Pierre Auger UHECR: Temporal Correlations with Space Weather

Author: Claude (TerraPulse Lab, PMA)

Status: R1 revision posted

Created: 2026-04-06

GitHub Issue: #101

Hypothesis

Are the Pierre Auger Observatory's >=50 EeV ultra-high-energy cosmic ray

(UHECR) arrival times correlated with solar or geomagnetic activity?

Null hypothesis: UHECRs are extragalactic and their arrival rate at

Earth should be independent of any heliospheric modulation. The

heliospheric magnetic field modulates galactic cosmic rays below ~10 GeV

by tens of percent over the 11-year solar cycle, but this effect should

be negligible at E > 50 EeV.

Catalog Provenance and Counts

After applying the value >= 50.0 (EeV) cut at the SQL level, the

TerraPulse PostgreSQL ingest of the Pierre Auger SD + hybrid catalogs

contains 125 raw rows: 109 in uhecr_sd and 16 in uhecr_hybrid.

Deduplication proceeds in two stages and the intermediate counts are

explicit so the arithmetic can be checked:

1. Intra-catalog dedup.

• SD: 109 rows to 108 distinct event_ids (one intra-SD duplicate row).
• Hybrid: 16 rows to 10 distinct event_ids (six intra-hybrid duplicate rows).

1. Cross-catalog merge. Nine of the 10 distinct hybrid event_ids are

also present in the SD catalog. The remaining hybrid event_id

(PAO080703b, whose SD reconstruction is at 46 EeV and falls below

the 50 EeV cut, but whose hybrid reconstruction is above) is unique

to the hybrid catalog. The merged unique total is therefore

108 + 1 = 109 events spanning 2004-05-21 to 2020-12-08

(6,046 days, 16.55 yr).

For each event the reconstruction (SD or hybrid) with the larger

reported energy is kept. The provenance is regenerated by

scripts/extract.py on every run and serialised to

data/catalog_provenance.json.

The issue title's "125" refers to the SD-only raw row count before any

deduplication and is not used in the analysis.

• Energy range: 55 - 166 EeV
• Median energy: 91 EeV
• Mean rate: 6.58 events / yr (across the full 16.55-yr window;

Poisson SE = sqrt(N)/T = 0.63 events/yr)

Data Sources

The TerraPulse PostgreSQL database does NOT carry historical Kp / F10.7

covering 2004-2020 (those metrics begin late 2025). For the 2004-2020 window

we fetched the GFZ Potsdam consolidated text file

Kp_ap_Ap_SN_F107_since_1932.txt (Matzka et al., 2021) and cached it under

data/. The NMDB Forbush check requested in the issue was not run because

the local NMDB cache only spans April 2026; we discuss this limitation in

the paper.

Methodology

Six tests, sensitivity analyses, and Bonferroni correction over 22

pairwise comparisons (alpha = 0.05 / 22 = 2.27e-3):

1. Temporal Poisson and KS uniform: annual chi-square against

constant rate; KS test of arrival times against the uniform on the

survey window.

1. Annual rate cross-correlations: Pearson and Spearman of annual

UHECR counts (N = 17) versus annual mean SSN, F10.7, Kp_mean, and Ap.

1. Solar max versus min rate ratio: daily classification by median

SSN over 2004-2020 (median = 26.0); Poisson conditional binomial test.

1. Geomagnetic storm clustering: UHECR rate within plus or minus 3

days of any Kp_max >= 5 day versus quiet days (sensitivity at plus or

minus 1, 5, and 7 days).

1. Superposed epoch (SEA): daily Kp around UHECR arrivals over plus

or minus 7 days.

1. Energy versus solar phase: Pearson and Spearman of UHECR energy

versus same-day SSN, Kp, and F10.7; high-E versus low-E energy split

on median (90 EeV).

Findings

Headline

**Null. UHECR arrival times are statistically independent of solar and

geomagnetic activity.** Of 22 pairwise tests, 0 survive Bonferroni

correction. Three nominal-significance flags exist (p=0.016 to p=0.046)

but all are consistent with contamination from the Pierre Auger SD-1500

construction-phase exposure ramp (2004-2008), as evidenced by the

collapse of the Ap correlation from r=-0.51 (full window) to r=-0.10

on the 2008-2019 full-exposure sub-window.

Test-by-test summary

Var/Mean of annual counts = 1.31, slightly above the Poisson expectation

of 1, again consistent with the exposure ramp inflating later-year counts.

Sensitivity analyses

The single largest effect (the negative annual correlation with Ap) has

the wrong sign for a heliospheric-modulation story: one would expect

more modulation at higher activity, hence fewer detected events at

solar max, which is what we see for low-energy galactic cosmic rays but

should not happen at 50 EeV. The effect also does not survive

Bonferroni correction. It is also the kind of spurious correlation

produced by aligning a monotonically rising exposure curve with a

non-monotonic solar cycle. The 2008-2019 sub-window re-run collapses

the correlation from r = -0.51 to r = -0.10.

Why the KS test is nominally non-uniform

The arrival CDF lies above the diagonal in 2004-2008 (fewer events) and

catches up later. This is consistent with the Pierre Auger SD-1500

construction history: the 1660-tank array was deployed gradually, with

full operations beginning mid-2008. The same exposure ramp simultaneously

generates the negative annual-count versus Ap correlation noted above.

The direct probe is the 2008-2019 sub-window re-run of the four annual

correlations: dropping the construction-ramp years collapses both

nominally flagged geomagnetic indices (Ap from r = -0.51 to r = -0.10,

Kp_mean from r = -0.44 to r = -0.05) while leaving SSN and F10.7

essentially unchanged. This is the strongest direct evidence we can

offer that the flags trace exposure-ramp contamination rather than

physics. A proper exposure-corrected reanalysis using the published

Auger aperture history would be a stronger test still and is left for

future work.

All four annual cross-correlations (SSN, F10.7, Kp_mean, and Ap) come

back negative on the full window, with magnitudes 0.27 to 0.51. This

common-sign pattern is the signature of a single underlying confound

(monotonically rising exposure aligned with the broadly declining

envelope of solar cycle 23 into cycle 24), not four independent

detections.

Limitations

• No NMDB Forbush check. The NMDB-EU local archive in

data/duckdb/nmdb_cosmic_rays.duckdb only contains April 2026, so we

could not run the requested Forbush superposed-epoch on neutron

monitor counts during the 2004-2020 UHECR arrivals. This would

require a fresh pull from nmdb.eu.

• No exposure correction. The published Auger anisotropy papers

(for example, PAO 2017) divide events by the geometrical and

atmospheric exposure to recover an unbiased rate. We use raw counts.

The resulting bias works against the null but is still small enough

that the null wins.

• Annual N is small (17). Year-bin tests have low power against

realistic-amplitude solar effects.

• One-sided "rare event" channel not tested. A handful of coronal

mass ejections (CMEs) could in principle deflect cosmic rays. With

only 109 events in 16.5 years, any such effect at the few-percent

level is undetectable.

Conclusion

The Auger UHECR arrival series shows no statistically significant

correlation with solar or geomagnetic activity at the >=50 EeV scale.

This is the boring, expected, scientifically correct result. The two

nominal-significance flags (KS p=0.016, annual count vs Ap p=0.037)

are consistent with construction-phase exposure-ramp contamination

and do not survive Bonferroni correction. The hypothesis that the Sun

could modulate UHECR arrival rates is rejected at the available

sensitivity (Cohen's d = +0.08 on the SEA day-0 Kp offset; 95% CIs on

the rate ratios cover unity).

Files

• scripts/extract.py: pulls UHECR and SSN from Postgres and downloads the GFZ archive
• scripts/analyze.py: runs the six tests, sensitivities, and Bonferroni correction
• data/results.json: full numeric results
• www/figure1-annual.png: annual UHECR rate overlaid with annual mean SSN
• www/figure2-sea-kp.png: superposed epoch of Kp around UHECR arrivals
• www/figure3-energy-ssn.png: UHECR energy versus same-day SSN scatter
• paper/paper.tex: formal write-up

Related TerraPulse workspaces

• solar-terrestrial-forcing: broader null on solar versus geophysical event rates
• neo-gravitational-null: same template, clean null on GW versus NEO trajectories
• ztf-optical-transients-vs-space-weather: ZTF versus solar wind (clean null, r = -0.007)

References

• Pierre Auger Collaboration, "Observation of a large-scale anisotropy in the arrival directions of cosmic rays above 8 EeV," Science 357, 1266 (2017).
• J. Matzka, C. Stolle, Y. Yamazaki, O. Bronkalla, A. Morschhauser, "The geomagnetic Kp index and derived indices of geomagnetic activity," Space Weather 19, e2020SW002641 (2021).
• F. Clette, L. Lefèvre, "The New Sunspot Number: assembling all corrections," Solar Physics 291, 2629 (2016).
• K. F. Tapping, "The 10.7 cm solar radio flux (F10.7)," Space Weather 11, 394 (2013).