What exactly causes a Dragon Break?

What kind of power is needed to cause these events? I know one was caused by the use of the Numidium(The Second time.. . At least I believe it's the second time) and another when the Maruhkathi Selective tried to split Akatosh and Auri-El. The first makes sense, the Numidium is a powerful machine/artifact/god/thing and the fact that it was used by six factions by the Agent. But the second one really stumps me. How did they ''split'' Akatosh from Auri-El? (or attempt to) and why did it cause non-linear time?