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First, some context: I am creating a habitable world with intelligent life present in the second main sequence of a star (hence why it needs to be re-stabilized). This life discovers the ruins of an old civilization that had reached about modern humanity's tech level that had gone extinct thanks to the red giant/sub-giant phase, and finds out that their time is limited, which is where the actual stories start. I do not wish for alien civilizations to get involved, however I do not care how unlikely the process is, as long as its natural and reasonably possible under known physics.

Now, the question: How do I achieve this? The post-giant star needs to have a similar (maybe slightly higher) luminosity of the original star, or at least the planets orbit needs to have been changed by the event such that it is habitable. The best thing I can think of is some sort of external force (perhaps a super earth or near miss with a star corpse) that causes the star to become more convective and supply the core with fresh hydrogen to fuse, however I am open to any possible explanation for a red giant to enter a second main sequence whilst the planet stays habitable.

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    $\begingroup$ You are perhaps asking the most complicated question I've seen here so far. We have a binary star system where one partner is close enough to somehow reignite a red giant but the red giant still was formed in the first place. You should perhaps take that to the physics stack exchange. Usually, answers here are (in my 4 year experience) just common sense approaches by random people to solve simple issues in fictional worlds for beginner world builders. Also, you should be open to options without that binary thing. Stars can be reborn, but having another star trigger it, that feels hard $\endgroup$
    – Raditz_35
    Dec 23, 2020 at 9:43
  • $\begingroup$ Thanks for the suggestion. I broadened the question a lot. $\endgroup$ Dec 23, 2020 at 10:05
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    $\begingroup$ I think you made it even more complicated. I'd still suggest the physics or astronomy exchange just because there are some real experts that write beautiful answers. But if you're ok with a common sense approach or the chance of an expert having a look at your post here, I won't stop you. I have one small issue: I dont get if you want humanoids to survive or if you're ok with some primitive life. The word civilization is perhaps not the luckiest choice. Which one is it? What do you want to have left? I'm sure you have a reason why you want to start fresh on an old planet $\endgroup$
    – Raditz_35
    Dec 23, 2020 at 11:06
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    $\begingroup$ Is there any advanced technology available to the habitants of the planet? if so I would think the question is better suited to this site than Astronomy or Space stack. If not than maybe asking on those would be better suited. $\endgroup$ Dec 23, 2020 at 15:05
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    $\begingroup$ @Tortliena If they have the right technology it might be easy. The problem is that technology will need to be based on scientific principles we don't know or believe might be possible. This can be hand-waved in science-fiction. If that's possible, then any reason will do. $\endgroup$
    – a4android
    Dec 25, 2020 at 7:09

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As you guessed, we'd likely need to make the star fully convective in order to move it to a sort of second main sequence, where hydrogen fusion begins anew at its center; it's imperative that the hydrogen-rich outer layers are allowed to mix with the hydrogen-depleted core. Ideally, this would happen sooner rather than later. Stars which become red giants typically spend up to a couple billion years as subgiants immediately after the main sequence, entering the red giant branch only when their cores become degenerate. Your civilization would want to restart convection before that occurs.

Let's talk about what gives rise to convective zones in stars. There are three mass ranges to consider:

  1. Stars with masses less than approximately $0.3M_{\odot}$ are fully convective and therefore actually never become red giants. The thorough mixing allows them to exhaust all of their hydrogen by the end of their (extremely long) lives. Their convective zones consist of the entire star because their low temperatures give rise to high opacities, and high opacities are quite conducive to convection.
  2. Stars that fall into the range $0.3M_{\odot}\lesssim M\lesssim1.3M_{\odot}$ (the outer boundary is uncertain), like the Sun, have radiative cores and convective envelopes - again, low temperatures imply high opacities, but here the cores are too hot, and radiative transport dominates in the inner regions.
  3. Stars with masses greater than $\approx1.3M_{\odot}$ have the opposite structure: convective cores and radiative envelopes. This is the critical mass at which the CNO cycle, rather than the proton-proton chain, becomes the dominant mechanism for hydrogen fusion. The CNO cycle's rate has a much higher temperature dependence, with $\varepsilon_{\text{CNO}}\propto T^{20}$, while $\varepsilon_{pp}\propto T^4$. Therefore, the CNO cycle implies a much higher temperature gradient than the p-p chain - and a higher temperature gradient is the other major factor that can lead to convection.

Red giants have more complicated structures. Their degenerate cores and shell burning regions are surrounded by an intermediate radiative zone, and finally the enormous convective envelopes they're best known for. Fortunately for us, these convective zones are far from stable. Indeed, at several points in a red giant's evolution, the star experiences what we call dredge-ups, there at convective envelope reaches deeper into the star and actually mixes some of the byproducts of fusion up to the surface. In short, evolved stars may be susceptible to some poking and prodding, and I suspect that the same might be true for subgiants.

Let's look, then, at what I'd guess are our two main options. Helium fusion via the triple-alpha process has an even stronger temperature dependence, at $\varepsilon_{3\alpha}\propto T^{41}$. That might seem conducive to convection, if it could be exploited. On the other hand, that's helium fusion, not hydrogen fusion; as such, it basically defeats the whole purpose of trying to jump-start a second main sequence!

Perhaps we could attempt to raise the opacity in the radiative zones of a subgiant's envelope - whether they be more akin to those of a red giant or of a massive main sequence star. It seems unlikely that we could manage to reduce core temperatures significantly, but perhaps instead would could change our opacity source. Unfortunately, radiative opacities (with the exception of temperature-independent Thompson scattering) tend to decrease with increasing temperature, as noted above, sometimes as severely as $T^{-7/2}$, in the cases of free-free, bound-free and bound-bound absorption. (They do, though, tend to increase with density!) An exception is electron scattering, ordinarily the major source of opacity in the radiative zone.

My proposed solution is to attempt to increase the metal content of the radiative zone. Most radiative opacities show linear or quadratic dependence on the mass fraction of metals in the gas; therefore, raising the fraction of heavier elements, $Z$ would increase the opacity. These notes indicate that in the scenario where electron scattering is the dominant source of opacity, the temperature and density are related to the mean molecular mass $\mu$ by $T\propto\mu$ and $\rho\propto\mu^4$. I believe that these two dependences mean that changes in temperature and density caused by changes in molecular weight would cancel out, and it's just the explicit $Z$ or $Z^2$ dependence that governs opacity changes.

How could we do this? Perhaps crashing several spare (!) terrestrial planets into the star would help; there are cases where a star has exhibited a noticeably higher metal content that appears to come from engulfing a planet. Ideally, if the subgiant's convective zone was deep enough, metals could be mixed downwards to the upper edge of the radiative zone; from there, it's possible that they could enter the zone itself.

This is all fairly handwavy, but it's not outside the realm of possibility. Increasing opacity could, at the very least, make it more favorable for convection to become more important in any radiative regions, and if the civilization gets lucky, perhaps hydrogen could get mixed into the core before it becomes degenerate. I don't know how to calculate the relevant timescales to determine how long this weird reborn star could stay on its second main sequence; I suspect it wouldn't be incredibly long, but it depends. Like I said, maybe they'll get lucky.

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    $\begingroup$ /attempt to lower the temperature of the radiative zone by decreasing the mean molecular weight in the region. Dumping heavy metals.. would certainly decrease this/ Wouldn't adding things of higher molecular weight increase mean molecular weight? That's just my third grade math talking, now. $\endgroup$
    – Willk
    Dec 24, 2020 at 19:24
  • $\begingroup$ How many heavier molecules would I have to dump in the star? Are we talking a super-earth or just a dwarf planet? Multiple super-earths? Stars are huge, so I imagine probably a lot. I could also start the star with a higher metallicity already by putting it much later in the universes lifespan, which would also allow for bigger rocky objects. Would that be useful? $\endgroup$ Dec 24, 2020 at 21:34
  • $\begingroup$ Wouldn't hurling a few gas giants into the red giant star achieve the higher radiative opacity? Or are the higher metallicity values typically found in terrestrial planets necessary? $\endgroup$
    – a4android
    Dec 25, 2020 at 6:32
  • $\begingroup$ @Willk You're quite right - I made a foolish typo when I started writing this, forgot to fix it, and extrapolated from that. Fortunately, I made a second foolish error elsewhere, and it looks like they effectively cancel out. Edit coming. Thank you. $\endgroup$
    – HDE 226868
    Dec 26, 2020 at 16:08
  • $\begingroup$ @InfiniteDelta I don't know how much heavier elements you'd need; it depends on the size of the radiative zone and how much of those elements would successively mix in the very lowest reaches of the convective envelope - and I honestly have no idea how to calculate that. $\endgroup$
    – HDE 226868
    Dec 26, 2020 at 16:24
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The planet's orbit changes to be farther away.

Your red giant will lose mass.

https://en.wikipedia.org/wiki/Stellar_mass_loss#Red_giant_mass_loss

Stars which have entered the red giant phase are notorious for rapid mass loss. As above, the gravitational hold on the upper layers is weakened, and they may be shed into space by violent events such as the beginning of a helium flash in the core. The final stage of a red giant's life will also result in prodigious mass loss as the star loses its outer layers to form a planetary nebula.

As the mass of the star decreases, so does its gravity. The velocity of the planet does not change. With same velocity and weaker gravity, the planet will move to a wider orbit around its star.

http://curious.astro.cornell.edu/our-solar-system/57-our-solar-system/planets-and-dwarf-planets/orbits/81-when-the-sun-converts-mass-to-energy-do-the-orbits-of-the-planets-change-advanced#:~:text=How%20does%20this%20affect%20the,it%20in%20the%20same%20orbit.

How does this affect the orbits of the planets? Intuitively, if we imagine a planet orbiting the Sun at some speed, as the Sun loses mass its gravitational pull on the planet will weaken, so it will have trouble keeping it in the same orbit. The planet's velocity will therefore take it further away from the Sun, and the orbital separation between the Sun and planet will increase.

The formula that governs this situation turns out to be that the orbital separation is proportional to 1 divided by the Sun's mass -- this can be derived from the fact that the Sun-planet system must conserve its angular momentum as the Sun loses mass. The orbital period of the planet, meanwhile, is proportional to 1 divided by the Sun's mass squared.

The event that gives your planet a good fry might be an ejection of a lot of hot mass from the star. But the planet is not cooked thru and thru and not enough to lose its atmosphere and water - maybe more of a dark toasting. The planet moves away and has time to cool. Life has found refuge in the deep places and can start anew.

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    $\begingroup$ @HDE 226868 is that your downvote? . If scientifically this does not hold water lay out why so I can learn something! $\endgroup$
    – Willk
    Dec 23, 2020 at 21:12
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    $\begingroup$ I don't think this should be downvoted. The easiest way for a planet around a red giant to be habitable again is to move it outward to keep it within the habitable zone. It's sort of like how the moons of Jupiter and Saturn will likely become habitable as our sun enters its red giant phase. $\endgroup$
    – H98
    Dec 23, 2020 at 22:26
  • $\begingroup$ I was the downvoter, yeah - and all the science here is correct! But the big issue is that the very same mass loss means that stars that enter the red giant phase (and, later, the AGB phase) give rise to strong stellar winds, which raise the possibility of ablating away atmospheres. Orbiting a red giant is quite the threat to life. Additionally, the planet might increase its orbital radius by a factor of 2-3, but the red giant will brighten by several orders of magnitude, and the orbit won't have nearly increased enough to compensate. $\endgroup$
    – HDE 226868
    Dec 24, 2020 at 16:51
  • $\begingroup$ @HDE226868 - so principle is sound but not enough to accomplished what is asked. Fair enough. Thanks for laying it out. $\endgroup$
    – Willk
    Dec 24, 2020 at 17:25
  • $\begingroup$ @Willk Basically, yeah. That said . . . I haven't crunched the numbers yet, so I don't want to say it's impossible - it's just that it seems likely to be a bit more complicated than suggested. $\endgroup$
    – HDE 226868
    Dec 24, 2020 at 17:57

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