Depth and size dependence of cosmogenic nuclide production rates in stony meteoroids

0016-7037/93/$6.00

Geochimica n Cosmochimica ACM Vol. 57, pp. 2361-2375 Copyright 8 1993 Rrgmnon Press Ltd. printed in U.S.A.

+ .CKI

Depth and size dependence of cosmogenic nuclide production rates in stony meteoroids N.BHANDARI,I K. J. MATHEW, I M. N. RAo, ’ U. HERPERS,~ K. BREMER,’ S. VOGT,~** W. WOLFLI,~ H. J. HOI=MANN,~R. MICHEL,~ R. BODEMANN,~and H.-J. LANGE~ ‘Physical Research Laboratory, Navrangapum, Ahmedabad, India ‘Abteilung Nuklearchemie, Universitiit zu Kiiln, Kijln, Germany ‘Institut fur Mittelenergiephysik, ETH Hbnggerberg, Zurich, Switzerland 4Zcntraleinrichtung tIir Strahlenxhutz, Universitit Hannover, Hannover, Germany (Received June 1 I, 1992; accepted in revised form November 5, 1992)

Ah&act-Depth profiles of the cosmogenic isotopes 3He, we, “Ne, 22Ne, “Be and 26A1have been measured by conventional and accelerator mass spectrometry in the chondrites Madhipura, Udaipur, and Bansur. Shielding depths of the samples and meteorite sixes were derived from cosmic ray track density data and from 2’Ne exposure ages. In addition, “‘Be and 26Al were measured in seven fragments of Dhajala. The measured data, together with the existing 53Mn pro&s in these meteorites and with other well-investigated depth profiles of cosmogenic radionuclides and rare gas isotopes in ALHA 78084, Keyes, St. Severin, Jilin, and Knyahinya, now provide an experimental data base describing the depth and size dependence of cosmogenic nuclides in ordinary chondrites for preatmospheric radii between 8.5 cm and about 100 cm. Production rates are found to change only slightly with depth in small meteorites (R s 15 cm). For larger bodies ( 15 cm 5 R 5 65 cm), the profiles show significant depth dependence, the cosmogenic production increases from the surface to the center by about 30%. The center production rates increase with meteoroid size and show a broad maximum for radii between 25 and 65 cm. The location of the maxima for different nuclides depends on the dominant energy of particles responsible for their production from the main target elements. For R 2 70 cm, a significant decrease of center production rates is seen for loBe, 26Al, 53Mn, and “Ne, the individual depth profiles being essentially flat with shallow transition maxima. The observed depth profiles and the dependence of the center production rates on meteoroid size are well reproduced by model calculations based on Monte Carlo calculations of the intra- and internuclear cascade of galactic protons in meteoritic matter and on experimental and theoretical excitation functions of the underlying nuclear reactions. The model calculations provide a basis for identification of meteorites with anomalous levels of radioisotopes and give information about the irradiation history of meteorites and changes in the cosmic ray intensity with time and orbital space of the meteoroid. The results of the Dhajala chondrite are discussed in this context. al., 1982, SARAPINet al., 1985; VOGT, 1988), Dhajala (POTDARet al., 1986) and Jilin ( BEGEMANNet al., 1985; HEUSSER et al., 1985; and references therein) and the L-chondrites Keyes (WRIGHT et al., 1973; CRESSY,1975; P. ENGLERT, pers. commun. ), Knyahinya ( GRAF et al., 199Oa), and St. Severin (SCHULTZ and SIGNER,1976; ENGLERT and HERR, 1980). The meteorites ALHA78084, Keyes, Knyahinya, and St. Severin cover the range of meteoroid radii between 14 and 45 cm. There is no indication of these meteorites having had a complex exposure history. Jilin is a more complicated case, having a two-stage exposure history, consisting of a 10 Ma exposure in the surface of a large body followed by a short (0.4 Ma) exposure as a meteoroid with a radius R r 85 cm (HONDA et al., 1982, BEGEMANNet al., 1985; HEUSSER et al., 1985). For Dhajala a radius of 45 cm was proposed by POTDAR et al. ( 1986) on the basis of track data. This radius assignment produces, however, contradictions when comparing the Dhajala radionuclide data (POTDAR et al., 1986) with those from Knyahinya, for which a 45 cm preatmospheric radius has been determined ( GRAF et al., 1990a). In order to resolve these discrepancies loBe and 26Al were measured in seven fragments of Dhajala in this work. For three more ordinary chondrites, namely Bansur (L6), Madhipura (L), and Udaipur (H4), depth profiles of 53Mn

INTRODUCTION

RADIOACTIVEAND STABLEnuclides produced by the interactions of solar and galactic cosmic rays with extraterrestrial rocks such as meteorites and lunar samples have been successfully employed in understanding a variety of phenomena like variations of cosmic ray flux and energy spectra over different time scales in interplanetary space and exposure history of meteorites and lunar regolith (e.g., ARNOLD et al., 1961; GEISSet al., 1962; LAL, 1972, BHANDARI,1981; REEDY et al., 1983; VOGT et al., 1990, MICHEL et al., 1991a). The production rates of these nuclides at different depths within bodies of different size and chemical compositions for typical energy spectra of cosmic rays should be known a priori for this purpose. Over the years a number of chondrites have been studied for depth profiles of several cosmogenic nuclides such as ‘He, “‘Be 2’*22Ne,26Al, 53Mn as well as for cosmic ray track profiles, which allow determination of the preatmospheric radii. These meteorites are the H-chondrites ALHA (MONIOT et

* Present address: Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, IN, USA 2361

N. Bhandari et al.

2362

and cosmic-ray tracks were measured by BHATTACHARYAet al. ( 1980)) and it was concluded that these meteorites resulted from meteoroids having radii between 6 and 15 cm, thus being good representatives of small meteoroids. In this work, the depth profiles of the cosmogenic isotopes ‘He, “Ne “Ne, “Be, and 26Al have been measured in core samples of Madhipura, Udaipur, and Bansur. These three meteorites are observed single falls with recovered masses of 1, 2, and 15 kg, respectively ( BHATTACHARYA,1979). The cores investigated were the same for which cosmic ray track production profiles and the 53Mn profiles were determined earlier by BHATTACHARYAet al. (1980). The experimental depth profiles for the cosmogenic nuelides previously mentioned allow description of the systematics of the depth and size dependence of cosmogenic nuclide production rates in ordinary chondrites covering the known range of preaiii;ospheric radii of stony meteoroids. Together with similar work on lunar samples, they provide a complete data base which is excellently suited to test models of the production of cosmogenic nuclides in rocks. In this work, the experimental depth profiles are interpreted in the framework of a physical model ( MICHEL et al., 1989b, 1990, 199 la) which describes, without free parameters, the complex occurrences of cosmic ray interactions with matter. In this model, for galactic cosmic ray (GCR) particles the depth and size dependent spectra of primary and secondary protons and of secondary neutrons are calculated by Monte Carlo techniques using the HERMES (CLOTH et al., 1988) code system. Production rates are calculated by folding these spectra with experimental and theoretical cross sections of the underlying nuclear reactions. This model has been validated in a number of terrestrial simulation experiments ( DITTRICH et al., 1989; HERPERS et al., 199 1; MICHEL et al., 1985, 1989a, 199lb,c). For small meteorites and samples with small shielding depths, the contribution of solar cosmic ray (SCR) particles is taken into account as described earlier (BHATTACHARYAet al., 1973a, MICHEL et al., 1982). EXPERIMENTAL PROCEDURE Samples, typically 100 mg, were taken from known depths of the same cores of Bansur, Udaipur, and Madhipura meteorites, which were formerly investigated by BHATTACHARYA et al. ( 1980). In case of Dhajala, aliquots from the samples investigated by POTDARet al. ( 1986) were taken. Aluminus and beryllium were separated and “Be and 26A1were measured by accelerator mass spectrometry (AMS) as described earlier in detail (GRAFet al., 1990a; V~GT and HERPERS, 1988; and references therein). Rare gas measurements were done at Physical Research Laboratory Ahmedabad using a Reynolds type UHV glass mass spectrometer. The sensitivity of the mass spectrometer for 22Ne was 2; IO-” cm3 STP/mV. Blank corrections were typically 20-40s for 2@Neand 2-3s for the 22Neamounts measured in the meteorite samples. Mass discrimination in the neon maSSrange was I to 1.5% per amu. Corrections for trapped components were made based on ‘%e assuming planetary composition of 2r’Ne/22Ne = 9.8 and 2’Ne/Z2Ne = 0.029 as given by OZIMAand POD~SEK ( 1983). The measured amounts of 3He were considered to be cosmogenic. The blanc corrections for this isotope are negligible. Details of the mass spectrometric measurements may be found elsewhere

( BHAIet al., 1978). “Be and 26Alwere measured in 6, 5, 3, and 9 samples of Bansur, Udaipur, Madhipura, and Dhajala, while rare gases were analyzed in 7, 7, and 3 samples of Bansur, Udaipur, and Madhipura, respectively.

EXPERIMENTAL RESULTS Rare gas and radionuclide data are presented in Tables l3. For Bansur, Udaipur, and Madhipura, the 53Mn data by BHATTACHARYAet al. (1980) and for Dhajala the rare gas data by GOPALAN et al. ( 1977) and the radionuclide data by POTDAR et al. ( 1986) have been included in these tables for sake of completeness. Exposure Ages of Meteorites Based on the measured 2’Ne concentrations and on cosmogenic neon isotope ratios (22Ne/2’Ne)c, “Ne exposure ages were calculated for each sample following the procedures of NISHIIZUMI et al. ( 1980) and EUGSTER (1988). The exposure ages calculated according to EUGSTER( 1988 ) are systematically lower by 7% than those based on the shielding depth correction by NISHIIZUMI et al. ( 1980) (Table 1). For the following discussion we prefer the Eugster ages because of their internal consistency with exposure ages obtained from other rare gases. The mean values of the exposure ages calculated from various samples according to EUGSTER ( 1988 ) are 22.4 + 0.8 Ma for Bansur, 36.4 + 2.5 Ma for Udaipur, 15.6 -t 0.6 Ma for Madhipura, and 8.9 + 1.8 Ma for Dhajala. The uncertainties reflect the scatter of the ages obtained for different samples. These ages, particularly for Bansur and Udaipur, are significantly larger than those reported earlier by BHATTACHARYA et al. (1980) calculated from 2’Ne concentrations measurements by GOPALAN and RAO ( 1976) using production rates of BHANDARIand POTDAR ( 1982). The difference has mainly arisen because BHANDARI and POTDAR ( 1982) normalized their production rates to an exposure age of 11.2 Ma for the St. Severin meteorite as given by MARTI et al. ( 1968 ). This value has subsequently been revised to 16.8 Ma ( EUGSTER, 1988) and the production rates given by BHANDARI and POTDAR (1982) should therefore be reduced by 30%. When this is done, a reasonable agreement with the exposure ages of EUGSTER ( 1988) is obtained. For Dhajala the mean “Ne exposure age of 8.9 f 1.8 Ma calculated (Table 1) is, however, in agreement with 8.3 rt 0.7 Ma given by POTDAR et al. (1986). Because of the long exposure ages of these meteorites, the radionuclides dealt with in this work, with the exception of 53Mn in Madhipura and Dhajala, are in saturation and thus represent production rates. “Mn in Madhipura is about 5% undersaturated if an exposure age of 15.6 Ma is taken. For Dhajala, a detailed discussion will be given later. Shielding Depth and Size of the Meteoroids In order to interpret the measured depth profiles of cosmogenic nuclides in Bansur, Udaipur, and Madhipura in terms of their production profiles, the depth along cores had to be converted to shielding depths in space. This was done on the basis of the measured track densities and exposure ages of the meteorites. BHATTACHARYA( 1979) and BHATTACHARYAet al. ( 1980) reported track densities in spot and core samples of Bansur, Udaipur, and Madhipura and estimated shielding depths, ablation, and preatmospheric radii

Cosmogenic nuclide production rates in stony meteoroids

2363

TABLE1. Cosmogenic “Ne and 3He/2’Ne, %e/2’Ne, and “Ne/*‘Ne ratios and Ne exposure ages of Bansur, Udaipur, and Madhipura calculatedaccordingto NISHIIZUMI et al. ( 1980) and to EUGSTER ( 1988). J

21

Ne

Core

Sample

( 2aNe/21Ne,

lW”Nm

m

(12Ne/2’Ne)

I

(“Ne/“Ne)

T

exe

Nihiizumi

Depth

et al.

[ 10-ecm’/gl

[aI

Baasur

T

E

l xp

Eugstar

(1980)

(1988)

(L6)

13B(B-13-l)

0.0

-

1.0

6.04

f

0.18

5.75

f

0.06

1.03

f

0.01

1.176

f

0.012

1.173

& 0.012

25.00

23.32

B-13-2

1.0

-

1.6

5.37

f

0.16

6.07

f

0.06

1.02

f

0.02

1.188

& 0.018

1.186

f

0.018

23.24

21.68

B-l

3.4

-

3.6

6.30

f

0.19

4.56

f

0.05

1.05

*

0.01

1.147

f

0.012

1.142

f

0.012

23.24

21.68

13A(B-13-4)

3.6

-

4.3

6.48

f

0.19

5.36

f

0.05

1.03

f.

0.02

1.142

k

0.017

1.139

f

0.017

23.63

22.04

14G(B-14-3)

8.3

-

9.0

6.68

f

0.21

5.52

f

0.06

1.03

f

0.01

1.124

f

0.011

1.121

f

0.011

23.29

21.73

B-14-1

9.5

-10.1

7.49

f

0.12

4.46

f

0.05

1.03

f

0.01

1.121

f

0.011

1.118

f

0.011

25.03

23.35

7.79

f

0.23

3.81

f

0.04

1.03

f

0.01

1.107

f

0.014

1.104

i

0.014

3-E

B-14-2

9.9

24.45 22.81 ___________________ 23.98 f

Udmipur

22.37

0.82

f

0.77

(Sl4)

U-6

0.4

-

0.6

8.30

f

0.41

5.86

f

0.06

1.14

f

0.01

1.204

f

0.012

1.190

f

0.012

39.14

36.51

u-s

1.5

-

2.0

8.14

f

0.25

6.92

f

0.06

1.08

f

0.01

1.207

f

0.012

1.199

f

0.012

40.30

37.60

u-7

1.0

-

1.25

8.40

f

0.42

5.70

f

0.06

1.15

*

0.01

1.205

f

0.012

1.190

f

0.012

39.61

36.95

u-5

1.7

-

2.1

8.05

f

0.25

1.22

f

0.01

1.200

f

0.012

1.178

f

0.014

36.45

34.06

8.23

f

0.25

f

0.014

37.01

34.53

36.28

33.85

ux-

1

2.3

u-2

2.8

-

3.9

7.85

f

0.24

5.97

u-3

4.7

-

6.1

9.10

f

0.46

5.41

1.24

f

0.01

1.200

f

0.012

1.176

f

0.06

1.08

f

0.01

1.192

f

0.012

1.184

f

0.012

f

0.06

1.04

f.

0.01

1.201

*

0.012

1.197

*

0.012

43.90 40.96 _____________________ 38.96 f

Mrdhipurm

36.35

2.71

f

(L)

HP-1

0.0

MP-3

1.0

HP-4

3.0

-

-

1.0

4.0

3.80

f

0.11

4.97

f

0.05

1.02

f

0.01

1.182

f

0.011

1.180

f

0.011

16.11

15.03

4.43

f

0.13

5.26

f

0.05

1.02

f

0.01

1.160

f

0.013

1.158

f

0.013

17.37

16.21

4.26

f

0.13

4.78

f

0.05

1.04

f

0.01

1.160

f

0.012

1.156

k

0.012

16.58 ~____--____~----_---

15.47

16.69 f Dhajah

2.52

(data

(II%4)

Fran Qopalm

at al.

15.57

0.64

f

0.60

(1977))

T-67

6.2’

2.613

1.25

f

0.01

1.12

f

0.01

1.16

f

0.01

11.10

10.35

T-11

14.0’

3.175

1.26

f

0.01

1.09

f

0.01

1.09

f

0.01

10.02

9.35

DH-9

42.0’

2.470

1.05

f

0.01

1.08

f

0.01

1.08

f

0.01

7.41 ~-_~_--___---__-_~_-

6.92

9.51 f

l

Thaso al.,

depths

rofmr

to lhioldinq

dapthm

aalaulatod

an the

bmmis

of

trmak

density

1.90

mmmmurmnmntm

8.87 f

(Potdar

1.76

et

1986)

based on track production rates in spherical bodies of BHATTACHARYA et al. ( 1973a,b). Because of the changed exposure ages previously discussed, the track data were reevaluated using the new exposure ages. The track production rates of BHATTACHARYA et al. ( 1973a,b) are based on the track den-

sity profile in the radial core of St. Severin meteorite for which they used an exposure age of 11.2 Ma (MARTI et al., 1968). As mentioned previously, the exposure age of St. Severin has now been revised to 16.8 Ma (EUGSTER, 1988). Hence the track production rates of BHATTACHARYA et ak ( 1973b) need

2364

N. Bhandari et al. TABLE 2. Cosmogonic radionuclides in Bansur, Udaipur, and Madhipura. The 53Mn measurements reported by BATTACHARYA et al. ( 1980) for Mn-53 have been included in this table wherever measurements have been made in the same samples. ~~~~~~~~~--~~~----~_-_--~~---__----__-_---_---_-__-_--__--____---_-_-_____ Sample loBe 53Mn Core Shielding 26Al Depth

Depth

[dpm/kg

[cm1 [d&kg1 Idpm/kgl -~~~~~--~_-~~~~_-_~~~__-~~__--~____-____-_-~~___-~~_---__--___--------__-_ [cm1

Bansur

(L6)

13B(B-13-1) B-13-2 13c 13-3 13D 13A(B-13-4) 14G(B-14-3) 14F(14-1) Udaipur

0.0 1.0 2.0 2.1 3.2 3.6 8.3 10.3

- 1.0 - 1.6 - 2.2

0.0 1.0 1.7 2.4 2.8 4.3 4.7 6.1

- 1.0 - 1.3 - 2.1

- 3.4 - 4.3 - 9.0 -10.5

4.5 5.2 6.0 6.7 1.1 7.5 11.7 13.4

-

5.2 5.8 6.2

58.6

+ 3.8

19.0

i 1.5

48.8

+ 3.4

19.4

+ 1.1

1.3 8.2 - 12.3 - 13.6

48.8 50.9 39.6 50.2

+ + + +

19.7 + 18.5 + 19.7 * 19.0 +

4.0 4.4 4.7 5.0 5.3 6.2 6.5 7.5

-

4.4 4.6 4.9

44.2 44.3 43.9

rt 3.1 + 2.9 * 2.9

17.2 + 1.3 17.6 + 1.4 19.4 * 1.5

-

5.9

46.2

+ 3.0

17.0

+ 1.3

-

7.5

46.6

+ 3.0

17.0

+ 1.3

3.0 3.8 5.5 6.0 7.3

-

3.8 5.0

44.0 41.6

& 2.7 it 3.1

16.8 16.7

+ 1.3 + 1.3

-

0.5

34.8

+ 4.5

17.0

& 1.4

U-S c-2 u-2 C-l u-3 4 Madhipura

339 + 17 6.8 4.3 4.2 4.8

1.1 1.5 1.1 1.1

352 k 18 357 + 18 378 f. 19

- 3.9 - 6.1

300 f. 15

296 + 15 314 & 15 317 + 16

(L)

MP-1 MA2 M-2 MP-4 M-3

0.0 - 1.0 1.0 - 2.2 2.5 3.0 - 4.0 4.3

recordable

272 * 13 290 + 17

to be reduced by 30%. This correction the measured

361 f. 19 351 & 17

(~4)

U-1(6-1) v-4

because

Fe]

is partly compensated track lengths in feldspars

are higher by about 20% than lo-’ m used by BHATTACHARYAet al. ( 1973b). Therefore, a net reduction of only 10% in track production rates is required. This, however, leads to significant change in shielding depths and in the estimated sizes of the meteoroids where the ablation is small. The track production rates yield meteoroid radii of 14 cm, 11.5 cm, and 8.5 cm under the assumption of spherical geometry for Bansur, Udaipur, and Madhipura, respectively. The inferred shielding depths of the individual samples are given in Table 2. For Bansur, the new radius is quite similar to the result of R = 15 cm obtained by BHATTACHARYAet al. ( 1980). For Udaipur and Madhipura the formerly assigned radii were 9 cm and 6.5 cm, respectively, significantly lower than our new results. For Dhajala, which fell as a shower, about 500 fragments were recovered (BHANDARI et al., 1978) and the measurements have been made in different fragments and not in a core taken through the main mass. The shielding depths of various fragments were determined from the cosmic ray track densities which correlate well with the measured @‘Codata ( POTDARet al., 1986 ) . The results of Dhajala will be discussed separately from those of the three small chondrites.

275 f 14

Radionuclide Depth Profiles The depth profiles of “Be and 26AI in Bansur, Udaipur, and Madhipura do not show any significant increase from surface to center in each ofthe specimen, as can be seen from Table 2. These profiles thus indicate only minor depth effects in this range of radii (8.5 to 14 cm) as already noted by BHA~ACHARYA et al. ( 1980) based on their “Mn data. There is no significant increase from surface to center within the limits of experimental errors for the three cosmogenic radionuclides (Fig. I ). This is in contrast to the observation of an about 30% increase of production rates of these three cosmogenic radionuclides from surface to center for larger meteorites such as Keyes, St. Severin, and Knyahinya. There is, however, a slight increase in the mean production rate with the radius of the meteoroid. Considering the apparent constancy of production rates with depth in these small stony meteoroids, these data have to be discussed in two ways: The first question is whether the flat depth profiles can be explained by GCR interactions with small bodies, or whether SCR contributions have to be invoked to explain them. The second one is how the average production rates measured in these chondrites fit into the general picture of size dependence of production rates. Both

%lI

_._._.r-‘-’

,_._,_._._,_,_._._._C.-._._.-._.-.~-.-.-.-.-.-

. . . . . . .._.__......

““‘.‘i

f“"""'I""""'I""""'I"

‘..‘.“...

loBe

MADHIPURA

. . . . . . . . . . . . . . . . . .._..............

MAOHIPURA +

14

r 8 1’0

UDAIPUR

10

‘I

5

SHIELDING

DEPTH

[cm]

10

UDAIPUR

.-..A....

..,-..r:

. . . . . . ..

d-‘-

^....I

I,

I~il:~~::~::1-_~1::::----:

&

f

0

__,......_~‘--...-”

5

‘:~~~_-*d.U.

10

15

._._._. _~,._... ,._,,_ __.-. 1’

I

.......'.........~......, ......___........___...............

+k

I

8

FIG.1. E:xperimental radionuclide concentrations of ‘a, 26A1,and S3Mn and theoretical production rate depth profiles for Madhipura, Udaipur, and Bansur. The “Mn data weretaken from the work of BHATTACHARYA etal.(1980).For the theoretical depth profiles the total production (full lines), the production by primary protons (dotted lines), by secondary protons (dashed lines) and by secondary neutrons (dasheddotted lines) are distinguished.

300

400

0

20

40

60

0

5

10

15

20

I’,

N. Bhandari et al.

2366

these questions are dealt with in the following text on the basis of detailed model calculations. MODEL CALCULATIONS

For any model which predicts the production rates of cosmogenic nuclides in extraterrestrial matter, both solar and galactic cosmic ray particles have to be considered. While there is clear evidence for both solar as well as galactic cosmic ray production of cosmogenic nuclides in lunar samples, in meteorites the production of cosmogenic nuclides is dominated by GCR particles. SCR effects am of minor importance since they are restricted to the outermost few (~5 cm) centimeters at the surface of meteoroids, which scarcely survives ablation during its atmospheric transit. So far, unambiguous experimental evidence for SCR effects in meteorites are restricted to Salein (NISHIIZUMIet al., 1990; EVANSet al., 1987) and St. Severin ( LAL and MARTI, 1977). In small meteoroids, generally, some contribution of SCR interactions cannot be excluded a priori. Thus, for modelling of cosmic ray interactions in small meteoroids both SCR and GCR interactions have to be taken into account. For small meteorites and samples with small shielding depths, the contribution of SCR particles can be calculated as described earlier (BHATTACHARYAet al., 1973a; MICHEL et al., 1982). The accuracy of these calculations mainly depends on the quality of the excitation functions of the underlying nuclear reactions. An uncertainty, however, arises from the fact that the SCR spectra in the meteoroid orbits are not yet known. Therefore, in practice, only when the observed levels of cosmogenic nuclides cannot be explained on the basis of GCR interactions alone, they are attributed to SCR effects. Constraints on SCR effects in meteorites and thereby on SCR spectra and fluxes in the meteoroid orbits, therefore, crucially depend on the accuracy of the GCR models used. In this paper, the experimental depth profiles will be interpreted in the framework of a physical model ( MICHEL et al., 1989b, 1990, 199 la) which describes the production of cosmogenic nuclides by galactic protons. In this model, the depth and size dependent spectra of primary and secondary protons and of secondary neutrons are calculated by Monte Carlo techniques using the HERMES (CLOTH et al., I988 ) code system. Production rates are calculated by folding these spectra with cross sections of the underlying nuclear reactions. A number of terrestrial simulation experiments ( DI~TRICH et al., 1989; HERPERS~~al., 1991; MICHELet al., 1985, 1989a, 1991 b,c) support this model. It also has been successfully applied to explain the depth profiles of cosmogenic nuclides in lunar core samples and in stony meteoroids such as ALHA78084, Keyes, St. Severin, and Knyahinya and to deduce long-term mean GCR spectra at 1 A.U. and at the meteoroid orbits ( MICHEL et al., 199 1a). Since the first reports about this model, several extensions have been successfully implemented. First, the range of calculations was extended to meteoroid radii of 120 cm and secondly, the range of cosmogenic nuclides has been enlarged. Presently, production rates for “Be, 22Na, 26Al, “Mn, 6oCo as well as for Ne- and Kr-isotopes can be calculated. Furthermore, the model has been applied successfully to differentiated meteorites, where the model calculations provide a

basis for the calculation of exposure ages for achondrites via the nuclide pair 2’Ne/53Mn ( HERPERS et al., 1990a,b). The theoretical production rates presented here are calculated for a long-term average GCR proton spectrum as described earlier (MICHEL et al., 1989b, 1990, 1991a). DEPTH PROFILES AND CENTER PRODUCTION RATES A useful framework for the depth and size dependence of cosmogenic nuclide production rates can be developed on the basis of the results for the three small chondrites, discussed previously, and by including earlier results for ALHA78084, St. Severin, Keyes, and Knyahinya. These seven meteorites had preatmospheric radii from 8.5 to 45 cm. Further, extensive experimental data exist for lunar surface conditions, representing a body of infinite radius. Jilin had a preatmospheric size of about 1 m but since it had a complex exposure history, it is not possible to derive information about the production function of long-lived isotopes from these measurements; only cosmogenic radionuclides with half-lives less than 50 ka can be used for this purpose. However, only 22Na and 6oCo have been measured so far. It has been shown earlier ( MICHEL et al., 199 la; HERPERS et al., 1991) that the model calculations describe shape and magnitudes of the experimental depth profiles of “Be, 26Al, “Mn, and “Ne in ALHA78084, Keyes, St. Severin, Knyahinya, and in the Apollo 15 drill core within less than lo%, without any systematic deviations. The results obtained for Madhipura, Udaipur, and Bansur are of the same quality (Fig. I). The flatness of the profiles measured for Madhipura, Udaipur, and Bansur does not imply that the action of secondary particles is negligible in small meteorites. Thus, even in the center of a meteoroid with 8.5 cm radius primary protons contribute only about 30% to isotope production and major (about 70%) contribution comes from secondary protons and neutrons. For a radius of 14 cm this primary contribution is only 23%, thus indicating that secondary neutrons dominate even in small meteoroids. Considering the importance of secondary production, one expects an increase of production rates from surface to the center of the meteoroid. The theory predicts, for instance, increases of 53Mn from surface to the center by 23%, 32% and 35% for radii of 8.5 cm, I I .5 cm, and 14 cm (Fig. 1). The largest gradient occurs in a small region near the surface of the meteoroids. The near constancy of the experimental profiles is just a result of the meteorite samples representing interior regions where the depth profiles are relatively flat, the surface regions where production rate gradients occur being lost due to ablation. There is no need to attribute significant parts of the observed activities to SCR interactions, since the GCR calculations adequately explain the measured 53Mn, 26A1,and “Be data in all the three meteorites Madhipura, Udaipur, and Bansur. The new data allow us to investigate the dependence of center production rates as a function of meteoroid radius. The mean center production rates were calculated from the experimental data for “Mn, 26Al, and “Be in Madhipura, Udaipur, Bansur, ALHA78084, St. Severin, Keyes, and Knyahinya. Only samples from interior, near-center positions

Cosmogenic nuclide production rates in stony meteoroids

were used for averaging for meteoroid radii above 15 cm. The uncertainty in the mean center production rates is equal to the empirical variance of the analytical error for the particular radionuclide. The systematic uncertainties adopted for the determination of “Be, 26A1(both using AMS), and s3Mn (using RNAA) were 7% 8.5% and lo%, respectively. These experimental center production rates for “Mn, 26A1, and ‘OBe,covering preatmospheric radii between 8.5 and 45 cm, are presented in Figs. 2-4 together with theoretical center production rates up to radii of 120 cm. The calculational precision of the theoretical center production rates for a given set of cross sections for the production of a particular nuclide is between 2% for small meteoroids and 4% for the largest. The center production rates increase with meteoroid size and show broad maxima for radii between 25 and 65 cm. Except for “Be, the increase is by about a factor of two. The magnitude of the increase as well as the location of the maximum depend on the energy of the particles responsible for its production. For larger radii the center production rates decrease slowly for *‘jAl and ‘3Mn, which are low-energy products, and somewhat more rapidly for “‘Be, which is a high-energy product. For 53Mn, the model calculations agree with the experimental data within the limits of experimental uncertainties (Fig. 2). Although for the determination of 53Mn by radiochemical activation analysis a typical experimental uncertainty of 10% can be assumed, the actual deviations of the observed center production rates from the calculated ones are below 5%. The smaller empirical variances of individual depth profiles probably originate from the fact that the data presented here are obtained from one set of analyses and the scatter in the data represents precision rather than accuracy. Figure 2 also shows the proton and neutron contribution to the center production rates. Proton production dominates

’

I

.’

0

53Mn

Center Production Rates in Chondrites

50

100

RADIUS [cm] FIG.2. *‘Mn production rates in the center of ordinary chondrites as a function of meteoroid radius. The experimental data for Knyahinya (Kn) are from GRAF et al. ( 199Oa), for Keyes (Ke) from P. ENGLERT, pm. commun., for St. Severin (Se) from ENGLERT and HERR (1980), for ALHA (Ah) from SARAFIN et al. ( 1985), and for Bansur (Ba), Udaipur (Ud), and Madhipura (Ma) from BHATTACHARYAet al. ( 1980). For the theoretical curves the total production and the production by protons (primaries + secondaries) and by secondary neutrons are distinguished.

I

v

I

I

I

I

2361 I

I

I,

I

*6Al Center

I

I

I

I

I

I

I

•i L-chondrites 0 R-chondrites ...L-chondrites - E-chondrites

0

I,

I

I

I

Production Rates

50 RADIUS [cm]

exp. exp. talc. talc. 100

FIG.3. %A1production rates in the center of ordinary chondrites as Cmction of meteoroid radius. The experimental data are from this worl~forMadhipura(Ma),Udaipur(Ud)andBansur(Ba)andfrom GRAFetal.(l99Oa)forKnyahinya(Kn),fkomCREssY(l975)and VOGT (1991) for Keyes (Ke), from SARAFINet al. (1985) for ALHA (Ah) and from BHANDARI (1986) and VOGT (1991)

for St. Severin (Se).

near the surface and, for a radius of about 10 cm, neutrons and protons contribute equal amounts. For larger radii, neutrons rapidly become dominating, reaching their maximum production rate at a radius of 65 cm. The broad maximum of total center production rates for radii between 25 and 85 cm is caused by the balance between decreasing pinduced and increasing n-induced production. The 26A1depth profiles measured in Madhipura and Udaipur are similar within the experimental errors. The experimental uncertainties in the center production rates are about 8.5%. For Bansur and Madhipura the calculated center production rates agree within the experimental errors (Fig. 3). For the H-chondrite Udaipur (R = 11.5 cm), however, the center production rate is found to be equal to that measured for ALHA78084, for which a larger radius of 15 cm was inferred ( SARAFIN et al., 1985 ). This discrepancy is not seen for the center production rates of 53Mn. If a terrestrial age of ALHA of 140 + 70 ka is assumed ( NISHIIZUMI et al., 1989), 26A1will decay by 12.6% after its fall and a better agreement with the experimental profile can be obtained. There is, however, one significant discrepancy in the systematics of center production rates of 26A1,which also shows up for “Be (Fig. 4)) between the data for St. Severin and Keyes. Both nuclides are too high in St. Severin compared to Keyes by 20%, St. Severin falling above the theoretical line of the center production rates. The 26Al profile was measured in St. Severin by BHANDARI ( 1986) and by CRESSY ( 1975 ) in Keyes. Recent re-analysis by S. Vogt confirms these measurements within limits of errors. An explanation of the high 26Al in St. Severin by a nonspherical preatmospheric shape is unlikely ( GRAF et al., 1990b) and, moreover, is not revealed by the likewise low-energy product 53Mn. A better agreement is obtained with the 26A1(57.2 -t- 10.0 dpm/ kg, HERPERSand ENGLERT, 1983) measured by coincidence techniques for sample DIIIb of St. Severin (preatmospheric depth 2 9 cm).

N. Bhandari et al.

2368

The calculated production rates of 26A1reveal 7% higher production in L as compared to H chondrites due to compositional differences. This is in agreement with the experimental observations for the mean production rates (FUSE and ANDERS, 1969; HAMPEL et al., 1980; HERPERS and ENGLERT, 1983). The difference between L-chondrite Bansur and H-chondrite ALHA both having similar preatmospheric size, however, vanish if one assumes a substantial terrestrial age of the latter as previously discussed. In our earlier work ( MICHEL et al., 199 1a), the production rates for “Be were not given because the assumption of equal cross sections for proton- and neutron-induced production of “Be resulted in underestimation by about a factor of two compared to the experimental data. Based on recent measurements of the thin-target cross sections and on simulation experiments, it is now possible to give theoretical production rates for “Be with some confidence. There now exists a consistent set of integral excitation functions for the proton-induced production of “Be from 0, Mg, Al, Si, Ti, Fe, and Ni from thresholds to 2.6 GeV ( DITTRICH et al., 1990; BODEMANN et al., 1992). For the production of “Be by neutroninduced reactions, a set of excitation functions was derived from the analysis of “Be production in 0, Mg, Al, Si, Ti, Fe, and Ni in an artificial meteoroid irradiated isotropically with 1600 MeV protons ( HERPERS et al., 199 1) . These data show unambiguously that the n-induced production cross sections of “Be are 3 to 4 times higher than those of p-induced reactions for all target elements between 0 and Ni, similar to those proposed by TUNIZ et al. ( 1984) based on the analysis of “Be in St. Severin. With these new cross sections, production rates of “Be were calculated for stony meteoroids (Fig. 5) and lunar drill cores. “Be data in Bansur, Udaipur, and Madhipura do not show any change with depth within the limits of errors. The model calculations describe the observed “Be. production rates in Madhipura, Udaipur, ALHA78084, Bansur, and Keyes

6

t loBe Center

0

Production

50

RADIUS [cm]

Rates

100

FIG. 4. “Be production rates in the center of ordinary chondrites as function of meteoroid radius. The experimental data are from this work for Madhipura (Ma), Udaipur (Ud), and Bansur (Ba) and from GRAFet al. ( 199Oa) for Knyahinya ( Kn), from VOGT( I99 1) for Keyes ( Ke) , from TUNIZet al. ( 1984) and VOGT( 199 1) for St. Severin (Se), and from SARAFINet al. ( 1985) and MONIOTet al. (1982) for ALHA (Ah).

25 loBe in H-chondrites % x ‘;i $$

d 2

20

15

10

P4 5

0 3

50 Depth

100

[cm]

FIG. 5 . Theoretical depth profiles for the production of “Be in Hchondrites for radii of 5, IO,25 32,40,50,65,85, 100, and 120 cm and for an H-chondritic asteroidal surface. The production rates are for the long-term averaged GCR spectrum in the meteoroid orbits.

within the experimental errors. They underestimate the data for St. Severin and Knyahinya by IO- 15%.Also the “Be data in the Apollo 15 core are reproduced within lo%, the theoretical data being slightly lower than the experimental ones but still within experimental errors. Since the new cross sections were derived indirectly from thick-target yields in a simulation experiment, further experimental investigations of thin-target cross sections for the production of “Be by neutron-induced reactions are needed and might improve the quality of future model calculations. There is some internal inconsistency between the “Be data for St. Severin and Knyahinya on the one hand and for Keyes on the other, “Be in Keyes being systematically low. “Be was measured in Keyes by S. Vogt and in St. Severin by TUNIZ et al. ( 1984) and by S. Vogt. The two data sets for St. Severin are in reasonable agreement, though a transition maximum seen in the depth profile by TUNIZ et al. (1984) was not reproduced by the data of S. Vogt ( 199 1). The depth profile by S. Vogt shows a continuous increase from surface to center, in agreement with the theory. Analysis of the experimental *‘Ne profiles allows us to test the consistency of the model used here. Comparison of the “Ne exposure ages calculated according to NKHIIZUMIet al. ( 1980), EUGSTER ( 1988), and the present model are given in Table 3. It may be noted that in general the theoretical exposure ages are slightly larger than those calculated according to NISHIIZUMIet al. ( 1980) and to EUGSTER( 1988 ). The average ratios are TexJTexp (Eugster) = 1.09 + 0.09 and Texp/ Terp (Nishiizumi) = 1.02 + 0.09. There is no systematic trend with meteoroid radius in the deviations even for the smallest meteoroids. In case of Madhipura, for which a radius of 8.5 cm was assigned, the theoretical exposure age is higher than that calculated from the shielding depth corrections, while that for Udaipur (R = 11.5 cm) is lower. It is important to note that the theoretical exposure ages allow us to set limits of uncertainties for the preatmospheric radii assignments for Madhipura, Udaipur, and Bansur. A recalculation of the radii and of the depth assignments on

Cosmogenic nuclide production rates in stony meteoroids

2369

TABLE3. Comparison of exposure ages [Ma] derived in this work from experimental 2’Ne data usingtheproposed "Ne production rates and those calculated according to NISHIIZUMI et al. ( 1980) and EUGSTER( 1988).

T5 Ts R T T sxps *xp axp "Nishiisumi" "Eugster" tl?s work [cm1 ____--__----_______--~~~~--~~~~~~~--~~~~---____---~~_------~~~-----~~~~---~~~~~~_

Meteorite

Type

Madhipura

L

Ddaipur

l

8.5

15.05

16.7 + 0.6

15.6 + 0.6

19.8 + 1.8 (1.6)

H4

11.5

22.05

49.0 * 2.7

36.4 + 2.6

35.7 f 2.0 (0.8)

Bansur

L6

14.0

15.05

24.0 + 0.8

22.4 + 0.8

25.5 f 3.5 (3.2)

ALHA 78084

H4

14.0

32.0'

32.9 f 1.2

30.7 + 1.1

34.1 * 1.5 (0.3)

St. Severin LL6

27.'

10.E4

16.9 f 0.8

15.8 & 0.8

16.2 k 0.9 (0.4)

Keyes

L6

30.0

23.01

29.3 f 0.6

27.3 + 0.6

29.8 + 1.5 (0.3)

Knyahinya

LS

45.0

40.s2

40.3 f 1.0

37.6 + 1.0

39.0 f 2.2 (1.0)

H3-4 see text 8.36 9.5 + 1.9 8.9 + 1.8 Dhajala ___-_______--____--_~~~~-~~~~~~~~~~-~~~~--~____----_-----~~~~--~~~~~~~~~~~~~~~~~~

#

radius of a sphere with a volume equal to that of an ellipsoid

with main

semiaxes of 40, 20, and 25 cm. *

exposure Graf

age given

(5) by Bhattacharya s

errors are

in first reports,

i.e.

(3) by Sarafin et al. (1985),

(1988),

(1) by Cressy

(1975),

(4) by Wright

(2) by

et al. (1973),

et al. (1980) and (6) by Gopalan et al. (1977).

standard deviations of exposure ages calculated

samples of a meteorite.

For

St.

for different

Severin only samples with d > 10 cm were

considered. 8

errors include center

samples

theoretical cm were

standard deviation of absolute "Ne (given in parentheses)

concentrations

and a 5 % adopted

of near

uncertainty

of

production rates, Samples with d > 7 cm, 12 cm, 15 cm, and 20

considered

for ALHA

78084,

St. Severin,

Keyes

and Knyahinya,

respectively.

the basis of these theoretical exposure ages results in uncertainties of less than f 1 cm in the radii. Since the cosmogenic nuclide data of Madhipura, Udaipur, and Bansur can be described consistently with the other wellinvestigated meteorites such as ALHA78084, St. Severin, Keyes, and Knyahinya, there is no necessity to invoke complex exposure histories for these meteorites. This is in agreement with BHANDARI( 1986) who came to the same conclusion based on the track density and ( Z2Ne/2’Ne)c correlation. Thus, there now exists a complete description of cosmogenic nuclide production rates for spherical meteoroids with radii between 8.5 and 45 cm. ACIIVI’IV PROFILES IN DHAJALA CHONDRITE Profiles of several cosmogenic nuclides in Dhajala (H3-4) have been reported by BHANDARI et al. ( 1978 ) and POTDAR et al. ( 1986). These authors measured “Be, “Na, 26A1,and

WC0 and, on the basis of the minimum track density observed, assigned a preatmospheric radius between 45 and 50 cm to this meteorite. Two samples of Dhajala have also been measured for the “Mn activity. BHANDARI etal. ( 1978) reported a value of 76 -t 9 dpm/ kg in fragment T- 11 (shielding depth 14 cm), which leads to a value of 27 1 f 32 dpm/kg Fe. HERPERS and ENGLERT ( 1983) reported a similar value of 265 + 15 dpm/ kg Fe in fragment T- 15 (having similar track density and shielding depth of 14 cm). Correcting for undersaturation during the exposure age of 8.87 Ma (Table 1 ), these values lead to a s3Mn production rate of about 327 dpm/kg Fe. A comparison of the 26A1and “Be production rates with those measured in Knyahinya (R = 45 cm, GRAF et al., 1990a) shows that the activity levels in Dhajala are significantly (up to a factor of 2) lower than those in Knyahinya. As for 53Mn, the values reported in Knyahinya range between 406 + 56 and 526 + 62 dpm/kg Fe except for one value of 378 f 58 in kn-8, a sample close to the surface.

N. Bhandari et al.

2370

TABLE4. Cosmogenic radionuclidesin the H3-4 chondrite Dhajala. ---_~----~_--~~_--~---~_--_-_-__--___--___--___-__--________--__--_______-______________________ Sample

Depth’ [cm1

loBe [dpm/kg] Potdar et this work (1986)

al.

26A1 [dpm/kg] this Potdar et work (1986)

al.

3.0

13.0

f

0.7

T-9-l

6.0

12.8

rt 0.6

21.8

f

40.8

f

3.6

1.5

47.9

f

1.7

45.0

f

4.0

T-11

14.

12.6

f

0.6

17.3

f

4.3

37.6

it 1.4

56.0

f

3.4

T-273

15.

15.2

f

0.8

20.8

f

0.9

59.2

rt 2.6

49.0

i

2.0

15.1

f

0.8

56.7

f

2.1

T-272

16.5

15.7

f

0.8

19.0

f

1.0

52.2

f

2.5

T-9 2

29.

11.2

f

0.6

17.3

f

0.7

48.0

i

2.1

12.3

f

0.6

46.9

f

3.1

14.6

f

0.7

46.4

f

3.1

DH-9

42.

18.2

f 0.7

+

according Heusser

to Potdar et (spectroscopy],

al.

( 1986)

priv.

comm. to Potdar

Therefore, 53Mn is also probably similarly lower in Dhajala

compared to Knyahinya. We have therefore remeasured seven samples of Dhajala, whose shielding depths were already determined from track density measurements and for “Be and 26Al by AMS. The new “Be and 26Al data are presented in Table 4. The results confirm that the average 26Al specific activities in Dhajala are 33% lower than the center production rates in Knyahinya. According to POTDAR et al. ( 1986), the sample DH-9 should have been close to the center of Dhajala. With 26Al = 46.4 dpm/kg, it is 36% lower than the Knyahinya center production rate. The compositional difference between Knyahinya (L-chondrite) and Dhajala (H-chondrite) is 7% for 26A1as noted earlier, and therefore the composition corrected difference in 26Al activity is about 26%. The new “Be data measured by AMS are significantly lower than those measured by counting techniques by POTDAR et al. ( 1986). The average “Be content from our new measurements (Table 4) is 13.6 + 1.6 dpm/ kg, while POTDAR et al. ( 1986) found 19.4 + 1.9 dpm/kg. The accuracy of the new data is confirmed by repeated analysis for two samples (Table 4). The reason for this discrepancy is not clear and can probably be attributed to an error in the “‘Be standard used by POTDAR et al. ( 1986) for calibration of their beta counter. In the following we consider the AMS data to be correct. The average “Be in Dhajala is lower by 46% than the center production rate in Knyahinya and by 42% if DH-9 is assumed to be near the center of Dhajala. Furthermore, the difference in ‘%e production between L- and H-chondrites is small (a-

et

spectroscopy

[ dpm/kg]

73.

f

11.

6.6

f

al.

2.3

105.

f

11.

19.0

it 2.3

135.

2 13.

25.0

f

3.0

rt 2.5

126.

f

12.

58.0

& 3.5

51.0

rt 2.0

115.

f

11.

83.9

& 9.0

6.0

110.

f

8.

71.6

f

al.

et

spectroscopy

49.5

48.0’2

# G.

“Co

Potdar (1986)

(1986)

AMS counting counting AI%.? ~--------~----~~--~---_----_--__---___---_-____-_____-__-__---__--_______--___---___------__--_A

22Na [dpm/kg ] Potdar et al.

6.0

(1986)

5%). In view of this discussion, it is clear that the “Be, 26Al, and 53Mn data of Dhajala and Knyahinya cannot be understood in a simple way if both had a single stage exposure history with a radius between 45 and 50 cm. Effects of nonspherical geometry, error in estimation of the radius of the two meteoroids, differences in GCR flux and shape of the energy spectrum and in the orbital space of the two meteoroids and complex exposure history may be some of the factors responsible for the observed differences in isotope production rates in Knyahinya and Dhajala and need to be investigated further. In case of Knyahinya, samples taken from a cross section of the main mass were investigated. GRAF et al. (1990a) measured cosmic ray tracks in ten samples of this cross section, which showed shielding depths between 4.5 ( + 1.5, - 1.O) cm and 3 1.3 (+4.2, - 1.5) cm. The center of the meteoroid was determined from a detailed mapping of cosmogenic He and Ne-isotopes (thirty six samples) and of “Be (sixteen samples) over this cross section. Since the relative locations of all the samples were known, the combination of track and cosmogenic nuclide information allowed for a fairly definite assignment of the radius of 45 +- 5 cm for the Knyahinya meteoroid ( GRAF et al., 1990a). It was, moreover, concluded that the uncertainty of this radius assignment of +-5 cm also includes possible deviations from spherical shape. GRAF et al. ( 1990b) also discussed the influence of nonspherical shapes. Therefore, the differences in activity of various radionuclides observed between Dhajala and Knyahinya cannot be explained by deviations from spherical geometry. In case of Dhajala there is some uncertainty about the

Cosmogenic nuclide production rates in stony meteoroids shape and size of the meteoroid since there is no main mass, and measurements have been made in different fragments. Dhajala fell as a shower following a fireball and two detonations on 28 January 1976 at about 8:40 p.m. (BHANDARI et al., 1976). About 500 fragments having a total mass of more than 60 kg were recovered. BAGOLIA et al. ( 1977) measured cosmic ray tracks in 278 fragments, most of which had fusion crust on them. They gave a preatmospheric radius of 38 f 2 cm assuming an exposure age of about 7 Ma. POTDAR et al. ( 1986) studied cosmogenic radionuclides and tracks in seven fragments and found a good correlation between track density, shielding depth and 6oCo concentrations. These authors concluded from the observed minimum track density that Dhajala had a preatmospheric radius between 45 and 50 cm. The orbit of#nyahinya is not known. However, BALLABH et al. ( 1978) determined fairly reliable estimates of the orbital parameters of the Dhajala chondrite. It may be mentioned here that 22Na/26Al of about 2.3 in Dhajala is the highest value ever observed in chondrites except for Jilin, which is a known case of complex exposure. This 2ZNa/26Al ratio has been explained on the basis of the highly inclined orbit (i.e., about 27.6’) of the Dhajala meteoroid as deduced by BALLABH et al. ( 1978), because of which it was irradiated to cosmic rays at high heliolatitudes for most of the time. The high 22Na in part could also be due to the fact that Dhajala fell at the time of a solar minimum, just before which the GCR fluxes in the near earth space were unusually high (BHANDARI et al., 1978). From our calculations, 22Na/26A1 ratios lie between 1.1 and 2.3 at the center of a 40 cm Hchondrite, if the average GCR-spectrum according to MICHEL et al. ( 199 1a) is taken for the production of 26Al and spectra with modulation parameters ( CASTAGNOLIand LAL, 1980) of 900 MeV (observed in 1969) and 300 MeV (observed in 1977) are taken for the production of 22Na, respectively. Lower long-term ( lo7 a) GCR fluxes in the interplanetary space at high heliolatitudes seems to be a plausible explanation for low loBe, 26Al, and s3Mn observed in Dhajala as significant heliolatitudinal gradients exist ( KOTA and JOKIPII, 1983). But this hypothesis remains to be confirmed by other observations. Having discussed the uncertainties in shape, radii, GCR flux, and orbital differences, we now consider the possibility of complex exposure history for Dhajala. Two different scenarios generally describe the complex exposure history of meteorites, one being a long exposure in an asteroidal regolith followed by exposure in space as a small body and the other being exposure as a meter-size body in space which undergoes fragmentation for later part of its lifetime in space and is thus exposed as a small body. In the context of the information on radio- and stable isotopes and tracks available for Dhajala, as previously discussed, the following possibilities may be considered. 1) A very long first stage of exposure deeply shielded in an asteroid or bigger meteoroid resulting in negligible 26Al, “Be, and 53Mn activities, but accumulating a significant part of the observed ‘He and 2’Ne, followed by a second stage in a meteoroid with R = 45 - 50 cm, long enough to built up 26Al, “Be, and 53Mn, but short enough to leave them under-saturated.

2371

2) A first atage in a large meteoroid (R about 130 cm), which produced most of the 2’Ne, saturated 26Al and IsBe, and nearly S3Mn, thus explaining the low production rates, and a second stage exposure in a smaller meteoroid saturating 22Na and ‘60Co and producing all the tracks observed but too short to a&t 26Al, “Be, and 53Mn. The first scenario can be ruled out because the radioisotope ratios in Dhajala are similar to that in Knyahinya although their absolute activity levels are smaller (Table 5 ). Any under-saturation would change these ratios as the half-lives of the three nuclides differ by about one order of magnitude. In the second scenario the observed activity ratios can be easily explained. The ratio 26Al/ ‘OBeis slightly larger in Dhajala than in Knyahinya, while the “‘BeJs3Mn ratios are smaller in Dhajala. These differences between Knyahinya and Dhajala are consistent with Dhajala being larger than Knyahinya, because the “Be center production rates decrease somewhat faster with radius than those of the low-energy products 26Al and 53Mn. The latter two nuclides are similar considering the energetics of formation, so that similar P( 26Al)/P( 53Mn) ratios in Dhajala and Knyahinya are to be expected. 22Na data ( BHANDARIet al., 1978) have too much spread to allow any constraints on size in the second stage in connection with the theoretical production rates (Fig. 8). However, this latter scenario cannot explain the observed track and 6oCo data, even if the exposure periods are arbitrarily adjusted for the following reasons. The strongest argument against the complex exposure history of Dhajala is that the depths derived from 6oCo and track densities are generally in agreement ( POTDARet al., 1986). Fragmentation or complex exposure during the period when the tracks were accumulated can therefore be ruled out. The lower limit for this period can be obtained from the highest track density of 1.6 + 1O6 cmv2 ( BAGOLIAet al., 1977 ) observed in olivines of fragment A. Since no solar effects are seen in the fragment A (Table 3), a minimum ablation of 2 cm can be assumed for the location of this fragment. Based on the track production rates of BHATTACHARYAet al. (1973b), a minimum exposure period of 3 Ma is required for producing the observed track density in fragment A. Thus from the foregoing discussion, it appears that both scenarios of complex exposure cannot explain the observed data of radioisotopes, tracks, and stable isotopes. Assuming a single stage exposure and taking the “Ne exposure age of 8.4 Ma, the loBe and 26Al activities should be in saturation and can be taken as production rates. A comparison of the observed “Be, 26A1,and “Mn activity (Table 3) with theoretical depth profiles (Figs. 5-7) demonstrates that the data of Dhajala can be understood by assuming a radius larger than 85 cm. Except for the observed @‘Coactivities for Dhajala, there is no principal problem with a preatmospheric radius larger than 85 cm for Dhajala meteoroid. Of course, in such a case one has to assume that the central main mass of Dhajala was not recovered and the about 500 fragments recovered represent the outer 30 or 40 cm material of this body. The large radius of the Dhajala meteoroid easily explains the track density profile, the concentrations of 26A1,“Be, “Mn, 22Ne, and 2’Ne, and also of 22Na if a +30% effect on the GCR flux due to the solar minimum or due to a heliolatitudinal gradient

N. Bhandari et al.

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TABLE5. Production rate ratios in Knyahinya and Dhajala, assuming a simple exposure history for Dhajala. For s3Mn production rates were calculated for the smallest and the largest exposure “Ne ages of individual samples for a hypothetical case of saturation ( TcXp> 15 Ma). _____________________________-____~~__---~~~~~~-~~~~_--~~~~_--~~~~~~ Production Rate

Knyahinya

Ratio

Center

Dhajala Average.

______________________----__----__~~____-~~~~~_-~~___---~___--~~~~~~ P(26Al)/P('oBe)

2.89

F 0.23

P(26Al)/P(53Mn)

0.15

+ 0.02

P('"Be)/P(53Mn)

0.052

+ 0.006

3.57

rt 0.69

0.13

+ 0.02

(Texp =

6.92

Ma)

0.16

+ 0.02

(Texp = 10.35

Ma)

0.18

F 0.03

(T

Ma)

0.037

+ 0.005

(Texp =

6.92

Ma)

0.045

+ 0.005

(Texp = 10.35

Ma)

0.051

+ 0.007

(Texp > 15.

Ma)

exP

> 15.

__-_____-_____--_____-------~---_-~---~~~~---~~~~----~~~---~~~~-----

* For loBe and 26A1 only AMS data were used.

is included ( BHANDARIet al., 1978). A large radius would, however, call for a redetermination ofthe exposure age, since it is known from the investigation of cosmogenic neon in Jilin ( BEGEMANNet al., 1985), that 2’Ne production rates are ambiguous for ( 22Ne/2’Ne), ratios near 1.08 and that a depth correction according to EUGSTER( 1988) or NISHIIZUMI et al. ( 1980) can only be applied for higher (22Ne/2’Ne), ratios. If Dhajala was a large meteoroid, the present exposure age is only a lower limit for its real age. Generally neutron capture products such as @‘Co, 4’Ca, and 36C1are the optimal size indicators in stony meteoroids. In Dhajala, only 6oCo has been measured and its profile is consistent with R s 40 cm if the calculations of EBERHARDT et al. ( 1963) are considered ( POTDAR et al., 1986 ). Without

discussing the adequacy of Fermiage theory to explain the problem of low-energy neutron transport in small non-equilibrium sized bodies, it must, however, be stated that the nuclear data used by EBERHARDTet al. ( 1963) are superseded in the meantime by more accurate data (MUGHABGHAB et al., 198 1). Thus, the resonance integral for neutron capture by 59Co changed from 38.5 b to 74.0 b. Moreover, assuming chemical compositions according to MASON (1979) and scattering and absorption cross sections according to MUGHABGHABet al. ( 1981), the macroscopic cross sections necessary for the calculations changed up to 15%. Taking the Co abundance of 720 ppm, as reported by POTDAR et al. ( 1986) for Dhajala, and updating the calculations of EBER-

600

%tn in Chondrites 26Al in H-chondrites :

2 z -

60

$

400

$ 8

40 ii 200 I: a

$ IL 20

0

0

0

0

50 Depth [cm]

100

FIG. 6. Theoretical depth profiles for the production of *‘$A1 in Hchondrites for radii of 5, 10,25,32,40,50,65,85, 100, and 120 cm and for an H-chondritic asteroidal surface. The production rates are for the long-term averaged GCR spectrum in the meteoroid orbits.

50

100

Depth [cm] FIG. 7. Theoretical depth protiles for the production of “Mn in ordinary chondrites for radii of 5, 10, 25, 32, 40, 50, 65, 85, 100, and 120 cm and for a chondritic asteroidal surface. The production rates are for the long-term averaged GCR spectrum in the meteoroid orbits.

Cosmogenic nuclide production rates in stony meteoroids

ZzNa in Ii-chondrites

120 f

100

$

80

2

60

% ;

40 20 0

0

50

Depth

100

[cm]

FIG. 8. Theoretical depth profiles for the production of **Na in H-chondrites for radii of 5, 10,25, 32,40, 50,65,85, 100, and 120 cm and for an H-chondritic asteroidal surface. The production rates are for the long-term averaged GCR spectrum in the meteoroid orbits.

HARDT et al. ( 1963) with the new nuclear data, we expect a maximum 6oCo activity in H-chondrites of 456 dpm/ kg for a radius of 70 cm. This is more than 45% higher than the old maximum production rate of 308 dpm/ kg ( EBERHARDT et al., 1963), calculated for the same radius and Co abundance and five times the maximum observed value. It may be noted that the three different model calculations of @‘Coproduction rates by EBERHARDTet al. ( 1963), revised with recent nuclear data, by SPERGEL et al. ( 1986) and by our group are in disagreement with respect to magnitude and depth dependence. In a H-chondrite with 720 ppm Co, the revised EBERHARDT et al. ( 1963) production rates give a maximum 6oCo activity of 456 dpm/ kg for a meteoroid radius of 70 cm. Our calculations give 465 dpm/kg for a radius of 85 cm. SPERGELet al. ( 1986) find the maximum in L-chondrites for a radius of about 83 cm with a production rate of about 2 10 dpm/ kg (renormalized to 720 ppm Co). For small meteoroids the EBERHARDT et al. ( 1963) production rates increase faster with meteoroid radius than our calculations and those of SPERGELet al. ( 1986). These uncertainties have to be kept in mind while determining meteoroid sizes from neutron capture nuclides like 36C1,4’Ca, and @‘Co. For a @?o center production rate of 83 dpm/kg, however, the differences between the radius estimates by the three models are low. We estimate radii of 35 cm, 30 cm, and 36 cm according to our calculations, to EBERHARDT et al. (1963), and to SPERGEL et al. (1986), respectively. Thus, the preatmospheric radius of Dhajala was 30-36 cm, assuming the sample DH-9 to represent the center of the meteoroid. But it must be noted that the 6oCo production also depends on the phase of the solar cycle during one or two decades before the fall of Dhajala and intensities of GCR fluxes during this period have to be taken into account. However, the last ten years before the fall of Dhajala, which are most important for the observed 6oCo activities, covered a broad range of modulation parameters as defined by CASTAGNOLIand LAL ( 1980). For the solar maximum of 1969 a modulation parameter of 900 MeV and for the solar minima of 1965 and 1977 modulation parameters of 450 MeV and of 300 MeV

2373

were measured, respectively. For modulation parameters ranging from 300-900 MeV the center production rates of 6oCo vary by a factor of about 2.6 according to our calculations, those with lower modulation parameters being higher than those with large modulation parameters. If Dhajala had a high inclination the solar magnetic shielding should be lower for Dhajala than for a meteoroid with an orbit in the planetary disk and consequently such an orbit should raise the mCo production rate. However, this is not seen in the data. Up to now, no adjustment of60Co production rates to GCR modulation as function of time has been made. This would be possible in principle on the basis of terrestrial neutron monitor data, but has not been done up to now. The actual correction should, however, be smaller than for ‘*Na since 6oCo due to its longer half-life averages over about one &ilar eleven-year cycle. In view of these uncertainties, measurements of 36C1and 4’Ca, which are equally sensitive to the size of the meteoroid are required. They will enable us to put more stringent limits on the size and hopefully resolve the discrepancies seen in the cosmogenic nuclide data of Dhajala and Knyahinya. CONCLUSIONS Measurements of the three cosmogenic mdionuclides “Be, 26A1,and 53Mn, of the rare gas isotopes 3He, ‘%e, 2’Ne, and “Ne, and of tracks in Bansur, Udaipur, Madhipura, and Dhajala have considerably enlarged the experimental data base of cosmogenic nuclide depth profiles. As a result, the depth and size dependence of cosmogenic nuclide production rates in ordinary chondrites are now available for radii between 8.5 cm and about one meter. The experimental depth profiles can be reproduced fairly accurately by the model of GCR interactions with matter developed and described earlier by MICHEL et al. ( 199 1a). The mode1 calculations adequately describe the cosmogenic nuclide production in lunar drill cores ( MICHEL et al., 1991a) and are well applicable to infinitely large bodies. Production rates of 2’Ne, calculated from this model give exposure ages within 10% of the values based on the well-established procedure of EUGSTER ( 1988). In view of the accuracy with which this mode1 predicts the isotope production rates, meteorites with an anomalous level of activity can be easily identified. The disagreement in isotope production rates of “Be and 26Al in Dhajala is significant and requires further investigations to understand its cause. Acknowledgments-This work was partially supported by DLR and ISRO and by the Deutsche Forschungsgemeinschaf. We thank J. T. Padia for his help at various stages of this work. Editorial handling: G. Crozaz

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