The Rise and Fall of the First Solar Cycle Model

Extract of a letter by the French astronomer Jérôme de La Lande (1732–1807) to fellow astronomer Franz Xaver von Zach (1754–1832), who reprinted it in his 1798 Ephemerides. “Seit 40 Tagen war nicht der geringste Flecken in der Sonne zu sehen, welches mir noch nie vorgekommen ist. Es ist doch zu verwundern, das zu gewissen Zeiten diese Licht-Materie die ganze Oberfläche des Sonnenkörpers überströmen und bedecken kann, und dass zu anderen Zeiten nicht genug dazu vorhandern ist; oder treibt eine Ebbe und Fluth diese Materie nach den Polen zu? welches mag wohl der Weltkörper seyn, der solche ungeheure Revolutionen auf der Sonne bewirken, und ihr so nahe kommen kann?” La Lande believed sunspots to be dark mountainous “islands” emerging above an “ocean” of luminous matter, so that the tides analogy probably imposed itself rather naturally upon him.

See Hoyt D. V. and Schatten K. H. , The role of the Sun in climate change (Oxford, 1997), 30. As noted by these authors, and especially given his favourable prejudice on the matter, it is indeed surprising that Horrebow did not discover the sunspot cycle sometime in the early 1770s, as the cycle stands out rather clearly in his dataset. Entries in Horrebow's notebook for 1776, the year of his death, also indicate that he had begun to contemplate some sort of relationship between planets and sunspots: “Es ist indeß zu hoffen, daß man durch eifriges Beobachten auch hier eine Periode auffinden werde, wie in den Bewegungen des übrigen Himmelskörper; dann erst wird es an der Zeit sein zu untersuchen, in welcher Weise die Körper, die von der Sonne getrieben und beleuchtet sind, durch die Sonnenflecken beeinflußt werden” (Rudolf Wolf, Geschichte der Astronomie (Munich, 1877), 654).

Schwabe Heinrich , “Sonnen-Beobachtungen im Jahre 1843”, Astronomische Nachrichten, no. 21 (1843), cols 234–6.

Meadows A. J. , Early solar physics (Oxford, 1970), 32–47, provides a lively description of these various ideas, and of the sometimes heated debates they generated.

Carrington Richard Christopher , Observations of the spots on the Sun (London, 1863), 1.

Originally published as: Wolf Rudolf , “Mittheilungen über Sonnenflecken VIII”, Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich, iv (1859), 183–205.

Wolf used mid-nineteenth-century orbital data and, more importantly, perihelion distances to set the relative amplitude of each planet's contribution; this explains the slight differences between his adopted amplitudes and the m/a2 values listed in Table 1.

Carrington , op. cit. (ref. 5), 247.

Carrington , op. cit. (ref. 5), 248.

Tait P. G. , “Obituaries: Balfour Stewart”, Proceedings of the Royal Society of London, xlvi (1889), pp. ix–xi, p. ix.

Stewart Balfour , “On sun-spots and their connection with planetary configurations”, Transactions of the Royal Society of Edinburgh, xxiii (1864), 499–504; although Stewart failed to identify a significant similar effect by Jupiter, he nonetheless endorsed what he interpreted to be Carrington's suggestion that Jupiter's heliocentric distance influences sunspot formation. That same year, Stewart published a second paper ( Stewart Balfour , “On the large sun-spot period of about 56 years”. Monthly notices of the Royal Astronomical Society, xxiv (1864), 197–8), pointing out that Jupiter and Saturn come close to aphelion simultaneously every 59 years, which is interestingly close to the 56-year sunspot periodicity suggested by Wolf a few years earlier.

De La Rue Warren , Stewart Balfour and Loewy Benjamin , “Researches on solar physics. Second series. On the behaviour of sun-spots with regard to increase and diminution”, Proceedings of the Royal Society of London, xiv (1865), 59–63.

De La Rue Warren , Stewart Balfour and Loewy Benjamin , “On the distribution of solar-spotted area in heliographic latitude”, Monthly notices of the Royal Astronomical Society, xxvii (1866), 12–14.

De La Rue Warren , Stewart Balfour and Loewy Benjamin , “Researches on solar physics. No. II”, Philosophical transactions of the Royal Society of London, clx (1870), 389–496; they had first inferred a similar trend involving the Jupiter-Venus and Mars-Mercury pairs (“Kew Observatory”, Monthly notices of the Royal Astronomical Society, xxx (1870), 92–94), but this evidently failed to hold as more data were analysed.

De La Rue Warren , Stewart Balfour and Loewy Benjamin , “Further investigations on planetary influence upon solar activity”, Proceedings of the Royal Society of London, xx (1872), 210–18; this is in fact a 9-page extended abstract of a much lengthier work, which was never published for reasons soon to be discussed.

De La Rue , Stewart and Loewy , op. cit. (ref. 15), 213–17.

De La Rue , Stewart and Loewy , op. cit. (ref. 15), 212.

De La Rue , Stewart and Loewy , op. cit. (ref. 15), 216.

Schuster Arthur , “The influence of planets on the formation of sun-spots”, Proceedings of the Royal Society of London, xxxv (1911), 309–23. In later writings, Schuster is even more explicit, e.g.; “[Loewy] saved himself trouble, and evolved the results out of his inner consciousness” (Arthur Schuster, Biographical fragments (London, 1932), 213).

This paper was to be the full-length version of the 1872 extended abstract discussed above. The whole episode is recalled by Schuster in his aforecited Biographical fragments, which also includes an account of the events leading to Stewart's resignation from Kew. Schuster's choice of words in the 1911 extract cited in the text, “… which it would be wrong now to conceal…”, suggests that Loewy's sins were not immediately publicized following their discovery. Up to February 1873 the sunspot investigations by “Messrs. De La Rue, Stewart and Loewy”, including planetary influence studies, are reported upon matter-of-factly in the Kew Observatory report included in the minutes for the Annual General Meetings of the Royal Astronomical Society. Then, in the minutes of the 54th Annual General Meeting, one reads: Some unforeseen interruption has occurred in the measurement and discussion of the Sun-spots, which will cause a delay of two years in the publication of the results. Arrangements are being made for the micrometrical measurements to be conducted at Kew Observatory, and the work will be completed as soon as possible by De La Rue Messrs and Stewart Balfour (“Kew Observatory”, Monthly notices of the Royal Astronomical Society, xxiv (1874), 163).

In some papers published in the late 1870s, Stewart did investigate possible correlations between planetary configurations and variations in terrestrial magnetism, in the course of which he mentions some of his pre-1872 sunspot-related results, without however commenting on the 1872 events. See, e.g., Stewart Balfour , “On the variations of the daily range of the magnetic declination as recorded at the Kew Observatory”, Proceedings of the Royal Society of London, xxvi (1877), 102–21; and Stewart Balfour , “On the diurnal range of the magnetic declination as recorded at the Trevandrum Observatory”, ibid., xxvii (1878), 81–88.

See, for example, Lockyer Norman J. , Contributions to solar physics (London, 1874), 386. Secchi's A. Le Soleil (Paris, 1875), 188–93, is somewhat more cautious in its assessment, even though the Kew team's work formed the centrepiece of Secchi's discussion of the possible causes of the sunspot cycle.

Another early proponent of this latter class of model was the American physicist Pliny Earle Chase (1820–86), who attempted to associate the waxing and waning of sunspots with the position of the solar system's centre of mass. See Chase Pliny Earle , “The sun-spot cycle of 11.07 years”, Proceedings of the American Philosophical Society, xxii (1872), 410–11; and Chase Pliny Earle , “Planetary relations to the sun-spot period”, ibid., xxiii (1873), 147–8. This variation was destined to be rediscovered repeatedly in the course of the twentieth century.

The possibility of magnetic influence between the Sun and planets was also considered to be a plausible mechanism, as mid-nineteenth century solar physicists began to contemplate the possibility that the Sun, like Earth, is magnetized. From 1852 onwards, Rudolf Wolf repeatedly alluded to this possibility in his writings. The American astronomer Francis E. Loomis, although primarily interested in variable stars, also discussed the idea in the introductory chapter of his inaugural doctoral dissertation entitled “Periodic stars” (Göttingen University, 1869), where he went on to propose that the small difference between the sunspot period and Jupiter's orbital period could perhaps be accounted for if the solar magnetic axis, like Earth's, undergoes secular variations in its orientation.

Hoek wrote: “Quu'on se représente des conditions d'équilibre instable, et la moindre force suffit à le rompre et à produire des phénomènes importants. Dans le cas actuel il n'est pas impossible de se représenter de telles circonstances. Les couches extérieures du Soleil, rayonnant leur chaleur dans l'espace, doivent par conséquent devenir plus denses. Il suffit que leur densité surpasse celle des couches situées plus près du centre pour avoir l'équilibre instable. Il viendra un moment où elles iront s'engloutir dans l'intérieur du Soleil pour être remplacées par des couches moins denses. Il est donc possible que les marées produites par les planètes, quelque insignifiantes quu'elles soient, suffisent à fixer ce moment” (extract from a letter to De La Rue, dated 26 January 1867, and published as Hoek M. , “Considerations on sunspots”, Monthly notices of the Royal Astronomical Society, xxvii (1867), 208–11). The American solar physicist Charles A. Young (1834–1908) was to echo similar thoughts as late as the 1897 revised edition of his popular Solar Physics textbook ( Young Charles A. , The Sun (New York, 1897), 159), although the general tone of his discussion makes it clear that he did not give great credence to the overall issue of planetary influence on sunspots.

See Ekholm Nils , “Ueber die Periodicität des Sonnenthätigkeit”, Bihang till Kungliga Svenska Vetenskapsakademiens Handlingar, xxv (1901), 1–71, for a fair, critical review of many of these attempts; and Anceaux Emile , “Sur la corrélation des taches et des marées du soleil”, Bulletin de la Société Astronomique de France, xix (1905), 73–78, for a reasonably succinct account of a multi-planet tidal model, including orbital eccentricity effects.

“Zum Schlusse mögen noch die von mir und andern gemachten Versuche erwähnt werden, die Coordinaten der Fleckenkurve durch Formeln darzustellen, oder den Verlauf der Erscheinung durch eine Art Rückwirkung der Planeten auf die Sonne zu erklären, obschon dieselben bis jetzt noch nicht zu ganz befriedigenden Resultaten geführt haben”, Wolf Rudolf , Handbuch der Astronomie, ihrer Geschichte und Litteratur, Band IV (Zürich, 1893), 410.

Birkeland Kr. , “Recherches sur les taches du soleil et leur origine”, Videnskabs selshabets skrifter (Christiania, 1899), 124.

“Le résultat négatif auquel nous sommes arrivés en ce qui concerne la période undécennale n'a d'ailleurs aucune influence sur nos résultats, à l'égard des variations de courte période, et n'infirment donc pas l'hypothèse, suivant laquelle les forces perturbatrices exercées sur le soleil par les planètes est à même de donner le branle à la production des taches et d'imprimer un certain rythme aux éruptions qui ont lieu sur le Soleil” (Birkeland, op. cit. (ref. 28), 125).

Brown Ernest W. , “A possible explanation of the sun-spot period”, Monthly notices of the Royal Astronomical Society, lx (1900), 599–606.

Birkeland immediately revisited his 1899 calculations in the light of Brown's paper, only to reiterate verbatim his earlier negative conclusion, however ( Birkeland Kr. , “Les taches du Soleil et les planètes”. Comptes rendus de l'Académie des Sciences, cxxxiii (1901), 726–9). Nonetheless, whenever discussing his own theory of the sunspot cycle, he continued to mention planetary influences as a plausible alternative; see, e.g. Birkeland Kr. , “Recherches sur les taches du soleil et leur origine”, Memorie della Societa degli Spettroscopisti Italiani, xxiv (1905), 14–18.

Newcomb Simon , “On the period of the solar spots”. The astrophysical journal, xiii (1901), 1–14.

The analysis is more complex than suggested by this brief sketch, in view of the impossibility of estimating the mean period independently of the data being tested. The issue of phase memory was revived by R. H. Dicke in the late 1970s (see Dicke R. H. , “Is there a chronometer hidden deep in the Sun?”, Nature, cclxxvi (1978), 676–80; also Dicke R. H. , “The phase variations of the solar cycle”, Solar physics, cxv (1988), 171–81), and continues to befuddle solar physicists to this day; see, e.g., Charbonneau Paul and Dikpati Mausumi , “Stochastic fluctuations in a Babcock-Leighton model of the solar cycle”, The astrophysical journal, dxliii (2000), 1027–43.

In saying so it is not at all my intention to belittle Schuster's contribution to the problem. But after working through the writings of the Kew team, Schuster's paper reads very much like Balfour Stewart's final tour de piste, relayed from beyond the pale by his former pupil, colleague, and successor at Owens College.

Schuster Arthur , “The influence of planets on the formation of sun-spots”, Proceedings of the Royal Society of London, lxxxv (1911), 309–23. A few years earlier, using his newly developed periodogram technique, Schuster had carried out a careful analysis of the Wolf sunspot number and Greenwich sunspot area time series ( Schuster Arthur , “On the periodicities of sunspots”, Philosophical transactions of the Royal Society of London, ccvi (1906), 69–100). Where Wolf and others had been assuming planetary-related periodicities and adjusting other model parameter to fit the data, here Schuster was extracting periodicities from the data, and comparing them to periodicities extracted in a similar way from the sunspot number time series. Whether at the synodic or sidereal orbital periods, he had not found any significant signal in the periodograms for either Mercury, Venus, or Jupiter. Yet he evidently felt compelled to revisit the problem.

Schuster , op. cit. (ref. 35), 317.

Maunder A. S. D. , “An apparent influence of the Earth on the numbers and areas of sun-spots in the cycle 1889–1901”, Monthly notices of the Royal Astronomical Society, lxvii (1907), 451–75. This curious hemispheric effect was already mentioned in the Kew team's 1872 paper and in Birkeland's 1899 tome, has shown up in later studies, and remains unexplained to this day.

Stratton F. J. M. , “On possible phase-relations between the planets and sun-spots phenomena”, Monthly notices of the Royal Astronomical Society, lxxii (1911), 9–26.

Stratton , op. cit. (ref. 38), 26. Interestingly, Stratton concluded his paper by reiterating his belief in the possibility of planetary influences on the Sun in much the same language as his nineteenth-century predecessors: “… the dynamical effects of planets upon what may be an atmosphere of very uncertain stability should be manifested in some solar phenomena” (ibid).

See Hale George E. , “On the probable existence of a magnetic field in sun-spots”, The astrophysical journal, xxviii (1908), 315–43, and Hale George E. , “The magnetic polarity of sun-spots”, The astrophysical journal, xlix (1919), 153–78.

See, e.g., Parker Eugene N. , “The formation of sunspots from the solar toroidal field”, The astrophysical journal, cxxi (1955), 491–507. This is sometimes referred to as the “sea-serpent” model of sunspot emergence, and has been amply vindicated by subsequent observational and modelling work.

For example, on an appropriately revised version of Figure 8, the Venus sector 8 count becomes a 2σ effect (p = 0.33 for chance occurrence in any one of 12 sectors), and the excesses in Mercury's Sectors 3 and 8 fall back to the 1σ level.

On these so-called “sunspot nests” see, e.g., Sawyer Constance , “Statistics of solar active regions”, Annual review of astronomy and astrophysics, vi (1968), 115–34; Castenmiller M. J. M. , Zwaan C. and van der Zalm E. B. J. , “Sunspot nests”, Solar physics, cv (1986), 237–55; Brouwer M. P. and Zwaan C. , “Sunspot nests as traced by a cluster analysis”, Solar physics, exxix (1990), 221–46. The existence of “active longitudes”, regions of recurrent sunspot activity persisting for many sunspot cycles, remains a topic of debate; see, e.g., Neugebauer M. , “The solar magnetic field and the solar wind: Existence of preferred longitudes”, Journal of geophysical research, cv (2000), 2315–24, and references therein.