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Presented here is a quaternary solar system consisting of two binary orbits. One consists of two red giants, each one 100 times as wide, one-third as massive and 100 times as bright as our sun. Both stars have been red giants for only 12 million years. One giant is orbiting the other giant from a distance of 12 AUs. The other binary consists of two yellow dwarves, each one 105% as wide, 110% as massive and 126% as bright as our sun. The one dwarf orbits the other from a distance of two AUs.

Each of the binaries has its own habitable zone, a stage in which liquid surface water can be possible. But in this case, one habitable zone is deep inside another. For any of the planets orbiting the yellow-dwarf binary, how different would "double habitability" be from the singular habitability that our Earth is currently under? In other words, how would the red giant binary's habitable zone affect the yellow-dwarf binary's habitable zone?

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    $\begingroup$ How far would one binary's barycenter be from the other? To be overlapping (the habitable zones, that is), it strikes me as hideously unstable in the order of not-much-time for a transplanted civilisation and certainly outside the realms of the possibility of complex life evolving. Can we also assume roughly (very roughly) circular orbits? $\endgroup$ Mar 9 '21 at 0:47
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    $\begingroup$ Why do you have such precise sizes for the yellow stars? (They're not dwarf stars, by the way. Our own sun is bigger than average, even if it isn't quite in the supergiant range. A dwarf star is just a big bigger than Jupiter.) Is it important for the worldbuilding that you're doing, or is it more important to find out what type of quaternary stellar system could exist that would support life as we understand it? $\endgroup$
    – Ghedipunk
    Mar 9 '21 at 2:03
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    $\begingroup$ @Ghedipunk Our sun is a main-sequence yellow dwarf. $\endgroup$ Mar 9 '21 at 2:36
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    $\begingroup$ I hate how people always illustrate a binary system, as one of the two standing still and the other orbiting it. It shows the illustrator has no clue whatsoever about celestial mechanics. $\endgroup$
    – PcMan
    Mar 9 '21 at 6:28
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    $\begingroup$ Higher-order star systems tend to be huge, or the the orbits of each pair of stars won't remain stable. For instance, Capella is a close match for your description, with a pair of larger stars and a pair of red dwarfs... except that these pairs are on the order of 10,000 AU from each other, 250 times the distance from the Sun to Pluto. Obviously, at that distance the effect on habitability is nil. $\endgroup$
    – Cadence
    Mar 9 '21 at 7:40
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No habitable zones at all.

Consider a habitable zone. It receives enough radiation from its star (or star pair) such that water does not freeze or evaporate.

From OP "one habitable zone is deep inside another." I take it that this is the habitable zone of the yellow stars which is deep inside the zone of the reds.

The habitable zone of the yellows is considered only in respect to the yellows. Now let us take that zone and add more radiation. It gets hotter, right? A zone habitable with the radiation of 2 star will be considerably hotter with the radiation of 4. How do I know it will be hotter? It is the habitable zone of the red stars, which is enough to prevent water from freezing.

I think, in fact, having 2 medium size stars within the habitable zone of your large stars means no habitable zones at all around either pair. If the yellow stars are within what would be the habitable zone of the reds, the addition of radiation from the red stars means there is no orbit around the yellow stars which will not cook the planet. The presence of the yellow stars in what would otherwise be the habitable zone of the red star means there is no orbit around the red stars which would not periodically bring the planet in close proximity to the yellow stars and have it pop. Like a piece of planet popcorn.

However here is the way to save your system. You will need to move the yellow pair way, way out to where the contribution of the red stars is a small percentage. Then the yellow pair can have a habitable zone safe from the influence of the red stars.

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    $\begingroup$ You don't have to be scared of downvotes, friend. Just be yourself. <3 $\endgroup$ Mar 9 '21 at 2:36
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    $\begingroup$ Please leave it as is, Dailey and don't delete bits. The idea of habitables around a double binary is an interesting one and I dont want to leave it as an impossibility. $\endgroup$
    – Willk
    Mar 9 '21 at 2:38
  • $\begingroup$ That last paragraph is still unnecessary. $\endgroup$ Mar 9 '21 at 2:50
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    $\begingroup$ I've edited the meta part out while keeping the content of the last paragraph. Hopefully that means we can both meet WB guidelines and keep the excellent content in this answer $\endgroup$
    – coagmano
    Mar 9 '21 at 4:18
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The "Habitable zone" concept becomes "The collection of all habitable orbits"

The habitable zone is a simplification depicting 2 circles around a sun (or barycentre of N suns) representing the boundaries on the possible orbits that could sustain life:

enter image description here
By defining the red and green circles, all those blue orbits (and infinitely more) are defined as "habitable"

This concept only applies to your 4-star system in three very special cases:

When the suns are really really hot and the habitable zone is very far away from your diagram, you get a really zoomed out version:

enter image description here

When two of the suns are very far away that they don't contribute much heat and can be ignored:

enter image description here

Or when the suns are weak, and the planet's atmosphere is thick and an extreme insulator that can hold heat for a full year (think venus here), you can theoretically have nested rings of habitability zones depending on the temperature gradient:

enter image description here

However none of these special cases probably apply to your system, your habitability zone probably can't be described using radii alone.

Consider this snapshot I just drew in mspaint - both the areas which are too hot, and areas which are too cold are not circles and the whole shape rotates, and there is no single circle which doesn't pass through through either boundary:

enter image description here

There is no single radius circular orbit that stays between the too hot and too cold mark.

There are still infinitely many orbits - including lots of elliptical ones, and circular ones with a specific phase, but they all have an orbit with the same period as the other sun pair, eg:

enter image description here

This ensures that the planet never cross the red line on its orbital ring. The 5 most stable (and I use that term loosely) of these are the Lagrange points:

enter image description here

Assuming the blue and yellow spheres in this diagram are your sun barraycentres: L1 only is a habitable orbit if your suns are weak enough / far enough away from each other, the other 4 are some of the habitable orbits.

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    $\begingroup$ Trying to keep a planet at a lagrange point in a ternary system for any period of time long enough to be relevant in habitability terms seems a bit futile; might be worth dropping that last bit. The rest seems OK though. $\endgroup$ Mar 9 '21 at 11:44
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    $\begingroup$ @Starfish hence "use the term stable loosely". I highly doubt even the 4 suns will last a long time before one is launched into space. $\endgroup$
    – Ash
    Mar 9 '21 at 14:50
  • $\begingroup$ @StarfishPrime: I kept reading until I found an answer that mentions the Lagrange points, because that's the only option, without drastically changing the system. It's worth keeping. (What I was thinking was "the habitable zones move", but this is better) $\endgroup$ Mar 10 '21 at 0:14
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how would the red giant binary's habitable zone affect the yellow-dwarf binary's habitable zone?

I think you should go with a superposition of the amount of received energy to determine the habitable zone in the system as a whole.

Let me explain my reasoning with a simplification: if an habitable zone is defined as the region of space where the total amount of radiation received by the outside is between 80 and 120 units, that has to be the total of the radiation coming from all the stars. In your case you would consider only the 4 stars of the system, given that the contribution of the others is negligible. If a certain location in the system receives in units 60 from A, 40 from B, 20 from C and 10 from D you can quickly see that it all sums up to 130 units, out of the habitable zone, unless for those moments where B or D are eclipsed.

In a very 0th order approximation, I think that either the overall habitable zone would be pushed outward with respect to the habitable zone of every star taken individually, or there can be no habitable zone at all, considering that the superposition can exceed or not meet the habitability score depending on the relative positions of the stars.

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    $\begingroup$ There will be a habitable zone or zones for the system, as there will be an area or areas which receive the appropriate amount of total radiation. Those areas may not be stable. It could also be that there's no stable orbit that stays within the zone or zones which are habitable. OTOH, I'd note that most people tend to think about such systems from a 2 dimensional point of view, which is encouraged by our representing the system as a 2D image. There might be some habitable stable orbits which are substantially outside the system ecliptic, as defined by the obits of the four stars. $\endgroup$
    – Makyen
    Mar 9 '21 at 18:54
  • $\begingroup$ @Makyen: 3d! Clever! A planet that circles the barycenter of all four, 90 degrees to the ecliptic could maybe be stable and in the habitable zone! No, on further thought, it's orbit would have to rotate as the suns all circled each other, and there's no mechanism for that. 3d won't cut it here. $\endgroup$ Mar 10 '21 at 0:17
  • $\begingroup$ If the orbit is inclined, you'll start to get kozai-lidov cycles where you start trading inclination for eccentricity. So at some point your orbit wont be inclined and will become very eccentric which will make having a habitable zone alot harder. $\endgroup$
    – Rob
    Mar 10 '21 at 10:25
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I think it has as much to do with the previous answers of 'add up all radiation' as to your definition of 'habitable'.

If you're talking about current day humans being able to survive there then look at the other answers (practically no chance). However, things change for bacteria or Tardigrades, which have a much larger bandwidth for habitable. Then after that imagine things like alien lifeforms, like silicon based biology or an intelligent robot civilisation just requiring energy and materials for operation and replication.

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  • $\begingroup$ habital zone is usually defined by liquid water, which even bacteria and Tardigrades need in order to reproduce and grow. But you raise an interesting point that maybe aliens could evolve to need liquid non-water? $\endgroup$ Mar 10 '21 at 0:20
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I think that the closet thing to what you are asking for is if a planet orbits just outside the habitable zone of class K or M star, and so would have a temperature slightly below the freezing point of water.

But the star the planet orbits happens to orbit a more massive and more luminous star at a relatively close distance. The distance between the two stars has to be at least several times the distance of the planet's orbit around it star, but also small enough for the planet to be almost within the habitable zone of the larger star,so that the combned luminosity of the two stars suffices to make the planet warm enough for liquid water and life.

During a year of the planet it's distance from the larger star will vary by twice the average radius of the planet's orbit. So the larger and brighter star should be sufficiently luminous for the variation in the planet's distance to not change the distance to the brighter star, and the amount of heat the the planet gets from that star, very much.

And it is possible that such an arrangement with the brighter star a spectral class G or F, and the smaller star a spectral type K or M, might work. And if it won't work with one brighter star, it might work if there are two brighter identical stars, a close binary. A binary of identical stars which has twice the luminosity of single star of that type would have have an outer edge of its habitable zone about 1.41 times as far as the outer edge for a single star of that type.

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There's no such thing as a habitable zone.

Well, OK, there are those ten thousand astronomers publishing their belief in it, but just look at it a moment:

  • A planet like Neptune, with oceans of supercritical water, is too hot for Earthlike life. Its habitable zone might be somewhere further from the Sun, or it may need more time to cool after the Sun dies down.
  • A tidally locked planet could revolve around the Sun at the distance of Mercury, yet as described in Niven's story "The Coldest Place", the night side might be far below a habitable temperature. Perhaps, however, there is a deep topological feature that can collect a thin atmosphere and retain water. Perhaps living organisms have developed metabolism using "anti-solar" photosynthesis.

The habitable zone is a pure abstraction, perhaps suitable for a spinning billiard ball, but telling us very little about where life may or may not be found in the cosmos. Your question illustrates that we can truly decide habitability only in a certain place on a given planet, knowing all the features of its geology and rotation.

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    $\begingroup$ This doesn't answer the question. $\endgroup$
    – Mermaker
    Mar 9 '21 at 14:37
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    $\begingroup$ Whilst you might have a point about the definition, (why not write a question about non-habitable-zone life? It could be useful and interesting) this doesn't answer the question. $\endgroup$ Mar 9 '21 at 16:51

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