The cosmogenic isotope 10Be is useful for long-term studies of solar activity because of its long half-life of around 1.5 × 106 years. Its concentration is usually measured in stratified ice cores allowing for independent dating. Because of its long life, the beryllium concentration is difficult to measure by the decay rate (Beer, 2000). Accordingly, the 10Be/9Be ratio needs to be precisely measured at an accuracy better than 10–13. This can be done using AMS (Accelerator Mass Spectrometry) technique, which make the measurements complicated and expensive. Correction for the decay is straightforward and does not include isotope fractionating. From the measured samples, first the 10Be concentration is defined, usually in units of 104 atoms/g. Sometimes, a correction for the snow precipitation amount is considered leading to the observable 10Be flux, which is the number of atoms per cm2 per second.
There exist different 10Be series suitable for studies of long-term solar activity, coming from ice cores in Greenland and Antarctica. They have been obtained from different cores with different resolutions, and include data from Milcent, Greenland (Beer et al., 1983), Camp Century, Greenland (Beer et al., 1988), Dye 3, Greenland (Beer et al., 1990), Dome Concordia and South Pole, Antarctica (Raisbeck et al., 1990), GRIP, Greenland (Yiou et al., 1997), GISP2, Greenland (Finkel and Nishiizumi, 1997), Dome Fuji, Antarctica (Horiuchi et al., 2007, 2008). We note that data on 10Be in other archives, e.g., lake sediments, is usually more complicated to interpret because of the potential influence of the climate (Horiuchi et al., 1999; Belmaker et al., 2008).
Details of the 10Be series and their comparison with each other can be found in Beer (2000); Muscheler et al. (2007).
The isotope 10Be is produced as a result of spallation of atmospheric nitrogen and oxygen (carbon is less abundant by far in the atmosphere and makes a negligible contribution) by the nucleonic component of the cosmic-ray–induced atmospheric cascade (Section 3.1.3). The cross section (a few mb) of the spallation reactions is almost independent of the energy of impacting particles and has a threshold of about 15 MeV. Thus, the production of 10Be is defined solely by the multiplicity of the nucleonic component, which increases with the energy of primary cosmic rays (see Figure 6). Maximum production occurs at an altitude of 10 – 15 km due to a balance between the total energy of the cascade (which increases with altitude) and the number of secondaries (decreasing with altitude). Most of the global 10Be is produced in the stratosphere (55 – 70%) and the rest in the troposphere (Lal and Peters, 1967; Masarik and Beer, 1999, 2009; Usoskin and Kovaltsov, 2008; Kovaltsov and Usoskin, 2010).Update
Computation of 10Be isotope production is straightforward, provided a model of the atmospheric cascade is available. The first consistent model was developed by D. Lal et al. (Bhandari et al., 1966; Lal and Peters, 1967; Lal and Suess, 1968), using an empirical approach based on fitting simplified model calculations to measurements of the isotope concentrations and “star” (inelastic nuclear collisions) formations in the atmosphere. Next was an analytical model by O’Brien (1979), who solved the problem of the GCR-induced cascade in the atmosphere using an analytical stationary approximation in the form of the Boltzmann equation, which has also been normalized per “star” formation. Those models were based on calculating the rate of inelastic collisions or “stars” and then applying the mean spallation yield per “star”. A new step in the modelling of isotope production was made by Masarik and Beer (1999), who performed a full Monte-Carlo simulation of a GCR-initiated cascade in the atmosphere and used cross sections of spallation reactions directly instead of the average “star” efficiency. A recent model by Webber and Higbie (2003) and Webber et al. (2007) is also based on a full Monte-Carlo simulation of the atmospheric cascade, using improved cross sections. The global production rate of 10Be is about 0.02 – 0.03 atoms cm–2 s–1 (Masarik and Beer, 1999; Webber et al., 2007; Kovaltsov and Usoskin, 2010), which is lower than that for 14C by two orders of magnitude (about 2 atoms cm–2 s–1; see Section 3.2.2). The yield function of 10Be production is shown in Figure 6A and the differential production rate in Figure 6B. One can see that the peak of 10Be sensitivity, especially in polar regions, is shifted towards lower energies (below 1 GeV) compared with both 14C and neutron monitor sensitivities. This implies that the 10Be isotope is relatively more sensitive to less energetic CR and is, therefore, more affected by solar energetic particles (Usoskin et al., 2006b). There is discrepancy of a factor of 1.5 between different production models of 10Be production that needs to be resolved. Comparison of model computations with direct beryllium production experiments (Usoskin and Kovaltsov, 2008; Kovaltsov and Usoskin, 2010), and also the results of modelling of the short-living 7Be isotope (Usoskin et al., 2009a) suggest that some numerical models (Masarik and Beer, 1999; Webber and Higbie, 2003; Webber et al., 2007) tend to underestimate the production. Update
Although the production of 10Be can be more or less precisely modelled, a simple normalization “surface”, similar to that shown in Figure 7 for 14C, is not easy to produce because of partial mixing in the atmosphere (see Section 3.3.3). Simplified models, assuming either only global (e.g., Beer, 2000) or polar production (Bard et al., 1997; Usoskin et al., 2004), have been used until recently. However, it has been recognized that a more realistic model of the limited atmospheric mixing should be used. Without detailed knowledge of 10Be transport in the atmosphere, it is impossible to relate the quantitatively-measured concentration to the production (as done for 14C using the carbon cycle), and one has to assume that the measured abundance is proportional (with an unknown coefficient) to the production rate in a specific geographical region (see Section 3.3.3).
After production, the 10Be isotope has a seemingly simple (Figure 4) but difficult-to-account-for fate in the atmosphere. Its atmospheric residence time depends on scavenging, stratosphere-troposphere exchange and inter-tropospheric mixing (e.g., McHargue and Damon, 1991). Soon after production, the isotope becomes attached to atmospheric aerosols and follows their fate. In addition, it may be removed from the lower troposphere by wet deposition (rain and snow). The mean residence time of the aerosol-bound radionuclide in the atmosphere is quite different for the troposphere, being a few weeks, and stratosphere, where it is one to two years (Raisbeck et al., 1981). Accordingly, 10Be produced in the troposphere is deposited mostly locally, i.e., in the polar regions, while stratospheric 10Be can be partly or totally mixed. In addition, because of the seasonal (usually Spring) intrusion of stratospheric air into the troposphere at mid-latitudes, there is an additional contribution of stratospheric 10Be. Therefore, the measured 10Be concentration (or flux) in polar ice is modulated not only by production but also by climate/precipitation effects (e.g., Steig et al., 1996; Bard et al., 1997). This led Lal (1987) to the extreme conclusion that variations of polar 10Be reflect a meteorological, rather than solar, signal. However, comparison between Greenland and Antarctic 10Be series and between 10Be and 14C data (e.g., Bard et al., 1997; Horiuchi et al., 2008) suggests that the beryllium data mostly depicts production variations (i.e., solar signal) on top of which some meteorological effects can be superposed (see also Section 3.6.3).
Since both assumptions of the global and purely-local polar production of 10Be archived in polar ice are over-simplified, several attempts have been made to overcome this problem. For instance, McCracken (2004) proposed several simple mathematical models of partial atmospheric mixing (without division in the troposphere and stratosphere) and compared them with observed data. From this semi-empirical approach McCracken concluded that M2 (full mixing above 60° latitude and a limited mixing between 40° and 60° latitude) is a reasonable model for Antarctica. Vonmoos et al. (2006) assumed that the production of 10Be recorded in Greenland is related to the entire hemisphere in the stratosphere (i.e, global stratospheric mixing) but is limited to latitudes above 40° latitude in the troposphere (partial tropospheric mixing). This approach uses either semi-empirical or indirect arguments in choosing the unknown degree of mixing.
Recent efforts in employing modern atmospheric 3D circulation models for simulations of 10Be transport and deposition, including realistic air-mass transport and dry-vs-wet deposition (Field et al., 2006; Heikkilä et al., 2007), look more promising. An example of 10Be deposition computed on the world grid using the NASA GISS model (Field et al., 2006) is shown in Figure 9. Precision of the models allows one to distinguish local effects, e.g., for Greenland (Heikkilä et al., 2007). A simulation performed by combining a detailed 10Be-production model with an air-dynamics model can result in an absolute model relating production and deposition of the radionuclide. We may expect this breakthrough to occur in the near future. The validity and usefulness of this approach has been recently demonstrated by (Usoskin et al., 2009a), who directly modeled production (using the CRAC model – Usoskin and Kovaltsov, 2008) and transport (using the GISS ModelE – Koch et al., 2006) of a short beryllium living isotope 7Be and showed that this such a combined model is able to correctly reproduce absolute level and temporal variations of the 7Be concentration measured in near ground air around the globe. Keeping in mind the similarity between production and transport of the two beryllium isotopes, 7Be and 10Be, this serves as support for the advanced modelling of 10Be transport. Update
In order to properly account for geomagnetic changes (Section 3.1.2), one needs to know the effective region in which the radionuclide is produced before being stored in the archive analyzed. For instance, if the concentration of 10Be measured in polar ice reflects mainly the isotope’s production in the polar atmosphere (as, e.g., assumed by Usoskin et al., 2003c), no strong geomagnetic signal is expected to be observed, since the geographical poles are mostly related to high geomagnetic latitudes. On the other hand, assuming global mixing of atmospheric 10Be before deposition in polar ice (e.g., Masarik and Beer, 1999), one expects that only changes in the geomagnetic dipole moment affect will the signal. However, because of partial mixing, which can be different in the stratosphere and troposphere, taking into account migration and displacement of the geomagnetic dipole axis may be essential for a reliable reconstruction of solar variability from 10Be data (McCracken, 2004). Therefore, only a full combination of the transport and production models, the latter explicitly including geomagnetic effects estimated from paleomagnetic reconstructions, can adequately account for geomagnetic changes and separate the solar signal. These will form the next generation of physics-based models for the cosmogenic-isotope proxy method. We note that paleomagnetic data should ideally not only provide the dipole moment (VADM or VDM) but should also provide estimates of the geomagnetic axis attitude and displacement of the dipole center.
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