Sun Pillar at Oslo, Norway by Steinar Midtskogen December 3, '08. ©Steinar Midtskogen, shown with permission.
Steinar produces daily time-lapse movies of the Oslo sky and these images are individual frames. The video is here.
The temperature was -3C and there was light snow before an ice fog which later cleared.
The pillar is unusually tall. It stretches up almost to the bright but diffuse upper tangent arc 22° from the sun.
No sundogs are visible in the movie. This combined with the tangent arc and pillar's abnormal height suggest that it might have been produced by horizontal column crystals rather than plates.
The majority of pillars are the collective glints from gently tilted plate crystals. How can column crystals with no permanently near horizontal faces produce a pillar?
The column side faces are responsible. The diagram below shows how a column crystal takes rotational positions about two axes (1) near vertical and (2) a near horizontal one lengthways through the column.
Now visualize the strong red arrow perpendicular to one of the side faces. The closer the arrow tip is to the zenith the more horizontal is the face and the more likely will it glint sunlight into a pillar.
As the crystal rotates about the vertical axis the tip sweeps out circles (lines of latitude) centred on the zenith. As the crystal rotates about its long axis the tip sweeps out lines of longitude.
We can simulate the tip positions by drawing a dot for random rotational positions of each axis.
The diagram has 7000 points computed in this way. They give a surprise, they show that the combination of the two motions leads to the tip spending more time at the zenith than anywhere else.
The corollary is that a side face spends more time nearly horizontal than at any other position.
Each crystal side face acts for a moment as a near horizontal mirror and glints the sun to form a sun pillar.
Columns can make pillars. Lowitz oriented crystals also produce them by the same mechanism.