Brown dwarfs are a celestial object that is too large to be a planet, but too small to be a true star. They are formed in the same way stars form in the collapse of a stellar nebula, but unlike a star, they do not have enough mass to fuse hydrogen into helium in the core.
To have enough energy to perform the proton-proton chain, the core of the stellar material must be at least 15 million Kelvin. Brown dwarfs just do not have enough mass to compress their cores down to reach that temperature. However, they may have enough mass to fuse deuterium (an isotope of hydrogen with a neutron as well as a proton in its nucleus) or even lithium. However, these reactions are not sustainable and therefore do not continue the process of fusion.
Brown dwarfs are also completely convective (i.e. the brown dwarf material is nearly homogeneous). If you took a sample of brown dwarf from its surface and then from its interior, the samples would be identical in composition. Our Sun, however, is layered. The outer layers do not mix with the inner layers. There is well-defined core, the radiation zone, and the convective zone. (See my post of the layers of the Sun).
Because brown dwarfs do not fuse any material in its center, brown dwarfs do not give off radiation (or at least, not a significant amount). Therefore, they are "dark". In the Hertzsprung-Russell Diagram, they occupy the farthest lower right region of the chart.
Since brown dwarfs exist, and are probably abundant, they are a valid and most probably candidate to explain dark matter.
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