Problems Related to Interplanetary Matter (1961)

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THE DISTRIBUTION OF RARE GASES IN IRON METEORITES Peter Signer and Alfred O. Nier School of Physics University of Minnesota This investigation is an attempt to deduce information on the production mechanism of cosmogenic nuclides in iron meteorites from the variation in the concentration of cosmogenic rare gases. In order to determine the variations in the concentration of the cos- mogenic rare gases, 35 samples, taken from locations scattered over a cross section of the 480 kg iron meteorite Grant (fine Octahedrite) were analyzed. In each sample the concentration of Ar38, Ar3", Ne22, Ne , Ne2 , He4 and He3 was determined in one single extraction process, using a statically operated mass spectrometer. Special techniques were used to prevent contamination of the gas mixture extracted from small meteoritic samples (200 - 400 mg) by rare gases from the atmosphere. For He, this problem could be solved com- pletely. The Ne20 was affected, in some runs, by air-contamination to the extent of a few percent, whereas for Ne22, Ne , Ar " and Ar ° contamination was negligible. The lowest measured ratio for Ar^/Ar40 was 0. 52, which after correction for air-argon becomes 0. 4. This is an upper limit for the ratio of cosmogenic Ar38 and Ar40, because the Ar4^ may still be contaminated with radiogenic Ar40 from the decay of K40. The concentration of the cosmogenic Ar, Ne and He has been found to vary systematically with the location of the sample. Contours of equal concentration could be constructed, as shown for four isotopes in Figure 1. The isopleths for helium agree within the limits of the procedure with those reported earlier by Hoffman and Nier (1958) and Fireman (1959). It is therefore assumed, that the isopleths of Ar and Ne also are closed curves of slightly elliptical shape. In the subsequent analysis of the variation of the concentration it will be assumed that the isopleths are circles and the straight line in Figure 1, extending from the position of the minimum concentration to the upper right in each diagram (referred to as "reference radius") is a 31

LEFT RIGHT •TCFERtNCt L»C H too Figure 1. Contours of equal concentration for Ne21, Ar38, He and He4. Crosses indicate the locations of the measured samples. Measure- ments were made only in the regions with the lowest concentration and the highest gradient in concentration of the He. Therefore, the curves are not drawn as closed contours. The reference radius is assumed to to be perpendicular to the outer isopleths. radius of the spherical isopleths. From the diagrams in Figure 1, the increase of the concentration along the reference radius can be con- structed. Figure 2 shows this radial increase for Ar38, Ne21, He4 and He3. To show the difference in the relative increase, the curves in Figure 2 are normalized to the concentration of each isotope found in the center. Ne21 exhibits the most variation with depth, He3 and Ar36 vary less but roughly the same, whereas He4 is the least variable nuclide. It should be noted that the Ar3" was found to increase slightly more than the Ar38. At the position of the minimum concentration, Ar3^/Ar38 is 0.61 and at the post-atmospheric surface it is about 6 percent higher. 32

I.SO- I.4O - 1.30 - 1.20 - 1.10- I.OO cm DISTANCE FROM CENTER Figure 2. Increase of the Ne21, Ar38 ancj He4 concentration along the reference radius. Amounts are normalized to the respective minimum amount. The abundance of the three Ne- isotopes was found to be, with- in the limits of error, constant over the whole cross section. (Ne20/Ne21 = 0. 96 ± 0. 05 and Ne22/Ne21 = 1. 06 ± 0. 05). The precise physical formulation of the production mechanism of the cosmogenic nuclides is not yet possible be- cause of lack of a complete understanding of some of the processes involved. Martin (1953) derived a formula for the production rates of cosmo- genic nuclides which has been slightly modified by Ebert and Wanke (1957). The equation given by the latter authors can be integrated so as to be valid for a spheri- cal target exposed to an iso- tropic radiation. Accordingly, the number of cosmogenic nuclides of a species "i" pro- duced in a volume is given by an expression of the form e-kaXsined8d* - Bi e-ksxsin«dfld* Ai. X describes the position of the volume under consideration rela- tive to the pre-atmospheric surface. ks are parameters which indicate the attenuation of the primary and secondary particles. These parameters are the same for all species "i". BJ are parameters composed of quantities such as individual pro- duction cross sections for the different species; absorption cross sections for primaries and secondaries (also contained in ka and ks); the number of secondaries produced per primary interaction, and finally the radiation dosage. 33

The basic assumptions made in deriving the stated equation for the production rates are the following ones: A). The intensity of the primary and secondary particles in an infinite-plane target decreases exponentially with depth, if the incident particles are unidirectional. B). The energy spectrum of the primaries and secondaries does not change with depth. C). In each primary interaction a definite number of secondary particles are produced. D). Wide angle scattering is negligible. E). Tertiary particles are negligible. F). The production of the cosmogenic nuclides by both primary and secondary particles can be described by average production cross sections for each species "i". G). The pre-atmospheric shape of the meteorite was a sphere and its size did not change during the exposure to the cosmic radiation. For more details refer to the publications by Martin (1953), Ebert and Wanke (1957) and also Signer and Nier (1960). The parameters ka and ks in equation (1) are the same for all species "i" whereas Ai and Bj^ have to be determined individually for each nucleus. Values of ka, ks, Ai, Bi (i = 38, 21, 4, 3) were found by adjust- ing these parameters to give the best agreement between the experimental data in Figure 2 and the amounts computed with equation (1). Figure 3 shows the agreement between the calculated values (solid curves) and ex- perimental data (dots). The close agreement provides evidence that at least in this case the production mechanism proposed by Martin and modified by Ebert and Wanke is adequate to explain the experimental data. The fitting process also yields the pre-atmospheric radius (R = 40 cm) of the spherical meteorite. The points on the post-atmospheric surface lay at a value of 0. 7 for r/R. With the parameter values determined in the fitting process it is possible to calculate average values for the absorption cross sections. The present investigation, however, allows only the calculation of produc- tion cross section ratios. Absolute values may be obtained if further in- formation such as radiation dosage or a single production cross section is available. 34

CENTER 15.0 - SURFACE - 15.0 — E.5 — 750 690 I7O0 3100 - 1700 00 CENTER 02 r/R 0.6 08 1.0 SURFACE Figure 3. Computed radial increase (solid line) compared with exper- imentally determined increase (dots). Note the position of the dots, corresponding to the post- atmospheric surface, lying at r/R = 0.7. The agreement of the values found here and those determined by Hoffman and Nier, as shown in Table 1, is satisfactory considering the limited precision of the whole procedure. Table 2 gives the ratios of the secondary to primary pro- duced nuclides. It is interesting to note, that the secondary produced amount is biggest for He4, less for He3 and Ar38 and negligible for Ne2l. This fact can be seen also from Figure 2, where the Ne2l de- creases most with depth, because of the insignificant secondary pro- duction. A comparison of production cross sections with results of target- studies may have only a limited validity. The values determined here are averages over the whole energy-range of the cosmic radia- tion, whereas targets are irradiated monoenergetically. Having determined the param- eters in equation (1) it is of interest to carry through the integration for some non-spherical bodies. Such a computation was made for prolate and oblate ellipsoids of revolution having masses of 2000 kg and a ratio of axes of 1:2. The calcula- tions were made for points along the axis of symmetry. The results agreed closely with those for a spherical body having the same mass and indicated that the assumption of a spherical shape is a reasonable approximation. A knowledge of the parameters also permits one to compute the rel- ative amounts of nuclides produced by primary and secondary particles. Figure 4 shows the variation of the primary production (long dashes) 35

TABLE 1 Comparison of Ratios of Production Cross Sections as Deduced from the Parameters* Present Work Hoffman &c Nier 0.67 0. 50 0. 13 0. 14 4.8 5.0 1.0 1.4 * The production cross sections for nuclides of the species "i1 for primary and secon and ffsi, respectively. for primary and secondary particles are designated by a • TABLE 2 Relative Contribution of the Secondary-produced Nuclides ffs4/ffp4 's2l/'p2l 0.21 1.0 0.0 0.30 and the secondary production (short dashes) as well as the total concentra- tion (solid line) along a radius in a spherical meteoroid having the mass of Grant (2000 kg). The parameters determined in the fitting process can be used for further applications. One can, for example, calculate the way the con- centrations of the four nuclides Ar38, Ne21, He4 and He3varyin spherical bodies of different mass. Figure 5 demonstrates the decrease of the con- centrations along a radius from the surface to the center of spherical meteoroids of 102, 103, 104, 105 kg and co mass. The amounts were normalized to the respective amounts calculated to be found in infinitely small meteoroids. The results of these calculations can be presented in different ways in order to analyze the variation of nuclide-ratios with depth in hypoththet- ical spherical meteoroids. One of the possible presentations is given in Figure 6. Here, the He4/Ar38 ratio is given as a function of the He4/Ne21 ratio along a radius in spherical meteoroids of 102. 2 x 102, 36

l.0r 0B- 0.6 04- 02- PRIMARY a SEC0NDARY PR0DUCED PRIMARY PR0DUCED SEC0NDARY PR0DUCED Ij0r Ne 21 Off— SURFACE 10 20 cm 30 OB 06 0.4- 00 Ar38 40 "" 10 CENTER SURFACE 20 30 40 cm CENTER l.0r 1.0 0.8 0.6V/ 04f. \ 02 SURFACE 30 40 CENTER SURFACE 2000 kg SPHERE (Ff~40cm) 10 20 cm 30 40 CENTER Figure 4. Contribution of the primary (long dashes) and secondary (short dashes) produced nuclides in a spherical meteoroid of 2000 kg mass, as computed with the parameters giving best agreement with measure- ments on Grant. The total amounts are given by the solid lines. The amounts are normalized to the respec- tive amount in an infinitesimally small meteoroid. 37

2 x 103, 2 x 104, and 2 x 105 kg mass. The big dots on the ends of the curve at the lower left correspond to values found on the surface of the respective meteoroids whereas the big dots on the upper right end of each curve represent the value at the center. The small dots on the curves represent values at relative depths corresponding to r/R = 0.8, 0.6, 0.4, and 0. 2 (surface 1. 0; center 0. 0). The crosses indicate seven arbitrarily chosen Grant samples. These are given to illustrate the agreement of the calculated curve (2 x 103 kg) for Grant with the experimental data. Ar1 SURFACE Id4 kg SURFACE Figure 5. Radial variation of the concentration of the four isotopes Ne21. He3, Ar3** and He4 for spherical meteorites of different masses as predicted by the assumed production mechanism. The amounts were normalized as in Figure 4. 38

According to the assumptions made, ratios found in meteorites of nearly spherical shape should lie close to the family of curves in Figure 6. A deviation can only be explained by a chemical composition for the par- ticular meteorite different from that in Grant or by an irradiation having a very much different energy spectrum than that to which Grant was ex- posed. The latter explanation can. with good reasons, be excluded. !/Ne" Figure 6. He4/Ar38 as a function of He3/Ne21 in spherical meteorites of different masses. Surface points lie at the left end of the curves, center points at the right end. Intermediate points correspond to r/R values of 0.8, 0.6, 0.4 and 0.2. Crosses (+) indicate some arbitrarily chosen samples of Grant and the symbols (X) represent some measurements of other iron meteorites. 39

Ar3* i lff*ce STP/g Figure 7. He3/Ne21 as a function of the Ar38 concentration in spherical meteorites exposed to the same radiation (with respect to radiation dosage and energy spectrum) as Grant. The mass is used as param- eter. Values found in the center lie on the dashed line designated as "center" and surface-values on the one designated "surface." The dots on the "mass-lines" correspond to depths with r/R values of 0. 2. 0. 4, 0. 6 and 0. 8. The crosses (+) and (X) have the same meaning as in Figure 6. The symbol (X) shows some preliminary measurements on other meteorites, where the meaning of the designating letters is given in Table 3. With the exception of Washington County (WC) all the measure- ments lie within the experimental error, on the family of curves. We conclude from this fact, that excluding Washington County*, all the mete- orites listed have a chemical composition similar to Grant. Figure 7 is a graph useful for investigating the size and radiation dosage of a meteoroid as well as the position from which the analyzed sample was removed. The He3/Ne2l ratio is given as a function of the * Schaeffer and Fisher (1959) have pointed out that Washington County has an exceptionally high He4 content, probably resulting from U and Th de- cay. The present work points also to a high Ne20 content which would suggest the presence of primordial gas in this meteorite. (The presence of Kr and Xe have not yet been investigated.) No primordial gas seems to have been reported for any other iron meteorite. 40

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Ar38 concentration in spherical meteoroids of different masses, assuming that all these hypothetical bodies were exposed to radiation similar (with respect to dosage as well as to energy distribution) to that irradiating Grant. Values measured at the center of spherical meteoroids should lie on the dashed curve designated with "center, " whereas surface values are expected to lie on the curve "surface." The curves between two big dots indicate the variation of the ratio He3/Ne21 with the Ar38 concentration in a meteoroid of a particular mass. The small dots represent again the values corresponding to a relative depth of r/R = 0.8; 0.6; 0.4 and 0.2. The solid line to the left gives the functional relationship in an infinitely large meteoroid. The points A, B, . . . G correspond to values found in this "meteoroid" at a depth equal to the radius of the 102, 2 x 102, . . . 105 kg meteoroids, respectively. The crosses represent the same Grant samples as in Figure 6 and indicate again the agreement of the experi- mental data with the calculation. As long as the radiation dosage and chemical composition of a meteoroid of any size is the same as for Grant, analysis of a sample of it should give rise to a point which lies in the restricted area shown in the figure. These requirements seem to be fulfilled in the case of Carbo. Two samples were measured on Carbo, one removed from the radiation center and one close to the pre-atmospheric surface (Fireman 1958; Hoffman and Nier 1959). The two measurements lead to points (X, designated with C) well on the "mass-line" for a 5000 kg sphere, one at the center and the other at a relative depth of about r/R = 0. 3. Points, such as the ones representing measurements on Sikhote-Alin, Odessa or Keen Mountain, can be explained by assuming that their radia- tion dosage was smaller than that of Grant. Note that the point for Wash- ington County is reasonably located in this graph, indicating that only the He4 of the four isotopes investigated here is not explainable by purely cosmogenic origin. Without any further information or assumptions, the graph shown in Figure 7 allows a determination of the radiation dosage with an uncertainty of about a factor of two. The use of similar graphs correlating other com- binations of isotopes provides restricting criteria. Furthermore, logical reasons may be used to limit the uncertainty in the interpretation. Table 3 gives some conclusions based on the graph in Figure 7 as well as three similar graphs, as indicated in the table. It should be re- membered that these conclusions are all based on the many assumptions entering into the model. Future investigation may show if these assump- tions were justified or if the model has to be modified. 42

Epstein: Is there any difficulty in applying this method of analysis to Canyon Diablo? Signer: No fundamental difficulty, except that the content of cosmogenic rare gases of some fragments of Canyon Diablo may be a little low to be measured with much accuracy. Many fragments of the meteorite are known, of course, and it would be interesting to see if they lead to a consistent picture in the model presented here. Arnold: It would be tempting to apply the infinite radius model to Canyon Diablo. Signer: Yes--the best tests of this method of analysis would be with samples of very large meteorites and of cosmic dust. Anders: How would erosion of the meteorite in space affect the analysis? Signer: One would have to combine curves for the concentration in objects of several different sizes. The result would be a flattening of the con- centration curves, especially near the post-atmospheric surface. [Anders, Arnold and Fireman were concerned about the disagreement be- tween Signer's suggestion of a 12 cm loss of material from the refer- ence axis during flight through the atmosphere and recent metallurgical arguments that this mass loss could not have exceeded 2-6 cm. On the basis of Signer's foregoing comment it has to be remembered that Signer's 40 cm preatmospheric radius for Grant is based on many assumptions as, for example, those of spherical shape and no altera- tion in the size during the irradiation. Therefore, if space erosion is indeed significant, no real disagreement may exist at all.] Anders: It should be possible to employ this method of analysis to deter- mine at last whether the cavities in iron meteorites are pre- atmospheric. Some of them are considerably larger than the typical scale of cosmic ray interaction (~15 cm). Signer: A serious difficulty here is that the holes automatically cause drastic departure of the meteorite from the assumed spherical shape. The effects would also be considerably smeared by virtue of the iso- tropy of the flux. Fish: The largest perturbation in the concentration contours would be ex- pected at the very bottoms of the holes. A study of the shape of the contours near these holes might be revealing even if a detailed analysis were not practical. 43

REFERENCES Ebert, K. H.. and Wanke. H. (1957) "Ueber die Einwirkung der Hoehenstrahlung auf Eisenmeteorite, " Z. f. Naturforsch. 12a, 766- 773. Fireman, E. L. (1958) "Distribution of helium-3 in the Carbo meteorite, " Nature. 181, 1725. Fireman, E. L. (1959) "The distribution of helium-3 in the Grant meteor- ite and a determination of the original mass, " Planet. Space Sci. 1, 66-70. Hoffman, J. H. and Nier, A. O. (1958) "Production of helium in iron meteorites by the action of cosmic rays, " Phys. Rev. 112, 2112- 2117. Hoffman, J. H. and Nier, A. O. (1959) "The cosmogenic He3 and He4 distribution in the meteorite Carbo, " Geochim. et Cosmochim. Acta, 17, 32-36. Martin, G. R. (1953) "The origin of meteoritic helium and the age of meteorites, " Geochim. et Cosmochim. Acta, 3, 288-309. Schaeffer, O. A. and Fisher, D. E. (1959) "Cosmogenic noble gases in Washington County meteorite, " Nature, 183, 660-661. Signer, P. and Nier, A. O. (1960) "The distribution of cosmic-ray pro- duced rare gases in iron meteorites, " J. Geophys. Research (in press). 44