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Are some L-type brown dwarves bright enough so that it would be dangerous to the eyes if one looked at them from habitable distance or closer? If not, are the weakest M-type stars undangerous to look at from habitable distance too? T-type brown dwarves are dim enough that there shouldn't be any danger, and Y-type ones are invisible.

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A typical L-type brown dwarf is about 1200-2200 K in surface temperature and is about the size of Jupiter. Using the Stefan-Boltzmann law, we can deduce that the hottest brown dwarfs have a luminosity of$$\Big(\dfrac{2200}{5778}\Big)^4 \cdot \Big(\dfrac{1R_J}{1R_\odot}\Big)^2 = 0.00021224 L_\odot$$

According to Wikipedia, the dimmest apparent magnitude that causes pain to look at is $-25$. We can use the luminosity formula for apparent magnitude and distance calculate how far away an observer must be to experience this magnitude: $$0.00021224 = 0.0813 \text{ ly}^{-2}d^2\cdot10^{-0.4\cdot(-25)}$$

Solving the equation gives $d=0.03232 \text{ AU}$, or $67.62 $ times the brown dwarf's radius. Using this useful HZ calculator and plugging in $T_{eff}=2200$ and $L=0.00021224$, we get the distance must be between $0.015$ and $0.032$ AU, which is inside that limit. This range is inside the limit for $-25$ apparent magnitude, so no, looking at brown dwarfs at their habitable zone is not guaranteed to be safe.

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    $\begingroup$ I don't quite understand the minus 25 number as "minimum magnitude that causes pain". You get eye damage even when looking from Neptune's distance (30 au) at the Sun for too long. They probably mean a pain in the way that you immediately look away from the Sun (but afaik that goes till Saturn's distance at 10 au). My question deals with the eye damage threat by looking at the star regardless of other circumstances. However, this means that L-dwarves definitely are dangerous to look at, so I'm accepting your answer. $\endgroup$
    – Giovanni
    May 26, 2021 at 13:40
  • $\begingroup$ @Giovanni I wonder the same. Do you have any sources which state maximum brightness for human eyes which is not harmful? $\endgroup$
    – planetmaker
    May 26, 2021 at 13:46
  • $\begingroup$ @Giovanni Simple test: Hold a 100 watt bulb 1 foot (30 cm) away from you. This is about -25 apparent magnitude. Doing the same thing but 16.5 ft (5 meters) away is -20 apparent magnitude, or the Sun when viewed from Neptune. Don't try it unless you are willing to risk losing eyesight!!! $\endgroup$
    – WarpPrime
    May 26, 2021 at 13:47
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    $\begingroup$ @fasterthanlight That's why I better won't try, especially with what I think to know stated above. $\endgroup$
    – Giovanni
    May 26, 2021 at 14:17
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    $\begingroup$ At a distance of 67.62 radii the star will appear about 1.7° wide, or 3.2 times wider than our Sun from Earth. That will have a modest impact on the unsourced, potentially unscientific and wrong "pain" threshold from Wikipedia which does not say anything about safety. Also, with a spectrum shifted to the IR and using human eyesight, the amount of heat focused on the retina per unit of perceived visible brightness will be much higher (if it were not for the fact that the spot of heat would be 10.1 times larger in area.) $\endgroup$
    – uhoh
    May 30, 2021 at 23:43

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