What are some pseudo-scientific ways to explain the qualities of a yellow dwarf hyperstar?

Question

Basically, in my stories, there’s a habitable, Earth-like planet called Ozarvis 32. It is the 32nd planet from the star of the Ozarvis Stellar System, which has 68 planets, 12 of which are in the Habitable Zone of the native star. This star is rather strange, and I’ve described as being a “Yellow Dwarf Hyperstar”.

So far, my explanation for why it’s a ‘Hyperstar’ is that it is within the same size range and has the some color as a Yellow Dwarf Star, but has a much higher luminosity and a much stronger gravitational field. In other words, Hyperstars are otherwise normal stars that have stronger gravitational fields and higher luminosities than their fully normal counterparts.

So what are some ways to explain why it has these qualities without contradicting the fact that Ozarvis 32 is both the 32nd planet in this stellar system and habitable?

Answer 1

The bottom line is that you can't get everything you want. Something called the Vogt-Russell theorem says that a star's structure and properties (radius, luminosity, lifespan, etc.) are almost entirely determined by its mass and metallicity.$^{\dagger}$ The mass in particular is the more important of the pair, and increasing it -- which you'll need to do to increase the star's gravitational pull -- will change radius, temperature and luminosity. If you want a higher luminosity, you have to accept that the radius and temperature will also increase, and with an increase in temperature will come a change in color.$^{\dagger\dagger}$ So there's no real way to achieve a yellow hyperstar without invoking some serious handwavium.

Maybe we can use some diluted handwavium, though. Let's say that we increase the mass and therefore the intrinsic luminosity, surface temperature/color and radius. We can try to mask the color change by surrounding the star with some dust. Dust has two major effects: dimming the light and inducing reddening, which would compensate for the shift to a bluer color we get with increasing the temperature. It might be possible to find some middle ground where the dust doesn't significantly dim the star but keeps it yellow. Perhaps the dust has an exotic composition due to the elements on the star's surface.

The 68 planets give me pause, because even though this star will be brighter than a typical yellow dwarf and will therefore have a wider habitable zone, it's still a stretch to 1) have that many planets and 2) have 12 within the habitable zone. It's possible to pack large numbers of exoplanets close together -- see TRAPPIST-1 for the canonical example -- but that relies on a careful set of orbital resonances. I don't have numbers, but to make the habitable zone wide enough for 12 planets, even with resonances, you'd need to significantly increase the star's luminosity, which would then make it much larger than a yellow dwarf and also much bluer. I'm not saying it's impossible, but it's definitely difficult.

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$^{\dagger}$For the stellar astrophysicists who will jump on me for this, yes, rotation and magnetic fields also play minor roles! But they're too minor for this situation.
$^{\dagger\dagger}$If you want some numbers: Stars can often be modeled as black bodies, meaning that we can the Stefan-Boltzmann law to relate their luminosity $L$, radius $R$ and surface temperature $T$: $$L=4\pi R^2\sigma T^4$$ where $\sigma$ is the Stefan-Boltzmann constant. Let's get to some numbers. The exact scaling between mass and the other properties depends on the energy generation mechanism in the star. If it's primarily using the $pp$ chain, then $R\propto M^{3/7}$. If it's primarily using the CNO cycle, then $R\propto M^{19/23}$. Over the entire main sequence, we can using $L\propto M^{\alpha_L}$ with $\alpha_L$ somewhere between 3 and 4 depending on your model; $\alpha_L=3.5$ is an okay middle ground. We can rewrite the Stefan-Boltzmann equation as $$T\propto L^{1/4}R^{-1/2}$$ We then see that stars using the $pp$ chain have surface temperatures scaling with mass as $T\propto M^{15/28}\approx M^{1/2}$, and stars using the CNO cycle have surface temperatures scaling with mass as $T\propto M^{31/92}\approx M^{1/3}$. So luminosity depends strongly on mass and radius and temperature depends weakly on mass.

Answer 2

Your star is a yellow supergiant.

If I understand correctly, you want Ozarvis to be a very large star with high energy emission (so something like a O or A-class star) while keeping to the spectrum of a F-class star.

Fortunately, not all the stars are part of the main sequence - and yellow supergiants exists.

Polaris A (The center of the triple system composing the North Star) is such an example.

Answer 3

The luminosity of a star is a function solely of its size and surface temperature, and it's color is strictly a function of temperature (modulo absorption lines from metallicity). Thus, the object you describe simply cannot be a natural object. You can't get something the color of tge sun and the size of the sun that has significantly higher luminosity than the sun.

....unless it isn't producing light by thermal emission after all. Your hyperstar could be an artificial structure which uses, e.g., LEDs to reproduce an approximation of the solar spectrum at a much higher level of power-per-square-meter, generating energy through artificial fusion. Heck, you don't even really need artificial fusion if you are allowed to cheat a little bit--all the planets lie in a plane, and who's really going to be checking on what the sun looks like from above anyway? So you can get away with a smaller, more efficient, longer-lived, but strictly less luminous star, and surround it in a Dyson shell of machinery that provides the extra mass and radius to replicate the properties of our sun, and then multiply the apparent luminosity of that star by a few thousand times by using that shell of machinery to direct all of the encased star's power output into a thin slice containing the plane of the planets.

Answer 4

This doesn't seem plausible at all. There's a maximum level of crowding that you can achieve around any object, given by the mutual Hill-radius of two planets/objects.

Two adjacent planets have to be further away than about ~20 mutual Hill radii from each other, in order to have orbital stability over billions of years. Systems we know of fulfill this criterion (whence we are able to observe them), with 1-3 planets in their HZ, but increasing this number tenfold, is going to destabilize the system.

Answer 5

Part One of Seven: The Problem.

In my humble opinion you can use almost any type of star as the star in the system, as long as some advanced civilization long ago more or less built all the planets in the system and seeded the ones in the habitable zone with life. And the planets in the habitable zone would have to be arranged in a ring in a shared orbit.

Others have explained how implausible your star is.

Astrophysicists were beginning to calculate the future evolution of stars at least as early as the early 1950s and 1960s.

Stephen H. Dole, in Habitable Planets for Man, 1964, discussed the qualities necessary for a world to be habitable for humans.

https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf

For example, a world has to have an atmosphere with a partial pressure of between 60 and 400 mmHg of oxygen to be breathable for humans. On pages 61 to 63 Dole discusses how long it co took Earth from its initial formation to acquire an atmosphere with enough free oxygen, produced by photosynthetic lifeforms. The present day answer is about 4 billion years, meaning that Earth has been habitable for humans for only about 600 million years.

Dole concludes that: "In general, it is probably safe to conclude that a planet must have existed for 2 or 3 billion years, under fairly steady conditions of solar radiation, before it has matured enough to be habitable."

On pages 67 to 72 Dole discusses the properties of the primary. Dole says that stars shine fairly steady on the main sequence until their available hydrogen is mostly used up, then swell into red giants, destroying life on any previously habitable planets, and then shrink to white dwarfs, perhaps having become novas during the process. More massive stars use up their hydrogen quicker and remain on the main sequence for shorter times.

Stars potentially capable of having habitable planets belong to spectral classes F, G, and K, in order of decreasing mass and luminosity. Spectral classes are further subdivided with numbers from 0 to 9 in order of decreasing mass and luminosity. Roman numerals are used to describe whether the stars are main sequence stars - V means main sequence.

According to the information available to Dole at the time of writing, stars with mass equal to or less than 1.4 solar masses and spectral types of F2V or colder, would remain on the main sequence for at least the minimum time of 3 billion years Dole considered necessary for a planet to become habitable.

Low mass dim stars have their circumstellar habitable zones (which Dole called "ecospheres"), where planets are expected to have the right temperatures for liquid water using life forms, so close to them that planets in them would become tidally locked, which Dole considered incompatible with habitability. Dole calculated that the inner part of the "ecosphere" of a star would be too close starting with a mass of 0.88 Sun and the whole ecosphere would be to close to the star starting with a mass of 0.72 Sun, a K1V class star.

So any science fiction writer who read Habitable Planets for Man in 1964 or later would realize that stars of type F2V to K1V were the only classes of stars likely to have planets with atmospheres breathable for humans. And if they wanted their stories to seem scientifically plausible to their more scientifically educated readers they would restrict depicting human habitable planets to those orbiting stars of spectral types F2V to K1V.

Scientific calculations show that a star which has gravity many times as strong as the Sun's must be many times as massive as the Sun, and thus must have a much higher surface temperature than the Sun, and so it couldn't be the same color as the Sun.

A star could have the same color as the Sun, and thus have the same surface temperature as the Sun, and at the same time be many times as luminous as the Sun, if it has a surface area many times that of the Sun, and thus had a larger radius and diameter than the Sun.

Such a star is called a subgiant, giant, supergiant, etc. depending on its size and luminosity. And the problem with having human habitable planets orbiting such a star is that giant stars are former main sequence stars which swell up into giant size at the ends of their main sequence lifetimes, and as they become much more luminous they roast any former habitable planets they had, killing all life on them. And the giant stage should not last long enough for the planets which are now getting the right amount of light from the star to become habitable for humans.

Part Two: Solution One.

However, some giant stars might have relatively stable luminosities for billions of years. So a planet suitable for life which happens to be the right position around a star might be thawed out and warm enough for life for billions of years while the star is a giant star.

But I am not an expert and can't say which mass of star would have the longest lasting habitable zone when in the giant phase, or how wide that giant phase habitable zone would be. So I don't know whether you could fit 12 planetary orbits into the habitable zone of such a star in the giant phase of its life.

Part Three: Solution Two.

Possibly an advanced civilization in the past has created a lot of habitable planets in the habitable zone of a star in the giant phase of its life. The civilization would have had to terraform planets in the new habitable zone to become habitable millions and billions of years before they would naturally become habitable. Or it would have to move habitable planets from other stars systems into orbit around the star. Or it would have to build planets in orbit around the star and then terraform them to be habitable.

That would be a vast project, but there is no scientific law which makes it impossible for a civilization to be powerful enough to complete such a project.

Part Four: Solution Three.

Or you could put the planets in orbit around several stars, whose combined luminosity would more than that of a single star. As you may remember from Part One, Dole in 1964 believed the most massive and luminous star which could remain n the main sequence for as long as three billion years would be a class F2V star with 1.4 times the mass of he Sun.

I will go with a class F3V star with 1.42 time the mass of the Sun, 1.578 times the radius, and 4.68 times the luminosity of the Sun, as the most massive star which might have habitable planets.

https://en.wikipedia.org/wiki/F-type_main-sequence_star#:~:text=An%20F%2Dtype%20main%2Dsequence,between%206%2C000%20and%207%2C600%20K.

Since the Sun has a radius of about 695,700 kilometers, an F3V star would have a radius of 1,097,814.6 kilometers, and a diameter of 2,195,629.2 kilometers, or 1,364,300.7 miles.

So imagine two F3V stars making a binary system, orbiting around their center of mass in almost circular orbits. They should be separated by ten times the diameter of one of the stars, or about 21,956,292 Kilometers.

Now imagine another binary pair of F3V stars, with the same separation between the two stars.

Now imagine that the two binary pairs orbit around their center of mass. The two pairs have a separation ten times the separation between stars in a pair, or 100 times the diameter of one of the stars. So they are separated by 219,562,920 kilometers. That is a separation of 1.4677 times an Astronomical Unit, or AU, which is the distance between Earth and the Sun and is defined as 149,597,870.7 kilometers.

If the planets in the system all orbit around all four of the stars, the closest planets should orbit at distances of at least three to five times the separation between the two pairs of stars, in order to have long terms stable orbits. Thus the nearest planets should orbit the four stars at a distance of at least 4.403 to 7.338 AU.

Each star has a distance at which an orbiting planet would receive exactly as much radiation from the star as Earth gets from the Sun. I call that the Earth Equivalent Distance, or EED. To find the EED of a star find the ratio between the star's luminosity and the luminosity of the Sun, and then find the square root of that ratio and multiply it by 1 AU.

Since in this case the "star" is actually four stars, each with 4.68 times the luminosity of the Sun, and thus a total luminosity of 18.72 times the luminosity of the Sun, the EED will be at 4.326 AU. Thus the habitable planets in such a system would have to orbit farther from the stars than than the EED.

Part Five: More Problems.

It is fine for the habitable planets to orbit beyond the EED of the quadruple star so long as they are still within the habitable zone of the stars.

And it would be easy to adjust the inner and outer limits of the Sun's habitable zone to account for the different luminosity of a star. Except for:

This list of estimates of the inner and outer edges of the sun's habitable zone made during the last 60 years shows that some estimates a very different from some others.

https://en.wikipedia.org/wiki/Circumstellar_habitable_zone#Solar_System_estimates

So which estimates should a writer use? A writer can be certain that a planet at the EED will be in the habitable zone of its star. And the farther a planet orbits inside or outside the distance of the EED, the less certain one can be that it will be in the habitable zone.

Worse, the spacing of planetary orbits is not random. The gravitational interactions between planets prevent two planets from having orbits too close to each other. Each planet has a forbidden zone around its orbit that any smaller planet would be ejected from.

I don't know how to calculate the sizes of planetary forbidden zones. The size of a plant's forbidden zone depends on the mass of the planet, the mass of the star, the eccentricity of he planet's orbit, and the distance at which the planet orbits the star. But I don't know the formula.

The orbits of the planets in the TRAPPIST-1 system are separated by distances of hundreds of thousands of kilometers. With an average orbital separation of one million kilometers, 12 planetary orbits could be squeezed within a distance range of 11,000,000 kilometers, and most stars should have habitable zones wider than that.

But I think that the true minimum separation between planetary orbits is probably a ratio between the orbits instead of a distance in kilometers.

the smallest known ratio between the semi-major axis of planets in between Kepler-36 b and Kepler-36 c. B orbits Kepler-36 at 0.1153 AU and c orbits at 0.1283 AU. So he orbit of c is 1.11275 times as far from the star as the orbit of b.

so if the innermost habitable planet in a system orbited at distance X, the next one out would orbit at 1.11275 X, the 3rd at 1.2382 X, the 4th at 1.3778 X, the fifth at 1.533 X, the sixth at 1.706 X, the seventh at 1.898 X, the eighth at 2.112 X, the ninth at 2.350 X, the tenth at 2.615 X, the eleventh at 2.91 X, and the twelfth at 3.128 X.

So to have space for 12 planetary orbits in the habitable zone of a star, the outer edge of the habitable zone would have to be at least 3.128 times as far from the star as the inner edge. And most estimates of the Sun's habitable zone don't have that great a range of relative distance.

If only scientists could find a theoretical basis for squeezing more planetary orbits into a habitable zone.

Part Six: Solution Four.

The PlanetPlanet Blog by astrophysicist Sean Raymond does have a solution. In our solar system all eight planets orbit around the Sun in the same direction as seen from "above: the plane of the planetary orbits. Most of the moons of the planets in our solar system orbit their planets in the same direction that those planets orbit the Sun. That is called having prograde orbits. But some moons orbit around their planets in the direction opposite to the planetary orbital direction, in retrograde orbits.

In this post: https://planetplanet.net/2017/05/01/the-ultimate-retrograde-solar-system/

Raymond mentions a paper by Smith and Lissauer which shows that planetary orbits can be closer together if prograde and retrograde orbits alternate.

https://ui.adsabs.harvard.edu/abs/2009Icar..201..381S/abstract

Raymond says that with Earth mass planets and all prograde orbits, only four planetary orbits can fit within the habitable zone of a star, but with Earth mass planets and alternating prograde and retrograde orbits eight planetary orbits can be fit within the habitable zone of a star.

This is a step in the right direction. And maybe you can be content with only eight planets in the habitable zone of your star.

But Raymond considers it impossible for such a star system to form naturally and says that it would have to have been created by a very advanced society in a tremendous feat of engineering entire worlds.

Part Seven: Solution Five.

IN the next post: https://planetplanet.net/2017/05/03/the-ultimate-engineered-solar-system/

Raymond finds a way to pack more than 12 planets in a star's habitable zone. At first he says that up to six planetary orbits can fit within a star's habitable zone.

Then he mentions another paper by Smith and Lissauer, which describes how a ring of planets sharing the same orbit could be long term stable. Their calculations work for 7 to 42 planets of equal mass equally spaced along he circumference of the shared orbit.

https://ui.adsabs.harvard.edu/abs/2010CeMDA.107..487S/abstract

So who says that scientists never do anything nice for science fiction writers?

So you could put your 12 planets in the same orbit within the habitable zone of your star, which can be any star capable of having habitable planets. And you can put the other 56 planets in one or two shared orbits closer to the star than the habitable zone, and in several shared orbits outside the habitable zone, and maybe have a few of them in individual orbits.

And Raymond also believes that a star system with many co orbital planets like this would have to have been created by an advanced civilization instead of forming naturally. Which means the star need not be a star which would naturally have habitable planets, so long as its radiation is not too harsh.