Mathematics – Probability
Scientific paper
Jul 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993metic..28..351g&link_type=abstract
Meteoritics, vol. 28, no. 3, volume 28, page 351
Mathematics
Probability
Argon, Argon-38, Cosmic Rays, Galactic, Solar, Cosmogentic Isotopes, Helium, Lunar Rocks, Neon, Neon-21, Neon-22, Noble Gases, Solar Proton Spectrum
Scientific paper
Oriented lunar rock 68815, with 2 x 10^6 years of surface exposure, has become the most widely studied detector of solar cosmic ray (SCR) products. Radio-nuclides ^10Be, ^26Al, ^53Mn, ^14C, and ^81Kr measured in 68815 by several investigators have been used to estimate the long term average solar proton flux, J(sub)>10(4 pi, E > 10 MeV) and rigidity, R(sub)o (MV) [1-4]. Reported ^26Al and ^53Mn depth profiles were consistent with J = 70 p/cm^2/s and R(sub)o = 100 MV [1], whereas depth profiles of SCR ^81Kr suggested J(sub)>10 = 160 p/cm^2/s and R(sub)o = 85 MV [2]. The nearly flat depth profile for ^10Be in 68815 suggested a softer proton spectral shape or a higher erosion rate [3]. Profiles of SCR ^14C, measured in the same 68815 column used for our noble gas analyses, were consistent with J(sub)>10 ~144 p/cm^2/s at R(sub)o = 85 MV, or with J(sub)>10 ~91 p/cm^2/s at R(sub)o = 100 MV [4]. As noted by [3], such combinations of spectral parameters are not unique and may vary widely. SCR profiles, therefore, typically yield comparable spectral parameters to those determined from track studies and contemporary spacecraft measurements. In this study we determined depth profiles of SCR ^21Ne, ^22Ne, and ^38Ar produced by nuclear interactions of energetic (~10-100 MeV) solar protons in documented depth samples of 68815. In addition, we resolved SCR Ne from GCR Ne by their distinct isotopic ratios, a resolution that has been obtained only for neon. We derived the most probable spectral values for solar protons from the measured datasets, placing no prior restrictions on the values of spectral parameters or of the rock erosion rate. We evaluated all combinations of J(sub)>10, R(sub)o, and erosion (Q) using a least squares techniques to measure the "goodness of fit" between measured and calculated SCR abundances. By fixing two parameters at a time (R(sub)o and Q), the third (J(sub)>10) was iterated to determine an optimal value for each set. Comparisons between parametric sets were based on the standard deviation of the profile fit, behavior of the residuals, neon isotopic ratios, and implied GCR exposure ages. No values of R(sub)o lower than 70 MV gave reasonable fits to the data, and R(sub)o values greater than 100 MV implied more SCR neon production at depth than permitted by either the measured isotopic ratios or the resulting GCR exposure ages. Our quantitative data analysis yielded an optimal fit combination (i.e., set with highest probability) of J~110 p/cm^2/s and R(sub)o~85 MV with an erosion of ~2 mm/Myr for ^21Ne, ^22Ne, and ^38Ar. Recently published SCR neon and argon data for lunar rock 61016 [6] have been reevaluated under the same criteria described above. Unique, self-reliant determinations of J(sub)>10, R(sub)o, or Q are difficult. Virtually all combinations of R(sub)o (70 to 125 MV) and Q (1-3 mm/Myr) resulted in SCR profiles of equal goodness of fit given some optimal flux between 50 and 135 p/cm^2/s. We have also applied this statistical treatment to SCR radionuclide data sets for 68815; results of this analysis will be compared with SCR Ne and Ar. References: [1] Kohl et al. (1978) LPSC XIV, 2299-2310. [2] Reedy and Marti (1991) The Sun in Time, 260-287. [3] Nishiizumi et al. (1988) LPSC XVIII, 79-85. [4] Jull et. al. (1992) LPSC XXIII, 639-640. [5] Garrison et al. (1993) LPSC XXIV, 521-522. [6] Rao et al. (1993) JGR, (in press).
Bogard Donald D.
Garrison Daniel H.
Rao Mallikharjuna N.
Reedy Robert C.
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