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Addressing solar modulation and long-term uncertainties in scaling secondary cosmic rays for in situ cosmogenic nuclide applications

journal contribution
posted on 2023-05-16, 17:23 authored by Lifton, NA, Bieber, JW, Clem, JM, Duldig, ML, Evenson, P, John Humble, Pyle, R
Solar modulation affects the secondary cosmic rays responsible for in situ cosmogenic nuclide (CN) production the most at the high geomagnetic latitudes to which CN production rates are traditionally referenced. While this has long been recognized (e.g., D. Lal, B. Peters, Cosmic ray produced radioactivity on the Earth, in: K. Sitte (Ed.), Handbuch Der Physik XLVI/2, Springer-Verlag, Berlin, 1967, pp. 551-612 and D. Lal, Theoretically expected variations in the terrestrial cosmic ray production rates of isotopes, in: G.C. Castagnoli (Ed.), Proceedings of the Enrico Fermi International School of Physics 95, Italian Physical Society, Varenna 1988, pp. 216-233), these variations can lead to potentially significant scaling model uncertainties that have not been addressed in detail. These uncertainties include the long-term (millennial-scale) average solar modulation level to which secondary cosmic rays should be referenced, and short-term fluctuations in cosmic ray intensity measurements used to derive published secondary cosmic ray scaling models. We have developed new scaling models for spallogenic nucleons, slow-muon capture and fast-muon interactions that specifically address these uncertainties. Our spallogenic nucleon scaling model, which includes data from portions of 5 solar cycles, explicitly incorporates a measure of solar modulation (S), and our fast- and slow-muon scaling models (based on more limited data) account for solar modulation effects through increased uncertainties. These models improve on previously published models by better sampling the observed variability in measured cosmic ray intensities as a function of geomagnetic latitude, altitude, and solar activity. Furthermore, placing the spallogenic nucleon data in a consistent time-space framework allows for a more realistic assessment of uncertainties in our model than in earlier ones. We demonstrate here that our models reasonably account for the effects of solar modulation on measured secondary cosmic ray intensities, within the uncertainties of our combined source datasets. We also estimate solar modulation variations over the last 11.4 ka from a recent physics-based sunspot number reconstruction derived from tree-ring 14C data. This approximation suggests that spallogenic nucleon scaling factors in our model for sea level and high geomagnetic latitudes can differ by up to ∼10%, depending on the time step over which the model sunspot numbers are averaged. The potential magnitude of this difference supports our contention that incorporating long-term solar modulation into secondary cosmic ray scaling is important. Although millennial-scale solar modulation clearly requires further study, we believe it is reasonable at present to use our S value record for scaling spallogenic nucleons during the last 11.4 ka, and the weighted mean S value for that period of 0.950 for longer exposure times. By accounting for solar modulation effects on the global variations in nucleon and muon fluxes, these models thus provide a useful framework on which to base CN production rate scaling functions. © 2005 Elsevier B.V. All rights reserved.


Publication title

Earth and Planetary Science Letters










School of Natural Sciences


Elsevier Science BV

Place of publication

Amsterdam, Netherlands

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  • Restricted

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