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What light spectrum would hit the surface of a planet orbiting a red dwarf star?

The planet has a humid, greenhouse, & cloudy atmosphere, and a strong ozone, 80%+ surface water.

Planet is tidally locked.

Trying to determine plant life on a world, and the type of light it would absorb or reflect. Any additional considerations would be appreciated as well.

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    $\begingroup$ What makes you believe that there is a direct relationship between the power spectrum of the electromagnetic radiation of a star and the color(s) of the photosynthetic pigment(s)? Here on Earth we have brown, green, and blue-green photosynthetic pigments. Also note that here on Earth the maximum of the power spectrum of solar light is in the green region (around 550 nm) but none of the common photosynthetic pigments is optimized to absorb green light... $\endgroup$ – AlexP Mar 15 at 20:19
  • $\begingroup$ I don't. I'm attempting to understand possible considerations. From my limited research I was under the impression that the power of that light spectrum would impact how plants responded in development. Does this not matter? I figured like you mentioned that earth plants are green to reflect the extremes of the our solar spectrum, and wondered if the plants receiving light from a red dwarf would do likewise, possibly being red, orange, or yellow? $\endgroup$ – CatoRockwell Mar 15 at 20:37
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    $\begingroup$ My comment tried to make two points: first, not all plants on Earth are green. It so happened, by accident, that land plants are descended from green algae, but they could just as well have been descended from brown algae, the Phaeophytae; and second, green plants reflect green, and absorb red and blue, which is unexpected given that most power is in the green part of the spectrum. $\endgroup$ – AlexP Mar 15 at 20:47
  • $\begingroup$ Thank you. I was under the impression that green plants evolved as a photosynthetic reaction to the sun, to reflect the excess green light. If this is not the case then, it definitely opens up my options for this world. Is there anything else I should take into consideration when developing plant life? $\endgroup$ – CatoRockwell Mar 19 at 3:32
  • $\begingroup$ I'm a bit confused about the use of "greenhouse"... Venus is a greenhouse planet and there's no plant life there... not at least the kind we know and understand... If, however, you're talking about a planet in the habitable zone, it turns out it will look pretty much like our sun (because the energy needs to be about the same), and most likely have about the same effect (i.e. other considerations might be more important). Here's a picture: phl.upr.edu/library/media/sunsetofthehabitableworlds $\endgroup$ – Erk Apr 21 at 2:18
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The planet would have to be closer to the red dwarf star.

https://www.spaceanswers.com/solar-system/what-if-we-replaced-our-sun-with-a-red-dwarf/

Also, on flora, plants would be differently colored.

"As a result, astrobiologists have suggested that photosynthetic plants on worlds orbiting lone red dwarfs could take on hues of red, blue, yellow, purple, or even grayish-black to best absorb the starlight," (From link below).

Red dwarfs give off less light and because the planet has to be closer (than, for instance, Earth's distance from the sun) to the red dwarf.

https://news.nationalgeographic.com/news/2011/04/110419-alien-trees-black-plants-planets-ras-space-science/

There is also the issue of solar flares though. Red Dwarfs give off solar flares more powerful than the suns. With the planet being closer these flares could easily kill all plant life unless it could somehow shrink away and hide during these flares.

https://www.universetoday.com/140302/a-red-dwarf-blasts-off-a-superflare-any-life-on-its-planets-would-have-a-very-bad-day/

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There is an episode of Stargate Universe which speculates that a red dwarf star would lead to purple plants.

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Speaking of a hypothetical Earth-like planet (plus tidally locked) it would resemble something like this:

source:https://steamcommunity.com/sharedfiles/filedetails/?l=czech&id=101632999

The planet itself would be divided into 4 zones, 3 of which would be technically uninhabitable: a perpetual hurricane on the side facing direct sunlight, a twilight zone (tormented by endless winds) and the icy biome, covering pretty much the other half of the planet. The only habitable zone would be the zone of indirect insolation, where life could thrive and evolve, in a range of temperature varying from over 104°F in the western regions to even less than 0°F in the Eastern part.

Now, Ozone is the major absorber of UV rays. If the layer was thicker than it is on Earth, then it could potentially absorb all UV rays. Less UV rays means less risks of skin cancers or insolations for us humans, but it could gradually lead our bodies to a Vitamin D deficiency (with consequent low calcium levels). Increased humidity levels could cause the hurricane located in the point of maximum insolation to grow bigger and thus more extreme temperatures in the transition "habitable" zone (with the tropical one becoming even more humid and the Eastern one colder).

Finally, as far as vegetation is concerned, we know that the chlorophyll in most plants here on Earth absorbs blue and red light, but (suprisingly!) less green light. Therefore, chlorophyll appears green to us. Green is still absorbed, but less than all the other colors. On a red dwarf world, since the light peak is in more in the infrared, leaves would try and catch every photon they could since it would require a larger amount of them to complete photosynthesis. I guess leaves would appear darker (even black) than here on Earth, but I'm not too sure about that. I don't even think there would be life in the oceans either, since light would be too weak to penetrate water below 10/20 meters.

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  • $\begingroup$ Got any sources on the hurricane? $\endgroup$ – TheDyingOfLight Apr 23 at 7:30
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Spectral Stuff

For the emission spectrum of the star you'll need two formulas. Wiens Displacement Law [1] and the Planks Law [2].

Wiens Displacement Law

$ λmax = (2.898 * 10^{-3}/T)*10^9$

$T$ = stellar temperature in Kelvin

Obtain temperature via this formula.

$T = M^{0.505}$

$T$ = stellar teperature relative to Sol (multiply by 5778 K)

$M$ = stellar mass relative to Sol

Planks Law

$Bλ(λ, T) = ((2*π*h*c^2)/λ^5)*(1/(e^{h*c/λ*kB*T}-1)$

Have fun figuring this one out. ;) Or use this calculator [3]

Atmosphere

You mentioned Water Vapor, Ozone and CO2, as greenhouse gases. If you aim for a human breathable atmosphere consider these limits.

O2 = 0,16 - 0,5 atm, but only up to 35 % of atmosphere (runaway wildfires will keep it this low)

O3 = 0.0000001 atm

Co2 = 0.02 atm (gets uncomfortable at 0.005 atm)

Be aware that greenhouse or hothouse atmosphere are used to describe Venus like conditions. You don't seem to aim for that. Should you want to calculate the greenhouse effect on this world I'm gonna have to stop you right there. Nothing short of a PHD grade physics simulation will give you precise values. But I do have a list of linear approximations derived from calculating stuff backwards. These are by no means scientifically accurate, but they will do for worldbuilding.

$H2O = 677 K/atm$

$O3 = 19600000 K/atm$

$CO2 = 13784 K/atm$

Don't let the planets teperature get above an average temperature 47 Celsius, as this marks the beginning of a runaway greenhouse effect [4] leading to Venus like conditions. This again is just a ballpark number. You shouldn't go under an average temperature of - 56,6 C as CO2 will have frozen out at this point. These are the limits of habitability. Using these a way more elegant than calculating habitable zones and dropping the planet there.

You will get the planets temperature without greenhouse effect [5] via the following equation.

$T = (\frac{ L_{\odot}(1 - a)}{16 \pi d ^ 2 ơ}\;.)^{1/4}$

$L$ = Luminosity in Watts

Obtained via

$L = M^3$ ($M$ is relative to Sol, Sol L is 3.828×10$^{26} W$)

$a$ is the planets albedo, [6] and [7] should help you there.

$σ = 5.670373 × 10^{−8} \;\mathrm{W}\; \mathrm{m}^{−2}\; \mathrm{K}^{−4}.$ this the the Stefan-Boltzmann constant.

All that said a these formulars are tuned to an earth like sun and many things like the albedo and greenhouse effects of the gases will be altered by the new spectral class. But going for something more accurate is material for several scientific papers and not for a SE answer.

Tidal Lock

Assuming that the planet is tidally locked is sensible, but tidal locking does not always mean that the same side points towards the sun. Mercury is an example of a tidally locked world in a higher than 1:1 spin-orbit resonance [8]. As the eccentricity of the tidally locked planets orbit increases, the most likely spin-orbit resonances go up from 1:1 to 3:2 to 1:2 to 5:2. Just be aware that you will get strong distance based "seasons" as eccentricity increases. Just run the temperature formula for pericenter, apoapsis and apocenter. As the average eccentricity of discovered exoplanets is at 0.3, higher than 1:1 resonances seem very realistic and increase habitability.

Additional Consideration

It is very likely that you came across the concept of an eyeball planet [9] during your research for this. Sources and people who give you this information are not up to speed. The eyball planets are an artifact of early simulatiins without oceanic and atmospheric heat transfer. There will be strong, constant winds carrying warm air from the near point to the far one. Temperatures on the night and day sides will be close to equal. And if there is a frozen ocean the ice free hole won't be round, it will be lobster shaped. (If you want I'll go source hunting, tell me in the comments.)

Small stars like red dwarfs tend to be variable, flare or UV-Ceti stars [10]. They can increase their luminosity suddenly be orders of magnitude. Imagine the sun suddenly getting way hotter and brighter for a few hours and you see the problem. It isn't clear if all small stars are variable, as they become calmer as they age. Yet even ancient Barnards Star has been observed to flare. This needs to be considered while designing the biosphere.

Plants

Color

There is no definitive answer here, just a jungle of possibilities that might all be true. Youtuber Artifexion made a video on the subject suggesting that plants use either the peak radiation of their star for photosynthesis or reflect it to use the other, less intensive light [11]. On earth the secound approach is used, resulting in green plants. On red dwarf planets this would result in black plants as they would want to use all the light. Should the star be variable some kind of biological flare warning system, maybe an UV-detector and the ability to protect against or survive the flare will be crucial. Land plants will be more affected than sea plants. So rolling up like Shameplants, burrowing, using the stellar inferno for reproduction like Mammoth Threes or springing up rapidly after the flare like Eukalyptus does after fires seem like useful strategies.

The first approach is great but there is one huge caveat. Biochemistry isn't a wonderbox. Xenobiology might hold many wonders but a chlorophyll equivalent for every set of wavelenghts seems unlikely. Earths green plants don't really use all the blue and red light, chlorophyll a and b just have absorbtion spectra covering a part of both wavelenghts. The various chlorophylls c and chlorophyll d have other functional wavelenghts and there are various bacteriochlorophylls. Interesting for our purposes is the recently discovered chlorophyll f, capable of using infrared light with wavelengths between 707 and 800 nm [12]. This would lead to plants which ignore the entire visible spectrum or only use some red light via chlorophyll din addition to the infrared light. This kind of vegetation could be white or bright blue-green-metallic respectively. This kind of reflectiveness could allow for flare survivability.

[1] https://en.m.wikipedia.org/wiki/Wien's_displacement_law

[2] https://en.m.wikipedia.org/wiki/Planck's_law

[3] http://www.spectralcalc.com/blackbody_calculator/blackbody.php

[4] https://en.m.wikipedia.org/wiki/Runaway_greenhouse_effect

[5] https://en.m.wikipedia.org/wiki/Planetary_equilibrium_temperature

[6] https://en.m.wikipedia.org/wiki/Albedo

[7] https://youtu.be/y3Kb_ik5f-I

[8] http://www.skymarvels.com/infopages/vids/Mercury%20Spin-Orbit%20Resonance.htm

[9] https://en.m.wikipedia.org/wiki/Eyeball_planet

[10] https://www.aavso.org/vsots_uvcet

[11] https://youtu.be/L9MNC45Jr6Q

[12] https://en.m.wikipedia.org/wiki/Chlorophyll_f

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