Sundogs, also called “mock suns” or “parahelia” (Greek for “beside the sun”), appear as one or two patches of light on either or both sides of the sun. Sundogs give the illusion that there are two or three suns in the sky. Sundogs may be white or colored, and often appear along the path of a 22 degrees halo (a thin ring of light around the sun).
These patches of light are occasionally seen around a very bright, full moon. In that case, they are called moon dogs.
Sundogs are produced by the refraction (bending) of sunlight through relatively large ice crystals. Sundogs and moon dogs form only in cold regions.
Sources: Ahrens, C. Donald. Meteorology Today: An Introduction to Weather, Climate, and the Environment, 5th ed., pp. 99-100; Engelbert, Phillis. The Complete Weather Resource, vol. 2, pp. 329-31.