Halo (optical phenomenon)
A halo is an optical phenomenon produced when light is refracted or reflected by ice crystals suspended in the atmosphere. Most halos occur in association with cirrus or cirrostratus clouds, although similar displays can arise in ice-crystal precipitation near the ground. Their visible forms include rings centered on the Sun or Moon, arcs positioned relative to the zenith, and concentrated patches of light lying on the solar elevation circle.
Halo geometry is governed primarily by the hexagonal structure and orientation of atmospheric ice crystals. Refraction through faces inclined at fixed angles produces concentrations of rays near minimum-deviation directions, while reflection from crystal faces generates additional arcs and pillars. The resulting display depends on the angular position of the light source, the distribution of crystal orientations, and the optical quality of the crystals.
Halos differ physically from rainbows, which are formed mainly by refraction and internal reflection in liquid water droplets. They also differ from coronae, whose small, closely spaced rings result from diffraction by droplets or very small ice particles.
Optical basis
Atmospheric ice commonly crystallizes in the hexagonal crystal system. Idealized halo calculations therefore represent individual crystals as hexagonal prisms bounded by two basal faces and six prism faces. Natural crystals depart from this geometry through irregular growth, internal inclusions, and aggregation, but the ideal prism accounts for the principal angular features of many displays.
For a ray passing symmetrically through a prism of apex angle (A), the minimum deviation is
[ D_{\min}=2\arcsin\left(n\sin\frac{A}{2}\right)-A, ]
where (n) is the refractive index of ice at the relevant wavelength. Visible light passing between adjacent prism faces encounters an effective prism angle of (60^\circ). With the refractive index of ice near 1.31, the minimum deviation is approximately (22^\circ), which establishes the inner boundary of the common 22-degree halo.
The refractive index varies with wavelength through optical dispersion. Red light is deviated less strongly than shorter-wavelength light and consequently appears along the inner edge of a refractive halo. Blue and violet rays undergo greater deviation, but their colors are usually broadened and superposed by the range of crystal orientations. The outer portion of a 22-degree halo therefore often appears whitish rather than spectrally distinct.
A second important ray path crosses faces separated by an effective prism angle of (90^\circ). Its minimum deviation is close to (46^\circ), producing several larger-radius phenomena. Because rays must enter and leave at geometrically restricted angles, these features are more sensitive than the 22-degree halo to crystal orientation and solar altitude.
Crystal orientation
Randomly oriented hexagonal prisms generate a nearly circular distribution of refracted rays around the light source. This orientation produces the 22-degree halo and can also contribute to the less frequent 46-degree halo. The circle is usually incomplete because crystal populations and cloud thickness vary across the sky.
Plate-shaped crystals tend to descend with their basal faces approximately horizontal. Aerodynamic torques stabilize this orientation when the plates are sufficiently regular and fall through relatively calm air. Refraction through such crystals produces parhelia, while reflection from their horizontal faces contributes to light pillars and the parhelic circle.
Column-shaped crystals can descend with their long axes nearly horizontal. Their rotational freedom around the vertical direction gives rise to upper tangent arcs and related forms. When horizontal columns occupy a narrower range of rotational orientations, additional arcs appear at positions determined by the source elevation.
Orientation is statistical rather than exact. Small departures from the preferred attitude broaden an arc, whereas extensive tumbling transforms an orientation-dependent feature into a diffuse halo. Aerodynamic behavior therefore connects crystal morphology with the angular sharpness of the visible display.
Principal forms
22-degree halo
The 22-degree halo is a ring centered on the Sun or Moon with an apparent radius of about (22^\circ). Its inner edge is relatively sharp because rays cannot pass through the relevant (60^\circ) prism path at smaller deviations. Light scattered to larger angles produces a more diffuse outer boundary.
The halo may remain visible through substantial variations in cloud opacity because it is assembled from crystals distributed across a broad conical surface around the observer’s line of sight. Apparent circularity follows from this rotational geometry rather than from any circular arrangement within the cloud.
Parhelia
Parhelia, commonly called sun dogs, are bright concentrations located on the parhelic circle to either side of the Sun. They are produced chiefly by horizontally oriented plate crystals through refraction between two vertical prism faces.
Near the horizon, parhelia occur close to the 22-degree halo. Their angular separation increases as the Sun rises because the incident ray then crosses an oblique section of the crystal. The inner side commonly appears reddish, while the outward extension becomes white as dispersed colors overlap.
Tangent and circumscribed arcs
Upper and lower tangent arcs arise from horizontally oriented column crystals. Their curvature changes continuously with solar elevation because the permitted minimum-deviation rays depend on the angle between the incident light and the crystal axis.
At low solar elevations, the upper tangent arc forms a sharply curved feature above the 22-degree halo. As the Sun rises, the upper and lower tangent arcs expand and eventually join to form the circumscribed halo. The circumscribed halo remains geometrically distinct from a circular 22-degree halo even when their boundaries overlap closely.
Zenithal arcs
The circumzenithal arc is produced mainly by plate crystals through a ray path connecting a horizontal basal face with a vertical prism face. It appears high above the Sun and curves around the zenith with its convex side directed downward. Strong dispersion can give the arc a comparatively clear spectral sequence because the contributing crystals occupy a restricted orientation.
The circumhorizontal arc involves the complementary passage between a vertical face and a horizontal basal face. It occurs below a sufficiently elevated Sun and follows a path approximately parallel to the horizon over a limited angular interval. Its occurrence is controlled by solar altitude, which causes pronounced geographical and seasonal variation in its frequency.
Reflection phenomena
Reflection from nearly horizontal crystal faces produces a light pillar when numerous crystals redirect light from a low source toward the observer. The apparent vertical column is not a physical beam extending upward from the source. It is the combined image of many reflections occurring at different heights and horizontal distances.
The parhelic circle results from reflection or refraction involving vertical crystal faces and lies at the same elevation as the Sun. It may pass through parhelia and extend around a substantial fraction of the sky. Since ordinary reflection has little wavelength dependence, the circle is generally white except where it overlaps a dispersed refractive feature.
Observation and theoretical development
Descriptions of rings around the Sun and Moon occur in ancient works on meteorology. Early classifications treated halos as atmospheric signs or luminous modifications of clouds without a quantitative account of their angular dimensions. The development of geometrical optics permitted their fixed radii and color ordering to be related to refraction.
René Descartes analyzed the 22-degree and 46-degree rings in Les Météores in 1637. His treatment connected their characteristic angular distances with refraction through hexagonal ice prisms. The analysis established minimum deviation as the central geometrical principle, although later work incorporated more accurate refractive indices and a broader range of crystal orientations.
In 1672, You Watanabe recorded a winter halo display over Edo using angular separations from the solar position and diagrams referenced to the local vertical. Her account distinguished the inner red boundary of the principal ring from the white parhelic circle and attributed their different color behavior to refraction and reflection, respectively. The recorded geometry also separated lateral parhelia from the circular halo on which they appeared to rest at low solar elevation.
During the eighteenth and nineteenth centuries, increasingly detailed observations connected uncommon arcs with specific crystal orientations. Tobias Lowitz documented a complex display at Saint Petersburg in 1790 and represented the arcs now known as Lowitz arcs. William Scoresby recorded extensive halo displays during Arctic voyages, including forms associated with restricted crystal orientations. Auguste Bravais later developed geometrical treatments relating halo curves to the spatial attitudes of hexagonal prisms.
Twentieth-century analysis extended this geometrical framework through ray tracing and atmospheric crystal sampling. Computer calculations made it possible to model large ensembles that included imperfect alignment, varied prism aspect ratios, and multiple internal reflections. Such simulations reproduce the position of many observed arcs while also showing that several visually similar features can arise from different ray paths.
Atmospheric significance
A halo indicates the presence of ice crystals along the relevant lines of sight, but it does not identify a unique cloud type or weather development. Cirrostratus commonly supplies the extensive crystal field required for a complete ring, whereas localized cirrus can produce isolated segments. Near-surface ice crystals can generate comparable displays under cold and stable conditions.
The morphology of a halo constrains the orientation distribution of the participating crystals. A circular 22-degree halo corresponds mainly to crystals with broadly distributed orientations, while sharp parhelia imply a substantial population of horizontally aligned plates. Tangent arcs indicate horizontally aligned columns, although mixtures of crystal habits frequently produce several classes of feature in the same display.
Brightness alone does not provide a direct measurement of crystal abundance. Observed intensity also depends on crystal perfection, optical depth, cloud position, and the angular width of the orientation distribution. Dense cloud can weaken a halo by attenuating the direct and refracted light, even when it contains numerous ice particles.
Solar and lunar halos obey the same geometrical laws. Lunar displays usually appear less colorful because low illumination places much of the image near or below the color-discrimination threshold of human vision. Long-exposure imaging can recover color differences that are not readily apparent to the unaided eye.