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For context: say I have a planet in a P-type orbit around a pair of binary stars. One's a K-type and the other is a red dwarf (M-type). I want it to be such that, planet-side, it looks as if there is only one sun, and would like a scientifically plausible mechanism for such. Said planet is in the habitable zone of the stars.

Would it have to be an atmospheric phenomenon? I suppose if there was a dense atmosphere or cloud layer, the light from the two stars would not be distinguishable, but I don't know how realistic that assumption is. Would any moons still be visible?

Or would the larger star simply outshine the smaller one to the extent that it looks like one large sun? Would the planet be too close to them for the stars to look like a singe light source?

Thanks!

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In order to make two bright objects look like one, you need them to be very close together (angular distance, at least, so their separation is small relative to the planet's orbital radius), and ideally close to the same brightness.

Here you have one that's significantly dimmer, smaller, and cooler than the other, so the best you'll get is to have the two stars so close together that one skims the other's atmosphere. The stars can then fill each other's Roche lobes, giving an overall "egg shape" to the pair (with the small end of the egg fairly sharp compared to the usual hen fruit), and the small end dimmer and redder. Exchange of gas between the two can further blur the distinction between the stars -- and of course people who evolved there will think it's entirely normal to have a star that isn't spherical or of uniform temperature.

What I don't know is whether main sequence stars in this proximity will affect each other's normal course of evolution, or whether the two will tend to equalize masses over geological time (or vice versa), make the smaller star unstable (or vice versa), etc. You'll need more astrophysics knowledge for that -- but it won't matter at all over the life of a human, a civilization, perhaps even a species (stars mostly change very slowly, and K and M type slower even than our Sun).

From comments (thanks, @Logan R. Kearsley), it seems that evolution of the stars won't be noticeably affected until the larger, shorter-lived star starts to leave the main sequence and blow up into a red giant, at which point the smaller star will steal mass and slow this process. How much this will affect the evolution of the smaller star (which would otherwise turn into a truly tiny white dwarf after a trillion years or more) is less clear; if it gains enough mass it might itself become a red giant in only a hundred billion years or less.

None of these stellar evolution changes will have any effect on a civilization on the circumbinary planet of this question, however; the lifetime of a K star (depending on its mass) ranges from almost twice to half a dozen times that expected of our own sun -- seventeen to seventy billion years, roughly.

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  • $\begingroup$ Thanks; do you know if such a star would be able to support a solar system like our own, with range of rocky and gas planets, or would it be too unstable? $\endgroup$
    – Ushumgallu
    Nov 30 '21 at 20:03
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    $\begingroup$ Given the proximity of the stars (orbital period in small number of days), I'd expect planetary orbits in or very near the plane of the stellar orbit to be stable well before they reach the habitable zone of even a K star (the M dwarf being barely a contributor to total radiation level). $\endgroup$
    – Zeiss Ikon
    Nov 30 '21 at 20:11
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    $\begingroup$ The smaller star will retard the evolution of the larger star by stealing mass from it as it expands, thus reducing core pressure and slowing the expansion. That will, in turn, speed up the evolution of the smaller star. None of that will matter for a few billion years at least, though--not until the larger star would've otherwise been scheduled to go off the main sequence. The masses will not generally equalize, but I do not recall which core is expected to die first.... $\endgroup$ Nov 30 '21 at 22:48
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So you want the two stars to be spectral class K and spectral class M.

Unless the planets in your star system are going to be lifeless and uninhabitable, you should restrict the stars to main sequence stars of luminosity class V, since it is usually believed that only main sequence stars can have planets with life.

Wikipedia has lists with properties of main squence stars of various spectral classifications and sub classifications.

The one for K class main sequence stars is here: https://en.wikipedia.org/wiki/K-type_main-sequence_star

and the one for main sequence M class stars is here: https://en.wikipedia.org/wiki/Red_dwarf

Unfortunately it doesn't give the diameters of the stars of various types. The diameter of a star is important to calculate how large it would look at a specific distance, such as the distance where a planet would be habitable.

The red dwarf star EBLM J0555-57Ab may be the smallest main sequence star known. It has a radius of about 0.08 that of the Sun, about 59,000 kilometers, smaller than Jupiter or Saturn, though many times as massive as those planets.

I believe that the maximum resolution of the human eye is about 30 arc seconds, or about half of an arc minute. An arc second is about 0.000000771 of a full circle.

So about 30 arc seconds would be about 0.000023148 of a full circle.

If the star EBLM J0555-57Ab is has a radius of 59,000 kilometers and diameter of 118,000 kilometers, for it to appear about 0.000023148 of a circle wide the circumference of the circle would have to be be 5,097,632,625 kilometers. So the radius of the circle would be about 811,314,115.6 kilometers. And that happens to be about 5.4233 times an Astronomical Unit or AU, the distance bwween Earth and the Sun, which is 149,597,870.7 kilometers.

Since an extremely tiny class M star such as EBLM J0555-57Ab would contribute only a tiny fraction of the heat and light that even the dimmest spectral class K star would, your planet would be frozen and lifeless unless it was close enough to the class K star to be within its circumstellar habitable zone.

Unfortunately, the circumstellar habitable zones of main sequence spectral class K stars are smaller than that of the Sun. It is possible that main sequence spectral class F stars could possibly have habitable planets with life. But even in the casse of an F0V star, the habitable zone would probably only extend to abut 3 AU from the star.

And of course the problem with being far enough away from the stars to not see the class M star as a disc would be similar to the problem of not seeing the separation between the two stars. As the two stars orbited each other, sometimes one star would be in front of the other, sometimes one star would appear to touch the other, and often the stars would appear to be separated.

You can't make the orbital period of the planet equal the orbital period of the two stars around each other so the two stars always have the same configureation as seen from the planet, since the planet would have to orbit the two stars at a distance at least several times as large as the distance between the stars. So sometimes people on the planet would see the two stars at their maximum separation.

There have been many questions about the habitability of giant, planet sized moons orbiting giant planets. Usually, those planetary sized moons are assumed to get their heat and light from the star in the system, and thus be orbiting within the circumstellar habitable zone of that star.

But scientific studies show that such a hypothetical moon could receive significant heat and life from the giant planet it orbits. That heat and light would be from the star's light reflected from the planet onto the near side of the moon, the infrared rays emitted by the planet at its temperature, and from tidal heating resulting from tidal interactions with the giant panet and any other large moons of the planet.

Those calculations showed that in some cases the moon could receive sufficient heating from the planet to suffer a runaway greenhouse effect and become uninhabitable. And of course if the planet and moon were farther away from the star in the system, that heating might be enough to keep the moon warm enough for life despite being outside the circumstellar habitable zone of the star.

So I think that you should make the two stars a very close binary, perhaps a contact binary, and make the habitable world a moon of a giant planet far beyond the usual outer ledge of the habitable zone, kept warm enough for life by tidal heating.

I suggest that you make the K type star in the system a K0V class star, the most luminous and hottlest subclass of K type star. The hotter a star is, the more intense its light will be, and the more painfull it will be to look at that star, and the brighter glare from the K type star will make it harder to notice the class M star.

In fact, you might want to reconsider and make the bigger star a class G star or even a class F star, since they would be hotter and thus harder to look at and make it harder to notice the M star beside it.

I don't know how advanced any civilzation of the planet will have to be to discover the smaller star. It is possible that people will notice fainter shadows from the smaller star pointing slightty away from the darker shadows from the brighter star.

Have you ever noticed the shadow of a tree on the ground with many spots of light on the ground where the light is passing trough gaps between leaf coverage? Long ago during a partial solar eclipse, I noticed that those spots of light on the ground were crescent shaped, like the Sun during the eclipse. So I think that would enable some people to notice that there is a smaller light source beside the main star.

So you should make the two stars as close together as possible, and make the giant planet with the habitable moon as far away from the stars as possible, to make all such effects as small as possible.

That means you need to look at previous questions about the habitability of exomoons and the answers to them, to figure out how to keep your exomoon warm enough to be habitable.

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Planet-side, it can look like this for two reasons.

Either:

  • The planet is so close to the stars that anything living on the planet can't look at them directly, since their eyes/ocular organs/whatever will be damaged, so they just assume it's one star

  • The planet is so far from the stars that they appear as a single point of light - the human eye, or the ocular organs of whatever lives on this planet, can't resolve the gap between the two, so they look like a slightly lopsided but unitary blob.

There's probably a "Goldilocks zone" in between, where the stars are dim enough to be observed with the naked eye (unlike ours) and yet close enough that they can be resolved as separate entities. You don't want your planet in this area.

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Planet never sees smaller star.

Your planet is at the L3 Lagrange point of the smaller star. Thus the big star is always interposed between the two. enter image description here

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    $\begingroup$ That was my thought too. Only problem is L3 is unstable - the planet will need some sort of station-keeping mechanism to keep it there. $\endgroup$
    – Gene
    Nov 30 '21 at 22:39
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    $\begingroup$ Beyond the instability I don't think this works anyway--L3 implies an object orbiting the central mass which implies the mass of the L3 object is negligible with regard to the central mass. A star isn't negligible--the two stars are going to be orbiting a point somewhere between the pictured star and L3, and thus have a shorter orbital period than the planet has about that point. I don't think the planet's orbit is stable, either, but I'm not as sure of that. $\endgroup$ Dec 1 '21 at 4:13
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    $\begingroup$ @LorenPechtel - L3 object in proposed scenario is the planet, not the smaller star. Do you mean that the orbiting body considered to have Lagrange points (Earth in diagram, smaller star in this scenario) must have negligible mass? Is the concept of Lagrange points not applicable to a binary star system? $\endgroup$
    – Willk
    Dec 1 '21 at 15:13
  • $\begingroup$ Yup, it's not relevant to binary systems. For the Lagrange points to exist you need star >>> planet >>> object. I think you could have Lagrange points in a wide enough orbit about a close binary, but they certainly don't exist in this form. $\endgroup$ Dec 1 '21 at 16:03
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We can clearly see the sharply-defined disk of our own sun, especially when it's filtered through a bit more atmosphere at sunrise and sunset. With a dimmer K-type star together with a M-type red dwarf, a habitable world would be closer and have an even better view.

A thick layer of cloud cover would be a plausible way of obscuring the true nature of the stars. The fuzzy blob in the sky might often be redder on one side or change color if one star eclipses or transits the other, but the nature of the system won't necessarily be obvious to observers on the surface. Moons would only be visible as dimmer fuzzy blobs that occur at night, though.

Another possibility is for the locals to have a very non-humanlike vision sense. Perhaps they can only clearly see short-wave light, though this would be odd considering the planet gets relatively little such light. Maybe they don't have clear vision at all, or are very nearsighted. Or their eyes just don't handle bright objects as well as ours. In any case, special viewing equipment would allow them to get a clear view.

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Megastructure. Aliens have surrounded one of the stars with a Dyson sphere, Ringworld, etc. which consumes the visible light and emits infrared that you are not quite able to see, until science.

Space oddity. Rather than a megastructure, electromagnetic life forms (distant descendants of the Common Sunspot) have taken up residence in the smaller star, and their ecosystem now releases only dim infrared light high in the coronasphere, after it has sustained the vast intellectual ferment of soaring prominences surrounding their Philosophers' Star.

Protoplanetary disk. Both stars are surrounded by a vast ring of debris, and light filters through this ring.

Tidal lock. To an approximation, your planet always shows one face to the two stars. (Because it is circumbinary, it can't just face one all the time) The part of the planet that directly faces the brighter star all the time is uninhabitable, as is the dark side; but in the habitable zone (of the planet, I mean) only the smaller star ever rises above the horizon.

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