Chapter XII: The Sun’s Rotation

The mode of the sun’s rotation is perhaps the most significant feature of his constitution. A thorough understanding of it would doubtless bring with it an explanation of many other outstanding difficulties. But it seems, unfortunately, a long way off. No more has been attained as yet than the representation of the observed facts by empirical formulæ. That is to say, a law of order has been discerned in them although their cause remains obscure.

No single period of rotation can be ascribed to the sun. Each element of the photosphere, probably each layer of the chromosphere, moves round the axis in a fashion of its own. The fundamental rate, if such there be, is so masked by local drifts as to be unrecognisable. The most hopeful road to its eventual detection seems to be by the gradual disentanglement of the solar influences affecting terrestrial magnetic phenomena. The immediate task in hand, however, consists in extending and giving precision to knowledge on the whole subject, in bringing varied methods to bear upon it, and in linking into some kind of sequence the circumstances ascertained.

Until spectroscopic and photographic means became fully available, the solar rotation could be determined only by timing the circuits of spots. And spots were very soon found to have “proper motions” precluding them from discharging the function of points of reference. Hence there could be no unanimity as to the sun’s rotation, the period arrived at by each observer depending upon his choice of spots. At length Carrington’s scrutiny during the years 1853 to 1861 showed the systematic nature of these baffling diversities. They proved to vary with heliocentric latitude, and the great solar swirl was brought into evidence. Once in about twenty-five days the visible surface of the sun sweeps round at the equator; but as the distance from it increases, the time lengthens progressively. The rate of retardation is given mathematically in the following expressions, which, being artificially adjusted to correspond with observation, might be multiplied and modified indefinitely:—

FORMULÆ OF SOLAR ROTATION.

X = 865′ − 165′ sin ⁷⁄₄ _l_ (Carrington).
X = 1011′ − 203′ sin (41° 13′+ _l_) (Spoerer).
X = 862′ − 186′ sin^2 _l_ (Faye).
X = 858′ − 157′ sin^2 _l_ (Tisserand),
X signifying the daily angular motion, _l_ the solar latitude.

Formulæ of the kind, moreover, are of restricted application. Based exclusively upon spot-measurements, they can scarcely be trusted outside of the spot-zones—that is, beyond 38° north and south of the equator. Carrington’s gives a period of 25^d 9^h 53^m where _l_ = 14°, of 26^d 9^h 9^m for _l_ = 30°; and he adopted as the standard period 25^d 9^h 0^m, conformed to in latitude 13½°. But what this average speed of transport actually represents, is the mean rate of motion of the multitude of sun-spots,[278] not the rotation of the body of the sun. Professor Bigelow argues from meteorological analogies that this prevails without disguise at the equator, while retrogressive currents of a “trade-wind” character lengthen the periods derived from observations in the spot-zones.[279] But such-like comparisons are plainly inadmissible. More plausible, although far from decisive, is his contention that the equatorial period must be the true one because it lends itself to the correlation of terrestrial phenomena—auroræ, magnetic storms, wind and weather changes—with solar outbreaks.

Solar rotational studies entered upon a new phase with the application to them of the spectroscope. The particular importance of the innovation lay in the change of venue which it involved. A new court, so to speak, was constituted, a fresh set of witnesses called. These were the Fraunhofer lines; and while requiring more delicate treatment, they seemed likely to prove more trustworthy than their predecessors. Spots do not float inertly on the photospheric tide. They are subject to individual hurryings and laggings that to some extent invalidate the record of their axial progress. Fraunhofer lines, on the contrary, are eminently steadfast. They fall short, it is true, of the absolute fixity formerly ascribed to them; yet after every deduction has been made, their reputation as natural constants remains substantially intact. It must, however, be borne in mind that what the Fraunhofer lines tell about the sun’s rotation is not strictly comparable with the information derived from spots. For they proceed from a different level, and may therefore obey a different law of revolution. They indicate the velocity, not of the sun itself, but of the absorbent strata in which they originate.

The eastern limb of the sun advances, the western limb recedes at the rate of 1·2 miles a second. The consequent line-displacements amount to just ¹⁄₁₅₀ the little gap between the D-lines of sodium. In 1871 their simple detection by Vogel was a feat of some moment.[280] Five years later, Young was enabled, by his early possession of a grating or diffraction spectroscope, to fix their range with approximate accuracy. Then Langley showed how, by their means, to distinguish at a glance lines of solar and telluric production. For in juxtaposed spectra from opposite ends of the equator, the solar lines, being affected by rotation, are manifestly “notched,” while atmospheric rays run straight on without a break. They stand self-announced as of domestic production.

The differential plan of measurement thus suggested obviates many forms of otherwise inevitable error. It was adopted by Dunér in his classic work on the sun’s rotation, presented to the Royal Society of Upsala 14th February 1891. He selected two iron lines in the red (λλ 6301·72, 6302·72) for comparison with a pair of adjacent oxygen lines from the “Alpha” band, known to be terrestrial, and therefore exempt from motion-shiftings.[281] They were then safely treated as fiducial; and the intervals between them and the solar lines differed, east and west of the equator, to an extent corresponding with rotation in a period of twenty-five and a half days. By the use of the utmost refinements, the observations were carried up to within fifteen degrees of either pole, where the period was found to be protracted to thirty-eight and a half days, the intervening zones showing intermediate velocities. Direct acquaintance with the sun’s axial movement was thus extended far beyond the regions of spot-occurrence; and only direct acquaintance is, in this matter, of any avail, since the formulæ devised to suit low latitudes break down nearer the poles, disclosing their unsoundness by a total want of agreement in the periods calculated from them.

“Carrington’s law” might have been true of spots only; it might have denoted some peculiarity in their mode of production, causing a systematic increase of backward drift, north and south of the equator. The Upsala measures, however, proved it to apply, irrespectively of spots, to the solar globe generally. They told, indeed, something more than this. The period deduced from them was longer than that given by spots. The difference amounted to about half a day, and it persisted in all latitudes—that is to say, the vapour of iron surmounting the photosphere gyrates more slowly than the spots _in_ the photosphere. A variation of angular speed with elevation above the sun’s surface was for the first time indicated. Confirmatory evidence was soon forthcoming.

The photographic investigation of facular movements was attempted by Dr. Wilsing at Potsdam in 1888.[282] From 1012 measurements executed upon 108 plates, he obtained a constant angular velocity of 14°·27 per diem, equivalent to a period of 25·23 days, which is just that of spots situated ten degrees from the equator. But the conclusion that faculæ in all parts of the sun conform to it was certainly fallacious. M. Bélopolsky made this apparent in 1892,[283] and M. Stratonoff of Taschkent still more decisively in 1894–96.[284] His research included the determination of 2158 positions of 997 faculæ on 316 Pulkowa plates, and furnished the clearest evidence of their poleward retardation. The Stonyhurst drawings, discussed by Fathers Sidgreaves and Cortie,[285] yielded similar results. Concomitant increase of period and latitude is, in fact, a rule without exception on the sun.

Faculæ, however, have a mean rate of their own. In the same parallels they are transported more rapidly than either spots or absorbent vapours. Their period of rotation is the shortest attributable to any solar formations. The main facts of the case can be taken in by a glance at the following little table:—

PERIODS IN DAYS
┌────────────┬───────┬──────┬─────────┐
│Heliographic│Faculæ.│Spots.│Reversing│
│ Latitude. │ │ │ Layer. │
├────────────┼───────┼──────┼─────────┤
│ 0°│ 24·66│ 25·09│ 25·46│
│ 15°│ 25·26│ 25·44│ 27·49│
│ 80°│ 25·48│ 25·81│ 31·83│
└────────────┴───────┴──────┴─────────┘

The equatorial facular period, it is worth noting, is nearly identical with that ascribed by Hornstein, on the ground of magnetic observations, to the mass of the sun.

The diversities exhibited above are as perplexing as they were unexpected. They do not even fall readily into any satisfactory order of progression. The slowest movement belongs to the reversing layer, or at least to the slice of it stopping out Dunér’s iron lines; for there is no certainty that the entire stratum rotates unanimously. It is, however, certain that it covers both spots and faculæ. The level of absorption is higher than the level of the photosphere with all its immediate appendages. This fact has been already insisted upon;[286] it may perhaps usefully be reasserted in the present connection. Fraunhofer-absorption is stamped in the prismatic rays of faculæ and sun-spots precisely as in those of the photosphere. They have then been demonstrably sifted through the same screen of incandescent vapours. We have yet to learn that they escape any minutest part of the absorptive effects produced in ordinary sunlight. They must accordingly be submerged beneath the whole series of strata occasioning them. At the same time, it has to be borne in mind that Dunér’s deductions rest upon a narrow basis. He measured only a single pair of lines, and we lack the specific assurance that those individual lines occur in the facular and spot spectra. Presumably they do; no reason is apparent why they should behave exceptionally; but a direct record of their actual presence would be satisfactory. They should also be looked for in the “flash” at the edge of the eclipsed sun. Their detection as brilliant lines would confirm and settle their status.

But here we encounter an anomaly. Since the reversing layer rotates more slowly, and lies higher than the photospheric formations, a law of retardation with altitude might be assumed. Its prevalence is, nevertheless, contradicted by the relations of spots and faculæ. Faculæ undeniably rise above spots, yet they wheel more rapidly; they give a shorter period. This seems to be established by Wolfer’s[287] confirmation of Stratonoff’s results. Thus while retardation outward is indicated by the reversing layer, acceleration outward is forcibly suggested by faculæ. And there is a general consensus of opinion that this rule applies generally, so that the comparative tardiness of the absorptive region stands over as an unexplained discrepancy. Even within the region itself, Mr. Lewis E. Jewell has found indications of diminishing angular velocity towards the photosphere, where also the equatorial quickening is small compared to its value higher up.[288] Moreover, Bélopolsky’s speculations as to the nature of the corona, which probably adumbrate, if they do not convey truths, require that it should rotate much more swiftly than the sun itself.[289] The forecast will doubtless be tested ere long by eclipse-spectrograms. Indeed, further evidence is much needed on a number of crucial points connected with the sun’s rotation.

Dunér confessed his inability to imagine a “Why” for the singular rotatory régime of which he had clearly expounded the “How.” “It constitutes,” he remarked, “one of the most difficult problems in astrophysics.” One theory after another has been proposed, and sunk out of sight, overweighted by manifest inconsistencies. A machine “going” like the sun the wit of man has not yet been able to devise. Nevertheless, a means of evading the difficulty has been found. The possibility has been perceived, and perhaps too readily admitted, of regarding it as a legacy from chaos to cosmos. The embarrassments surrounding the subject may be relegated to a far-distant age, and to a state of things for which the investigators of to-day disclaim responsibility. The anomaly, on this view, is a survival of nebulous conditions, which, so far from having a present sustaining cause, is, and has always been, subject to the destructive agency of friction. Why then, it may be asked, has it persisted throughout the æons of the sun’s growth? Should it not have been quite early abolished, if it be nothing more than a residual inequality, begun to be smoothed away in the dim foretime when the solar globe took shape? Mathematicians reply in the negative. Wilczynski of Berlin gave in 1896 an apparent demonstration that internal resistance cannot change the diurnal arc described by any point on the sun to the extent of two minutes in twenty-seven million years.[290] But Harzer showed it to be applicable only to cases non-existent in nature.[291] It would be valid under ideal circumstances; things being as they actually are, it falls to the ground.

Starting from less questionable premisses, however, Wilsing of Potsdam in 1891,[292] and Sampson of Durham in 1894,[293] reached practically the same conclusion. They agreed that millions of years must elapse before the sun comes to rotate “all of a piece,” like a solid body. There is, indeed, one flaw in their reasoning. Both limit convective circulation within the solar globe to a relatively thin shell of material. They assign to radiation an essentially superficial character. In the attempt to prove that the rotational currents flow without impulsion, they sacrifice the functional efficiency of our great light-giver. For assuredly its immense output of radiant energy can only be supplied from interior stores, rendered available by powerful and _deeply rooted_ vertical currents. But the continued activity of such a system should speedily efface inequalities of surface drift, unless some countervailing force maintained them.

Dr. Wilsing asserts that, in the comparatively late “phase of celestial evolution represented by the fixed stars, radial currents are beginning to disappear.” It might more plausibly be argued, considering the intense brilliancy of such bodies, that radial currents are in them at a maximum of strength and volume. “We are therefore relieved,” the author continues, “from the difficulty of accounting for ‘Carrington’s law of rotation’ on mechanical and physical principles, since it appears as the result of earlier conditions of motion.”[294]

We leave a good deal to the coming time; why should we not shift an occasional perplexity back to the broad shoulders of antiquity? Much that is inconceivable in a sun might be possible in a spiral nebula. No such expedient, however, will answer the present purpose. The originating cause of the sun’s rotational anomalies, whatever it may have been, continues to act. In a globe so profoundly disturbed, they could not possibly have survived of themselves.

Professor Young finds the necessary driving power in falls of cooled materials, bringing with them to the photosphere the swifter motion appertaining to a wider circumference. The consequent accelerative impulse would be greatest at the equator, and would diminish to nothing at the poles, according, so far, with the observed facts. Spots, moreover, by onrushes at epochs of reconstruction or recrudescence, formally acknowledge the receipt of supplies from above. But Carrington’s “law” governs all the solar formations, and the rationale by continuous downward precipitations seems to be of very partial applicability. Faye tried to solve the problem on an inverse principle. Instead of descents from without, he postulated ascents from within, the equatorial retardation being less than that in high latitudes because the rising matter comes from nearer the surface. This, however, was a purely artificial arrangement, with no voucher for its reality. The explanation needed to be explained. Speculation here, as elsewhere, must await the progress of direct inquiry.