Statistically significant clusters in the cosmic ray exposure age distributions of some groups of iron and stone meteorites were observed, suggesting epochs of enhanced collision and breakups. Fourier analyses of the age distributions of chondrites reveal no significant periods, nor does the same analysis when applied to iron meteorite clusters

Marti, K.

Woodard, M. F.

English

NASA Technical Reports Server

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SH 7.1-11
CLUSTERS AND CYCLES IN THE COSMIC RAY AGE
DISTRIBUTIONS OF METEORITES
Martin Fo Woodard* and K. Marti
University of California, San Diego
La Jolla, California 92093
ABSTRACT
Statistically significant clusters in the cosmic ray exposure
age distributions of some groups of iron and stone meteorites
are observed, suggesting epochs of enhanced collisions and
breakups. Fourier analyses of the age distributions of chon-
drites reveal no significant periods, nor does the same analy-
sis when applied to iron meteorite clusters.
*Present address: Smithsonian Astrophysical Observatory, Mail Stop 16, 60
Garden Street, Cambridge, Massachusetts 02138°
Introduction. Cosmic ray interactions in meteorites produce a variety of spal-
lation products which depend on the target element abundances, the size and
location within a meteorite. Radioactive and stable cosmogenic nuclide pairs
with half-lives ranging from a few years to 109 years can be used to determine
the cosmic ray exposure history of an object. The radioactive nuclides with
half-lives short, compared with the time interval of exposure to cosmic rays,
are in secular equilibrium and define the production rates. For a constant
exposure geometry measured amounts of the stable integrating nuclides coupled
with radionuclide measurements are used to obtain the integral time of exposure
to cosmic rays. The advantage of this approach is that reliable exposure age
information can be obtained in samples reflecting variable degrees of cosmic
ray shielding as in large meteorites or in cases of incomplete development of
the secondary cascade typically observed in small meteorites. A number of
methods were developed for the calculation of production rates and of cosmic
ray exposure ages (e.g. Voshage, 1962; Nishiizumi et al., 1980; Marti, 1984;
Lavielle et alo, 1984). Exposure ages for iron met_eo_tes based on 40K-41K
and 38Ar data indicate some cl_stering of exposure ages for several groups of
irons (e.g. Voshage and Feldmann, 1979; Lavielle et al., 1984). Exposure age
distributions for chondrites were studied several times (e.g. WUnke, 1966;
Crabb and Schultz, 1981) o Noble gas data were recently compiled by Schultz
and Kruse (1983)o
Methods of Analysis. To test the significance of a cluster of M samples with-
in a given group of N (>M) meteorites, we first assign an age span, T, to the
group as a whole, Based on the rough appearance of the age distribution of the
group. We then select a value, W, much shorter than T, similar to the age
spread of the candidate cluster. Under the assumption that the N group mem-
5ers are uniformly and randomly distributed over the age interval [O,T], we
calculate the probability of finding at least M samples within some subinter-
val of duration W.
The cluster probabilities were computed by performing Monte Carlo
simulations on a vax 11/780 computer° For each trial of the simulation, N
pseudo-random numbers were generated on the interval [O,T]o A set of overlap-
ping subintervals, each of duration W, were defined so that their starting
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SH 7.1-11
points form a uniform grid in which successive subintervals overlap by 90% so
as to cover the interval [O,T]. If at least M of the N random numbers is
found in one or more of the subintervals, a "success" is recorded. The esti-
mated occurrence probability for a cluster of M meteorites is the number of
successes divided by the total number of trials°
Various tests of the Pseudo-random number generator have been made,
including a comparison with a direct calculation of the cluster probability in
a limiting case where a simple analytic expression applies.
We have also searched for periodicity in the age distributions of
both individual meteorite groups and in the age distributions of clusters. A
discrete time series is formed by assigning to each of a set of uniformly-
spaced time bins, the number of samples lying within the bino A Fourier spec-
trum is then computed for these time series and is examined for outstanding
peaks, the significance of a peak in the power spectrum is evaluated by com-
puting the probability of finding a peak at least as high as the real one in
the spectrum of a randomly generated age distribution (using a Monte Carlo
procedure quite analogous to the above method of establishing cluster proba-
bilitieso
Results. A cluster is designated "probable" if its probability of occurrence,
by the previously described test, is less than 10% and "very probable" if the
probability is less than 1%o Groups of probable and very probable clusters
are listed in the table below.
Table List of SignificantExposure Age Clusters and CalculatedProbabilities.
Average
Group N T Age of M W Probabillty
(Myr) Cluster
(Myr)
£
H Chondrites 95 20 2 45 3 0/105
Enstatlte
Achondrltes 9 115 60 5 8 94/104
Irons IA 13 i03 440 5 50 207103
Irons IIA 7 103 25 4 50 111/104
Irons IID 3 ' 103 360 3 50 60/104
IronsIlia 19 103 650 7 50 2/103
IronsIIIE 6 103 475 3 50 104/103
Irons IVA 13 103 375 i0 150 17104
400 6 75 60/104
400 4 40 198/2000
Irons IVB 5 . 103 875 3 50 50/103
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SH 7.1-ii
Column 1 gives the group containing the cluster, columns 2 and 3 give the size
of the group, N, and its age span, T. Column 4 gives the estimated age and
column 5 the number of samples in the cluster. Columns 6 and 7 give, respec-
tively, the age span, W, of the cluster and the probability of random occur-
rence (the latter expression displays explicitly both the number of successes
and the total number of trials from which the successes were derived). The
table does not list all clusters found because some of these overlap in time.
A Fourier analysis of the H chondrite group, using only meteorites
with exposure ages between i0 and 40 Myr (i.e., ignoring the big peak at 7Myr)
yielded no significant periods° Similarly, no significant peaks were found in
the fourier spectrum of the L chondrites between 0 and 40 Myr. A power spec-
trum of the age distribution of the iron meteorites (see table) also yielded
no significant periods.
Discussion. We regard the clustering as real since probable or very probable
clusters occur in most of the major subgroups. The statistical significance
assigned to the clusters depended on the assumed test model of a uniform dis-
tribution over the stated ranges, T. For instance, for each of the iron
groups T = i000 Myr is roughly the cutoff age for the irons as a whole. A more
realistic hypotheses against _lich to test cluster significance might be to
distribute the samples exponentially, to simulate the gradual decrease in the
number samples of increasing age.
To obtain some idea of the sensitivity of the results to our assump-
tions, we have also computed the cluster probabilities by choosing a width W
in excess of the apparent age range of the cluster, thereby overestimating the
probability, for example, for the iron IIIE subgroup, changing W/T from 5%
(corresponding to the result in the table) to 7% increases the probability from
"10% to ~20%, therefore, this cluster must be considered marginal. On the
other hand, the probability of the cluster in the IA iron group increases from
~2% to ~9% when the assumed width of the cluster changes from 5% to 8%o The
IA cluster and most of the clusters listed in the table are at least probable
even when their age ranges are overestimated.
One interpretation of the clusters is that they represent epochs of
increased meteorite formation resulting from individual collisions of asteroids
or comets. In this case, one would expect to see a cluster of width corres-
ponding to uncertainties in the age values° However, secondary breakups of
the original collision products, complex exposure histories, and spatial
variations in the cosmic ray flux, can all degrade the sharpness of the clus-
terso Thus it is important to know whether the actual spread in the ages of
samples from a given cluster can be accounted for by any of the above factors.
Multiple collisions with asteroids might produce meteorites over an
extended period° One possible example of such an enhancement is the iron IVA
cluster at 400 Myr, extending over an age interval W = 150 Myr. The fact that
this interval, containing i0 samples is exceptionally long leads us to sus-
pect that two or more clusters are present° Belonging to the aforementioned
i0 are 6 samples of average age 400 Myr, which themselves constitute a very
probable cluster listed in the table. The remaining four samples do not
constitute a cluster by our criterion, however a more sophisticated test might
reveal a second cluster.
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Conclusions. The record of cosmic ray effects in iron and stone meteorites
was studied° Statistically significant clusters in the exposure age distribu-
tions of these objects were found, suggesting epochs of enhanced meteorite
formation, possibly as the result of collisions and breakups° Significant ex-
posure age clusters are found or confirmed for the following groups of meteo-
rites: H-Chondrites at 7 Myr, enstatite achondrites at 60 Myr, iron group IA
at 450 Myr, IIA < 50 Myr, IID at 350 Myr, IIIA at 650 Myr, IIIE at 475 Myr, IVA
at 400 Myr and IVB at 875 Myro A Fourier analysis of the age distributions of
both H and L chondrites reveals no significant periods, nor does the same
analysis when applied to the age distributions of iron meteorite clusters
Acknowledsements. This research was supported by NASA NAG 9-41.
References°
Crabb, Jo and Schultz, Lo (1981), Geochim. Cosmochim. Acta 45, 2151-60.
Lavielle, B., Marti, Ko and Regnier, S. (1984), Proceedings of Conf. on
Isotopic Anomalies in the Solar System, Paris°
Marti, Kurt (1984), Abstract, Workshop on Cosmogenic Nuclides, July, Los
Alamos, New Mexico.
Nishiizumi, K., Regnier, S. and Marti, K. (1980), Earth Planet° Sci. Lett. 50,
156-70.
Schultz, Lo and Kruse, H. (1983), Helium, Neon and Argon in Meteorites; A Data
compilation. Special publication of the Max-Planck-Institute for Chemis-
try, Mainz.
Voshage, H. (1962), Zo Naturforscho 17a, 422-32.
Voshage, Ho and Feldmann, H. (1979), Earth Planet. Sci. Lett. 45, 293-308.
WHnke, Ho (1966), Z. Naturforsch. 21a, 93-110.


Clusters and cycles in the cosmic ray age distributions of meteorites

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