This is really easy. You argued that the D must have been made by the BD. I challenged that. (It's an unanswered question.) You presented your own reasonable arguments backed up with even a quote that agreed you might be wrong. I thanked you for your concession Any questions?
In absence of consensus, I don't see how my opinion on the matter is wrong.
How does the origin of Deuterium help your argument that a planet-sized ball of burning gas can vary in temperature by over a million degrees?
When you state that X is true when X is not know to be true or false, then you've erred. When did you prove that that BD's temperature varies by over a million degrees? Are you assuming that D burning continues in all BDs forever? Are you applying typical cases to a specific one without justification?
As previously discussed, if the minimum temperature is not achieved, the power source cannot be maintained, and the Brown Dwarf is no longer a Brown Dwarf. Is is a black ball of inert gas, the final stage.
No, there is no requirement that all BDs must fuse deuterium as per the source you cited. Why are you asserting that the BD in question burns deuterium without evidence?
The source I quoted in the second post says that Brown Dwarfs burns deuterium.
http://en.wikipedia.org/wiki/Deuterium_burning"Since hydrogen burning requires much higher temperatures and pressures than deuterium burning does, there are objects massive enough to burn deuterium but not massive enough to burn hydrogen. These objects are called brown dwarfs"
Perhaps ithe theory does not exist. Perhaps it does and you are not aware of it. Either way, that has no bearing on the existence of the BD being described and it's sub-zero C temperature. Would a lack of germ theory make the existence of germs impossible? Hardly.
I don't see how your argument that Astronomy is wrong supports your position.
No, I mentioned that in my first post. Hot matter leaves the core. It cools as it expands. After it cools it falls back down toward the core where it is heated again and process continues. It's like a big circle. That's what convection is. Convection doesn't automatically lead to instant thermal equilibrium.
Heat transfer takes time. Stars are huge. The end.
Not instant, but the systems are attempting to equalize at all levels.
The primary cooling comes from radiation loss, not "cooling as it expands". If there were no radiation loss, there would be no convection. This is a ball of gas. Heat rises to the top. Gas cooled by radiation loss at the surface falls to the core via convection, just as the cold air in a heated room falls to the floor, where it is recycled into the heater and brought up anew.
The argument that in an environment like that, a difference of a million degrees can be maintained in an equalizing, convective body, is simply absurd. Heat is constantly being moved to the top. It's nothing like earth.