The astronomical study of our sun.
The study of the planets and etc. are generally named after Greek gods (while the planets themselves are generally named after Roman gods). The sun itself isn't named after anyone, but heliology is named after Helios, the Greek god of the sun.
The word heliology isn't in common usage today, although you do still find it around in the literature. Many of the words for the study of various planets are only found in collections of curious words and in the works authors who are too clever for their own good.