<p>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<span class="math-container">$$\Big(\dfrac{2200}{5778}\Big)^4 \cdot \Big(\dfrac{1R_J}{1R_\odot}\Big)^2 = 0.00021224 L_\odot$$</span></p>
<p>According to <a href="https://en.wikipedia.org/wiki/Apparent_magnitude#List_of_apparent_magnitudes" rel="nofollow noreferrer">Wikipedia,</a> the dimmest apparent magnitude that causes pain to look at is <span class="math-container">$-25$</span>. We can use the luminosity formula for apparent magnitude and distance calculate how far away an observer must be to experience this magnitude: <span class="math-container">$$0.00021224 = 0.0813   \text{ ly}^{-2}d^2\cdot10^{-0.4\cdot(-25)}$$</span></p>
<p>Solving the equation gives <span class="math-container">$d=0.03232 \text{ AU}$</span>, or <span class="math-container">$67.62 $</span> times the brown dwarf's radius. Using <a href="http://depts.washington.edu/naivpl/sites/default/files/hz_0.shtml#overlay-context=content/hz-calculator" rel="nofollow noreferrer">this useful HZ calculator</a> and plugging in <span class="math-container">$T_{eff}=2200$</span> and <span class="math-container">$L=0.00021224$</span>, we get the distance must be between <span class="math-container">$0.015$</span> and <span class="math-container">$0.032$</span> AU, which is inside that limit. This range is inside the limit for <span class="math-container">$-25$</span> apparent magnitude, so <strong>no, looking at brown dwarfs at their habitable zone is not guaranteed to be safe.</strong></p>

CC BY-SA 4.0
2021-05-27T08:10:05.033Z
As a comment, and somehow in line with comments above. Eyes don't feel pain by light (not in time scale to trigger a response. If we turn from a bright source is by a kind of discomfort but not pain). So it would be better to speak of damage or whatever was meant in order to fix the threshold used for the calculations.
Alchimista
CC BY-SA 4.0
2021-05-27T08:49:17.673Z
@Alchimista Right, my threshold would be the one where there is no threat of an eye damage whatsoever. Given fasterthanlight's answer, it is safe to say that all L- and M-type stars are dangerous to look at from too close, and maybe even T-dwarves but I can't believe they would be too. T-dwarves are very dim.
Giovanni
CC BY-SA 4.0
2021-05-27T09:58:56.360Z
@Giovanni just for curiosity. As researchers and workers with arc soldering know. One can work hours with almost no annoyance and hours later get "sand in the eyes". This is anyway out of this discussion. Just to stress that eyes bulbs have not pain signalling cells until damage is done.
Alchimista
CC BY-SA 4.0
2021-05-30T23:43:50.803Z
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.)
uhoh
CC BY-SA 4.0
2021-05-26T13:40:26.033Z
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.
Giovanni
CC BY-SA 4.0
2021-05-26T13:46:13.717Z
@Giovanni I wonder the same. Do you have any sources which state maximum brightness for human eyes which is not harmful?
planetmaker
CC BY-SA 4.0
2021-05-26T13:47:45.120Z
@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!!!**
WarpPrime
CC BY-SA 4.0
2021-05-26T14:17:43.837Z
@fasterthanlight That's why I better won't try, especially with what I think to know stated above.
Giovanni
CC BY-SA 4.0
2021-05-26T14:19:45.500Z
@planetmaker I can't find the link about the sun from Saturn/Neptune, but that's also insightful: https://astronomy.stackexchange.com/questions/22231/at-what-distance-would-it-be-safe-for-humans-to-stare-at-the-sun
Giovanni
CC BY-SA 4.0
2021-05-26T13:17:25.747Z
2021-05-26T13:17:25.747Z
WarpPrime
<p>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 <em>un</em>dangerous 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.</p>

<luminosity><habitable-zone><brown-dwarf><visible-light>
Is it dangerous to look at an L-type brown dwarf from too close?
Giovanni
# Is it dangerous to look at an L-type brown dwarf from too close?

(Asked by: username_0 on 2021-05-26)

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 *un*dangerous 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.

**Tags:** luminosity, habitable-zone, brown-dwarf, visible-light

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## 1 answers

### Answer by username_1 on 2021-05-26. Score: 4 | Accepted answer

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,](https://en.wikipedia.org/wiki/Apparent_magnitude#List_of_apparent_magnitudes) 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](http://depts.washington.edu/naivpl/sites/default/files/hz_0.shtml#overlay-context=content/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.**

> **Comments:**
> **username_0**: 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.  
> **username_4**: @Giovanni I wonder the same. Do you have any sources which state maximum brightness for human eyes which is not harmful?  
> **username_1**: @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!!!**  
> **username_0**: @fasterthanlight That's why I better won't try, especially with what I think to know stated above.  
> **username_0**: @planetmaker I can't find the link about the sun from Saturn/Neptune, but that's also insightful: https://astronomy.stackexchange.com/questions/22231/at-what-distance-would-it-be-safe-for-humans-to-stare-at-the-sun  
> **username_2**: As a comment, and somehow in line with comments above. Eyes don't feel pain by light (not in time scale to trigger a response. If we turn from a bright source is by a kind of discomfort but not pain). So it would be better to speak of damage or whatever was meant in order to fix the threshold used for the calculations.  
> **username_0**: @Alchimista Right, my threshold would be the one where there is no threat of an eye damage whatsoever. Given fasterthanlight's answer, it is safe to say that all L- and M-type stars are dangerous to look at from too close, and maybe even T-dwarves but I can't believe they would be too. T-dwarves are very dim.  
> **username_2**: @Giovanni just for curiosity. As researchers and workers with arc soldering know. One can work hours with almost no annoyance and hours later get "sand in the eyes". This is anyway out of this discussion. Just to stress that eyes bulbs have not pain signalling cells until damage is done.  
> **username_3**: 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.)  

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