Why does temperature always rise in stars?

[astrolollo]

Hello everyone,
I know that pre-main sequence stars do heat up because of gravitational contraction, and the increase in internal energy (and so in temperature) comes from this shrinking and is governed by the virial theorem ( http://www.astro.wisc.edu/~townsend/resource/teaching/astro-310-F08/19-stellar-energy.pdf) . In the previous link they say that only those stars who haven't still ignited hydrogen in their core contract the way the virial theorem states. But I've been told that throughout its whole life a star contracts to increase its temperature, and the virial thm is obviously valid in every moment of a star's life since it only requires hydrostatic equilibrium. Why should the contraction stop then when it comes to H ignition? I know that also nuclear reactions can play a role in making the temperature rise. So, who is wrong?

Thanks everyone!

 

[Ken G]

Core nuclear fusion self-regulates the temperature of the core to supply just the heat that is leaking out of the star as light diffuses out and escapes. The situation is very much like what a house does in the winter time, it simply burns fuel to replace heat leaking out. Prior to core fusion, when heat leaked out, the star had to release gravitational energy via contraction, in order to sustain hydrostatic equilibrium. Fusion replaces that need, so there is no further contraction. The evolution that does occur while the star fuses hydrogen is mostly due to the fact that hydrogen fusion swallows up electrons into helium, altering the rate that light diffuses out because electrons are a source of opacity. So there can be some further contraction and rising of temperature during core fusion, but it is quite slow. I'm not sure if that makes anyone wrong-- the virial theorem is always satisfied, and contraction occurs or doesn't occur depending on whether there is a net heat loss and whether the composition is changing.

 

[astrolollo]

Thanks for the reply!
Is this further contraction due to nuclear burning governed by the virial thm too?

 

[Ken G]

Yes, as you correctly pointed out, the virial theorem is simply a way to express hydrostatic equilibrium in global energy units instead of local force units. The main-sequence contraction typically occurs over trillions of sound crossing times, so is occurring very close to hydrostatic equilibrium.