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I've read many accounts of our sun's distant fate, but what I've never heard is on what time scale these events occur.

For instance, when the sun runs out of hydrogen, I presume it doesn't just WHAM! become a red dwarf suddenly, engulfing the inner planets in seconds. But how long would it take for the sun to expand? Would anyone left on Earth have days, weeks, months, years to escape? Centuries? What kind of time scales are we talking about, here?

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There's a nice paper by Drs. Klaus-Peter Schroder and Robert Smith on the distant future of the Sun and Earth; it's available at the arXiv:

Table 1 in that preprint summarizes a number of parameters, but in simplified form the radii (in terms of the current value) at different times (given in billions of years) are:

            Age   Radius
ZAMS       0.00   0.89
present    4.58   1.00
MS:final   10.00   1.37 
RGB:tip   12.17   256.
ZA-He     12.17   11.2
AGB:tip   12.30   149.

(hopefully that will render correctly.) For comparison, the current orbit of the Earth is 215 times the current solar radius. ZAMS is the zero-age Main Sequence, present is today, MS:final is the end of the Main Sequence, RGB:tip is the maximum size during the Red Giant branch, ZA-He is the start of core Helium burning and AGB:tip is maximum size during the asymptotic giant branch phase. After that the Sun will fade away as a white dwarf.

While there is 2.17 billion years between the end of the Main Sequence and the start of core Helium burning (which also marks the end of the Red Giant phase), for more than two billion years the Sun is less than ten times its current radius - it's only during the last 200 million years when the expansion towards the Earth's current orbit happens. This is plotted in Figure 1 of the preprint, which the radius of the Sun during the final three hundred million years.

So in the context of the Sun's overall lifetime, the expansion in the giant phase is extremely rapid. Of course, on our timescales it's a very long time...!

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What a fascinating paper. What caught my eye is the mention that the energy requirements to keep the Earth in a habitable orbit during the Sun's evolution, by causing close flyby encounters with a largish asteroid every ~6000y or so, are less than the energy requirements for interstellar travel. – ghoppe Aug 10 '11 at 0:09
This is also quite an interesting paper The search for a strategy for mankind to survive the solar Red Giant catastrophe. – Jus12 Aug 24 '11 at 15:54
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I can't give a precise answer, but the time scales are much longer than human timescales, or even the typical lifetimes of species. The red giant phase of the sun won't happen for over five billion years, which is longer than our planet has been around. Baring heroic planet moving technology, our planet will have been slowly fried long before then. The sun is currently brightening at about one percent per hundred million years, and that rate is gradually increasing. At some point within roughly a billion years, the planet will cross the threshold for runaway steam-driven global warming, i.e. steam is a greenhouse gas, warms the planet, evaporates more of the oceans etc. That will effectively end life on the planet. Even the red giant phase is many millions of years long. But any evidence that our rock ever supported life will have been eliminated long before then.

According to Wikipedia, the red giant phase begins when the Hydrogen in the stars center is completely converted to Helium. Hydrogen is then fused to Helium in a shell surrounding the inert Helium core. This occurs a few thousand times faster than the earlier phase, so its lifetime is a few thousand times less than the main sequence phase that completed just before the red giant phase. They give a lifetime of a few million years, which is consistent with the high luminosity. So I think your answer is it is reasonably stable for timescales of a few million years.

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Okay, but my question isn't really about life on Earth. I just used that as an example to get some idea what the time frame would be. If someone were to miraculously be still on Earth, would the transition to red giant be fast (like would they have to leave in a few days or hours) or slow (like could they take months or years)? My underlying assumption is that something noticeable happens sort of all at once and not gradually over millions of years. Maybe that's an incorrect assumption about how the sun will become a red giant. – Gary Jul 23 '11 at 0:05
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Nope, it doesn't really happen "all at once". As the Sun evolves off the main sequence to become a red giant, it goes through a "subgiant" phase, where its luminosity (on the HZ diagram) is between the main sequence stars and red giants (stars like Procyon are already in this phase). The curious thing is that there are so few subgiant stars - why do we observe so few of them on the HR diagram?

Well, it's because (a) subgiants have short lifespans compared to MS stars, and (b) subgiants are still significantly dimmer than red giant stars. So it's possible that we have more subgiants than we have red giants - it's just that we just don't see most of the subgiants

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