Symmetry in halo displays and symmetry in halo-making crystals

Abstract

The relation between the symmetry in halo displays and crystal symmetry is investigated for halo displays that are generated by ensembles of crystals. It is found that, regardless of the symmetry of the constituent crystals, such displays are always left-right (L-R) symmetric if the crystals are formed from the surrounding vapor. L-R symmetry of a halo display implies here that the cross sections for formation of a halo arc on the left-hand side of the solar vertical and its right-hand side mirror image are equal. This property leaves room for two types of halo display only: a full symmetric one (mmm-symmetric), and a partial symmetric one (mm2-symmetric) in which halo constituents lack their counterparts on the other side of the parhelic circle. A partial symmetric display can occur only for point halos. Its occurrence implies that a number of symmetry elements are not present in the shape of the halo-making crystals. These elements are a center of inversion, any rotatory-inversion axis that is parallel to the crystal spin axis P, a mirror plane perpendicular to the P axis, and a twofold rotation axis perpendicular to the P axis. A simple conceptual method is presented to reconstruct possible shapes of the halo-generating crystals from the halos in the display. The method is illustrated in two examples. Halos that may occur on the Saturnian satellite Titan are discussed. The possibilities for the Huygens probe to detect these halos during its descent through the Titan clouds in 2005 are detailed.

Formation of atmospheric halos and applicability of geometric optics for calculating single-scattering properties of hexagonal ice crystals: Impacts of aspect ratio and ice crystal size

“…Several studies have simulated circumscribed halos and other optical phenomena by calculating ray paths that depend on the relative positions between the Sun and ice crystals (or orientations of ice crystals) and on the sunlight path through the faces of crystals [7][8][9][10][11][12][13][14][15][16][17]. For example, the 221 and 461 halos are caused by the minimum deviation of sunlight due to the refraction through a 601 prism formed by alternate side faces, and a 901 prism formed by the side and basal faces of hexagonal crystals, respectively.…”

A note on the radiance distributions of halos due to scattering by randomly orientated crystals

“…As in our previous papers dealing with a conceptual approach to halos [20,35], the formalism outlined in the present paper is not meant to compete with the computational Monte Carlo ray-tracing approach for simulating halos. Rather, the present paper is meant to complement the computational approach in order to get a better understanding of halos.…”

Reflection halo twins: subsun and supersun

“…The image of the resulting halo is, however, not a simple inversion of that of the subsun: due to the curvature of the Earth, the reflecting basal faces of distant plate-oriented crystals are not parallel with the aircraft's horizontal, but instead with respect to their own local horizontals. In this scattering geometry, the Spin Vector Assumption [2,3] is not satisfied in the line of sight of the observer and the ensemble of crystal basal faces acts as a hollow fun house mirror, causing the reflected image to appear as a distinct vertical band of uniform width extending upwards to the supersolar point-which is the point directly above the sun, equally high above the aircraft's true horizon as the sun is below it.…”