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After reading this question on wordbuilding. I saw that a brown dwarf emits most of its energy in the infrared which made me wonder: How bright would such a star appear from it's exoplanet in the visible light range? Could an exoplanet orbit a brown dwarf and be warm enough for life with liquid water and a similar temperature to Earth, yet be cast into eternal night?

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Source: https://www.eso.org/public/images/eso9709b/

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    $\begingroup$ visible light is not exactly essential to reach that temperature - the infrared emissions can just suffice and life probably could evolve such that infrared light is visible (our vision is probably for good reason in the maximum of the sun's light). The real question is: how far in is such orbit, how quickly will such planet be tidally locked and can life evolve on a planet tidally-locked with respect to its star? However each brown dwarf emits enough light onto a planet in its habitable zone to not consider it pitch dark. $\endgroup$
    – planetmaker
    Commented Jan 11, 2022 at 17:22
  • $\begingroup$ There's a lot of other variables to this question. What counts as life for you? Could sub-surface creatures living near geothermal vents still count? In which case, your planet can be pretty darn cold. Not to mention most of Earth's internal heat budget is radiogenic. I could imagine a planet where this radiogenic heat is knocked up lot and that could significantly affect the whole heat budget equation. $\endgroup$
    – zephyr
    Commented Jan 11, 2022 at 18:09
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    $\begingroup$ Temperature goes down rather quickly as the star’s spectrum is shifted towards the infrared. A 100 W incandescent lamp releases most of its energy as heat, yet despite its visual brightness, it’s not warm enough. Granted, located a few million kilometres away, you would probably not see it, but even a few metres away from it, you won’t feel its heat. A toaster’s elements are basically all infrared (some visible red), but you don’t feel their heat even close to the toaster (supposing it’s broken open). A brown dwarf’s planet would have to be extremely close to it in order to sustain life… $\endgroup$
    – Pierre Paquette
    Commented Jan 12, 2022 at 0:12
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    $\begingroup$ @PierrePaquette or a photosynthetic pathway based on infrared photons would have to evolve. I'm trying to thing of a question to ask about that possibility, torn between an astrobiology question in Biology SE and a photochemistry question in Chemistry SE, and whether it should be more hypothetical or a reference request. $\endgroup$
    – uhoh
    Commented Jan 12, 2022 at 0:29
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    $\begingroup$ @uhoh - you could also posit such a question on Worldbuilding $\endgroup$
    – Rory Alsop
    Commented Jan 12, 2022 at 9:27

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Disclaimer: I'm not an astrophysicist, merely someone interested in astronomy. That being said I thought it worthwhile to mention the below paper, as it may provide you with some insight into Brows Dwarfs themselves and the specific problems involved with habitable planets around them. I would have added it as a comment, but I do not yet have that privilege.

Answer: The paper Habitability in Brown Dwarf Systems (Bolmont E., 2018) provides an introduction to the topic you are interested in: properties of Brown Dwarfs (BD), loss of water in the early phase; time spent in the habitable zone (HZ); tidal interactions; one planet system vs. multiple planet systems; volcanism. You will see that there are a lot of parameters that play a role, only some of which: mass of the BD, age of the system; where in the system did the planet originate (inside, in, outside the HZ, which itself moves inward as is mentioned in one of the comments); "cold traps" on tidally locked planets; volcanism.

Of interest to you might be Figure 4b in the paper, where three possible planets are compared, one losing very little water but spending little time in the HZ (bad for natural evolution, I guess), another one losing some water but spending a lot of time in the HZ, and a planet losing a lot of water once it reaches the HZ. So, planet 2 might be something for you.

Giving a clear answer to your original question -- How bright would such a star appear from it's exoplanet in the visible light range? Could an exoplanet orbit a brown dwarf and be warm enough for life with liquid water and a similar temperature to Earth, yet be cast into eternal night? -- is obviously far from straight-forward, and different astrophysicists will answer it differently. Many parameters are involved, but the paper offers a few parameters you might tweak in your favour.

Anyway, since you are interested in world-building, the question is, how "sciency" and reliable has your "universe" to be? How much "handwavium" are you willing to apply? What are your readers (or players etc.) like? How much are they willing to accept about a fictional universe before their willingness or ability to "suspend disbelief" is overtaxed? These are further parameters in world-building, and perhaps even more important than the ones science can tell us about. But at least this paper (and the ones it refers to) should provide you with some ideas how you can tweak your universe/planetary system.

Addition (18 January 2022): The web-site planetplanet.net has an article called Real-life sci-fi world #4: Earth around a brown dwarf. The article is dated 2014, but it is definitely more accessible than the paper mentioned above, and it should be a lot more useful worldbuilding-wise.

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  • $\begingroup$ Does this paper show the luminosity of the star in the visible range only? $\endgroup$
    – SurpriseDog
    Commented Jan 17, 2022 at 19:49
  • $\begingroup$ Figure 2 of the paper gives the spectral energy distribution for several dwarfs, from a bit less than 1 to a bit more than micrometers. See, for example, the band-descriptors J, H, K (near infrared) at the bottom of the figure. See my edit of my answer. $\endgroup$
    – CR131873
    Commented Jan 18, 2022 at 20:26
  • $\begingroup$ The brown dwarf would appear reddish-brown (and gigantic) in the sky. But look just to the side and you can see the stars! It would basically look like nighttime except in the direction of the brown dwarf! Clouds would simply be black patches blocking the stars. Very Interesting. $\endgroup$
    – SurpriseDog
    Commented Jan 18, 2022 at 23:15

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