Correspondences

What is linked, what is not

Each arc joins two phenomena tested on this site. Green and animated: clear link (correlation significant at 5 % after correcting for autocorrelation, or a response outside chance in an event study). Grey: inconclusive test. A statistical link alone does not establish causation.

Clear link
Inconclusive

Hypotheses tested

Clear links

correlation p < 0.05 or epochs outside chance

Causation demonstrated

a correlation demonstrates none

Arc width from |r| of the stored result; several tests between the same phenomena are drawn as stacked arcs.

Hypothesis tested: The solar wind and its magnetic field push galactic cosmic rays back: the more active the Sun, the fewer reach us (heliospheric modulation). Particles drift in the heliospheric field, whose polarity flips at every maximum: depending on its sign they come in over the poles or along the current sheet, which should make the response fast every other cycle and slow in the others (Jokipii et al., 1977).

Pearson correlation r (lag 5 month(s))

-0.85

95% interval [-0.90; -0.79] (block bootstrap)

Aligned points

751

effective n ≈ 36 (autocorrelation)

p-value

0.00000

two-sided, Fisher z transform, effective n

Mean delay, even cycles (months)

cycles 20, 22 and 24

Mean delay, odd cycles (months)

cycles 21 and 23 (25 is in progress)

Period analysed

1963-11 → 2026-05

computed on Oct 25, 2026 · engine v1.0

Aligned series (standard deviations, after preprocessing)

Show the data as a table

Sunspots of month M and cosmic rays of month M + the chosen lag, in standard deviations (z), with no other filtering: the two curves move in opposition at the pace of the 11-year cycle. Original values in the table and the CSV export.

Correlation by lag (month(s))

Show the data as a table

Pearson coefficient for each lag; a positive lag means the second series follows the first. The table gives n, effective n and p for each lag.

Delay of cosmic rays behind sunspots, cycle by cycle

Cycle	Period	Parity	Best lag	r	r without lag
20	1964-10 → 1976-02	even	2 month(s)	-0.87	-0.87
21	1976-03 → 1986-08	odd	16 month(s)	-0.87	-0.62
22	1986-09 → 1996-07	even	0 month(s)	-0.92	-0.92
23	1996-08 → 2008-11	odd	14 month(s)	-0.90	-0.78
24	2008-12 → 2019-11	even	4 month(s)	-0.90	-0.86
25 (in progress)	2019-12 → 2026-09	odd	11 month(s)	-0.92	-0.82

Same lag search (0 to 24 months, most negative r) within each cycle, bounded by the SILSO minima. Only five complete cycles: the alternation is clear but rests on five values, and the best lag of a cycle is uncertain by a few months (flat correlation curve near its peak).

Aligned series (CSV)

Method and sources

Monthly sunspot number (SILSO, version 2); monthly mean of the corrected count rate of the Oulu neutron monitor (months with at least 80 % of days measured). Lags of 0 to 24 months paired on the calendar; the expected sign is negative, the most negative r is kept. Bretherton et al. effective size (the 11-year cycle strongly reduces the number of independent values), block bootstrap with 24-month blocks. Same search cycle by cycle, between the official minima.

Computation parameters

{
    "x": "monthly mean sunspot number (SILSO V2)",
    "y": "monthly mean corrected count rate of the Oulu neutron monitor (months with at least 80 % of days)",
    "cycles": "same lag search within each solar cycle (SILSO minima 1964-10, 1976-03, 1986-09, 1996-08, 2008-12, 2019-12), at least 36 pairs",
    "pairing": "calendar months",
    "bootstrap": {
        "seed": 20261023,
        "block": 24,
        "draws": 1000
    },
    "lag_choice": "most negative r (sign expected a priori)",
    "lags_months": [
        0,
        24
    ]
}

Inputs : silso.ssn.monthly (3,333 pts, run #48) · oulu.nm.daily (22,811 pts, run #3730)

Reading this result

The anticorrelation is one of the strongest on the site, but its significance rests on a small effective number (about thirty): there are only six cycles. The alternating delay (a few months for even cycles, more than a year for odd ones) is the signature, in cosmic rays, of the 22-year magnetic cycle of the Sun. The current cycle 25 follows the odd-cycle behaviour. Correlation is not causation: common factors (seasons, cycles, trends) or coincidence can produce it. The p-values account for autocorrelation (effective n) but not for preprocessing choices; the confidence interval comes from a block bootstrap. The limits of the source data apply.

SOURCES OF THIS PAGE

SILSO monthly mean total sunspot number V2.0: SILSO World Data Center. The International Sunspot Number, V2.0. Royal Observatory of Belgium, Brussels. · source page ↗
Licence : CC BY-NC 4.0 · retrieved on Oct 23, 2026 · SHA-256 4749cc16c68e…
Oulu neutron monitor, daily corrected count rate (Sodankylä Geophysical Observatory): Oulu neutron monitor data, cosmicrays.oulu.fi, Sodankylä Geophysical Observatory of the University of Oulu (6NM64 standard neutron monitor at 65.05° N, 25.47° E, geomagnetic cutoff rigidity ≈ 0.8 GV). · source page ↗
Licence : Research, educational and public non-commercial use; acknowledge cosmicrays.oulu.fi and the Sodankylä Geophysical Observatory (commercial use: contact the station manager) · retrieved on Oct 25, 2026 · SHA-256 fc2f77ecf31e…
Jokipii et al. (1977): Jokipii, J. R., Levy, E. H., & Hubbard, W. B. (1977). Effects of particle drift on cosmic-ray transport. I. General properties, application to solar modulation. The Astrophysical Journal, 213, 861–868. · doi:10.1086/155218
Licence : Published literature; cited
Usoskin et al. (2011): Usoskin, I. G., Bazilevskaya, G. A., & Kovaltsov, G. A. (2011). Solar modulation parameter for cosmic rays since 1936 reconstructed from ground-based neutron monitors and ionization chambers. Journal of Geophysical Research, 116, A02104. · doi:10.1029/2010JA016105
Licence : Published literature; cited

Solar cycle and cosmic rays An active Sun shields the Earth, with a delay that changes from one cycle to the next

What is linked, what is not

Delay of cosmic rays behind sunspots, cycle by cycle