A brown dwarf is a self-gravitating object too light to sustain ordinary hydrogen fusion. Electron degeneracy limits its contraction, leaving radii near that of Jupiter across a broad mass range.
The conventional deuterium-burning boundary is near Jupiter masses, with composition-dependent variation. It is a useful classification scale rather than a sharp formation-based distinction between planets and brown dwarfs.
The hydrogen-burning minimum mass is the lowest mass that can sustain core hydrogen fusion, about -- solar masses for near-solar composition. Less massive brown dwarfs cool continually after any deuterium burning ends.
A fixed stellar homology profile with giveswhere . As a function of this is a concave quadratic; its maximum is , at . At the maximum, the central electron degeneracy pressure and thermal pressure are equal. If this temperature is insufficient for sustained hydrogen burning, the object becomes a brown dwarf. Only the positive-temperature segment represents a physical sequence.
For a homologous stellar polytrope of index , take and zero surface pressure. The stellar virial theorem, with , givesThe normalized density profile fixes independently of mass and radius at fixed composition. Writing shows that its maximum is , at . Below this radius contraction increases the fraction of support provided by electron degeneracy pressure and lowers the thermal temperature. A fixed normalized profile also fixes the ratio of central to mass-averaged temperature, giving a hydrogen-burning minimum mass.
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A brown dwarf is a type of celestial object that falls between the largest planets and the smallest stars in terms of mass. Specifically, brown dwarfs have masses ranging from about 13 times the mass of Jupiter (approximately 0.012 times the mass of the Sun) to around 80 times the mass of Jupiter (about 0.07 times the mass of the Sun). They are not massive enough to sustain hydrogen fusion in their cores, which is the defining characteristic of true stars.