By taking account of a size distribution of planetesimals, we show that noble gases gravitationally trapped by planetesimals in the solar nebula can explain the isotopic fractionation of terrestrial Xe relative to Xe in primitive meteorites, leaving Kr and other lighter noble gases almost unfractionated. However, this model is not successful in explaining noble gas elemental abundances in the Earth

Igarashi,George

Ozima,Minoru

National Institute of Polar Research Repository

Proc. NIPR Symp. Antarct. Meteorites, 1, 315-320, 1988 ORIGIN OF ISOTOPIC FRACTIONATION OF TERRESTRIAL XENON George IGARASHI* and Minoru OzIMA Geophysical Institute, Faculty of Science, University of Tokyo, 11-16, Yayoi 2-chome, Bunkyo-ku, Tokyo 113 Abstract: By taking account of a size distribution of planetesimals, we show that noble gases gravitationally trapped by planetesimals in the solar nebula can explain the isotopic fractionation of terrestrial Xe relative to Xe in primitive meteorites, leaving Kr and other lighter noble gases almost unfractionated. How­ever, this model is not successful in explaining noble gas elemental abundances in the Earth. 1. Introduction Isotopic composition of terrestrial Xe (not only atmospheric Xe, but also Xe in mantle-derived materials) is severely fractionated (about 3.5% per atomic mass unit) rela­tive to that in primitive meteorites, whereas surface correlated Xe in lunar soil (SUCOR Xe), which approximates the solar Xe, has almost identical isotopic composition to that in primitive meteorites (cf OzIMA and PooosEK, 1983). Moreover, it seems to be a rule rather than an exception that Xe in the mantle-derived materials is characterized by excess 129Xe due to the decay of 1291 (T112 = 16 Ma) relative to the atmospheric Xe (e.g., PHINNEY et al., 1978; STAUDACHER and ALLEGRE, 1982). This observation strongly suggests that isotopic fractionation of terrestrial Xe must have occurred at a very early stage of the Earth's accretion, say, before the decay of 129!. In contrast to Xe, isotopic composition of Kr is almost identical among terrestrial materials, meteorites and SUCOR (BASFORD et al., 1973). Therefore, to explain the isotopic fractionation of terrestrial Xe, one needs a special mechanism which could cause severe isotopic fractionation only in Xe, the heaviest noble gas, leaving Kr (and other lighter noble gases) almost unfractionated. 2. The Planetesimal-Type Noble Gases As a possible mechanism of origin of isotopic fractionation of terrestrial Xe, OzIMA and NAKAZAWA (1980) proposed gravitational trapping of noble gases by planetesimals in the solar nebula. According to their theory, the enrichment factor a t, the ratio of the amount of a noble gas atom i gravitationally trapped by planetesimals to that when gravity is not taken into account, is expressed as, * Present address: Laboratory for Earthquake Chemistry, Faculty of Science, University of Tokyo, 3-1, Hongo 7-chome, Bunkyo-ku, Tokyo 113. 315 316 George IGARASHI and Minoru OZIMA ai =3 exp (Aµi ) J: x2 exp (-Aµix2)dx, A=(mH/kT)(2r./3)p8GR2, x=r/R, ( 1 ) where k is Boltzmann's constant, T the absolute temperature, µ1 the atomic weight of the noble gas i, mn the mass of hydrogen atom, R the radius of the planetesimal and Ps the density of the planetesimal. Because the enrichment factor ai increases expo­nentially with an atomic weight, isotopic fractionation becomes larger in a heavier noble gas element than in a lighter one. OzIMA and NAKAZAWA (1980) showed that isotopic fractionation is the largest in Xe among all noble gas elements and that observed isotopic fractionation of terrestrial Xe could be approximately explained by Xe gravitationally trapped by a planetesimal of about 600 km in radius. However, there remains a prob­lem in their theory that gravitationally trapped Kr also should show non-negligible isotopic fractionation when the planetesimal becomes large enough to produce Xe iso­topic fractionation, which is contrast to the observation. 3. A Size Distribution of Planetesimals We worked to circumvent the above difficulty by taking account of a size distri­bution of planetesimals. The radius of planetesimals around the Earth's orbit was estimated to be about a few km (e.g., HAYASHI et al., 1985) when they were formed by fragmentation of a dust layer due to gravitational instability at the ecliptic plane in the solar nebula. Planetesimals then collided with each other to form larger planetesimals. The size distribution of planetesimals growing in the solar nebula was simulated by NAKAGAWA et al. (1983). Although the size distribution could not be expressed by a simple function, they showed that it could be approximated by an exponential function of the radius of a planetesimal for larger bodies than a typical size of the growing planetesimals (for smaller bodies, the size distribution is proportional to R- 912). Because the noble gas amount trapped in planetesimals becomes significant for large-sized planetesimals, we may approximate the size distribution of planetesimals by a 'T dis­tribution", N(R)==.(R/R0) exp (-R/R0), (2) where R0 is the radius at the maximum of N(R) (the mode of the radius). Planetesi­mals growing in the solar nebula continued to trap noble gases gravitationally from ambient nebula gases. The Earth was then formed by accretion of planetesimals of various sizes containing various amounts of noble gases. Therefore, noble gases trapped by the Earth would be a mixture of those gravitationally trapped by earth-accreting planetesimals of various sizes. 4. Isotopic Fractionations of Noble Gases in the Earth-Accreting Planetesimals The enrichment factor for a mixture of noble gases in the earth-accreting plane­tesimals which have the size distribution (eq. 2) is expressed as, Origin of Isotopic Fractionation of Terrestrial Xenon 317 ( 3 )  where Rmax is the maximum radius of the planetesimals. Isotopic fractionation is conventionally expressed in terms of a-values relative to the solar isotopic composition. In the case of Xe, o1 wilI be defined as 01= {(1Xe/130Xe)/(1Xe/130Xe)soiar - l} X 1000, 01 is then expressed in terms of a1 defined in eq. 3, Table 1. Isotopic fractionation (01 in per mil) for noble gases in planetesimals which have a size distribution with various Rmax, We also assumed Ro=30 km (the mode of the radius of planetesimals). Rmax (km) 300 600 900 1080 1200 4He 3.7 4.1 4. 1 4.1 4.1 R (single planetesimal)a 20Ne 3.8 4.4 4.4 4.4 4.4 730 10 a OZIMA and NAKAZA w A (1980). 01 36Ar 84Kr 1soxe - -�--�-4.0 4.4 4.9 4.7 6.1 9.1 4. 7 6.3 14.9 4.7 6.3 35.2 4. 7 6.4 100. 7 20 30 40 (4 )  (5 )  Table I shows o1 per atomic mass unit for various Rmax in the case of R0 = 30 km. The 01 for a single planetesimal (OZIMA and NAKAZAWA, 1980) is also listed for comparison. As the Rmax becomes large, 01 is enhanced significantly only in the case of Xe. Con­sequently, compared with the case of planetesimals of the same size, difference of o1 between Kr and Xe becomes very large when a size distribution of planetesimals is taken into account. For Rmax = 1080 km, Xe isotopic fractionation amounts to the observed value in terrestrial Xe (about 3.5%/AMU), while Kr isotopic fractionation is only 0.6%/AMU. Moreover, if we choose smaller R0 and larger Rmau the difference of 01, between Kr and Xe becomes still larger, for example, we obtain Kr isotopic fractiona­tion of 0.4%/AMU for R0 =25 km and Rmax= 1500 km, 0.2%/AMU for R0 = 20 km and Rmax= 2I00 km, with Xe isotopic fractionation of about 3.5%/AMU. EBERHARDT et al. ( 1972) reported isotopic fractionation of terrestrial Kr relative to solar Kr in the opposite direction (-0.4%/AMU). It is impossible for this model to explain such a Kr frac­tionation in the opposite direction. However, BASFORD et al. (1973) observed two principal isotopic fractionations in solar Kr, the first closely resembling the terrestrial Kr within 1 o-s at all isotopes and the second apparently fractionated with respect to the terrestrial isotopic composition by about -0. 25%/AMU, which is smaller than that observed by EBERHARDT et al. (1972). It seems that the fractionation of terrestrial Kr relative to solar Kr is not well established and needs further confirmation. ______ , __ _., .,,,,,,,_ .... 318 George IGARASHI and Minoru Oz1MA 400 300 200 -200 -300 o=� SUCOR 124 126 128 130 132 134 136 Mass no. Fig. 1. Isotopic fractionation pattern for Xe in planetesimals which have a size distribution. Lines indicate the fractionation patterns for planetesimals with various Rmax in the case of Ro=30 km. An isotopic fractionation pattern for Air Xe relative to SUCOR Xe (PODOSEK et al., 1971), which is regarded to be close to the solar Xe composition, is also shown for comparison. Isotopic fractionation lines calculated for various Rmax are shown in Fig. 1. An isotopic fractionation pattern for Air Xe relative to SUCOR Xe, which is regarded to be close to the solar Xe composition, is also shown for comparison. 129Xe excess in Air Xe can be attributed to a contribution of 129I decay. In addition, although there seems to be a difference of the isotopic fractionation pattern between Air Xe and the planetesimal­type Xe in heavy Xe isotopes (134X and 136Xe), it may be explained by a lunar fission component in SUCOR Xe, that is, SUCOR Xe cannot be directly identified with the solar Xe, but may contain a heavy Xe component such as a lunar fission component implanted on the grain surface by ion pumping processes (PooosEK et al., 1971). From the difference of isotopic fractionation pattern between Air Xe and Xe predicted by this model, we could estimate that the fission component in SUCOR Xe amount to (10+ 5)% of total 136Xe. In the above argument, we assumed that noble gases in planetesimals are in gravita­tional diffusion equilibrium. The time constant for heavy noble gases within a plane­tesimal of a radius of R is of the order of R2/(4 X I010 )y (R in cm) (OzIMA and NAKAZAWA, 1980), for example, R=2000 km (2 X 108 cm) gives the time constant of 106 y. On the other hand, NAKAGAWA et al. (1983) showed by numerical calculations that the maximum size of planetesimals growing in the solar nebula exceeds R = 2000 km within the order of 106 y. Hence, it is plausible that the noble gases in a planetesimal with a radius up to a few thousand kilometers are nearly in gravitational diffusion equilibrium. Origin of Isotopic Fractionation of Terrestrial Xenon 5. Elemental Fractionations of Noble Gases in the Earth-Accreting Planetesimals 319 In Table 2, we show enrichment factor a1 for various Rmax in the case of R0 =30km. The enrichment factor for a single planetesimal (OzIMA and NAKAZAWA, 1980) is also listed for comparison. By taking account of a size distribution of planetesimals, noble gas elemental fractionations become much smaller than that for a single planetesimal; the values of enrichment factor become only 2-4 for 130Xe, whereas those in single planetesimals of the same sizes are 103-104. Consequently, if we take the same values of porosity of planetesimals and nebular conditions as those used by OZIMA and NAKAZA w A (1980), the total amount of heavy noble gases contained in the earth-accreting planetesi­mals is too small to account for heavy noble gas abundances in the Earth, by about two orders of magnitude in Ar, about three orders of magnitude in Kr and Xe, whereas total Ne amount in the earth-accreting planetesimals is about the same order of magnitude as that in the Earth. Thus, this model is not successful in explaining both absolute and relative elemental abundances of noble gases in the Earth. Table 2. Enrichment factor «1 for noble gases in planetesimals which have a size distribution with various Rmax, We also assumed R0=30 km. Rmax (km) 3(X) 6(X) 900 1080 1200 4He · · - ···---- -- - -l. 01 1.02 1.02 1.02 1.02 R (single p1anetesima1)a 730 1.08 20Ne - ·--- -- - -- - -1.07 1. 09 1.09 1.09 1.09 2.10 Air/Solar (normalized to 20Ne= l)b :::::1.00 «1 36Ar B4Kr 1soxe --- --- ---�------ -1. 15 1.40 1. 73 1. 17 1. 51 2. 11 I. 17 1. 51 2.27 1. 17 1. 51 2.62 1. 17 1. 51 4.01 4.34 67.3 1.46X JOS 61. 5 3. 8X 10s 3. Ox 103 -------�--- - ---···---- -- ---- ----��---- - --- - ---- -- --�-- ----- -a OzIMA nd NAKAZAWA (1980). b 0ZIMA and PODOSEK (1983). 6. Conclusion We have reconsidered the gravitational segregation model proposed by OzIMA and NAKAZAWA (1980) by taking account of a size distribution of planetesimals growing in the solar nebula, and found that the difference of isotopic fractionation factor o1 be­tween Kr and Xe becomes very large compared with that in a single planetesimal; when Xe isotopic fractionation amounts to that observed in terrestrial Xe (3.5%/AMU), Kr is left almost unfractionated (less than 0.6%/AMU). However, this model is not suc­cessful in explaining noble gas elemental abundances in the Earth. A more complicated model will be needed to explain both isotopic and elemental abundances of noble gases in the Earth. 320 George loARASHI and Minoru 0ZIMA Acknowledgments We would like to thank Prof. K. NAKAZAWA of Tokyo Institute of Technology, Ors. S. SASAKI and K. 0HTSUKI of University of Tokyo for valuable discussions. We also appreciate critical comments from two anonymous reviewers. References BASFORD, J.R., DRAGON, J. C., PEPIN, R. O., Coscm, M.R., JR. and MURTHY, V.R. (1973): Krypton and xenon in lunar fines. Proc. Lunar Sci. Conf., 4th, 1915-1955. EBERHARDT, P., GEISS, J., GRAF, H., GROGLER, N., MENDIA, M.D., MORGELI, M., SCHWALLER, H. and STETTLER, A. (1972): Trapped solar wind gases in Apollo 12 lunar fines 12001 and Apollo 11 breccia 10046. Proc. Lunar Sci. Conf., 3rd, 1821-1856. HAYASHI, c., NAKAZAWA, K. and NAKAGAWA, Y. (1985): Formation of the solar system. Protostars and Planets II, ed. by D.C. BLACK and M.S. MATTHEWS. Tucson, Univ. of Arizona Press, 1100-1153. NAKAGAWA, Y., HAYASHI, C. and NAKAZAWA, K. (1983): Accumulation of planetesimals in the solar nebula. Icarus, 54, 361-376. OzIMA, M. and NAKAZAWA, K. (1980): Origin of rare gases in the Earth. Nature, 284, 313-316. OzIMA, M. and PoDOSEK, F.A. (1983): Noble Gas Geochemistry. Cambridge, Cambridge Univ. Press, 367 p. PHINNEY, D., TENNYSON, J. and FRICK, U. (1978): Xenon in CO2 well gas revisited. J. Geophys. Res., 83, 2313-2319. PODOSEK, F.A., HUNEKE, J.C., BURNETT, D.S. and WASSERBURG, G. J. (1971): Isotopic composition of xenon and krypton in the lunar soil and the solar wind. Earth Planet. Sci. Lett. , 10, 199-216. STAUDACHER, T. and ALLEGRE, C.J. (1982): Terrestrial xenology. Earth Planet. Sci. Lett., 60, 389-406. (Received October 15, 1987; Revised manuscript received November 26, 1987) 

Origin of isotopic fractionation of terrestrial xenon

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Origin of isotopic fractionation of terrestrial xenon

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