I was arguing on a forum with somebody, who claims himself to be a historian, that the heavily armoured cataphracts themselves used bowes, at least in some periods. My source was this book, which I sadly don't possess, just read once, and I don't remember the exact page and paragraph.
If I remember correctly though, one of the authors (whose name I sadly also don't remember) stated that in the XIIth century, more specifically in the battle of Haramvár, 1127, the cataphracts used bows as a secondary weapon.
However, the person, who I was arguing with, said it was nonsense, and the heavily armoured riders themselves never used bows, this myth comes from the fact, that on many occasions there were more lightly armoured horse-archers among their ranks to support them.
So can somebody confirm or deny that the most heavily armoured riders used bows as well, at least in some periods? Or did they always rely on specialists in that matter?
Yes they did sometimes carry bows. In the 'Praecepta militaria' of Nikephoros Phokas you get a very detail description of how a heavy cavalry attack plays out. Some of the back ranks of the blunted edge formation would be carrying bows, but not all of them.
At least at this period their were no light horse archers mixed into the formation. They would screen and flank the attack.
See a full translation and analysis in the book 'Sowing the Dragon's Teeth: Byzantine Warfare in the Tenth Century'.