Comment by mncharity

The canonical Q/A pair "Why does the Sun shine?"/"Fusion in its core" perhaps contributes confusion here? Where the question is silently swapped out for "Why is the Sun still shining after 4+ Gyr?". You're primed for a close connection between core and surface photons. Asking "Why is there fog over the uncovered corner of the pool?", one seems unlikely to appreciate "the fog comes from a small aquarium heater somewhere on the bottom!" (IIRC the magnitudes). "The Sun is hot, and hot things glow" creates less of that association between core and light.

> You could calculate how long it would take to notice anything if the core suddenly stopped fusing.

FW(little)IW (very not my field, just AI, quick&sloppy), for a Sun magically switched to contraction-dominated heating, I'm sloping order 10^6-7 yr for a 1% increase in surface temp, with core contraction dynamics being just one uncertainty.