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It is believed that our sun will become a red giant with a diameter of about 1 AU. When the fusion slows down, gravity will collapse the sun. Since the energy release from the fusion diminishes slowly (maybe hundreds of years for a significant change of 1%).

Let's assume that only a small fraction of the sun (10%) is needed to collapse (to 1/1000 the volume) to produce a nova. Would it still be possible for a star to collapse in a few hour (instead of decades)?

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This is not how the Sun will end its life. –  Rob Jeffries Dec 20 at 13:56

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Technically, collapsing of a star as a whole at any point of time happens dynamically, but due to the thermal timescale being much higher, the compression can be considered nearly adiabatic, which causes the star to become hotter and brighter and maintains hydrostatic equilibrium at a dynamical timescale. (There is little involvement of the core here since the photon diffusion timescales are high - ~ 100,000 years - and any effect of the core on the star will be seen much much later.) This is why you never see a 'star' collapse. You can, at best, see them pulsate. Typically the core is what collapses, which alters fusion rates and hence is NOT adiabatic. I will try to explain this process in a little detail; let me know if that answers you question.

When the star is almost out of fuel, it cannot burn fuel as effectively as before, so, the core compresses a little, increasing the temperature, which increases the efficiency and rate of fusion, which makes the 'running out of fuel' part faster leading to a positive feedback process (compression $\rightarrow$ faster exhaustion $\rightarrow$ more compression). This gradually keeps 'collapsing' and burning fuel faster till a point where it cannot counter the collapse using an increased fusion rate due to lack of sufficient fuel (this might still take a few million years, maybe, but it keeps collapsing faster in a runaway fashion till that point). Beyond this point, the collapse happens at the dynamical timescale till it hits degeneracy (or ignition temperature of the previously inert core), which leads to puffing, novae and supernovae based on the mass of the core and its composition.

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Well, I'm not sure exactly what you mean by "collapse" (if it takes $10^9$ years to die, the last few hours satisfy what your asking about). However, maybe some explanation would help:

You're asking about the interaction between two timescales - the Dynamical Timescale, which is the time it takes for a star to free fall into a nova, and the Nuclear time scale (I think), which is the rate at which the sun exhausts it's fuel. The dynamical timescale for the Sun is like 1000 s, and the nuclear timescale is like a Gyr (usually what we think of when we think "lifetime of the Sun").

Any nuclear effects would totally dominate over dynamical effects (since they take much, much longer), and without some specific collusion of behavior (angular momentum, metalicity, what have you), collapse would occur with the burning of fuel and not with the dynamical timescale until the Sun exhausted all it's fuel, and would collapse in a matter of minutes.

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I am looking for how fast the rate of fission changes from being capable of maintaining the sun radius at 1 AU and when the sun collapses to a nova. How do you determine when the fuel is spent? Since the nuclear reactions are diffuse, the only way a star would collapse is when the rate slow significantly. –  LDC3 Jul 7 at 5:44
Takku's comment gives a little bit more detail about how the process happens, and I found a site when even more details: faculty.wcas.northwestern.edu/~infocom/The%20Website/end.html –  cduston Jul 7 at 17:15

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