Those who lament the timely closure of Pattern Recognition in Physics should lament no more: while the sun orbits the barycentre, papers that argue that this affects solar variability will get published. As evidence for this conjecture, I offer you McCracken et al (2014) and its precursor Abreu et al (2012).

Both papers discuss spectral peaks in a 9400-year record of solar activity reconstructed from the cosmogenic isotopes 14C and 10Be, from tree rings and ice cores respectively (high concentrations of the cosmogenic isotopes indicates a high flux of cosmic radiation and an inactive sun), and relate these spectral peaks to the influence of planets on the sun. Rather than invoking the “vanishingly small” planet-induced tides on the sun, both papers invoke the torque that the planets’ gravity imposes on the solar tachocline, the non-spherical layer that separates the inner and outer parts of the sun. The mechanism by which the very small torque forcing could be amplified into the reconstructed solar variability is left unspecified.

Figure 5 of Abreu et al shows the spectra of solar activity and their calculations of torque over the Holocene. Five of the peaks in the two spectra coincide. It’s looking promising. Nature certainly thought so.

Alas, there is problem. As Poluianov & Usoskin (2014) demonstrate, the data processing of Abreu et al will cause spurious spectral peaks in their torque spectrum. Abreu et al calculate the torque on a daily basis, but perform the spectral analysis on annually averaged data. This will cause aliasing of the sub-annual torque frequencies of Mercury and Venus, making them appear as low frequency spectral peaks. Poluianov & Usoskin (2014) repeat the analyses of Abreu et al, but using daily rather than annually averaged torque.

None of the spectral peaks found by Abreu et al remain – they are all aliasing artefact. The correct peaks don’t align with the peaks in the solar variability record. The aliasing problem should have demolished Abreu et al (Poluianov & Usoskin also argue the test for coherence between the torque and the solar record is too liberal), but in their response, Abreu et al (2014) basically declare that “tis but a scratch”. They admit that they have an aliasing problem, get confused about the effect of a constant term in their equation for calculating torque, and other things. Some how, the frequencies they originally found are still present, but as minor spectral peaks. It would be most curious for the sun to ignore major peaks in torque but respond to minor peaks.

Abreu et al maintain that using a Monte Carlo procedure, the odds of having the five peaks coincide is “is lower than 10−4“. They estimate this by counting the number of time the five spectral peaks are found in white or red noise processes, and from these calculate the probability of the five spectral peaks co-occurring. There are at least two problems with this, firstly the torque spectrum does not resemble red or white noise and second there are not just five spectral peaks in the solar reconstruction – there are at least eight. The relevant test is not finding the five peaks selected by Abreu et al in random data, but in finding any five out of eight peaks. There are 56 ways to do this – Abreu et al’s estimate of the odds is at least 56 times too low.

McCracken et al (2014) is a review of the evidence for planetary influences on solar activity. The three authors, who were all part of the Abreu et al team, declare

Despite our initial view that we would be able to prove beyond all reasonable doubt that no such correlation exists, it became clear that the contrary is true.

Six lines of evidence persuaded McCracken et al.

1) Four of the most prominent spectral peaks in the solar activity record approximate integer multiples of half the Neptune-Uranus synodic period of 171.42.

This looks like numerology to me.

It stretches credibility to believe that any physical mechanism links the Neptune-Uranus synodic period to one frequency in solar activity let alone four, especially given that Neptune and Uranus are much smaller and more distant than Jupiter. Yet McCracken et al write

The probability of these correlations occurring by chance is shown to be <10−4

This is, at the very least, a sloppy way to express the results of their Monte Carlo procedure, and is an example of the Texan sharpshooter fallacy. Given the eight planets, the number of orbital times and synodic periods is large, so it is really not that surprising that the solar spectral peaks are an integer multiple of one of these multiplied by a arbitrary fraction.

2) The frequencies in the solar proxy record match those in the torque applied by the planets to the solar tachocline, citing Abreu et al. These peaks in the torque spectrum are the ones that Poluianov & Usoskin demonstrated were spurious, arising from inappropriate data processing. McCracken et al neglect to cite Poluianov & Usoskin. They cannot claim not to have been aware of the work as together with Abreu they submitted their reply to Poluianov & Usoskin’s comment before McCracken et al was accepted. This does not look good.

Because torque diminishes with the cube of distance this second argument of McCracken et al contradicts the first as Neptune and Uranus are so remote from the Sun they apply very little torque compared with Jupiter and Venus.

3) The ~2300-year Hallstatt cycle in the solar activity data proxy approximates the half the period between the syzygy (alignment) of the four gas giants at 5272 BP and at 644 BP. Not the strongest of arguments: one peak of unknown statistical significance in the solar activity spectrum can be related to a transient planetary alignment of with no obvious mechanism for affecting the sun.

4) There is no new evidence at number 4. The argument is simply to state that if you multiple the miscalculated probability of argument 1 by that of argument 3 you get a very small and irrelevant number. That’s not quite how McCracken et al phrase it.

5) The barycentre, the centre of mass of the solar system about which the sun orbits, sometimes in a ordered pattern, sometimes in a disordered pattern depending on the alignment of the gas giants. These different modes of free fall, which comprise the Jose cycle, are compared with the solar activity spectrum to find patterns. Mechanisms are not so obvious.

Over the last thousand years, four of the seven periods with disordered phases of falling coincide with minima in solar activity. Not impressive evidence.

Sunspot cycle 20 is smaller than most others and coincides with a small rather than a large wobble of the sun about the barycentre. A single data point. Not impressive evidence.

During the Dalton minimum in solar activity some unusual sunspot cycles matched some small wobbles around the barycentre.

The figure in McCracken et al isn’t very good so I’ve plotted the sunspot data from WDC-SILSO and the sun-barycentre distance from the Horizon ephemerides. I cannot see any strong relationships here.

More interesting is the claim that the 20 Grand Minima in the Holocene (including the Maunder Minimum) all occurred during disordered phases of the Sun’s motions. Although this “close association” in figure 7 is not so obvious in the figure 8. McCracken et al rate the probability of the association occurring by chance if the wobble had no effect as 0.01. This is the only evidence I’ve found interesting, but it is hardly conclusive evidence.

So out of the six lines of evidence in McCracken, only one is in the least interesting, meriting some further investigation. The other five lines are very dubious.

Finding patterns of planetary dynamics that correlate with solar activity is easy. There are a multitude of patterns, some are bound to correlate (occasionally, at least if you squint). Testing if these patterns are real is complicated by the lack of a suitable test case – using the same data for exploratory analysis and confirmatory analysis is an easy way to get Type 1 errors, results that appear to be statistically significant but are no more than by chance. Fitting models with half the data and testing the fit for the other half would be a good strategy (but no peeping allowed).

One of two things is required to make planetary-solar interactions convincing 1) good predictions of the next few sunspot cycles, 2) a physical model of solar activity that can only match observed record of solar activity when planetary alignment is considered. The first will take decades to be realised, so might the second.

Abreu J.A., Albert C., Beer J., Ferriz-Mas A., McCracken, K.G. & Steinhilber, F. 2012. Is there a planetary inﬂuence on solar activity? Astronomy and Astrophysics 548, A88.

Abreu J.A., Albert C., Beer J., Ferriz-Mas A., McCracken, K.G. & Steinhilber, F. 2014. Response to: “Critical Analysis of a Hypothesis of the Planetary Tidal Inﬂuence on Solar Activity” by S. Poluianov and I. Usoskin Solar Physics 289, 2343–2344.

McCracken, K.G., Beer J. & Steinhilber, F. 2014. Evidence for Planetary Forcing of the Cosmic Ray Intensity and Solar Activity Throughout the Past 9400 Years. Solar Physics 289, 3207-3229.

Poluianov S. & Usoskin, I. 2014. Critical Analysis of a Hypothesis of the Planetary Tidal Inﬂuence on Solar Activity Solar Physics (2014) 289, 2333–2342.