Evidence for Planetary Forcing of the Cosmic Ray Intensity and Solar Activity Throughout the Past 9400 Years

Abstract

Paleo-cosmic-ray (PCR) records based on cosmogenic ¹⁰Be and ¹⁴C data are used to study the variations in cosmic-ray intensity and solar activity over the past 9400 years. There are four strong correlations with the motion of the Jovian planets; the probability of occurring by chance being < 10⁻⁵. They are i) the PCR periodicities at 87, 350, 510, and 710 years, which closely approximate integer multiples of half the Uranus–Neptune synodic period; ii) eight periodicities in the torques calculated to be exerted by the planets on an asymmetric tachocline that approximate the periods observed in the PCR; iii) the maxima of the long-term PCR variations are coincident with syzygy (alignment) of the four Jovian planets in 5272 and 644 BP; and iv) in the time domain, the PCR intensity decreases during the first 60 years of the ≈ 172 year Jose cycle (Jose, Astron. J. 70, 193, 1965) and increases in the remaining ≈ 112 years in association with barycentric anomalies in the distance between the Sun and the center of mass of the solar system. Furthermore, sunspot and neutron-monitor data show that three anomalous sunspot cycles (4th, 7th, and 20th) and the long sunspot minimum of 2006 – 2009 CE coincided with the first and second barycentric anomalies of the 58th and 59th Jose cycles. Phase lags between the planetary and heliospheric effects are ≤ five years. The 20 largest Grand Minima during the past 9400 years coincided with the latter half of the Jose cycle in which they occurred. These correlations are not of terrestrial origin, nor are they due to the planets’ contributing directly to the cosmic-ray modulation process in the heliosphere. Low cosmic-ray intensity (higher solar activity) occurred when Uranus and Neptune were in superior conjunction (mutual cancellation), while high intensities occurred when Uranus–Neptune were in inferior conjunction (additive effects). Many of the prominent peaks in the PCR Fourier spectrum can be explained in terms of the Jose cycle, and the occurrence of barycentric anomalies.

Appendix

1.1 A.1. Properties of the Jose Cycle

Jose (1965) examined the periodic motion that the Sun executes about the center of mass of the solar system (the barycenter). Based on his calculations for the interval 1655 – 2012, he estimated the period of this motion to be 178 years. As outlined below, we have used the position of the barycenter for the interval 9337 BP to 10 000 years in the future, as given by the NASA/Jet Propulsion Laboratory Ephemeris DE-408 J2000 (see Abreu et al., 2012, for more details). Note that the barycenter we used includes the effects of all the planets, but it is easily shown that the four Jovian planets provide the dominant effect. Thus the small planets (Mercury through Mars) contribute < 2×10⁻³ solar radii to the position of the barycenter, while the combined effects of the Jovian planets are in the range 2>R _b≥0.15 solar radii. Identifying the ordered (quasi-sinusoidal) phases throughout this interval of 19 339 years, we conclude that a sequence of 97 Jose cycles lasted for a total of 16 635 years. From this we conclude that the long-term average Jose period is 171.49±0.21 years. Independently, Sharp (2013) has concluded that the Jose period is ≈ 172 years averaged over the past 6000 years. For the purposes of this article, we defined the first Jose cycle to commence at the start of the ordered phase in 10 332 BP. This places the modern era in the 59th Jose cycle.

1.2 A.2. Calculations of Probabilities

• i) Correlation with the Uranus–Neptune synodic period. Figure 2 shows an apparent agreement between the four observed consensus periodicities in Table 1 and the four harmonically related periods T=N(T _UN/2) years, where N are the integers 1, 4, 6, and 8, and where T _UN is the Uranus–Neptune (U–N) synodic period of 171.42 years (see Section 2). We assess here the statistical probability that this same correlation has occurred by chance independently for both the ¹⁰Be and ¹⁴C records. We performed this analysis in the frequency domain for the ten periodicities observed in the range 40<T<1000 years in both the ¹⁰Be and ¹⁴C data, as listed in Table 1. The resolution of the Fourier analyses is independent of frequency, being 2.12×10⁻⁴ cycles year⁻¹ for a sample length of 9400 years. T _UN/2 corresponds to a frequency of 116.67×10⁻⁴ cycles year⁻¹. For the ¹⁰Be data, we divided the frequency range 10×10⁻⁴<f<250×10⁻⁴ cycles per year into 60 equal bins in frequency space, each of width 4×10⁻⁴ cycles year⁻¹, and identified the four bins containing the four frequencies given by N=1, 4, 6, and 8. Assuming white noise, a noise-derived period has equal probability of falling into any of the 60 bins. For ¹⁰Be, we then used binomial statistics to compute the probability [P]=2.7×10⁻³ that the four periods in Figure 2 (out of a total of ten observed periods) fell within the bins corresponding to N=1, 4, 6, and 8. The sequestration processes for ¹⁰Be and ¹⁴C are different, and these data therefore represent independent measurements of the cosmic radiation intensity in the past. Table 1 shows that similar periods (within the resolution of the Fourier analyses) were observed in the ¹⁰Be and ¹⁴C data. In the case of ¹⁴C we used 40 frequency bins of width 6×10⁻⁴ cycles year⁻¹. The probability that the four observed periods in the ¹⁴C data would fall in the bins corresponding to the periods P=N (T _UN/2) was computed to be P=1.1×10⁻². The independence of the meteorological, climate and measurement noise in the ¹⁰Be and ¹⁴C therefore indicates that there is a probability of <10⁻⁴ that the same four periods, N×(T _UN/2), would occur in the ten periodicities observed in the two independent data streams between 40 and 1000 years.

• ii) Correlation of the Hallstatt spectral peak [2310 years] with the repetition period of syzygy of the Jovian planets (Grand Jovian Alignment − Section 4). Working in the frequency domain as above, we defined bins of width 2×10⁻⁴ cycles year⁻¹ for both the ¹⁰Be and ¹⁴C data for the interval 1000<T<5000 years. For white noise, the probability that the Hallstatt periodicity would coincide with the independently known repetition period of the Grand Jovian Alignments by chance for ¹⁰Be and ¹⁴C individually is then 0.2, and for both 4×10⁻².

1.3 A.3. Astronomical Quantities and Terms

• i) The synodic period [T _s] of planets 1 and 2 is given by 1/T _s=1/T ₁−1/T ₂. The periods of the planets are known to a precision of one part in 10⁵ out to Saturn, and one in 10⁴ for Uranus and Neptune. For the latter, T _s=171.42 years. For Jupiter and Saturn, T _s=19.858 years. The sidereal periods used here were Jupiter =11.862 years; Saturn=29.457 years; Uranus=84.02 years; and Neptune=164.79 years.

• ii) Syzygy: a straight-line configuration of three or more planets and the Sun.