[Formendacil]

before it stood stern, untouchable now by pity, a figure robed in white, but at its breast it held a wheel of fire. Out of the figure there spoke a commanding voice.
'Begone and trouble me no more! If you touch me ever again, you shall be cast yourself into the Fire of Doom.'

I thought I'd toss my opinion on this passage into the brew...

I have often seen this episode as a foreshadowing of Frodo's claiming the Ring only a short while later, in the Cracks of Doom.

As a general rule, I am not a fan of direct intervention of this sort by Eru, and I do not tend to like the idea of Gandalf or anyone being behind it...

So that leaves, as the source of power, the Ring, at least according to my preferences of thought.

Why would the Ring want Gollum gone? I have no idea... Would it care if Gollum was there or not? I have no idea...

But I do know that FRODO would want Gollum gone. I think everyone here knows why Frodo would want Gollum gone. And if Frodo was acting with such power, the Ring seems the most likely source of it, as well as the most likely object to be the "Circle of Fire".

If so, then this is Frodo's first real use of the Ring's power. He has, Bilbo-esque, used it to turn invisible and escape, but this is his first use of it as if he were a lord, using its power for dominion over another person. As I said, it forebodes, to me, his claiming of the Ring only paragraphs later.

And, as an addendum, Frodo's curse/prophecy here is remarkably similar to this passage in the "Taming of Smeagol":

For a moment it appeared to Sam that his master had grown and Gollum had shrunk: a tall stern shadow, a mighty lord who his his brightness in a grey cloud, and at his feet a little whining dog. Yet the two were in some way akin and not alien: they could reach one another's minds. Gollum raised himself and begin pawing at Frodo, fawning at his knees.