Selecting a Red dwarf for my planet

Question

I am currently designing a world orbiting a red dwarf M type star and I would like to know what type of red dwarf do i need to choose (M0V - M9V stars) that can meet the requirements for my world.

For starters, here's a description of the world I am making:

My world is an Earth like planet that orbits an M type red dwarf in it's habitable zone. The planet is a bit larger that Earth with it being 1.5 times more massive (by thay i mean that gravity is 1.5 g compared to Earth's 1 g) although I am not entirelly certain about it and I'm considering making it only 1.2 times more massive. Anyways, the planet is tidally locked around its parent star with its rotation around its axis taking just as long as its rotation around the star. Despite this, its atmosphere, who's composition is almost entirelly similar to Earths, is thick enough and its winds strong enough that the heat is transmitted around the planet resulting in the day side hosting oceans and one large continent full of various plant and animal organisms. Now I wanted my plants to be mainly red with a few species being black. As for the sky I wanted it to be an orange color, kinda like the Earth's sky during a sunset.

So what kind of star should i go for here? Also, how big would that star appear on the sky to someone standing on the surface and what color would it appear?

Edit: As I've read so far from the answears I've recieved, a red dwarf probably can't fill out the conditions for the world I'm designing. So I'm changing my question a little. What star should i use for my planet to exhibit the following characteristics:

•Orange sky

•Red plants

•Tidally locked (Can stars bigger than red dwarfs even have tidally locked planets around their habitable zone?)

Answer 1

I should preface this by saying that this is an active area of research and speculation. New papers come out all the time that consider new limitations and possibilities for habitability of exoplanets, leading to habitable zones growing or shrinking as we consider ever more detailed models. Nobody would call you out for being inaccurate if you picked a star mass a little lighter than the most recent published lower bound estimate - this is all well within the error bars of known science.

That said, the short answer is that more massive stars (M0V-M3V) are your best bet:

• Lower Limit - This article suggests that tidal heating could cause a runaway greenhouse effect on worlds tidally-locked to their stars at very close distances, making any planet orbiting a star with $< 0.3$ solar masses uninhabitable. This would rule out M4V-M9V dwarfs. I wouldn't put too much stock in such a simple inequality coming out of an atmospheric model, however, since these things are incredibly complex. It's highly possible that M4V or M5V might be habitable if the planet has a weird atmosphere or high albedo or something.
• Upper Limit - Intuitively, the upper limit comes from the fact that you want this planet to be tidally locked, which would be difficult to achieve around a star that's too massive since you'd have to be far away from it to avoid being cooked. In practice though, even the brightest M0V dwarf, Lacaille 8760, permits tidally-locked habitable worlds. Using Earth mass and radius for the planet orbiting at distance $a = 0.268$ AU (I'll explain how I got that in the next section), we get a tidal locking time of about a million years. So it seems that any M-dwarf permits tidal locking, even the most massive ones.

Habitable Zone Shorthands

Figuring out habitability constraints for worldbuilding like this is actually super straightforward if you're willing to use a shortcut: just start with Earth and the sun, and then scale appropriately. For example:

• Orbital Radius: The Earth orbits at 1 AU and the sun has $1 L_{\odot}$ of luminosity, which are the nicest numbers we could ask for. If you want your planet to be about as warm as Earth, and you know that luminosity decays with the square of distance, then $L = (\frac{a}{\text{1 AU}})^2 L_{\odot}$. Rearrange, and your planet's orbital radius in AU is simply the square root of its luminosity in $L_\odot$. This is how I got 0.268 AU for Lacaille. Keep in mind that "about as warm as Earth" can be anywhere from a jurassic hothouse to an ice age, so I assume it encompasses any range of temperatures you might want.
• Apparent Size in the Sky: To answer your question about how big the star would look in the sky, we do the same thing. Since apparent size is proportional to actual size and inversely proportional to distance, the size of your sun in your planet's sky appears $\frac{\text{1 AU}}{a} \times \frac{R}{R_\odot}$ times as large as our sun looks in our sky. For Lacaille, this is about 1.9 times the apparent size of the sun. So, big in the sky, but not that big (the sun's apparent size is about half a degree. It's tiny).

Wikipedia is your friend for finding all the numbers you need. A handy table of approximate masses, luminosities, and radii for M-dwarfs can be found here.

As for your last question, how the star looks will depend on the thickness of your atmosphere. You don't want it to be too thick, or the pressure will be too much for life and will likely result in a runaway greenhouse effect. I imagine that at the lower end of habitable atmospheric thickness, the star is too bright to look at directly (like the sun) but has maybe a reddish tint, while at the upper end, the star is a deep red disk, like a setting sun on Earth.

All in all, your planet seems very plausible. The Earthlike size, the black/red plants, the tidal locking and high winds - it all checks out. Good luck on your worldbuilding!

Answer 2

TL;DR: red stars emit much of their light in the IR spectrum, which is bad for photosynthesis. Make your star as hot and bright as you can to avoid this issue.

Photosynthesizers under red light could be any color but red.

---

Other answerers have already covered things like apparent sizes and distances of stars, so I won't go into them here. Instead, I'll concentrate on your plant life, because it is pretty important and isn't often thought about very hard.

---

A very important thing to remember is that the light that cooler stars emit is not simply redder, but it contains much less short-wavelength light (eg. UV) and much more long-wavelength light (eg. IR).

You can use Planck's law to show you the relative proportion of the energy emitted by a black-body radiator (and for this sort of problem, stars can be reasonably modelled as one of those):

Spectral radiance is a slightly awkward thing to work with, but the area under the curves represents the proportion of the energy of the star that's emitted in those wavelengths. I've added a (rather poor) visualisation of the visible light spectrum below, so you can see that for all M-type stars most of their energy is in the near-IR spectrum.

There's a nice calculator on hyperphysics (don't be fooled by its deeply old-school presentation, the site remains very useful) which will do the integration of Planck's law for you and work out the proportion of the emitted light in a particular frequency band. For example, an M0V star emits just 28% of its total power in the 380nm to 780nm band (which is basically "visible light"). By comparison, a G2V star like the sun emits more like 46%.

"No big deal", you might think, "my photosynthesizers will just work on near-infrared". The problem you have now is that photosynthesis relies on the energy of single photons, and the energy of an individual photon scales inversely with wavelength. The peak of the emission spectrum for a G2V star is ~500nm, but for M0V it is more like 750nm, which means it has only 2/3rds of the energy. By the time you get to M6V it is longer than 1000nm, and hence has less than half the energy. Your photosynthetic process might be super efficient, but the energy it produces is just much lower than for visible light, which makes it much harder to do interesting chemistry and therefore make complex chemicals and evolve complex organisms.

Still, you can handwave it. Real world photosynthetic bacteria in the ocean can certainly manage to photosynthesize near-IR light, like Blastochloris.

Next problem: infrared absorption by the atmosphere.

Our atmosphere is transparent to a nice range of frequencies that we've no termed "visible light". Sure, it gets scattered quite a bit, but scattered light isn't "lost" as such. Look at those IR absorption peaks in the water vapor spectrum though. On cloudy days, your red-IR world will find a significant proportion of its light simply absorbed by the clouds, making it seem much darker than an equivalent cloudy day on Earth! Handwaving away clouds risks desertification, and all the problems that brings, so this probably isn't avoidable. This makes plant growth limited both in places with little cloud (no rain, so no water!) and places with too much cloud (not enough light!) which is a interestingly different to plant life on Earth.

I wanted my plants to be mainly red

Unfortunately, this is one area in which you are definitely out of luck, and handwaving won't help you.

Chlorophyll-bearing plants like you tend to see on Earth's surface are green because they have photosynthetic pigments that absorb red and blue light, and reflect the green bit they don't use.

Red plants (such as red algae) have other pigments like phycobilicoproteins that absorb green light and reflect red. Here's the thing though... the light spectrum emitted by a G2V star like the Sun has plenty of red and green and blue light to go around, as 46% of the Sun's output is in the visible band. Your red stars? Not so much. By far the largest part of the visible spectrum of light they emit is, obviously, red. By bouncing back red light, your plants would be wasting their most useful power source, and would struggle to compete with plants which could consume red light.

This means your vegetation is more likely to be blue, green or yellow to our eyes, if it had visible light color at all. Black vegetation is probably just fine, though.

Answer 3

ΓΙΑΝΝΗΣ ΜΙΧΑΗΛΙΔΗΣ made an erronious assumption about designing their world.

The planet is a bit larger that Earth with it being 1.5 times more massive (by thay i mean that gravity is 1.5 g compared to Earth's 1 g) although I am not entirelly certain about it and I'm considering making it only 1.2 times more massive.

They seemed to assume that the surface gravity of their world campared to Earth's surface gravity would be directly proportional to their world's mass compared to Earth's mass.

Actually there are two gravitational factors that world builders have to calculate when designing their planets, especially the ones they want to be habitable. The surface gravity and the escape velocity.

The surface gravity determiens how fast objects fall, and how heavy people feel. The escape veloctiy determines how long the planet can retain its atmosphere before it escapes into space. The two factors don't change in the same amount when the mass, radius, volume, or average density of a planet is changed.

Earth has a radius of 6,371 kilometers, and an averge density of 5.514 grams per cubic centimeter. The surface gravity of Earth is 1 g, or an acceleration of 9.80665 meters per second per second. The escape velocity of Earth is 11.186 kilometers per second.

Here is a link to an online surface gravity calculator:

https://philip-p-ide.uk/doku.php/blog/articles/software/surface_gravity_calc

And here is a link to an online escape velocity calculator:

https://www.omnicalculator.com/physics/escape-velocity

So we can try giving your world a mass 1.5 Earth mass while having the same radius (and thus volume) as Earth. It will have an average density 1.5 times that of Earth, or 8.271 grams per cubic centimeter.

This planet will have a surface gravity of 1.5 g, and an escape velocity of 13.7 kilometers per second, 1.2247 times that of Earth.

Now try giving your world a radius 1.5 that of Earth (or 9,556.5 Kilometers), and thus a volume 3.375 that of Earth. With 1.5 the mass of Earth of Earth in 3.375 times the volume, it will have 0.44444 the density of Earth, or 2.45 grams per cubic centimeter.

So it will have a surface gravity of 0.66 g, and an escape velocity of 11.186 kilometers per second, 1.00 times that of Earth.

Now try giving your planet the same density as Earth with 1.5 times the mass. That requires having 1.5 times the volume of Earth, and thus about 1.1447142 the radius of Earth, or 7,292.8837 kilometers.

That gives the planet a surface gravity of 1.14 g, and an escape velocity of 12.805 kilometers per second, 1.1447344times that of Earth.

In those examples, changing one factor by X amount will not change the other factors by X amount.

As a shortcut, changing the average density of a plent relative to Earth should change the surface gravity in approximately the same proportion.

As another shortcut, if you change the radius and the mass of a world by the same proportion relative to Earth, the planet will have approximately the same escape velocity as Earth.

As a third shortcut, giving a planet the same average density as Earth should change its radius and its escape velocity with approximately the same proportion.

So if you want your world to have a surface gravity of 1.5 g, you can give it the same radius and volume as Earth, with 1.5 times the mass and density.

And if you want your world to have 1.5 times the mass of Earth, of course there are many other possible volumes, surface gravities, and escape velocities for worlds with 1.5 times the mass of Earth.

If want your planet to be mostly made out of rock, with enough liquid and gas to be habitable, there are limits to its possible density range.

Many small rocky astronomical objects have very low densities, because they are made of smaller object with mergered with gentle forces and still have large vacuum spaces with them.

Your planet would be a planemo, an planetary mass object large enough to be gravitationally compressed into a spheroidal shape, for all of its internal spaces to be collapsed and filled in, for its interiod materials to be compressed to higher densitys than they have on the surface, and to have enough escape velocity to retain a substantial atmosphere, and liquid surface water.

As far as I know, there are only seven mainly rocky planemos known in our solar system. Earth has the highest average density, 5.514 grams per cubic centimeter, and the two lowest are the Moon, 3.334 grams per cubic centimeter, about 0.60464 tha tof Earth, and Europa, a moon of Jupiter with 3.103 grams per cubic centimer, 0.5627 that of Earth. And Europa has much more water proportionally than Earth, its entire surface being covered with liquid water covered by a thick ice shell with a total depth of about 100 kilometers.

There are many planemos in the other solar system, moons and dwarf planets with density lesser than the Moon. But they are either giant planets with escape velocities high enough to have vast amounts of hydrogen and helium, or objects made of mixtures of rocks and low density ices.

The highest estimated average density for any of those icey planemos is that of the dwarf planet Eris, 3.013 grams per cubic centimeter, 0.5464 that of Earth.

I think it is safe to assume that any planet or other planemo which is not entiely covered by liquid or ice but has at least some exposed solid surface area, should have an average density over 3.000 grams per cubic centimeters, and probably higher if it will be massive (and thus gravitationally compressed) enough to retain a substantial atmosphere and necessary for human breathing and for retaining liquid surface water necessary for life.

And htere are upper limits to the mass, surface gravity, escape velocity, density, etc. of worlds which are habitable for humans and beings with similar requirements in particular, and even for liquid water using lifeforms in general.