Why don’t stars collapse?
Assume no nuclear fusion so only energy source is gravity.
Star is “almost” in hydrostatic equilibrium
Star radiates energy:
nothing else happened T would drop, P would
drop, star would shrink.
Star does shrink, but in doing so gravitational energy is converted to heat,
preventing T from continuing to drop.
In fact, since star is now more compact, gravity is stronger and it actually
needs higher P (so higher T) to prevent catastrophic collapse
As star shrinks, ½ of gravitational energy goes into heating up
star, ½ gets radiated away
Rate at which it radiates energy, so rate at which it shrinks, is
limited by how “insulating” intermediate layers are