Thanks Tim and Ken.

I just realized that I was a bit confused about the gravitational energy component or the relativistic energy of the matter. Are these the same thing? Sure, if you let all the matter fall in from infinity it will make the Sun hot, but not necessarily exactly as hot as it is. The thing that I am really trying to get (I think) is the relativistic mass content of the Sun. I had been assuming that this was mainly in radiation because the matter was not going fast enough. But of course the matter has a lot more mass, so even a small relativistic factor comes out to a lot.

I guess that I am back somewhere near where I started in having a variable range for the correct answer on the radiation, but understanding a bit more about the background of that variation. It was also very valuable to get a fix on the matter relativistic or gravitational component which is now really more important for my purposes than the radiation question. Well at least I think I have the correct question now. ;-)

When my present ATM thread comes to an end in the next week I will probably start another one in which the answers to these questions are very relevant. It concerns the sunspot cycle.