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A brown dwarf is a body on the edge of being a very large planet or a very small star. Brown dwarfs range from 13 to about 90 Jupiter masses. The International Astronomical Union puts the line between large planets and small brown dwarfs at 13 Jupiter masses, because this is the mass threshold necessary for the fusion of deutrium.
Deutrium is an isotope of hydrogen that includes a neutron in the nucleus, rather than solely a proton as in common hydrogen, and is the easiest type of atom to fuse. As deutrium is quite rare compared to common hydrogen — 6 atoms in 10,000 for Jupiter, for instance — not enough is present for the formation of a true star, and thus brown dwarfs are often called "failed stars."
At around 0.075 solar masses, or 90 Jupiter masses, brown dwarfs become capable of fusing normal hydrogen - albeit at a much slower rate than main sequence stars like our Sun - making them red dwarfs, stars with about 1/10,000 solar luminosity. Brown dwarfs in general display very little or no luminosity, generating heat primarily through radioactive elements contained within them, as well as temperature due to compression. As brown dwarfs are very dim, it is difficult to observe them from a distance, and only a few hundred are known. The first brown dwarf was confirmed in 1995. An alternate name that was proposed for brown dwarfs was "substar."
An interesting property of brown dwarfs is that they all have almost the same radius - about that of Jupiter - with only 10% to 15% variance among them, even if their mass ranges up to 90 times that of Jupiter. At the low range of the mass scale, brown dwarf volume is determined by the Columb pressure, which also determines the volume of planets and other low-mass objects. At the higher range of the mass scale, the volume is determined by the electron degeneracy pressure - that is, atoms are pressed as closely together as possible without the electron shells collapsing.
The physics of these two arrangements is such that, as density increases, the radius is roughly maintained. When additional mass is added past the upper limits of brown dwarf masses, volume begins to increase again, producing large celestial bodies with radii closer to that of our Sun.