Comparison of the extended solar minimum of 2006–2009 with the Spoerer, Maunder, and Dalton Grand Minima in solar activity in the past

1 Introduction

The sunspot, geomagnetic, and auroral records show that the average level of solar activity during the “space age” was remarkably high, being equalled, or exceeded on only a handful of occasions during the past ~10,000 years [Solanki et al., 2004; McCracken et al., 2004, 2013]. On the other hand, by comparing sunspot, auroral, and cosmogenic ¹⁴C data, Eddy [1976] concluded that there had been extended intervals of low solar activity now known as the Maunder (1645–1715) and Dalton (1790–1830) Minima. Auroral records and the paleocosmic radiation records (PCR; see below) indicate that there were earlier periods of low solar activity; the Spoerer (1400–1540), Wolf (1320) and Oort (1050) Minima, and 19 more in the previous 8000 years [McCracken et al., 2013]. Solar records indicate sunspot cycles of relatively low amplitude in the interval 1890–1910 as well. Over the past millennium, these intervals of very low solar activity have been interspersed with intervals of 60–100 years exhibiting high sunspot numbers at solar maximum. That is, the historical record suggested that the interval of high solar activity since 1945 would cease circa 2000 and that the Sun would enter a period of relatively low solar activity. That expectation appears to have been fulfilled with the occurrence of the extended sunspot minimum of 2006–2009 and the subsequent low sunspot numbers and solar activity that have characterized the 24th sunspot cycle.

Based on their observations of the solar magnetic fields, both in the sunspot groups and in the intervening ephemeral regions, Schrijver et al. [2011] concluded that “the best estimate of magnetic activity….for the least active Maunder Minimum phases appears to be provided by (the) direct measurements in 2008–2009.” While not disputing this statement regarding the surface magnetic fields, this paper shows that the cosmic ray record indicates that this statement is unlikely to be valid for the large-scale heliospheric and solar magnetic fields.

Before proceeding, we state the nomenclature we will use. We refer to the 11 year solar cycle as the Schwabe cycle. As noted above, the extended intervals (typically 40–100 years) of low sunspot number are collectively referred to as Grand Solar Minima (GSMin). The intervening intervals (60–100 years) of high-amplitude Schwabe cycles are called Grand Solar Maxima.

Considering the longer term, the paleocosmic ray record [Steinhilber et al., 2012] shows that there have been 24 Grand Solar Minima similar to the Maunder Minimum in the past 9400 years [McCracken et al., 2013]. During that time, there have been four sequences of GSMin, each sequence extending over intervals of up to ~1000 years, separated by intervals of relatively high solar activity, each of duration ~1200 years. One such sequence of five GSMin started with the Oort Minimum followed by the Wolf, Spoerer, Maunder, and finally the Dalton Minimum. The long-term PCR record [Steinhilber et al., 2012] shows that this sequence is a good representative example of the earlier sequences of Grand Minima.

The galactic cosmic radiation (GCR) incident on Earth is strongly “modulated” by the heliospheric magnetic fields (HMF) entrained in the outward sweeping solar wind [Jokipii, 1991; Potgeiter, 2013]. As Figure 1 shows, the GCR intensity is highest during Schwabe cycle minima when the HMF strength is low, decreasing to low values near sunspot maximum when the fields (and their disordered nature) are high. As a result of the theoretical work of Parker [1965], Gleeson and Axford [1968], and Jokipii [1991], and others, there is now a good understanding of this process, as described by the cosmic ray modulation equation. The GCR intensity has been recorded by neutron monitors since 1951 and by the sequestration of cosmogenic radionuclides in terrestrial archives prior to that [Beer et al., 2012]. In the following we use those cosmic ray records as proxy measurements to compare the properties of the extended sunspot minimum (2006–2009) with those of three Grand Minima and Grand Maxima in the interval 1391–2012.

2 Instrumentation and Observations

2.2 The Paleocosmic Ray Record

As discussed by Beer et al. [2011], the cosmogenic radionuclides constitute a “natural neutron monitor” that provides a record of the cosmic ray intensity that extends > 100,000 years into the past. Briefly, on entering the atmosphere, each >500 MeV cosmic ray initiates a nucleonic cascade leading to subsequent nuclear reactions with atmospheric atoms [Beer et al., 2012]. The resulting radionuclides (primarily ¹⁰Be, ¹⁴C, and ³⁶Cl ) make their way to the surface of Earth and are sequestered in ice (¹⁰Be, ³⁶Cl), tree rings (¹⁴C), and sediments.

Using nuclear propagation codes such as GEANT, Masarik and Beer [1999, 2009] and Clem and Dorman [2000] computed the NM and PCR yields from the GCR spectrum incident on the heliosphere. McCracken and Beer [2007] used these results to intercalibrate the instrumental NM data, and the “paleocosmic ray” (PCR) data provided by ¹⁰Be and ¹⁴C. This intercalibration is used here to compute the neutron monitor response that is equivalent to the PCR data in the past; we refer to these as the pseudoneutron monitor data. The nuclear propagation codes on which this intercalibration is based are comprehensive and accurate; the McCracken and Beer [2007] procedure is relatively insensitive to uncertainties in the “local interstellar spectrum” of the GCR; and therefore, the pseudo NM data can be compared with confidence over intervals of many centuries.

Figure 2 displays the variability of the cosmic radiation at Earth for the interval 1391–2012; the interval 1391–1952 displays the pseudo NM data, and 1953–2012 are the NM data from Figure 1. The pseudoneutron monitor record was obtained by combining the annual ¹⁰Be data derived from ice cores from Dye 3 and the North Greenland Ice Core Project (both in Greenland) [Berggren et al., 2009]. There are relatively small long-term changes in the ¹⁰Be data due to atmospheric and climatic effects [Beer et al., 2012]: they differ between the Arctic and Antarctic and within those regions. In addition, the atmospheric and climate effects are quite different for ¹⁰Be and ¹⁴C data. Steinhilber et al. [2012] have minimized these differences by combining all the existing ¹⁰Be and ¹⁴C data from both hemispheres to provide an intercalibrated record of the paleocosmic ray data (22 year averages) for the past 9400 years. That record was used to minimize atmospheric and sampling effects in Figure 2. In addition, the geomagnetic dipole moment decreased by ~10% over the past 600 years, resulting in a similar reduction in the geomagnetic cutoff for the GCR. The data in Figure 2 have been corrected for this effect [McCracken, 2004].

Table 1. The Maximum Cosmic Ray Intensities and Estimated HMF Strengths for Each of the Three Grand Solar Minima, Together With the Same Parameters for the Interval 1880–1910, and the Schwabe Minima of 1954–1996 and 2006–2009a

Grand Minimum	Duration	Rise	Number of Cycles	11 Year Means		Schwabe Minima
		Period		Peak Pseudo NM (%)	Minimum HMF (nT)	Peak Pseudo NM (%)	Minimum HMF (nT)
Spoerer	1440–1540	1400–1443	4	107.1	3.6	111.3	2.4
Maunder	1645–1715	1645–1697	5	111.7	2.5	117.0	<2.0
Dalton	1790–1830	1790–1810	2	106.5	3.6	110.9	2.6
Gleissberg	1880–1910	1880–1891	1	102.1	4.6	104.5	3.8
Extended minimum	2006–2009					102.8	3.9
Modern epoch minima	1954–1996					97.7	5.4

• ^a Column 2: the nominal duration of the Grand Minima; column 3: the duration of the rising intensity phase; column 4: the number of Schwabe cycles in the onset phase; column 5: the maximum 11 year average pseudoneutron monitor intensity; column 6: the minimum 11 year average of the estimated HMF; column 7: the maximum yearly value of the pseudoneutron monitor intensity; column 8: the minimum yearly value of the estimated HMF. Notes: (1) Figure 1 shows that the Spoerer Minimum commences closer to 1400 than 1440–1469 as cited in the past. (2) Note that the estimates of absolute intensity of the HMF are subject to error as discussed in text. (3) The data for 1880–1910 are averaged over the Schwabe minima of 1891 and 1902 and exclude the enhancement in 1892–1894 as discussed in the text.

3 Comparison of the Extended Solar Minimum 2006–2009 With the Dalton, Maunder, and Spoerer Minima

Figure 2 shows that the cosmic ray intensity increased to relatively high values during the Spoerer, Maunder, and Dalton Solar Minima. There are 44 well-defined peaks of duration ~5 years in the data in Figure 2 that are well correlated with the sunspot minima since 1609, and we henceforth associate them and those before 1609 with the Schwabe minima. Likewise, the recurrent short-term minima of ~5 year duration in Figure 2 correlate well with the majority of the maxima of the Schwabe cycle. As first reported by Beer et al. [1998] and discussed by Usoskin et al. [2001] and McCracken et al. [2004], Figure 2 shows that the Schwabe cycle of solar activity persisted through the Maunder and Dalton Grand Minima, as well as during the Spoerer Grand Minimum.

The interval 1890–1910 illustrates a remaining uncertainty in the interpretation of the paleocosmic ray data. The highest value of the pseudo NM data (108.2%) in the interval 1890–1910 occurred in 1892–1894, near sunspot maximum, and in close association with a total of 18 “great” geomagnetic storms that occurred in the interval 1892–1894 (of 112 such storms recorded at Greenwich from 1874 to 1954) [Jones, 1955]. In a similar manner, the second, smaller pulse during the Dalton Minimum coincided with the sunspot maximum of 1816. Two possibilities for these increases have been discussed: (a) the production of a very large fluence of solar cosmic rays [McCracken et al., 2001] or (b) reduction of the strength of the solar axial dipole relative to the equatorial dipole during weak solar cycles [Wang and Sheeley, 2013]. The 1892–1894 peak, in particular, results in an underestimate of the strength of the HMF compared to the well-constrained estimates based on the geomagnetic record. Comparison of the sunspot and paleocosmic ray record shows that significant increases coincident with sunspot maxima are rare. The enhancement of 1892–1894 has been excluded from the subsequent discussions on the basis that it probably represents a phenomenon unrelated to the modulation of the cosmic radiation by the magnetic field entrained in the solar wind. The enhancements coincident with the Schwabe minima of 1891 and 1902 were not removed, as they are consistent with the cosmic ray modulation associated with all Schwabe minima.

To compare the minimum of 2006–2009 with the three Grand Minima in greater detail, Table 1 lists the maximum cosmic ray intensities and estimated HMF strengths for each of the three Grand Solar Minima, together with the same parameters for the Schwabe minima 1954–1996 and 2006–2009. In Figure 2, the highest annual value (102.8%) during the extended solar minimum 2006–2009 is shown as a horizontal dotted line. This and the fourth and sixth columns of Table 1 show that the annual cosmic ray intensity in 2009 was significantly less than the peak values associated with the three Grand Minima. Thus, the pseudo NM data attained peak values of ~111% during the Spoerer Minimum, ~117% during the Maunder Minima, ~111% during the Dalton Minimum, and ~104.5% averaged over the two Schwabe Minima of 1891 and 1902. These values are also significantly greater than the annual NM intensities for the Schwabe minima between 1954 and 1996, these being in the range 97–99%. The average of the annual values for these five Schwabe minima is 97.7%, and this is shown as a horizontal line in Figure 2 as well.

The intervals between the Maunder, Dalton, and Gleissberg Minima (i.e., 1730–1790 and 1830–1880) were periods with high Schwabe maxima comparable to those during the modern Grand Solar Maximum (1944–1996). The PCR values at the Schwabe minima during these two intervals averaged 97.1% and 100.7%, respectively (i.e., comparable to the value of 97.7% for the modern era 1954–1996). The PCR intensities for the Schwabe minima in the interval of enhanced solar activity (1540–1645) between the Spoerer and Maunder Minima averaged 103.0%. We have identified 15 Schwabe minima in these three intervals; the average PCR intensity being 100.2%, and the standard deviation 3.5%. As noted above, the highest annual PCR intensity during the long sunspot minimum of 2006–2009 was 102.8%. On the basis of this value, we conclude that the peak cosmic ray intensity for 2006–2009 is consistent with it being a member of the population of 15 Schwabe minima that occurred during the three intervals of strong solar activity that occurred between 1540 and 1880.

4 Detailed Comparison of the Extended Solar Minimum 2006–2009 With the Maunder Minimum

The PCR record shows that the Maunder Minimum was one of the most profound of the 24 GSMin that have occurred in the past 9400 years [McCracken et al., 2013]. The Sun was well observed during this time; an archival search by Hoyt and Schatten [1998] located records made by 70 observers, and they concluded that sunspot activity was recorded on >50% of all days in each year between 1645 and 1715. Figure 2 has shown that the highest cosmic ray intensities were not observed until the fifth Schwabe cycle after the commencement of the Maunder Minimum. We now use the sunspot record to examine this “slow-onset” feature of the Maunder Minimum and to further compare the extended minimum of 2006–2009 with the solar activity therein.

Figure 3 presents the pseudo NM data for the interval 1600–1750, together with the group sunspot record [Hoyt and Schatten, 1998]. Table 2 gives the maximum and minimum PCR values for each Schwabe cycle, together with the corresponding estimates of the HMF intensity. Note that the group sunspot record uses a logarithmic scale for values <10. The two horizontal lines in Figure 3 (top) correspond to the pseudo NM values for the Schwabe minima 1954–1996 and for the extended sunspot minimum 2006–2009. With only one exception (1671) the annual group sunspot numbers remained consistently ≤ 3 throughout the interval 1645–1700. By way of contrast, the peak values of the paleocosmic ray intensity at the Schwabe minima increased from 102.2% in 1650 to a maximum of 117.0% in 1697. We discuss features of this increase in the following paragraph.

The strong Schwabe cycle modulation of the cosmic radiation is very striking throughout the Maunder Minimum (MM). Figure 3 and Table 2 show that the annual cosmic ray intensity (102.2%) at the minimum of the Schwabe cycle at the commencement of the MM was similar to that for the extended minimum of 2006–2009 (102.8%). The estimated annual HMF intensity was 4.6 nT in 1650 compared to 3.9 nT in 2009. The group sunspot numbers for the 7 years (1645–1651) preceding the Schwabe minimum of 1650 were zero. There was a similar long interval of zero sunspot numbers 1662–1670, and the pseudo NM increased to 108.5% in 1675, and the estimated HMF decreased to 3.1 nT. The interval 1690–1699 was another extended interval of very low sunspot numbers, and the pseudo NM reached 117.0%, and the estimated HMF decreased to <2 nT. That is, while these three intervals within the MM exhibited a similar prolonged absence of sunspots, the cosmic ray conditions at Earth were strikingly different, consistent with a factor of >2.3 decrease in the strength of the HMF between 1651 and 1698. It has been estimated by Livingston and Penn [2009] that visual and telescopic observations of sunspots will not detect sunspots with magnetic fields < 1500 G, and this allows the possibility that there was a substantial but steadily decreasing level of solar magnetic activity which was below the sunspot detection threshold at that time. We now briefly consider that possibility.

The dynamo model of the solar magnetic field [Charbonneau, 2010] postulates that the subduction of the magnetic flux at the solar poles during one Schwabe cycle leads to the generation of the solar magnetic field in the subsequent cycle. Convection of portion of that field in the radially expanding solar wind gives rise to the HMF. The continuation of the 11 year Schwabe cycle of cosmic ray modulation indicates that the dynamo continued to operate during the six Schwabe cycles in the MM.

Table 2 examines the characteristics of these cycles in greater detail. Writing the estimated HMF intensity at each Schwabe maximum (row 6) as B_max, and the intensity at the preceding Schwabe minima (row 3) as B_min, row 8 gives the ratio (B_max / B_min) for the six Schwabe cycles within the Maunder Minimum. The average of this ratio is 1.54 (range from 1.30 to >1.85 (set to 1.85)). The fact that this ratio falls in this relatively restricted range suggests that the dynamo operates in a consistent manner during each Schwabe cycle in the MM. For the modern era, the annual average OMNI data yields B_max / B_min in the range 1.31–1.63 with an average of 1.52 for the interval 1965–2002. The similarity of the ratio for the MM (1.54) and the modern era (1.52) suggests that the dynamo operated in a quantitatively similar manner during both eras.

It is important to note that there may be other possibilities for the slow onset of the Maunder Grand Minima. For instance, Moraal [2013] pointed out that Voyager 1 did not see a well-defined cosmic ray maximum in 2009 in the heliosphere beyond the termination shock. This can be quantitatively understood as due to the factor of > 3 reduction in the solar wind velocity there. This causes modulation conditions to “accumulate” in time in the heliosheath and may delay cosmic ray variations in the outer heliosphere resulting in time scales longer than the Schwabe cycle at low energies. A slow monotonic reduction in solar wind velocity throughout the heliosphere, or a change in its 3-D geometry, might have a similar effect. Clearly, the slow onset of the cosmic ray counterpart of the Maunder Grand Minima is an important topic for research in the near future.

The observation (Table 1) that the onset of the Spoerer and Maunder Minima occupied four and five Schwabe cycles, respectively, suggests that this feature of a slow onset extending over a number of Schwabe cycles may be a common feature of the most profound Grand Minima. We speculate that the paleocosmic ray data indicates that the solar dynamo continues to operate in a manner similar to that observed in the modern epoch throughout the Grand Minima, while exhibiting a characteristic relaxation time that is well in excess of the 11 year period of the Schwabe cycle, and which only becomes evident during the most profound Grand Minima.

Finally, we consider the minimum values of the pseudo NM record during the MM. These values correspond to the maxima of the Schwabe cycle. The values for the first two (1645 and 1655) are 94.6% and 94.8%; that is, comparable to the level of modulation soon before and after the Schwabe minima during the instrumental era, 1951–2006, and they imply HMF ≈ 6.0 nT. The next three (97.7%, 100.6%, and 97.5%) are comparable to the values at the Schwabe minima 1954–1996 and imply HMF in the range 4–5 nT. The PCR intensity (105.3%) and HMF strength during the last (1704) was the only Schwabe maximum that was less active than observed during the minimum of 2006–2009. In summary, the cosmic ray and magnetic conditions during the maxima of the Schwabe cycles in the Maunder Minimum appear to have been comparable with the activity observed at the sunspot minima since 1954.

5 Conclusions