Halo

Halo, a word derived from the Gr. ἄλως, a threshing-floor, and afterwards applied to denote the disk of the sun or moon, probably on account of the circular path traced out by the oxen threshing the corn. It was thence applied to denote any luminous ring, such as that viewed around the sun or moon, or portrayed about the heads of saints.

In physical science, a halo is a luminous circle, surrounding the sun or moon, with various auxiliary phenomena, and formed by the reflection and refraction of light by ice-crystals suspended in the atmosphere. The optical phenomena produced by atmospheric water and ice may be divided into two classes, according to the relative position of the luminous ring and the source of light. In the first class we have halos, and coronae, or “glories,” which encircle the luminary; the second class includes rainbows, fog-bows, mist-halos, anthelia and mountain-spectres, whose centres are at the anti-solar point. Here it is only necessary to distinguish halos from coronae. Halos are at definite distances (22° and 46°) from the sun, and are coloured red on the inside, being due to refraction; coronae closely surround the sun at variable distances, and are coloured red on the outside, being due to diffraction.  
  
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Fig. 1. | Fig. 2.  
  
The phenomenon of a solar (or lunar) halo as seen from the earth is represented in fig. 1; fig. 2 is a diagrammatic sketch showing the appearance as viewed from the zenith; but it is only in exceptional circumstances that all the parts are seen. Encircling the sun or moon (S), there are two circles, known as the inner halo I, and the outer halo O, having radii of about 22° and 46°, and exhibiting the colours of the spectrum in a confused manner, the only decided tint being the red on the inside. Passing through the luminary and parallel to the horizon, there is a white luminous circle, the parhelic circle (P), on which a number of images of the luminary appear. The most brilliant are situated at the intersections of the inner halo and the parhelic circle; these are known as parhelia (denoted by the letter p in the figures) (from the Gr. παρά, beside, and ἥλιος, the sun) or “mock-suns,” in the case of the sun, and as paraselenae (from παρά and σελήνη, the moon) or “mock-moons,” in the case of the moon. Less brilliant are the parhelia of the outer halo. The parhelia are most brilliant when the sun is near the horizon. As the sun rises, they pass a little beyond the halo and exhibit flaming tails. The other images on the parhelic circle are the paranthelia (q) and the anthelion (a) (from the Greek ἀντί, opposite, and ἥλιος, the sun). The former are situated at from 90° to 140° from the sun; the latter is a white patch of light situated at the anti-solar point and often exceeding in size the apparent diameter of the luminary. A vertical circle passing through the sun may also be seen. From the parhelia of the inner halo two oblique curves (L) proceed. These are known as the “arcs of Lowitz,” having been first described in 1794 by Johann Tobias Lowitz (1757-1804). Luminous arcs (T), tangential to the upper and lower parts of each halo, also occur, and in the case of the inner halo, the arcs may be prolonged to form a quasi-elliptic halo.

The physical explanation of halos originated with René Descartes, who ascribed their formation to the presence of ice-crystals in the atmosphere. This theory was adopted by Edmé Mariotte, Sir Isaac Newton and Thomas Young; and, although certain of their assumptions were somewhat arbitrary, yet the general validity of the theory has been demonstrated by the researches of J. G. Galle and A. Bravais. The memoir of the last-named, published in the Journal de l’École royale polytechnique for 1847 (xviii., 1-270), ranks as a classic on the subject; it is replete with examples and illustrations, and discusses the various phenomena in minute detail.

The usual form of ice-crystals in clouds is a right hexagonal prism, which may be elongated as a needle or foreshortened like a thin plate. There are three refracting angles possible, one of 120° between two adjacent prism faces, one of 60° between two alternate prism faces, and one of 90° between a prism face and the base. If innumerable numbers of such crystals fall in any manner between the observer and the sun, light falling upon these crystals will be refracted, and the refracted rays will be crowded together in the position of minimum deviation (see Refraction of Light). Mariotte explained the inner halo as being due to refraction through a pair of alternate faces, since the minimum deviation of an ice-prism whose refracting angle is 60° is about 22°. Since the minimum deviation is least for the least refrangible rays, it follows that the red rays will be the least refracted, and the violet the more refracted, and therefore the halo will be coloured red on the inside. Similarly, as explained by Henry Cavendish, the halo of 46° is due to refraction by faces inclined at 90°. The impurity of the colours (due partly to the sun’s diameter, but still more to oblique refraction) is more marked in halos than in rainbows; in fact, only the red is at all pure, and as a rule, only a mere trace of green or blue is seen, the external portion of each halo being nearly white.

The two halos are the only phenomena which admit of explanation without assigning any particular distribution to the ice-crystals. But it is obvious that certain distributions will predominate, for the crystals will tend to fall so as to offer the least resistance to their motion; a needle-shaped crystal tending to keep its axis vertical, a plate-shaped crystal to keep its axis horizontal. Thomas Young explained the parhelic circle (P) as due to reflection from the vertical faces of the long prisms and the bases of the short ones. If these vertical faces become very numerous, the eye will perceive a colourless horizontal circle. Reflection from an excess of horizontal prisms gives rise to a vertical circle passing through the sun.

The parhelia (p) were explained by Mariotte as due to refraction through a pair of alternate faces of a vertical prism. When the sun is near the horizon the rays fall upon the principal section of the prisms; the minimum deviation for such rays is 22°, and consequently the parhelia are not only on the inner halo, but also on the parhelic circle. As the sun rises, the rays enter the prisms more and more obliquely, and the angle of minimum deviation increases; but since the emergent ray makes the same angle with the refracting edge as the incident ray, it follows that the parhelia will remain on the parhelic circle, while receding from the inner halo. The different values of the angle of minimum deviation for rays of different refrangibilities give rise to spectral colours, the red being nearest the sun, while farther away the overlapping of the spectra forms a flaming colourless tail sometimes extending over as much as 10° to 20°. The “arcs of Lowitz” (L) are probably due to small oscillations of the vertical prisms.

The “tangential arcs” (T) were explained by Young as being caused by the thin plates with their axes horizontal, refraction taking place through alternate faces. The axes will take up any position, and consequently give rise to a continuous series of parhelia which touch externally the inner halo, both above and below, and under certain conditions (such as the requisite altitude of the sun) form two closed elliptical curves; generally, however, only the upper and lower portions are seen. Similarly, the tangential arcs to the halo of 46° are due to refraction through faces inclined at 90°.

The paranthelia (q) may be due to two internal or two external reflections. A pair of triangular prisms having a common face, or a stellate crystal formed by the symmetrical interpenetration of two triangular prisms admits of two internal reflections by faces inclined at 120°, and so give rise to two colourless images each at an angular distance of 120° from the sun. Double internal reflection by a triangular prism would form a single coloured image on the parhelic circle at about 98° from the sun. These angular distances are attained only when the sun is on the horizon, and they increase as it rises.

The anthelion (a) may be explained as caused by two internal reflections of the solar rays by a hexagonal lamellar crystal, having its axis horizontal and one of the diagonals of its base vertical. The emerging rays are parallel to their original direction and form a colourless image on the parhelic circle opposite the sun.

References.—Auguste Bravais’s celebrated memoir, “Sur les halos et les phénomènes optiques qui les accompagnent” (Journ. École poly. vol. xviii., 1847), contains a full account of the geometrical theory. See also E. Mascart, Traité d’optique; J. Pernter, Meteorologische Optik (1902-1905); and R. S. Heath, Geometrical Optics.

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