<p>If we take 1 atmosphere of optical depth to mean looking though the Earth's atmosphere at zenith, then the optical depth to scattering is small - probably of order 0.3 for blue light and much smaller (according to <span class="math-container">$\lambda^{-4}$</span>) for red light.</p>
<p>That means that when the Sun is at zenith, most of the light reaches the ground but some blue light is scattered out of the line of sight.</p>
<p>If we look to other sight lines then the optical depth will increase roughly as <span class="math-container">$\sec z$</span>, where <span class="math-container">$z$</span> is the zenith angle (<a href="https://en.wikipedia.org/wiki/Air_mass_(astronomy)" rel="nofollow noreferrer">more complicated functions</a> are available). When we look in those directions, we mainly see scattered (blue) light. If we look towards the Sun at large <span class="math-container">$z$</span> (don't look at the Sun) then the optical depth to scattering is considerably larger and blue light is scattered out of the line of sight, leaving red light to come towards us.</p>
<p>The amount of blue light we see in the sky then depends on the intrinsic spectrum of the Sun and the angle between the sightline and the Sun.</p>
<p>M-dwarfs and especially brown dwarfs, have very little blue light in their spectra. A typical <span class="math-container">$B-R$</span> colour for an M-dwarf would be about 3 magnitudes, whereas for the Sun is about 1. That means the flux ratio of red to blue light is a factor of 6.3 bigger in an M-dwarf.  The ratio of the scattering cross-section of red to blue light is about <span class="math-container">$(400/700)^4 = 0.1$</span>, which would just about compensate.</p>
<p>So I think the best you could get is sort of a yellow-ish scattered light at large angles from the direction of the M-dwarf, due to Rayleigh scattering.</p>
<p>However, this ignores the <a href="https://en.wikipedia.org/wiki/Mie_scattering#:%7E:text=Mie%20scattering%20occurs%20when%20the,common%20causes%20of%20Mie%20scattering." rel="nofollow noreferrer">Mie scattering</a> component. The cross-section for Mie scattering is almost flat, or slightly rising towards red wavelengths. This is caused by aerosols and larger particles in the atmosphere; and tends to wash out the colour and make it more similar to the illumination spectrum. From that point of view, and depending on the aerosol content, I think the yellow-ish sky due to Rayleigh scattering will end up a more salmon pink because of Mie scattering.</p>
<p>This is the view from the ground. I'm not sure what you mean by viewing it from space. The Earth's atmosphere is almost transparent except where there are clouds. I guess if you look right at the limb of the Earth you see Rayleigh back-scattered light; in which case my answer would be the &quot;yellow-ish&quot; answer I gave above, because Mie scattering is quite biased in the forward scattering direction.</p>
<p>Brown dwarfs really have almost no blue light in their spectrum. It is completely absorbed by molecules in their atmospheres and re-radiated at infrared wavelengths. However, what matters is I suppose the ratio of red to blue light and although this is very small, I doubt you can say it is zero. So I'll pass on that one - I'm not sure. But to the human eye it is going to be very dark (assuming that your planet is illuminated by 1.4 kW per square metre of infrared light).</p>

CC BY-SA 4.0
2020-12-01T11:32:19.627Z
By viewing it from space I mean this: https://media.nationalgeographic.org/assets/photos/000/276/27620.jpg So it would also be yellow-ish.
Greenhorn
CC BY-SA 4.0
2020-12-01T11:37:04.417Z
@Greenhorn Yes. I'd go with "yellow-ish" for an M-dwarf.
ProfRob
CC BY-SA 4.0
2020-12-01T11:39:27.573Z
This proves my impression: the planets around weak red dwarfs (as well as those close enough around brown dwarfs) seem to have red-to-yellow atmospheres regardless of their composition.
Greenhorn
CC BY-SA 4.0
2020-12-01T12:02:34.910Z
What do you mean regardless of their composition. Your question asks about an Earth-like atmosphere. If the composition and/or density changes, then the answer can change. @Greenhorn
ProfRob
CC BY-SA 4.0
2020-12-01T14:07:29.937Z
Just my impression. Many planets have CO2 atmospheres anyway and these are per se orange-ish (such as Mars' and Venus' one).
Greenhorn
CC BY-SA 4.0
2020-12-01T11:23:50.780Z
2020-12-01T11:30:01.320Z
2020-12-01T11:30:01.320Z
ProfRob
<p>I have the impression that in brown dwarf and weak red dwarf systems, everything looks more reddish on a planet, including its atmosphere regardless of composition. Suppose there's a planet having an atmosphere at the same surface pressure and composition as that of Earth, circling either a brown dwarf or a below-average-luminous red dwarf at habitable distance, would this planet's atmosphere still look blue when seen from either the surface or outer space? Or would its atmosphere look more orange/red?</p>

CC BY-SA 4.0
2020-12-01T10:41:28.777Z
@RobJeffries You state that the sky rather isn't blue in the line of sight towards the red dwarf Sun, but elsewhere (such as close to horizon) it would still look blue?
Greenhorn
CC BY-SA 4.0
2020-12-01T11:05:15.983Z
It's a complicated calculation, that depends on the optical depth to scattering. Red and brown dwarfs have next to no blue light in their spectra so it is hard to see how you can get light that appears blue, even with a $\lambda^{-4}$ scattering cross-section. I see now that this ISN'T a duplicate.
ProfRob
CC BY-SA 4.0
2020-12-01T11:20:50.923Z
@RobJeffries I don't think it's a duplicate either because this question includes brown dwarfs and focuses on the entire sky. My question is on planets circling T9V to M2V stars in the habitable zone. I'm actually quite surprised that if there isn't a blue light in the star's spectrum you can't see blue in its system anywhere at all.
Greenhorn
CC BY-SA 4.0
2020-12-01T14:12:59.913Z
@fasterthanlight Just because it's a duplicate doesn't give a reason to downvote it.
Greenhorn
CC BY-SA 4.0
2020-12-01T16:30:11.183Z
And I'd completely forgotten this: https://astronomy.stackexchange.com/questions/34726/how-would-the-sky-look-if-earth-orbited-a-red-giant-at-a-safe-distance/35237#35237
ProfRob
<brown-dwarf><atmospheric-effects><red-dwarf><electromagnetic-spectrum>
If the Earth circled a red dwarf/giant or a brown dwarf, would its sky still look blue?
Greenhorn
# If the Earth circled a red dwarf/giant or a brown dwarf, would its sky still look blue?

(Asked by: username_0 on 2020-12-01)

I have the impression that in brown dwarf and weak red dwarf systems, everything looks more reddish on a planet, including its atmosphere regardless of composition. Suppose there's a planet having an atmosphere at the same surface pressure and composition as that of Earth, circling either a brown dwarf or a below-average-luminous red dwarf at habitable distance, would this planet's atmosphere still look blue when seen from either the surface or outer space? Or would its atmosphere look more orange/red?

**Tags:** brown-dwarf, atmospheric-effects, red-dwarf, electromagnetic-spectrum

> **Comments:**
> **username_0**: @RobJeffries You state that the sky rather isn't blue in the line of sight towards the red dwarf Sun, but elsewhere (such as close to horizon) it would still look blue?  
> **username_1**: It's a complicated calculation, that depends on the optical depth to scattering. Red and brown dwarfs have next to no blue light in their spectra so it is hard to see how you can get light that appears blue, even with a $\lambda^{-4}$ scattering cross-section. I see now that this ISN'T a duplicate.  
> **username_0**: @RobJeffries I don't think it's a duplicate either because this question includes brown dwarfs and focuses on the entire sky. My question is on planets circling T9V to M2V stars in the habitable zone. I'm actually quite surprised that if there isn't a blue light in the star's spectrum you can't see blue in its system anywhere at all.  
> **username_0**: @fasterthanlight Just because it's a duplicate doesn't give a reason to downvote it.  
> **username_1**: And I'd completely forgotten this: https://astronomy.stackexchange.com/questions/34726/how-would-the-sky-look-if-earth-orbited-a-red-giant-at-a-safe-distance/35237#35237  

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## 1 answers

### Answer by username_1 on 2020-12-01. Score: 3 | Accepted answer

If we take 1 atmosphere of optical depth to mean looking though the Earth's atmosphere at zenith, then the optical depth to scattering is small - probably of order 0.3 for blue light and much smaller (according to $\lambda^{-4}$) for red light.

That means that when the Sun is at zenith, most of the light reaches the ground but some blue light is scattered out of the line of sight.

If we look to other sight lines then the optical depth will increase roughly as $\sec z$, where $z$ is the zenith angle ([more complicated functions](https://en.wikipedia.org/wiki/Air_mass_(astronomy)) are available). When we look in those directions, we mainly see scattered (blue) light. If we look towards the Sun at large $z$ (don't look at the Sun) then the optical depth to scattering is considerably larger and blue light is scattered out of the line of sight, leaving red light to come towards us.

The amount of blue light we see in the sky then depends on the intrinsic spectrum of the Sun and the angle between the sightline and the Sun.

M-dwarfs and especially brown dwarfs, have very little blue light in their spectra. A typical $B-R$ colour for an M-dwarf would be about 3 magnitudes, whereas for the Sun is about 1. That means the flux ratio of red to blue light is a factor of 6.3 bigger in an M-dwarf. The ratio of the scattering cross-section of red to blue light is about $(400/700)^4 = 0.1$, which would just about compensate.

So I think the best you could get is sort of a yellow-ish scattered light at large angles from the direction of the M-dwarf, due to Rayleigh scattering.

However, this ignores the [Mie scattering](https://en.wikipedia.org/wiki/Mie_scattering#:%7E:text=Mie%20scattering%20occurs%20when%20the,common%20causes%20of%20Mie%20scattering.) component. The cross-section for Mie scattering is almost flat, or slightly rising towards red wavelengths. This is caused by aerosols and larger particles in the atmosphere; and tends to wash out the colour and make it more similar to the illumination spectrum. From that point of view, and depending on the aerosol content, I think the yellow-ish sky due to Rayleigh scattering will end up a more salmon pink because of Mie scattering.

This is the view from the ground. I'm not sure what you mean by viewing it from space. The Earth's atmosphere is almost transparent except where there are clouds. I guess if you look right at the limb of the Earth you see Rayleigh back-scattered light; in which case my answer would be the "yellow-ish" answer I gave above, because Mie scattering is quite biased in the forward scattering direction.

Brown dwarfs really have almost no blue light in their spectrum. It is completely absorbed by molecules in their atmospheres and re-radiated at infrared wavelengths. However, what matters is I suppose the ratio of red to blue light and although this is very small, I doubt you can say it is zero. So I'll pass on that one - I'm not sure. But to the human eye it is going to be very dark (assuming that your planet is illuminated by 1.4 kW per square metre of infrared light).

> **Comments:**
> **username_0**: By viewing it from space I mean this: https://media.nationalgeographic.org/assets/photos/000/276/27620.jpg So it would also be yellow-ish.  
> **username_1**: @username_0 Yes. I'd go with "yellow-ish" for an M-dwarf.  
> **username_0**: This proves my impression: the planets around weak red dwarfs (as well as those close enough around brown dwarfs) seem to have red-to-yellow atmospheres regardless of their composition.  
> **username_1**: What do you mean regardless of their composition. Your question asks about an Earth-like atmosphere. If the composition and/or density changes, then the answer can change. @username_0  
> **username_0**: Just my impression. Many planets have CO2 atmospheres anyway and these are per se orange-ish (such as Mars' and Venus' one).  

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