quality:correction
Theory

The standard mechanism for star birth is through the gravitational collapse of a cold interstellar cloud of gas and dust. As the cloud contracts, it heats due to the Kelvin–Helmholtz mechanism. Early in the process the contracting gas quickly radiates away much of the energy, allowing the collapse to continue. Eventually, the central region becomes sufficiently dense to trap radiation. Consequently, the central temperature and density of the collapsed cloud increase dramatically with time, slowing the contraction, until the conditions are hot and dense enough for thermonuclear reactions to occur in the core of the protostar. For a typical star, gas and radiation pressure generated by the thermonuclear fusion reactions within its core will support it against any further gravitational contraction. Hydrostatic equilibrium is reached, and the star will spend most of its lifetime fusing hydrogen into helium as a main-sequence star.

If, however, the initial mass of the protostar is less than about 0.08 M, normal hydrogen thermonuclear fusion reactions will not ignite in the core. Gravitational contraction does not heat the small protostar very effectively, and before the temperature in the core can increase enough to trigger fusion, the density reaches the point where electrons become closely packed enough to create quantum electron degeneracy pressure. According to the brown dwarf interior models, typical conditions in the core for density, temperature and pressure are expected to be the following:

This means that the protostar is not massive or dense enough ever to reach the conditions needed to sustain hydrogen fusion. The infalling matter is prevented, by electron degeneracy pressure, from reaching the densities and pressures needed.

Further gravitational contraction is prevented and the result is a brown dwarf that simply cools off by radiating away its internal thermal energy. Note that, in principle, it is possible for a brown dwarf to slowly accrete mass above the hydrogen burning limit without initiating hydrogen fusion. This could happen via mass transfer in a binary brown dwarf system.