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I was reading about red giants and came across this statement:

Some research suggests that, during the evolution of a 1 M☉ star along the red-giant branch, it could harbor a habitable zone for several billion years at 2 astronomical units (AU) out to around 100 million years at 9 AU out, giving perhaps enough time for life to develop on a suitable world.

Red giants have luminosities of $\sim 3000 L_\odot$. According to the inverse square law, the habitable zone must be $1^{+1.5}_{-0.2} \cdot \sqrt{3000} \approx 54.772^{+82.158}_{-10.954} \text{AU}$ away from the star. If the star is exhibiting variability, its luminosity may change by about/over $50\%$. This will make the habitable zone vary by a factor of $2\sqrt{0.5}=\sqrt2 \approx 1.414$. So do any stable orbits (in terms of habitability) exist for planets orbiting such a red giant star, assuming the variability timescale is within the orbital period of such a planet?

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  • $\begingroup$ At what timescale are they variable? $\endgroup$
    – planetmaker
    Apr 21, 2021 at 5:40
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    $\begingroup$ How do you define habitabity? $\endgroup$
    – ProfRob
    Apr 21, 2021 at 6:35
  • $\begingroup$ @ProfRob By habitability, I mean the circumstances where humans can colonize the planet and survive without major additions (i.e. spacesuits) $\endgroup$
    – fasterthanlight
    Apr 28, 2021 at 22:57
  • $\begingroup$ Then I don't understand what information you require beyond what you have already put in your question. A planet can orbit in a stable way at 54 au from a star. You seem to be asking about some sort of timescale though that you haven't defined in your question or in your comment. $\endgroup$
    – ProfRob
    Apr 28, 2021 at 23:10

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