 32S-rich [19].
7. Conclusions I have considered the isotopic anomalies that would be carried in the K and Ar of interstellar grains, especially in the SUNOCONS that precipitate in the ejecta of explosive burning. Their identification in Allende inclusions seems likely, either from excess K-Ar ages, from excess 36Ar/38Ar ratios, or from any of several very plausible isotopic anomalies in K. I present this discussion primarily to aid the planning and interpretation of experiments that can help establish the extent of the survival of presolar grains. Unfortunately, the absence of the predicted effects will not disprove the survival of such carrier effects, because both of these elements can have a chemistry that has been more subject to homogenization that in the case of more successful searches. But it will be very difficult for the SUNOCON picture of the origin of the Ca-Al-rich inclusions if 41K excesses cannot be detected in Ca-rich mineral separates of Allende inclusions.
6. Other Ar effects Acknowledgements 1 wish to return briefly to the other effects (6) and (7) listed in the introduction. The explosive burning of oxygen synthesizes 36Ar and 38At in the ratio and absolute yields that they are observed to have in the solar system. However, the amount of 4°Ar synthesized along with them is less than 10 - s of 36Ar, and can be thought of as zero for practical cosmochemical purposes. Thus ambient Ar trapped in SUNOCONS instead of in the solar system will have such properties, modified by cosmic ray effects in the interstellar medium. In practice it would be difficult to distinguish such Ar from Ar gas in the presolar nebula. When oxygen burning merges into silicon burning [8,9], the Ar shifts to isotopically pure 36At. Thus it is in principle possible to have excess 36/38 ratios in SUNOCONS that have trapped Ar during the ejection
I have been encouraged by helpful discussions with F. Begemann, G. Herzog, E. Jessberger and T. Kirsten. This work was supported by the Alexander von Humboldt Foundation, U.S. National Science Foundation grant AST74-20076, and by NASA.
References 1 D.D. Clayton, 22Na, Ne-E, extinct radioactive anomalies and unsupported 4°Ar, Nature 257 (1975) 36-37. 2 D.D. Clayton, Extint radioactivities: trapped residuals of presolar grains, Astrophys. J. 199 (9175) 765-769. 3 D.D. Clayton, Cosmoradiogenic ghosts and the origin of Ca-Al-rich inclusions, Earth Planet. Sci. Lett. 35 (1977) 398-410.
390 4 A.G.W. Cameron, Abundances of the elements in the solar system, Spat. Sci. Rev. 15 (1973) 121-146. 5 W.A. Fowler, Nuclear cosmochronology, in: Cosmology, Fusion and Other Matters, F. Reines, ed. (Associated Univ. Press, Boulder, Colo, 1972). 6 A.G.W. Cameron and J.W. Truran. The supernova trigger for the formation of the solar system, Icarus 30 (1977) 447-461. 7 E.K. Jessberger, T. Staudacher, B. Dominik and G.F. Herzog, 40Ar-39Ar dating of the Pueblito de Allende meteorite, Meteorities 12 (1977) in press. 8 D. Bodansky, D.D. Clayton and W.A. Fowler, Nuclear quasi-equilibrium during silicon burning, Astrophys. J. Suppl. 16 (1968) 299-371. 9 S.E. Woosley, W.D. Arnett and D.D. Clayton, The explosive burning of oxygen and silicon, Astrophys. J. Suppl. 26 (1973) 231-312. 10 F. Begemann and W. Stegrnann, Implications from the absence of a 41K anomaly in an Allende inclusion, Nature 259 (1976) 549-550. 11 R.N. Clayton, N. Onuma, L. Grossman and T.K. Mayeda, Distribution of the presolar component in Allende and other carbonaceous chondrites, Earth Planet. Sci. Lett. 34 (1977) 209-244.
12 L.M. Hobbs, Interstellar absorption in intercloud regions, II. Detection of the Na 1 lines, Astrophys. J. Lett. 206 (1976) L117-L120. 13 F. Hoyle and N.C. Wickramasinge, Dust in supernova explosions, Nature 226 (1970) 62-63. 14 J.G. Peters, W.A. Fowler and D.D. Clayton, Weak s-process irradiations, Astrophys. J. 173 (1972) 637-648. 15 W.M. Howard, W.D. Arnett, D.D. Clayton and S.E. Woosley, Nucleosynthesis of rare nuclei from seed nuclei in explosive carbon burning. Astrophys. J. 175 (1972) 201-216. 16 S.P. Smith, J.C. Huneke, R.S. Rajan and G.J. Wasserburg, Neon and argon in the Allende meteorite, Geochim. Cosmochim. Acta 41 (1977) 627-648. 17 F. Begemann, H.W. Weber and H. Hintenberger, On the primordial abundance of argon-40, Astrophys. J. Lett. 203 (1976) LI55-L157. 18 R. GObel, U. Ott and F. Begemann, On trapped rare gasses in ureilites (submitted to J. Geophys. Res.). 19 D.D. Clayton and S. Ramadurai, On presolar meteoritic sulphides, Nature 265 (1977) 427-428.
381
© Elsevier Scientific Publishing C o m p a n y , A m s t e r d a m - Printed in The Netherlands
I21
INTERSTELLAR POTASSIUM AND ARGON DONALD D. CLAYTON 1 Max-Planck-Institut far Kernphysik, Heidelberg (Federal Republic of Germany)
Received June 30, 1977
Isotopic anomalies are calculated in K and Ar that will be expected to be carried in interstellar grains. Special attention is given to the supernova condensates (SUNOCONS) that precipitate during the expansion of the explosive oxygen-burning zone of the interior, because that is where 39,41K and 36,38Ar find their natural origins. Expectations are given for: (1) K-Ar ages in excess of the solar age in accumulations of presolar grains, and (2) K anomalies in Ca-rich minerals within Allende inclusions, because experiments searching for such effects are currently underway. Considerable attention is also given to predictions of excess 36Ar owing to extinct 36C1 within presolar grains, and to descriptions of new correlations that can confirm its existence.
1. Introduction In preparation for new K-Ar studies o f primitive objects, especially inclusions of the carbonaceous chondrite Allende, I present herein a detailed theoretical description of isotopic anomalies in these elements that can be expected from presolar grains. While reinterpreting extinct radioactivities as being daughter excesses trapped in grains during the expansion and cooling o f supernova interiors, I have predicted [1 ] excess or unsupported 4°Ar due to prior 4°K decay within the interstellar grains and also excess 41K due to 41Ca decay there. Unsupported 4°Ar is that in excess o f what the 4°K concentration could yield in 4.6 Gyr. The present study gives details of those predictions and also presents the astrophysical basis for contemplating other isotopic anomalies in those same two elements. The context is the same as that I have advanced for reinterpreting apparent ages based on 129Xe, 244pu xenon, and carbonaceous-chondrite fission xenon [2], and on 26Mg/ 24Mg, 87 Sr/ 86 Sr, and 206 ' 207 Pb/ 204 Pb variations within Allende inclusions [3]. These alternate interpretations are of importance if the solids in the pre1 O n leave from Rice University, Houston, Texas, as H u m b o l d t Awardee, J a n u a r y - A u g u s t , 1977.
solar nebula were never vaporized and if the formation of meteorites and planets occurred more rapidly than can be accommodated by the conventional picture of live radioactivities at the time the solar system formed. To make matters clear from the outset, I wish to repeat the basic physical assumptions o f my model [3] of the formation of primitive unequilibrated inclusions. Regard the interstellar grains as having within their cores a collection of refractory thermal condensates, some of which precipitated during the expansion of the supernova interior and some of which condensed as mass was being lost from other types of stars. The supernova condensates (SUNOCONS) provide an especially important refractory component in the initial cold presolar nebula, and can, in principle, replace "the initial high-temperature condensation in the early solar system" as the parents [3] of the Ca-Al-rich inclusions. Before, during and after the collapse o f the solar nebula to a disk, the remainder of the condensibles will attach themselves by sticking cold to pre-existing grains. The resulting presolar condensates (PRESOLCONS) will then have volatile-containing mantles surrounding refractory cores (SUNOCONS and STARDUST from other types of stellar mass loss). In a large mechanical collection o f small (10 -4 cm) PRESOLCONS all con-
382 densibles will have roughly normal solar abundance, but local variations in the ratio of SUNOCONS to other matter will be expected, both as dust/gas fluctuations and as gradients in space and time in the accumulation process [3]. The Ca-Al-rich inclusions are then regarded [3] as being suddenly heated centimeter-sized samples that lose many volatiles while fusing the refractory cores in a partial melt so brief that equilibration cannot occur. The presolar grains themselves do not survice entirely, but the isotopic anomalies that they have carried are not homogenized in the inclusions, Within this framework we can first enumerate the K and Ar anomalies expected before discussing each. In K we expect the following anomalies: (1) 41K/39K variations owing to preferential residence of 41K in Ca-rich SUNOCONS, where it was preferentially incorporated as 1.3 X l0 s yr 41Ca, which is the nucleosynthetic progenitor of 41K in explosive oxygen burning [1 ]. This preferential incorporation of 41Ca depends on the capability of the element Ca to condense more readily than the element K. (2) 4°K/39K variations resulting from the fact that 4°K has a wider spectrum of nucleosynthetic origins than have the two stable isotopes of K, both of which are primarily products of explosive oxygen burning. (3) 4°K/39K varations owing to difference in average age between the gas atoms and the grains in the presolar nebula. In Ar we expect the following sources of anomalies: (4) 4°Ar/38Ar variations in the initial solar system resulting from excess 4°Ar from radiogenic 4°K decay in the interstellar dust [1 ]. Excess 4°Ar is by definition the 4°Ar that cannot be accounted for by subsequent decay of 4°K over the age of the solar system; i.e., samples with excess 4°Ar have apparent K-Ar ages greater than the age of the solar system. (5) 36Ar/aaAr ratios greater than normal owing to the decay of extinct 3 X 10 s yr 36C1in interstellar grains. (6) 4°Ar/38Ar ratios smaller than normal in any K-free SUNOCONS that may condense in explosive oxygen-burning ejecta, where 36Ar and 38Ar are normal but 4°Ar is absent. (7) 36Ar excesses in Ar trapped in SUNOCONS formed in ejecta of explosive silicon burning. These are not the only sources of variations in
these isotopes in meteorites, of course, for which other in situ processes (e.g., gas loss, cosmic rays) are well known. However, it is my purpose to emphasize those variations deriving from my picture. With this list as guide, we turn to a brief exposition of nucleosynthetic arguments pertaining to them.
2. Average fraction of ';OK remaining live at solar formation Relevant to all points above is a calculation of how much of all 4°K ever produced remained live at the time the solar system was formed. At that time, roughly 4.6 Gyr ago, the average isotopic composition of K will be taken to be 39K = 3910, 4°K = 5.76, and 41K = 289 on a scale Si = 106 [4]. The abundance that 4°K would have had had it been stable involves the age distribution of 4°K nuclei. The presolar galactic nucleosynthesis rate p(t) for 4°K cannot be known with certainty, but sufficient accuracy is obtainable by assuming that its time dependence was the same as for uranium. Instead of considering arbitrary histories of nucleosynthesis, moreover, it will suffice to characterize its rate by the well-studied exponential models of nucleosynthesis [5]:
Pi(t) = Pi exp ( - A t ) ,
t = 0 to to --- T
(1)
Here Pi is the relative production rate of the different nuclear species i, each of which for simplification is assumed to have the same time dependence. That assumption should be good enough for our purposes, although it may not be strictly correct. It will be noted that equation (1) does not consider a late spike that may have been associated with the formation of the solar system [6]. I am supposing for this paper that such a late spike injecting radioactive anomalies did not occur, so that the elements as we know them reflect their abundances in the interstellar cloud that gave birth to the sun. In particular, I take it that 4°K and 23SU were residuals of continuous exponential galactic nucleosynthesis (CONEXP). For this problem one can ignore the small free-decay interval, so that A and T in equation (1) must satisfy the relation:
2350 ~
-- 238Xl exp(-ZaSXT) - e x p ( - A T
(2)
383
were 0.32 is taken to be the U isotope ratio when the solar system began about 4.6 Gyr ago, and ru = p(235U)/p(238U) is taken to be the production ratio for these isotopes and has been estimated to lie in the range 1.4 < ru < 1.8 [5]. In Fig. 1 the values o f A ( G y r ) - l yielding this U ratio for each T are noted as points along three separate curves belonging to r = 1.4, 1.6, and 1.8. For those concordant solutions the ratio o f solar4°K to the total amount ever produced, 4°K, can be calculated from:
4°K
[
exp(-4°hT)- exp(-AT)
A
(3)
1 - exp(-AT)
=
These ratios provide the ordinate o f Fig. 1. F o r an astrophysically plausible case, T = 6 Gyr and r = 1.6
I --
\\~nl \hi 9
I
I
~
I
I
I
235U
.15
-
r
•~ 0.9
16 A-0
~
_
ru = 1.8/
~ 0.8 IP07
o.1
I
I 2
I
I 4
I
I 6
I 8 T (Gyr)
Fig. l. The ratio of the abundance of 4OK remaining at the origin of the solar system to the total production 4pOKis displayed for those cosmochronological models that also result in the isotopic abundance ratio 235U/238U = 0.32 at that time. The upper set of three curves are for three different values of the production ratio r U = P(235/P(238), and .Ploints along these curves are labeled by the value of A (Gyr)- that satisfy the U ratio for that galactic age T, plotted as abscissa. The lower three curves, with an inserted ordinate, measure the ratio of the average age T at solar birth to the age T of the Galaxy at that time. Numerical values are in Table 1. A best model is r U = 1.6, T = 6 Gyr at solar birth, and A = 0.154 (Gyr) - I , for which 4°K/4°K = 0.24 and~-/T = 0.576.
(for which A = 0.154 G y r - ] ) , we see that 24% o f all 4°K remained live at the beginning o f the solar system. For other choices of T and r the results are not much different. They are included in Table 1. For the same CONEXP models the average age ~-of the stable nuclei is given by: ~/T = [1 - e x p ( - A T ) ] - l - (AT) -1
(4)
and that ratio is both listed in Table 1 and included in Fig. 1. It has the value 0.576 for the T = 6 example above, meaning that the average age o f such nuclei at formation o f the solar system was ~ = 3.46 Gyr. Equality o f p ( t ) for 4°K and U may not be a correct assumption, but it would have to be a very bad one to invalidate the basic magnitudes. I f a late spike made 12% o f 23Su b u t no 4°K, for example, equation (2) shows that the proper A, T relationship is obtained formally by imagining ru to be increased by 12%, say from r u = 1.6 to ru = 1.8. Fig. 1 then shows that for each galactic age T the remaining 4°K is reduced by about 9%. This is not a big change in the total 4p°K that must be produced or in the amount o f cosmoradiogenic decay preceding the solar system. On the other hand, i f a late spike injected 4°K but no 23Su, the required galactic production o f 4°K is proportionately reduced. Only if a neighboring supernova injected most [6] o f 4°K will a large error be made in the cosmoradiogenic estimates. On that picture [6], however, fluctuations in 4°K/39K at least as large as the 160 variations [11 ] will be expected. With that clarification, I will return to the simpler models without the late spike that are m y concern. These models allow one to calculate quantities o f cosmochemical interest. Taking for a standard o f expectation the case r u = 1.6 and T = 6 Gyr, we see that if 24% o f 4°K remains, then 76% had already decayed before the sun formed. The fraction o f 4°K decays leading to 4°Ar will be taken to be 10.5%. A simple calculation independent of the 4°K branching ratio shows that the total cosmoradiogenic 4°Arcosmo is 3.5 times greater than the total amount o f 4°ArT® that can accumulate over the age T~ = 4.6 Gyr of the solar system. This result means that there exists a potentially great reservoir o f cosmoradiogenic 4°At, and the chemically interesting question is: How much o f it is in presolar grains making it capable o f being trapped in the formation o f solid bodies? If no 4°Ar is degassed from the interstellar grains containing
384 TABLE 1 4$!K in CONEXP models yielding 235U/238U = 0.32 T(Gyr)
i-u = 1.4
q~ = 1.6
A(Gyr)- ’
7/T
40
h(Gyr)-
ru = 1.8
’
;;/T
6F PK
8 6 5 4 3
0.045 0.154 0.274 0.522 1.20
0.530 0.576 0.611 0.663 0.750
40 gK
A(Gyr)-*
ru = 1.6, AG = 0.5 A IIT
40PK
0.207 0.238 0.259 0.287 0.321
0 0.078 0.182 0.394 0.959
0.500 0.539 0.575 0.602 0.712
0.230 0.267 0.287 0.313 0.345
40
>
40PK
0.092 0.216 0.350 0.634 1.45
0.561 0.605 0.639 0.692 0.783
0.185 0.216 0.239 0.266 0.301
0.515 0.538 0.557 0.585 0.642
0.218 0.269 0.301 0.343 0.392
Notes: T is time before solar system when nucleosynthesis began; exponential decline A is chosen to give U ratio for each ru; ru is production ratio P(235)/P(238);7 is average nuclear age at solar formation; 4zK/4iK is fraction of all 4oK produced remaining at solar formation; subscript G refers to a grain component younger than the gas.
some fraction f(K) of presolar K, the 40Ar/40K ratio today will be:
today = 11 + 35f(K)l
(z),,
(5) 0
where (40Ar/40K)T, is the ratio that would result from decay only over the age of the solar system, and has the value (40Ar/40K)~, = 1.137 if To = 4.6 Gyr and 4oX = 0.5373 (Gyr)-’ ; however, the real point of equation (5) is the enrichment factor 1 + 3.5 f(K), which leads to an excess in the apparent age given by: Anapparent)
in this model example is 40Arcosmo = 1.9 per lo6 Si atoms, but the corresponding amount and the corresponding analog to equation (5) is easily calculated for other choices of the galactic age T and of U production ratio Q. However, examination of Table 1 shows that no large differences can be expected within the set of models listed there, so that I can recommend the example I have given as a standard astrophysical expectation. Only if one considers models with greatly different physical assumptions will the numerical expectations be significantly different.
= 1.86 In [ 1 t 3.2 f(K)] Gyr
It seems not unreasonable to presume that 20% of 40K resided in presolar grains, in which case a mechanical assembly of PRESOLCONS would carry ab initio a quantity of 40Ar that is 70% of all that can have been generated by subsequent decay. Its apparent age would be greater than the true age of the solar system by AT = 0.92 Gyr, or T(K-Ar) = 5.5 Gyr. It is therefore of very great interest that such measurements on coarse-grained white inclusions of Allende [7] have indicated T(K-Ar) = 4.9 Gyr. This is a quantitatively plausible result of my model. It will also be evident that heating of this initial assembly could trap Ar gas with high 40Ar even in K-free phases, which would otherwise be regarded as later-generation minerals. The total amount of cosmoradiogenic 40Ar
3. 40K age difference between gas and dust As a physical assumption one could imagine that the K isotopic composition entering interstellar dust is exactly the same as the isotopic composition being injected into the interstellar gas. Even then a 40K anomaly could be expected owing to a different average residence time for gas and dust in the interstellar medium. I have previously suggested that the interstellar grains may have been substantially younger than the gas in the presolar nebula because of the greater ease with which gas can escape being incorporated into new star formation [3]. In that case there would be less 40K in the older gas than in the younger presolar grains at the time of formation of
385 the solar system. I have included the last columns of Table 1 to illustrate a sensible astrophysical parameterization of this effect. A younger presolar grain fraction could be easily and logically characterized by a value of A, say A G, that is smaller than the value of A characterizing the gas. The maximum age T would be equal for the two components. I have illustrated this by the choice AG = 0.5 A, so that the average grain age rG is from equation (4) less than the average for all nuclei. For the standard example T = 6 the value YG/T = 0.538 instead of 0.576, and the fraction of 4°K remaining live is increased to 0.269 instead of 0.238, corresponding to a fractional excess of 4°K in grains equal to 4°8 G = 13%. If 20% of K were trapped in grains, the gas would have a negative "ghost" [3] equal to 408 (ghost) = -3.2%. Variations in dust/gas ratio during accumulation could in this way result in variations in the primitive 4°K/39K ratio. Unfortunately, this model is probably too simple, and we must now turn to the likelihood that the isotopic composition of dust and gas differ for other reasons that are likely to have a greater magnitude.
4. Isotopic composition of K in SUNOCONS The tentative assumption of the last section, that the K composition in initial SUNOCONS is equal to that initially injected into the gas, is not likely to be correct. The largest effect has been predicted to be [1 ] a 41K excess in SUNOCONS from the decay of 41Ca. Our calculations [8,9] show that in explosive oxygen and silicon burning the 41K is synthesized almost entirely as this 1.3 × l0 s yr radioactive isotope of Ca, which is likely to be one of the first elements to condense during the expansion of the supernova interior. This condensation will fractionate 41Ca from 39K, which are otherwise synthesized in the proper abundance ratio. Following the subsequent decay in the interstellar medium, the Ca-rich SUNOCONS will have very large 41K/39K ratios when compared with normal mixes. To quantitatively examine this effect, consider that the explosive ejecta have the normal 41/39 ratio, but that a fraction.t(Ca) of Ca and f(K) of K condence in the SUNOCONS. I will later take f(Ca) = 0.5 and f(K) = 0.2 as examples of such chemical fractionation. Preferential condensation of Ca during quick expansion is expected for
thermal condensation. It follows that the SUNOCON 41K/a9K ratio will later be increased by the ratio f(Ca)/f(K), whereas the gas will be correspondingly depleted in 41K. The mixture of both reservoirs produces by definition normal (41K/a9K)o. Now during accumulation in the solar system, let the local mechanical mixture be enriched in the SUNOCON/ volatile ratio by a factor (1 + e) in comparison with the average normal ratio. The 41/39 ratio is thereby altered to: 4 ' K e/(Ca)+ 1 (~IK ] 39K - el(K) + 1 \39K ]o
(6)
which corresponds to a normal ratio for e = 0, the SUNOCON ratio for e = o% and the volatile ratio for e = - 1 . Taking the estimates f ( C a ) = 0.5 and f(K) = 0.2, and taking the SUNOCON/volatile enrichment to be e = 0.1, one finds a 41/39 ratio increased by 2.9%. This may be typical of what to expect for variations in Ca-Al-rich inclusions in Allende. Unfortunately for these predictions, preliminary searches [10] have not yet revealed such large effects. Perhaps I have overestimated the degree of separation of Ca and K in SUNOCONS or the degree of fluctuation that can be preserved in the subsequent chemistry that has fused the inclusions from the mechanical mixture [3], or even in the correctness of that picture itself. If the inclusions really were high-temperature condensates, no such effects would be expected, but then neither would oxygen anomalies [11 ]. The example of chemical fractionation is conservative, however, because the apparently old coarse-grained inclusion [7] has a K/Ca ratio 12 times smaller than AUende matrix, suggesting f(Ca)/f(K)/> 12 for SUNOCONS or that K was lost when they fused to make the inclusion itself. Of course, not all refractory interstellar cores are SUNOCONS, because other types of stars (e.g., red giants) lose hot gas in large amounts in which thermal condensation can also occur. Oxides of Ca, for example, that condense in red-giant mass loss should be isotopicaUy normal, at least in contrast to SUNOCONS. Arguments involving SUNOCONS must therefore be reduced by a factor measuring the dilution of SUNOCONS by other refractory STARDUST. Astronomical observations of interstellar Ca [ 12] show, however, that more than 99% of Ca is condensed in cold clouds, and more than 90% is condensed even
386 in the hot interstellar component. Since the Ca is born in a supernova from which it is first ejected, and since it can be expected to condense there [1,13], I regard the large depletions of interstellar Ca to signify that the Ca was condensed from the time of its very first appearance in the interstellar medium. To reach some other conclusion it would be necessary for Ca to be ejected in condensed forms from other types of stars at a rate that is 102 times greater than the rate of injection of Ca from supernovae. I calculate the latter rate to be 3 X 10-4Ms per year of Ca from supernovae, but it is presently difficult to know whether this rate is greater or less than that from other types of stars. I have tentatively taken them to be comparable in choosing for SUNOCONS the condensation f(Ca) = 0.5, but future work in astrophysics can clarify this choice. I must add, however, that such considerations also impact the presolar 16Ocomponent [11 ], and may play a role in limiting J 66 ~< 5% if the Ca-Al-rich inclusions are primarily fused interstellar grains as I have advocated [3]. Turning now to the origin of 4°K, I immediately find that the SUNOCONS may be deficient in it because the explosive burning of oxygen, which is the major origin of 39K and 41 K, is apparently not the major origin of 4°K. From the previous section we have that the primordial solar abundance 4~K = 5.76, corresponding as it does to only about 24% of all ever synthesized, indicates a nucleosynthesis requirement 4°K = 24. It is of interest to compare that abundance as a nucleosynthesis requirement with the yield expected from explosive oxygen burning, which is the origin of 39'41K. This calculation is readily carried out with satisfactory accuracy. The neutron density nn at the nuclear freeze-out [9] temperature T9f, in units of 109 K, of the oxygen-burning matter can be, on the average, obtained by the requirement that the 36Ar/ 38Ar isotopic ratio be well reproduced [9]. This results in: aSAr C(38Ar; Tgf) nn2 36Ar = 0.19 - C(36Ar; Tgf)
(7)
where the coefficients C(AZ;T) are defined and evaluated by Bodansky et al. [8]. This simple criterion has been shown to be astrophysically correct by Woosley et al. [9]. Solving it for the neutron density n n for any reasonable freeze-out temperature, which were also shown to lie in the range 3.0 < T9f
< 3.8 Gyr [9], allows the calculation of other key abundance ratios. In particular the freeze-out abundance of 4°K, and of 36C1, which will also be of interest, depends linearly on nn: 4°K = C(4°K; T9f) 39K C(39K, Tgf)nn ,
(8) 36C1 C(36C1;T9f) 3Sc-~= 'C(3sC1; 7-9t.)"g/" When these equations (8) are combined with equation (7) by elimination of nn, the self-consistent set of abundances that result are numerically: 36C1/3Sc1 = 1.282 X 10 -a'757/T9f, 4°K/39K = 1.913 × 10 -12"668/T9f
(9)
These are realistic estimates of the isotopic yields from explosive oxygen burning, and they are accompanied by normal ratios for 35C1/37C1 and 39K/41K, although 37C1 and 41K are, as we have emphasized, ejected as radioactive isotopes of Ar and Ca respectively. The yields in equation 9 are evaluated in Table 2, which also includes an absolute yield on the scale Si = 106. From there it is immediately obvious that for all reasonable freeze-out temperatures the total yield of 4°K is much less than the required 24 atoms• 106Si. Thus, explosive oxygen burning is not the primary source of 4°K. Taking T9f = 3.6 as most probable [9], I estimate that 2.3•24 = 9.6% of 4°K was synthesized in the explosive nucleosynthesis responsible for the bulk of the K isotopes. The immediate result is that 4°K/39K in SUNOCONS should be multiplied by the same factor. This deficiency of 4°K is seen to be larger than the age-difference effects discussed in the preceding section. The limit to ';OK deficiencies in the only study of K in Allende inclusions [10] is therefore just as strong as the limit from the normalcy of the 39/41 ratio there. There are several processes that tend to normalize the isotopic ratios, and I do not want to speculate about their relative importance at a time when so little data are available. I do predict the detectability of K variations and call for further studies of mineral separates of Allende inclusions. The actual origins of 4°K have been uncertain for a long time, and have been much discussed by astro-
387 TABLI~ 2 36C1 and 40K yields from explosive burning Yield *
36C1/3Sc1 40K/39K 36C1 ** 40K **
Freeze-out temperature T9f (109 K) 3.0
3.2
3.4
3.6
3.8
1.5 X 10-3 1.1 X 10-4 6.5 0.43
2.4 X 10-3 2.1 X 10-4 10 0.82
3.4 X 10-3 3.6 X 10-4 15 1.4
4.7 X 10-3 5.8 × 10-4 20 2.3
6.4 X 10-3 8.9 X 10-4 28 3.5
* Assuming 38Ar/36Ar = 0.19 in explosive oxygen burning. ** Per 106 Si atoms assuming chondritic 35C1, 39K result from the explosive burning of oxygen.
physics theorists. A quantitative study [14] of its origin in weak s-process irradiations has shown that it can be produced there if SaFe, another problem nucleus, is produced there. If their assumption that only 10% of 4°K remained live at solar formation is replaced by the present estimate of 24%, the combined overabundance factors for 4°K from Peters et al. [14] in their table 1 sum to about 100, comparable to that for SaFe, for weak fluences between r (1024n/cm 2) = 0.04 and 0.25. The problems with this origin lie in doubts [14] that this is the proper origin of SaFe and in the large associated overabundances of 37C1 and 41Ca, which, as 1 have described earlier, are almost surely due to the explosive oxygen burning. Larger neutron fluences, like those responsible for large Ba overabundances in red-giant atmospheres, may also produce significant amounts of 4°K, but no good calculation exists. For the interim I hold it likely that about half of 4°K owes its existence to the s-process irradiations. If that be the case, refractory condensates during mass loss from red giants (STARDUST) will be increased in the 4°K/a9K ratio. During solar accumulation processes, the PRESOLCONS will contain in their refractory component both STARDUST and SUNOCONS. In the subsequent partial melt [3] leading to the Ca-Al-rich inclusions, the STARDUST and SUNOCONS and matrix K may conceivably fuse to normal 4°K/a9K, considering that they are normal in bulk, but I think it more likely that inhomogeneities will persist. The 41K excesses in Ca-rich SUNOCONS still seem to me the best bet. The natural 4°K abundance has also been shown to be a possible product of neutron reactions on seed
nuclei during explosive carbon burning [15]. In this case the 4°K overabundance yields are comparable to those of the major products, Ne, Na, Mg and A1. The difficulty is that they are seen to be very temperature.sensitive from table 2 of Howard et al. [15] so that accurate statements are not possible. Nonetheless, I regard these results as having established the plausibility that a significant part of 4°K is due to such events. This raises the unanswered question of the mixing of explosive carbon products with those from explosive oxygen before the thermal condensation a few years later in the expanding gasses. This very question will impact not only the 4°K concentration in SUNOCONS, but also the very important question of the identity of the major host minerals. In summing up the cosmochemical implications, I estimate that the origins of 4°K = 24 are: 4°K = 2.3(explosive oxygen) + 10 (explosive carbon neutrons) + 12 (s-process). The question of its variability with respect to explosive-oxygen-produced 39K is then a question of the cosmochemical fate and mixing of these ejecta. The first source, explosive oxygen, has produced most of 39K and 41Ca [9]; the second source, explosive carbon is also believed to occur in a different shell of the same massive supernova; however, the third source, the s-process of slow neutron capture, which is not a major source of 39K and 41K, probably occurs primarily in red-giant stars of moderate mass. Although my emphasis has been on the SUNOCONS, I also urge close study of K isotopes in the carbonaceous-chondrite matrix. If matrix originated as a cold accumulation, the K isotopes will occupy
388 different physical sites. In that case preheating or some other physical treatment might drive off more 39K than 41K.
5. Excess 36Ar owing to extinct 36C1 There is another radiogenic Ar isotope that can be expected in STARDUST and SUNOCONS; 36Ar from decay of 3 X l0 s yr 36C1 in the grains. If it is possible to find excess 4°Ar due to presolar decay, it may be possible to find in the same samples excess 36Ar. Because the 36C1 would have been extinct at solar formation, unlike 4°K, no excess 36Ar will be expected in objects degassed in the solar system. One must search instead for 36Ar/38Ar ratios in excess of the normal ratio in primitive undegassed objects. Table 2 showed that the production of a6C1 in explosive oxygen burning is an order of magnitude greater than that of 4°K, being 36C1 = 20 per 106 Si for T9f = 3.6. SUNOCONS from this zone can therefore contain correspondingly more excess 36C1. In the other physical origins of 4°K, one also finds comparable production of 36C1. In the weak s-process 36C1 is made from 35C1 and 34S seed [14] with yields about equal to those of 4°K from 39K and 38Ar seeds. Thus I estimate 36Cls = 4°K s = 12. For the rapid neutron interactions in explosive carbon burning, the production of 36C1 is similar to that of 4°K, and although we [ 15 ] did not actually calculate 36C1 yields, I can see that it is plausible from those calculations to take 36Clr = 4°K r = 10. Thus the total nucleosynthesis yield of 36C1 is estimated by me to be a~C1 = 42 per 106 Si, in contrast to 4°K = 24. It follows that if the fraction trapped in grains is equal to that for K, the excess presolar 36Ar exceeds that of 4°Ar. Since 98% decays to 36Ar, as opposed to the 10.5% of 4°K that decays to 4°Ar, the average ratio of cosmoradiogenic abundances generated prior to the solar system is: [36Ar~ = 4 2 X 0.98 ~4---0~Ar]cosmo 24 ~ × 0.761"0= 21.5 whereas the ratio in grains must be modified still by the additional factor f(C1)/f(K). Nonetheless it is clear that large trapped 36Ar/38Ar ratios are possible in interstellar grains, and the question becomes that
of recognizing it unambiguously in meteoritic accumulates. What one wants is a Reynolds-type experiment that associates excess 36Ar* with Cl.bearing sites, in analogy to the 129Xe*-I correlation. This is commonly believed to be impossible owing to the absence of another reference isotope in Ar, but I have devised a way to demonstrate an analogous straight-line correlattion with the use of only two isotopes. Assume that the sample can be divided into accurate aliquots, labeled 1 and 2. Let aliquot 2 be irradiated with neutrons, converting some 37C1 into 38Ar*. Let 36Ar* designate that derived from the presolar decay of extinct 36C1. Assume that the total Ar is a mixture between a trapped component designated by subscript zero and the Cl-derived 36Ar* and 38Ar*. Then measure in temperature steps the 38Ar/36Ar ratio in both aliquots. Define for each temperature fraction the quantity: A(T)= ~-~ 2
l
36o+36"
and the ratio ~,(T) = (38/36)2/(38/36)1 = 1 + (38"! 380). Under the usual two-component mixing assumptions, there exists a straight-line correlation between the quantity 1/A(T) and the quantity [7(T) - 1] - I with intercept measuring the Cl-correlated ratio (36"/38")o and the slope measuring the isotopic composition of the ambient trapped gas; viz.: 1 /36"] --,--, A(T) \38"1 o
(36o/38o) "y(T)- 1
(,1)
where the subscript zero denotes the trapped component. This straight line could unambiguously associate excess 36Ar* with CI sites. Unfortunately it could not distinguish extinct 36C1 from excess 36Ar produced from in-situ neutron capture in the meteorite, which preferentially makes 36Ar from 3SC1(n,T) reactions. Very large 36Ar/38Ar ratios have in fact been found in inclusions of Allende [ 16], although those authors ascribed it to such in-situ neutron captures. The correct Cl-correlated cause can however, be identified by other noble-gas measurements on the same two aliquots. For example, the Kr isotopic composition in the irradiated and unirradiated aliquots will reveal how much in-situ neutron irradiation had previously occurred. I suggests such a program to identify extinct 36C1.
389 Another good program of the same type that I wish to here advocate irradiates the second aliquot with fast neutrons as are used in the schemes of K-Ar dating. The 36/38 ratio in the unirradiated aliquot can then be compared with the 4°Ar/39Ar ratio in the irradiated aliquot. A correlation could associate "carried" 36Ar with "carried" 4°Ar. It seems likely that the exploitation of such techniques can produce unique information for this problem, which has the potential to greatly clarify the presolar carrier phenomenon. It is perhaps worth emphasizing that the ratio (4°Ar/36Ar)0 in the ambient gas of the early solar system is expected on nucleosynthesis arguments to be very small, perhaps [4] about 2 X 10 -4. That the primordial gaseous value was in fact so small seems now confirmed by published measurements as low as 1.4 X 10 -3 in diamonds from Haver6 [17], and a value 2.8 × 10 -4 in Dyalpur is in press [18] by the same research group. I f these diamonds formed in the solar system, they must have trapped nearly primordial Ar gas. Larger 4°Ar/36Ar ratios are radiogenic, as commonly assumed, but I here re-emphasize that the decay need not have been in the solar-system body we study today. 4°Ar-rich internal atmospheres can exist even initially in an accumulation rich with presolar carriers, even if the carriers themselves are destroyed.
of the explosive silicon-burning zones. These 36Ar excesses would not be associated with C1, because the C1 yield also vanishes along with the 38Ar yield. Such 36Ar excess would instead be associated with sulfides [19] of Ca, Ti, and Cr-Fe-Ni. These sulfides would in this burning stage be 32S-rich [19].
7. Conclusions I have considered the isotopic anomalies that would be carried in the K and Ar of interstellar grains, especially in the SUNOCONS that precipitate in the ejecta of explosive burning. Their identification in Allende inclusions seems likely, either from excess K-Ar ages, from excess 36Ar/38Ar ratios, or from any of several very plausible isotopic anomalies in K. I present this discussion primarily to aid the planning and interpretation of experiments that can help establish the extent of the survival of presolar grains. Unfortunately, the absence of the predicted effects will not disprove the survival of such carrier effects, because both of these elements can have a chemistry that has been more subject to homogenization that in the case of more successful searches. But it will be very difficult for the SUNOCON picture of the origin of the Ca-Al-rich inclusions if 41K excesses cannot be detected in Ca-rich mineral separates of Allende inclusions.
6. Other Ar effects Acknowledgements 1 wish to return briefly to the other effects (6) and (7) listed in the introduction. The explosive burning of oxygen synthesizes 36Ar and 38At in the ratio and absolute yields that they are observed to have in the solar system. However, the amount of 4°Ar synthesized along with them is less than 10 - s of 36Ar, and can be thought of as zero for practical cosmochemical purposes. Thus ambient Ar trapped in SUNOCONS instead of in the solar system will have such properties, modified by cosmic ray effects in the interstellar medium. In practice it would be difficult to distinguish such Ar from Ar gas in the presolar nebula. When oxygen burning merges into silicon burning [8,9], the Ar shifts to isotopically pure 36At. Thus it is in principle possible to have excess 36/38 ratios in SUNOCONS that have trapped Ar during the ejection
I have been encouraged by helpful discussions with F. Begemann, G. Herzog, E. Jessberger and T. Kirsten. This work was supported by the Alexander von Humboldt Foundation, U.S. National Science Foundation grant AST74-20076, and by NASA.
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