Sunday, June 29, 2008

Sun, Jupiter, Saturn: spin-orbit coupling?

In this dose of skeptical peer-reviewed literature about the climate, we visit PASA, Publications of the Astronomical Society of Australia. Ian Wilson, Brad Carter, and I.A. Waite propose a new, provoking mechanism that may influence the intensity of solar cycles:
Does a spin-orbit coupling between the Sun and the Jovian planets govern the solar cycle?
The paper costs AUD 25 = USD 24 (it used to be USD 12 a few years ago).
Commercial break: Roy Spencer gives a popular presentation of his recent journal article.
It is helpful to review some facts about the orbits of Jupiter and Saturn. Jupiter's mass is about 300 Earth's masses while Saturn's mass is close to 100 Earth's masses. So you would expect Saturn to play a smaller role. However, you should be a bit more careful: role for what?

If you look where the center of mass of the Solar System is, the Sun, Jupiter, and Saturn are the key players. The distance "r" of the barycenter from the Sun's center is modified by a planet to be nonzero, namely
r = a / (1 + m/M)
where "a" is the Sun-planet distance, "m" is the planetary mass, and "M" is the Solar mass. You see that for small "m/M", using Taylor expansions, the deviation is proportional both to the orbital radius "a" as well as the planetary mass "m'.

Consequently, Saturn moves the barycenter by roughly 2/3 of the distance contributed by Jupiter: their effects are comparable. The barycenter is not too far - it is actually close to the Solar surface.

Now, can the relative position of the Sun's center and the barycenter of the Solar System influence things like the Sun's rotation? By the equivalence principle, the answer should be No. Physical phenomena in the free fall should be indistinguishable from phenomena outside any gravitational field.

However, it is plausible that more refined quantities such as tidal forces etc. will depend on the position of both Jupiter and Saturn (although the ratio of their contributions could be smaller than 2/3). Also, the equivalence principle can be wrong but I am not among those who are ready to believe such things just in order to support a skeptical theory. So let me continue to think about some kind of tidal forces.

Now, it takes 11.86 (normal) years for Jupiter to revolve around the Sun while Saturn's orbit takes 29.66 (normal) years. How much time does it take for the Sun, Jupiter, and Saturn to be re-aligned? Well, the rate of de-aligning is 1/11.86 - 1/29.66 = 1/19.8 years so the "synodic period" of Jupiter and Saturn is around 19.8 years.

This is different from the 22.3-year flow period (in the convective zone of the Sun; responsible for normal sunspot cycles; probably an internal feature of the Sun) and from the 178.7-year repetition period for the solar orbital motion found by Jose (1965) - these periodic processes modulate the sunspot cycles and bring Maunder, Dalton, and 2020 (?) minima (see also Sunspot-climate relationships) - but the authors propose a "synodic resonance" between these three periods. 178.7 is pretty much 8 times 22.3 or 9 times 19.8 (noted already before Jose 1965). Eight and nine are not two random integers. In fact, they differ by one:
1/(1/9) - 1/(1/8) = 1,
1/19.86 - 1/22.3 = 1/178.7 (approx)
I guess this is what they build upon but I don't have the full paper. (Update: Willie Soon kindly allowed me to look at it, and yes, they write what I say.) Whether this resonance actually works beyond the numerology is an open question for me. But it's certainly not crazy that the first modulation of the Sun's internal 22-year period comes from the star's interactions with the heaviest planets. And it's not crazy to think that the solar activity does influence the climate on Earth. Even if the application to climatology is irrelevant, the result of the authors would be fascinating for astrophysics.

If you believe these hints, there are all kinds of possible results that you may derive from them. For example, you won't be too surprised that solar cycle 24 sunspots haven't occurred for more than 2 months. It is plausible that Jose underestimated the cycle a bit and it should be 180+ years. We are living 180 years after the (cool) Dalton minimum. In fact, Ian Wilson claims the following:
[Our work] supports the contention that the level of activity on the Sun will significantly diminish sometime in the next decade and remain low for about 20 - 30 years. On each occasion that the Sun has done this in the past the World’s mean temperature has dropped by ~1-2 °C.
The paper is effectively another peer-reviewed case for global cooling.

Hat tip: Marc Morano


  1. I've no opinion on spin-orbit coupling, except that the phrase exists in chemistry. However, cyclic behavior sometimes yields new understanding if one looks for the radian of the cycle. In this case I divided 4*365.25 = 1461 by 2*pi to get 323.5253.. days. What is this? It's about 7 months 20 days... For some reason the Earth locked onto that four year cycle to reach an integer number of days in its solar orbit when it could have locked onto 365 days exactly. Since such things may involve coupling to anything in the solar system, your site appeared to be an interesting place to contribute this comment.

  2. Hello.

    You write about tidal influence of Jupiter and Saturn on the Sun. This forgets to say, that Venus has got biggest tidal influence on the Sun, bigger than Jupiter (on average, but in its perihelion the Jupiter is strongest), then is Mercury (but at Mercury's perihelion it is almost as influent as Jupiter in its aphelion), then Earth at approximatelly half of the Jupiter. Usually Venus+Earth outweight Jupiter's tidal force on V+E syzigies. All other planets are negligible (Saturn is somewhere at 2% of Jupiter's influence) - the reason is, that for tidal influence, the distance to planet is cubed (^3), which completelly disfavours far objects...

    It has been calculated by K.Georgieva (the paper is pending, but there have already been some conference presentations), that horizontal/meridional component of the tidal force (on the order of 3e-10 N/kg at J-V heliocentric opposition at 45° north of Solar latitude) may be significant for meridional flows (during duration of 11 years) - by more or less bracketing them, modulating the Sunspot cycle amplitudes and lengths... (Which is somewhat different standpoint from the Landscheidt and these aussies works, who preffer spin-orbit couppling, where actually the Jup+Sat would be most important, then Ura,Nep...)

    It has already been shown by Ching Cheh Hung (2007), that 27 of 30 major flares he examined occured directly below some of the 4 major tide-generating planets (J,V,E,M) or below their anti-points (since the tidal force is symmetric), and that the chance for this to happen at random is utterly small - so the tidal influence is really not a complete nonsense...

    You write:
    It is plausible that Jose underestimated the cycle a bit and it should be 180+ years

    No. It is 178.847 julian years. (Calculated from JPL ephemerides DE406 by taking 5 successive cycles from 1128-03-06 (JD=2133124.87746) to 2022-06-14 (JD=2459745.00239) (these boundaries I choosed arbitrarily, but on the same place in the cycle) and dividing the length by 5 to avoid minor irregularities in one cycle)