A brown dwarf is a self-gravitating body that does not sustain ordinary core hydrogen burning. Contraction initially heats it, but growing electron degeneracy pressure limits further compression before long-lived hydrogen fusion can establish the thermal balance of a main-sequence star. It subsequently cools and becomes fainter.
Some brown dwarfs temporarily burn deuterium; the deuterium-burning mass is a composition-dependent classification scale rather than a unique formation test. Their radii can be close to Jupiter's across a broad mass range. Consequently, exoplanet transit photometry alone cannot distinguish a giant planet from a brown dwarf. The transit and Doppler spectroscopy measurements of CoRoT-3b illustrate why independent mass information is decisive for characterizing such compact companions.
CoRoT-3b is a short-period transiting companion with roughly Jupiter masses but a radius close to Jupiter's. Its discovery combined a sequence of exoplanet transits with ground-based Doppler spectroscopy and additional checks. This measured both a large mass and a compact radius, placing it above the ordinary giant-planet population in mean mass density.[ref]
Transiting exoplanets from the CoRoT space mission VI by Magali Deleuil and others. Abstract: 34 transits, combined photometric and spectroscopic analysis, mass and radius
The object illustrates why a measured radius alone does not distinguish a giant planet from a brown dwarf: electron degeneracy pressure can give very different masses similar radii. Its mass also does not uniquely reveal its formation mechanism. The discovery paper explicitly left the formation-based interpretation open between a low-mass brown dwarf and an unusually massive planetary companion.
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.