Also harkens back to:

“Hm,” Harry said. “Suppose you threw it into the Sun? Would it be destroyed?”
...
“It seems unlikely, Mr. Potter,” Professor Quirrell said dryly. “The Sun is very large, after all; I doubt the Dementor would have much effect on it. But it is not a test I would like to try, Mr. Potter, just in case.”

Also, on Quirrell's particular attitude toward the sun:

Harry had lost. There had been moments when the cold anger had faded entirely, replaced by fear, and during those moments he’d begged the older Slytherins and he’d meant it...
“Is the Sun still in the sky?” said Professor Quirrell, still with that strange gentleness. “Is it still shining? Are you still alive?

Harry lost, and Quirrell's is basically asking "was it the end of the world to lose?"