The Annual Cosmic-Radiation Intensities 1391 – 2014; The Annual Heliospheric Magnetic Field Strengths 1391 – 1983, and Identification of Solar Cosmic-Ray Events in the Cosmogenic Record 1800 – 1983

The annual cosmogenic \(^{10}\mathrm{Be}\) ice-core data from Dye 3 and the North Greenland Ice-core Project (NGRIP), and neutron-monitor data, 1951���– 2014, are combined to yield a record of the annual cosmic-ray intensity, 1391 – 2014. These data were then used to estimate the intensity of the heliospheric magnetic field (HMF), 1391 – 1983. All of these annual data are provided in the Electronic Supplementary Material. Analysis of these annual data shows that there were significant impulsive increases in \(^{10}\mathrm{Be}\) production in the year following the very large solar cosmic-ray events of 1942, 1949, and 1956. There was an additional enhancement that we attribute to six high-altitude nuclear explosions in 1962. All of these enhancements result in underestimates of the strength of the HMF. An identification process is defined, resulting in a total of seven impulsive \(^{10}\mathrm{Be}\) events in the interval 1800 – 1942 prior to the first detection of a solar cosmic-ray event using ionization chambers. Excision of the \(^{10}\mathrm{Be}\) impulsive enhancements yields a new estimate of the HMF, designated B(PCR-2). Five of the seven \(^{10}\mathrm{Be}\) enhancements prior to 1941 are well correlated with the occurrence of very great geomagnetic storms. It is shown that a solar cosmic-ray event similar to that of 25 July 1946, and occurring in the middle of the second or third year of the solar cycle, may merge with the initial decreasing phase of the 11-year cycle in cosmic-ray intensity and be unlikely to be detected in the \(^{10}\mathrm{Be}\) data. It is concluded that the occurrence rate for solar energetic-particle (SEP) events such as that on 23 February 1956 is about seven per century, and that there is an upper limit to the size of solar cosmic-ray events.

The research at the University of Maryland was funded by US NSF grant 1050002. The research at EAWAG is supported by the Swiss National Science Foundation under the grant CRSI122-130642 (FUPSOL). K.G. McCracken acknowledges the consistent support that he has received since 2005 from the International Space Science Institute (ISSI), Bern, Switzerland. This work was completed in association with the ISSI Long-term Solar/Solar Wind Workshop (2012 – 2013) and profited from discussions during the PAGES workshops in Davos (2012 and 2014). The assistance and critical comments of M. Owens and E. Cliver and those of the referee are acknowledged with gratitude. All of the data and methods used here have been provided in the references cited.

Authors and Affiliations

1. Institute for Physical Science and Technology, University of Maryland, College Park, MD, USA

   K. G. McCracken

2. Eawag, Duebendorf, Switzerland

   J. Beer

Corresponding author

Correspondence to K. G. McCracken.

Disclosure of Potential Conflicts of Interest

The authors declare that they have no conflicts of interest.

Appendix 1: The Annual \(^{{10}}\mathrm{Be}\) Data; Processing; Normalization; Removal of Climatic and Geomagnetic Effects

Two extended annual data sets of \(^{10}\mathrm{Be}\) concentrations are available at present; they are from Dye 3 in Greenland (\(65.18^{\circ}\mathrm{N}\), \(43.83^{\circ}\mathrm{W}\), 2480 m a.s.l., Beer et al. 1990) and NGRIP (\(75.10^{\circ}\mathrm{N}\), \(42.32^{\circ}\mathrm{W}\), 2917 m a.s.l., Berggren et al. 2009). The \(^{10}\mathrm{Be}\) data suffer from several uncertainties such as occasional loss of core; uncertain identification of year, and several long-term changes (e.g. climatic and geomagnetic changes that differ from place to place on the Earth). To minimize these uncertainties, the data from the two cores have been processed as follows. Throughout the following, \(^{{10}}\mathrm{Be}(t)\) refers to the annual measurements of the \(^{{10}}\mathrm{Be}\) concentration:

• Time homogenization. We have used the time assignments for both records as determined by Berggren et al. (2009). The average \(^{10}\mathrm{Be}(t)_{\mathrm{av}}\) was computed for each year; where there was a gap in one record the average was estimated using the other record.

• Baseline correction. As discussed in the Introduction, normalization of the cosmogenic data to the present epoch depended on the data from three ice cores; Dye 3 (Beer et al. 1990), North GRIP (Berggren et al. 2009), and South Pole (Bard et al. 1997), and close examination showed that the Dye 3 decrease in \(^{10}\mathrm{Be}\) concentration between 1950 and 1960 was substantially greater than those for North GRIP and South Pole. The contemporary atmospheric transport and mixing of the \(^{10}\mathrm{Be}\) prior to sequestration in the polar caps indicates that all three should be equal (Heikkila, Beer, and Feichter 2009). We have used this equality to conclude that the concentrations observed at Dye 3 after 1950 were erroneously low. Applying a baseline correction based on the North GRIP and South Pole data to the Dye 3 concentrations, we have computed \(^{10}\mathrm{Be}(t)_{\mathrm{stein}}\), the revised average for the normalization interval 1944 – 1987 (as used by Steinhilber et al. 2012). The ratio \(X_{\mathrm{stein}}(t) =^{10}\mathrm{Be}(t)_{\mathrm{av}} /^{10}\mathrm{Be}(t)_{\mathrm{stein}}\) was then computed for each year.

• Removal of long-term variations of atmospheric origin. The measured \(^{10}\mathrm{Be}\) and \(^{14}\mathrm{C}\) data contain significant contributions of climatic, atmospheric, and (in the case of \(^{14}\mathrm{C}\)) oceanic origin. Using the data from seven ice cores, and the most recent \(^{14}\mathrm{C}\) data, Steinhilber et al. (2012) isolated the cosmic-ray signal from these contributions of terrestrial and instrumental origin. The sampling times for the \(^{10}\mathrm{Be}\) and \(^{14}\mathrm{C}\) data ranged from one to ten years. To minimize aliasing from the Schwabe (11-year) and Hale (22-year) cycles, Steinhilber et al. (2012) converted the data to contiguous 22-year samples. After applying the baseline correction outlined above, we believe that this is presently the most reliable record of the long-term changes in the paleo-cosmic-ray intensity for the past 9400 years. We have therefore adjusted the annual data record [\(X_{\mathrm{stein}}(t)\)] to a new normalized annual record [\(Y_{\mathrm{stein}}(t)\)] where the 22-year averages of \(Y_{\mathrm{stein}}(t)\) are consistent with the same time intervals in the baseline-corrected Steinhilber et al. (2012) data set. We stress that this removes the long-term contributions of atmospheric origin, while having minimal effect on the short-term production variations of \({<\,}22\mbox{-year duration}\).

• Geomagnetic cut-off correction. The geomagnetic dipole moment and the location of the geomagnetic poles have both changed significantly since 1391. For example, the geomagnetic dipole moment changed from \(8.5 \times 10^{22}\) to \(8.0 \times 10^{22}\) [\(\mathrm{Am}^{2}\)], thereby reducing the geomagnetic cut-off rigidities; and as a consequence there was a \({\approx\,}3~\%\) increase in \(^{10}\mathrm{Be}\) concentration due to this effect alone between 1391 and 2013. The ratio \(Y_{\mathrm{stein}}(t)\) was corrected to the 2013 epoch as detailed by McCracken (2004), and this is denoted \(Y_{\mathrm{stein}, \mathrm{GM}}(t)\).

• Other \(^{10}\mathrm{Be}\) reference values. As stated above, the annual \(^{10}\mathrm{Be}\) concentrations were initially expressed relative to the average for the interval 1944 – 1987 for consistency with Steinhilber et al. (2012). Two other reference values are convenient for computation and conceptual purposes, and they are also given in the Electronic Supplementary Material in the interest of uniformity among future workers. These reference values are: i) McCracken et al. (2004) introduced the nomenclature \(^{10}\mathrm{Be}(\mathrm{LIS})\) to represent the estimated value of the \(^{10}\mathrm{Be}\) concentration if the cosmic-ray local interstellar spectrum (LIS) were incident on Earth (that is, the modulation function \(\Phi= 0~\mbox{MeV}\)). The reader is referred to that article for discussion of the concept and its estimation. The annual values of \(Y_{\mathrm{LIS},\mathrm{GM}}(t) =^{10}\mathrm{Be}(t)_{\mathrm{av}}/^{10}\mathrm{Be}(\mathrm{LIS}) = 0.434 Y_{\mathrm{stein}},_{\mathrm{GM}}(t)\). ii) Oh et al. (2013) combined the data from eight high-latitude NMs for the interval 1964 – 2010; NM data are frequently expressed as a percentage relative to the monthly value for February 1987. For consistency with this practice the pseudo-NM data (see next paragraph) in Figure 1 and in the Electronic Supplementary Material are expressed relative to that reference.

• Data averaging used herein. To this point, all of the calculations were made on an annual basis. In view of the large standard deviation of the annual data, two numerical filters were used in the figures and the discussions. They are:

  • A “(1,4,6,4,1) binomial filter” where the filtered (average) value of the data file \(X(t)\) for year \(t\) is given by

    $$ X_{14\mbox{,}641} (t) = \bigl\{ X (t-2)+ 4 \times X(t-1) + 6 \times X(t) + 4 \times X(t+1) + X(t+2)\bigr\} /16. $$

    (1)

  • The 11-year running average.

Appendix 2: Estimation of the Pseudo-Neutron Monitor (PNM) Counting Rate

The neutron monitor provides one of the most important instrumental records of the intensity of the cosmic radiation near Earth. The record commenced in 1951, and since 1957 there have always been \({>\,}50\) instruments in the world-wide network. They have provided a great deal of our understanding of the temporal, energy, and directional dependence of the \({>\,}1~\mbox{GeV}\,\mbox{nucleon}^{-1}\) cosmic radiation near Earth. The \(^{10}\mathrm{Be}\) data can be regarded as the output of a natural neutron monitor (Beer et al. 2011) and it is convenient to use them to estimate the NM counting rate that would have been observed in the past. Using the procedure described by McCracken and Beer (2007), \(Y_{\mathrm{LIS},\mathrm{GM}}(t)\) defined above was used to compute the annual \(\mathrm{PNM}(t)\) using the look-up table in Figure 6.The resulting estimates are given in Figure 1 and Supplementary Table S-1. The relationship between the \(^{10}\mathrm{Be}\) data and the NM counting rates is substantially non-linear (Figure 5, McCracken and Beer 2007). This is the consequence of two factors: i) the \(^{10}\mathrm{Be}\) response extending to lower energies, and ii) the amplitude of the modulation increasing rapidly towards lower energies. For example, the ratio between the percentage changes in the \(^{10}\mathrm{Be}\) and the NM data is 1.45 for the intensities observed during the sunspot minima of 1954 – 1996, while it increases to 4.4 during the Grand Minima such as the Maunder Minimum (1645 – 1715). This results in the differences that are evident for the highest cosmic-ray intensities in the top two panels of Figure 1.

The look-up tables for the PNM data, and the diffusion coefficient [\(\kappa\)] used in the estimation of \(B(\mathrm{PCR})\).

Full size image

Appendix 3: Estimation of the Heliospheric Magnetic Field, B(PCR)

This procedure is based on Caballero-Lopez et al. (2004) and McCracken (2007a). Using a 3D model of the heliosphere that included a solar-cycle-dependent current sheet, latitude-dependent solar-wind velocities, and the Hale cycle of solar magnetic fields, Caballero-Lopez et al. (2004) computed the production rate of \(^{10}\mathrm{Be}\) in the Earth’s atmosphere as a function of the diffusion constant of cosmic rays [\(\kappa (t)\)] in the heliospheric magnetic field. In view of the high value of the standard deviation of the \(^{10}\mathrm{Be}\) data, we have averaged over the \(\kappa (t)\) computed for the two polarities of the solar polar field, the resulting functional dependence being displayed in Figure 6. As a consequence, the Hale-cycle modulation of the \(^{10}\mathrm{Be}\) (due to particle drift effects; see Potgieter 2013) remains in the tabulated data.

Caballero-Lopez et al. (2004) further developed the relationship between the diffusion coefficients [\(\kappa (t)\)] and the near-Earth HMF intensity [\(B(t)\)]. Writing \(B_{\mathrm{cal}}\) and \(\kappa_{\mathrm{cal}}\) for those parameters for the calibration interval, and \(B(t)\) and \(\kappa (t)\) for time \(t\), we have

where the exponent \(\alpha\) takes into account the scattering properties of the heliospheric magnetic field. McCracken (2007a) used the annual neutron-monitor data and the satellite measurements of the near-Earth heliospheric magnetic field for the interval 1970 – 2005 to determine \(\alpha = 1.75\). Figure 6 and Equation (2), together, provide the means to use the PCR to estimate the HMF in the past. This was done using a look-up table derived from the \(\kappa\) versus \(^{10}\mathrm{Be}\) curve in Figure 6. The Caballero-Lopez et al. method applies to values of \(^{10}\mathrm{Be}(t)_{\mathrm{av}}/^{10}\mathrm{Be}(\mathrm{LIS}) <0.8\). Equation (2) of McCracken (2007a) shows that this corresponds to \(B(\mathrm{PCR}) >2.5~\mbox{nT}\), and consequently no estimates for \(B(\mathrm{PCR}) <2.5~\mbox{nT}\) are given for those years in the Electronic Supplementary Material. This occurred for four years in the Spörer Minimum (1420, 1421, 1442.1, and 1460.1); six years in the Maunder Minimum between 1692.7 and 1698.7), and two years in the Dalton Minimum (1810 and 1811).

Appendix 4: Supporting Information

Table S1: Definition of columns in the data file given in the Electronic Supplementary Material.

Column 1. Date the recording was made. Prior to 1770, the date is that determined by Berggren et al. (2009). Subsequent to that date, the data were converted to calendar years using a cubic-spline interpolation. See Section 2 for further details.

Column 2. The year in which the majority of the \(^{10}\mathrm{Be}\) was produced in the stratosphere.

Column 3. \(Y_{\mathrm{stein},\mathrm{GM}}(t)\) as defined in Section 2 for 1391 – 1950. This is the ratio between the average of the Dye 3 and North GRIP \(^{10}\mathrm{Be}\) concentrations for that calendar year, and the average for the interval 1944 – 1987 as used by Steinhilber et al. (2012) after correction for the baseline shift and other factors described in Section 2. Correction has been made for the changing strength of the geomagnetic dipole; the tabulated values correspond to the present-day strength of the geomagnetic dipole. The data in this column are given in the upper panel of Figure 1.

Column 4. \(Y_{\mathrm{LIS},\mathrm{GM}}(t)\) as defined in Section 2 for 1391 – 1950. This is the estimated ratio between the average of the Dye 3 and North GRIP \(^{10}\mathrm{Be}\) concentrations for that calendar year, and the value that would be observed if the local interstellar spectrum (LIS) of the galactic cosmic radiation were incident on Earth, the value corresponds to the present-day strength of the geomagnetic dipole.

Column 5. 1391 – 1950; Annual estimates [nT] of B(PCR-1) as described in Section 3 and plotted in the upper panel of Figure 2. This is the estimated strength of the heliospheric magnetic field near Earth, before the removal of the \(^{10}\mathrm{Be}\) produced by solar energetic particle events. See Appendix 3 regarding the present-day restriction of estimates to B (PCR) \({>\,}2.5~\mbox{nT}\). These upper limits are given in the tabulation as \({<\,}2.5~\mbox{nT}\).

Column 6. Annual average estimates of the pseudo-neutron-monitor counting rate. For 1951 – 2013; annual average instrumental neutron-monitor-counting rate. For 1391 – 1950; annual estimate based on the \(^{10}\mathrm{Be}\) record. All data are normalized to the value for February 1987. These data are given in the middle panel of Figure 1.

Column 7. Annual average of selected high-latitude neutron monitors. 1965 – 2010 from Oh et al. (2013). 1951 – 1964, Climax, normalized to Oh et al. (2013), after correction for altitude and cut-off rigidity; 2011 – 2014, Oulu normalized to Oh et al. (2013).

Column 8. 1775 – 1950; Annual estimates [nT] of B(PCR-2) as described in Section 5 and plotted in the lower panel of Figure 2. This is the estimated strength of the heliospheric magnetic field near Earth, after the removal of the \(^{10}\mathrm{Be}\) produced by solar energetic-particle events.

Column 9. The \(^{10}\mathrm{Be}\) impulsive enhancements identified by the selection criterion described in Section 4, and verified by subtraction of the 11-year and longer variability (see Figures 3 and 4). These data are given as the percentage increase in \(^{10}\mathrm{Be}\) concentration compared to the concurrent mean. Note that these data are tabulated against the year in which they occurred in the \(^{10}\mathrm{Be}\) time series; no allowance has been made for the one-to-two year delay between production and sequestration in polar ice (see Section 4).

Table S2: A summary of some acronyms used in the article. Further descriptions are given in the text. The references are to the initial definitions of these acronyms.

PCR Paleo-Cosmic ray Referring to estimates of the cosmic-ray intensity based on measurements of the cosmogenic radionuclides preserved in polar ice (McCracken and Beer 2007).

PNM Pseudo-neutron monitor Referring to estimates of the neutron-monitor counting rate that would have been observed prior to the commencement of the NM record in 1951. In this article, based on measurements of the cosmogenic radionuclides preserved in polar ice (McCracken and Beer 2007).

\(B\) (PCR-1) Estimate of the field strength of the heliomagnetic field derived from the PCR data before removal of the contributions made by cosmic rays produced by the Sun (Section 3 of this article).

\(B\) (PCR-2) Estimate of the field strength of the heliomagnetic field derived from the PCR data after removal of the contributions made by cosmic rays produced by the Sun (Section 3 of this article).

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