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Brown dwarfs are a class of "sub-stellar" objects that have mass that is above the range of mass of gas giant planets, but not enough for their cores to sustain nuclear fusion of hydrogen-1 and turn them into proper stars. That's why they are often described as "failed stars".
The upper limit of a brown dwarf mass is about 75 and 80 times the mass of Jupiter (for comparison, the Sun is considered to be a "yellow dwarf" and it's about 1000 times the mass of Jupiter). The lower limit that distinguishes them from gas giants is less clear, but it's considered to be around 13 times the mass of Jupiter. Anything above the lower limit fuses deuterium (hydrogen-2), and anything above about 65 times the mass of Jupiter fuses lithium.
 Planet X/Nibiru
Planet X/Nibiru proponents like to claim that brown dwarfs are "invisible" and can be detected only in infrared light, and this is why no amateur astronomers have been able to spot the "incoming" Planet X/Nibiru. (Infrared telescopes operated by professional astronomers have no problem detecting brown dwarfs, but conspiracy theorists tend to dismiss "official" astronomy as controlled by the TPTB.)
As with many conspiracist beliefs, this claim is based on a distortion of actual scientific facts about brown dwarfs' low visibility:
- brown dwarfs fuse deuterium, which heats them up and everything heated emits infra-red light (and if it's hot enough, visible light too: think of red-hot iron, or see Planck's law at Wikipedia);
- small brown dwarfs may be cold enough to emit mostly infrared light;
- thus, if we consider only light emission, a small, cool brown dwarf will be fainter in the visible spectrum and brighter in the infra-red spectrum.
- light sources become fainter with distance, so if a brown dwarf is far away enough, its visible light may be too faint to be detected by the human eye or a telescope, while its infrared light may be still above the threshold of detection.
That doesn't mean that brown dwarfs are "invisible" to non-infrared observation, though. A brown dwarf is at least the size of Jupiter or larger and will reflect light in the same way. If one was close to our Solar System (or in it, as some claim), it would look like Jupiter at the same distance due to reflected sunlight. A brown dwarf inside the orbit of Jupiter would be as bright as or brighter than Jupiter in the night sky. (And Jupiter is one of the brightest objects in the night sky after the Moon, Venus and the International Space Station.) And even if the brown dwarf was located in the outer fringes of the Solar System and invisible to the largest telescopes, as it approached the Sun it would be brighter and brighter to the point that sooner or later an astronomer would catch it (and there would be absolutely no way to hide it once it became bright enough to be visible with the naked eye).
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 Planetary Systems
In 2013, a planet about twice the mass of Jupiter was confirmed to be orbiting a brown dwarf. As with stars, they can potentially have planets, comets, asteroids, meteoroids, planetoids, and dwarf planets.
 Sub-brown dwarf
This is where the line between brown dwarf and rogue planet gets tricky. Sub-brown dwarves are so small that they can't even fuse deuterium. The difference is that sub-brown dwarves are created from the gravitational collapse of gaseous nebulae, as brown dwarves and stars are. Meanwhile, rogue planets used to be part of a planetary system, but were kicked out.
 In a nutshell
- Brown dwarf on Wikipedia, if you are interested in more details
- Crash Course Astronomy's video about brown dwarfs, if you can't be arsed to read the article