Star post-main sequence timescale

[Sherrod]

Hi guys,

I am trying since a while to put in equation the evolution of a star's central density, temperature as it leaves the main sequence but has not reached yet the burning of Helium. So there is no nuclear reaction in the centre and the core is slowly collapsing.
Does anyone have some experience with this issue? Is it fair to assume that the star is still in hydrostatic balance?
Thank you.

 

[Chronos]

All stars are in a state of hydrostatic equilbrium until they either expand or contract. Both conditions have observational signatures.

 

[Sherrod]

Thanks Chronos. But since the contraction at the end of main sequence is very slow( Helmotz-Kelvin timescale, millions of years), can we still consider the star to be in hydrostatic equilibrium (dynamic timescale, minutes). In that case, how can we still model the evolution of the core radius?

 

[Chronos]

It is a long drawn out process as you noted unless the star is massive enough to undergo core collapse, where things happen relatively briskly. For a star of modest mass like the sun, the white dwarf core is not exposed until the stellar atmosphere is blown off - which - can take many millions of years. A principle intermediate step is shell burning, which is initiated when the core temperature reaches about 100 million degrees. This further compresses the core as it accumulates helium ash at an increased rate. Modeling the core radius of a star moving off the main sequence is pretty complicated. i don't know if the details have yet been entirely worked out. There is a lot going on in stellar interiors, like convection that are poorly understood and obviously impact core temperature, hence radius.

 

[Ken G]

Thanks Chronos. But since the contraction at the end of main sequence is very slow( Helmotz-Kelvin timescale, millions of years), can we still consider the star to be in hydrostatic equilibrium (dynamic timescale, minutes).

And note that hydrostatic equilibrium is also an approximation when on the main sequence. There's a common misconception that stars on the main sequence are put in equilibrium by fusion, but go out of equilibrium when fusion ceases. This simply isn't true, all that changes when fusion ends is the evolutionary timescale gets shorter, but it's still very long as you point out. That means the star gets slightly farther from equilibrium than it already was, but it's still very very close, so close that we would generally not include the evolutionary timescale in the force equation, any more than we would on the main sequence. The distinction about whether there is a dynamical term in the force equation is essentially the difference between "contraction" and "collapse"-- contraction happens slowly, so hydrostatic equilibrium remains a good approximation, whereas collapse happens rapidly and must appear in the force equation (as Chronos points out for the core collapse).

In that case, how can we still model the evolution of the core radius?

Interestingly, the core continues to contract, even in force balance, because helium ash is being added by the shell fusion, as mentioned. So we have the interesting case where a dynamical change, contraction, appears in the force equation not because of a dynamical term (as the A in F=mA), but because of time dependence in the forces themselves. So the core stays in force balance, and the envelope makes a jump from one (compact) force balance to another (puffed out) force balance, in order to relieve pressure on the shell burning region (such pressure would cause the shell burning to happen way too rapidly for equilibrium to be maintained). So even in a red giant, you still never really need to consider force imbalance to get a working model, but you do need to consider the driving time dependence of piling up helium ash in the core.