Parhelia are their candidate. They are caused by light refraction by tiny ice crystals, sometimes referred to as "diamond dust", that are often associated with high cirrus clouds. If the tiny crystals are really tiny and up in the sky, you can get a halo around the sun. If they are a little less tiny and there's an weak upper atmosphere wind to orient them just right, you can get what appear to be bright lights with tails pointing away from the sun, just a bit above an imaginary horizontal line passing through the sun's center. If atmospheric conditions hit a rare perfect condition, you can get a diamond dust halo with the parhelia riding the halo. A super-rare condition can let you see halo and parhelia plus reflections of the parhelia off clouds below the horizontal lines. An extremely-super-rare condition can give you all of the above plus a "light pillar" that appears to rise from the ground through the center of the halo/sundog/reflected-sundog/sun configuration. For this to work you have to have the dogs and halo in the background and the pillar in a perfectly calm foreground through which "diamond dust" is falling -- they will line up naturally because both are dependent on the position of the sun.
This combination of conditions is so rare that it has seldom ever been seen, but, when it is seen, it's certainly memorable. I was lucky enough to see it one morning, in November 1970, high in the plains of Wyoming just before I drove my VW Bug off the road in surprise. There were other folks off the road in the same place and all for the same reason. None of us had ever even heard of or seen the phenomenon. After about a half hour, it all just winked out. I guess upper atmospheric conditions just changed or God pulled the plug.
Anyway, the great Historian Eusebius wrote that Constantine had seen a Christian cross in the sky the night before his great victory at Saxa Rubra, nine miles north of Rome, and, according to Eusebius, Constantine wouldn't lie. After Saxa Rubra, the pursued army of the defeated Maxentius made its mad dash for the Milvian bridge. The bridge was too narrow, and by some accounts it actually collapsed. Maxentius was found later, drowned in the River, and Constantine got to put up his Triumphal Arch next to the Colosseum. "The Battle of the Milvian Bridge" must have sounded better to Constantine than "the Battle of Saxa Rubra" -- it had historic echoes of saving Rome -- because that's what he publicized in his attempt to woo Roman loyalty. But most Romans didn't buy it -- the remaining pagans and the large Mithraist population of the city resisted Constantine's efforts to support Christianity, and he rather quickly decided to make his new capital, Constantinople, on the Bosporus in Christian territory.
For centuries, the Christian symbol Constantine saw in the sky was pictured not as the Roman cross that appears over him in Renaissance art but rather as the Greek "chi" (looks like an X) overlaid with the Greek "rho" (looks like a P), those two letters being the first letters of the word "Christ" in Greek. The extremely-super-rare configuration outlined above might also be interpreted to look like the chi and rho, and, therefore, the scientists -- a least some scientists -- say that Constantine "must have seen" a halo, parhelia, reflected parhelia, and a light pillar.
But wait! Sun dogs, etc. are normally phenomena of the winter high plains or the frozen north! Skeptics might say he just made the whole thing up. The scientists-who-want-to-believe say that the very rarity of the phenomena and the fact that it was never reported near Rome before or since is what convinces plain-folks-that-want-to-believe that it was a miracle.
Internet links for sun dogs (some
with pix) are:
http://www.ems.psu.edu/Courses/Meteo200/lesson1/halo.htm (an artsy picture of sun
http://www.umich.edu/~urecord/9596/Dec12_95/artcl16.htm (no pix, but a concise explanation of dogs and pillars)
The account of Eusebius's, who actually knew Constantine and says he wouldn't lie: http://www.fordham.edu/halsall/source/conv-const.html
Milvian bridge events are at http://www.mmdtkw.org/VMilvianBridge.html