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Degenerate Objects

Brown Dwarfs

Hydrogen provides the first source of thermonuclear power to stars.  The most massive stars, those over 100 times the Sun's mass, blast through this fuel in 1 million years or less.  The Sun, with its dramatically lower rate of power generation, takes about 9 billion years to burn through its smaller reservoir of hydrogen.  This trend of slower power generation by smaller stars continues down to the common 1/4 solar mass stars, which are expected to burn their fuel in about 100 billion years.  Below 0.072 solar masses, the thermonuclear fusion of hydrogen becomes impossible.  The objects immediately below this critical mass are called brown dwarfs.

More precisely, a brown dwarf is a massive ball of hydrogen, helium, and trace amounts of metals that is not massive enough to burn hydrogen, but is massive enough to burn deuterium.  Brown dwarfs are expected to have masses ranging from just below 0.072 solar masses (78 times Jupiter's mass), the mass below which hydrogen fusion becomes impossible, down to 0.012 solar masses (13 time Jupiter's mass), the mass below which deuterium fusion becomes impossible.  Anything smaller than 0.012 solar masses is a giant gaseous planet.  From its spectrum, the brown dwarf appears to be simply an exceedingly cool star, but a brown-dwarf's inability to burn hydrogen betrays a fundamental physical difference between it and a star: unlike a star, a brown dwarf does not need thermonuclear fusion to hold itself up.

The absence of thermonuclear fusion in a brown dwarf may seen odd.  As a body of hydrogen radiates away energy, it shrinks, causing its core density and temperature to rise, so that the thermal pressure exerted by the electrons, atomic nuclei, and photons within the star counteract the force of gravity.  This rise in temperature is inversely proportional to the radius of the body, because the core temperature is equal to the gravitational potential energy of the atoms in the gas.  Eventually the core density and temperature of the body is high enough to initiate the thermonuclear fusion of hydrogen.  This is what happens with a protostar: it shrinks until its interior temperature is in the range of 5 to 20 million degrees Kelvin, initiating thermonuclear fusion, and the protostar becomes a main-sequence star

But this does not happen to a brown dwarf, and the reason is that a new source of pressure—the degeneracy pressure on electrons—comes into play.  This is the pressure that hold up the degenerate dwarfs and the planets Saturn and Jupiter (Degeneracy pressure is described in more detail in the pages just cited).  It is a consequence of the Pauli exclusion principle of quantum mechanics, and at sufficiently-high densities, it becomes the dominant source of pressure.  This pressure halts the shrinkage of a brown dwarf before its core temperature reaches the thermonuclear range.

When the electrons in a gas become degenerate, they occupy all of the lowest energy states in the gas.  The pressure of a gas in this state becomes independent of the temperature, depending instead only on the density of the electrons.  The pressure is proportional to the density to the 5/3 power.  On the other hand, the kinetic pressure of the electrons in an object with an internal temperature of 5 million °K, which characterizes the temperature at the core of the M dwarf stars, is directly proportional to its density.  This means that as the density at which an object has a core temperature of 5 million °K increases, at some point the degeneracy pressure exceeds the kinetic pressure.  Such an object is stabilized by degeneracy pressure before its internal temperature rises to 5 million °K.  Because the density increases as the mass decreases for an object of a given internal temperature, it is the low-mass objects that are stabilized by degeneracy pressure before they reach a high enough temperature to permit thermonuclear fusion.  This is also why there is a range of masses over which deuterium can burn, but hydrogen cannot burn: deuterium burns at a much lower temperature than hydrogen.  But even for deuterium, there is a mass below which degeneracy pressure stabilizes the object before the core temperature reaches the burning point; the objects below this critical mass are the giant gaseous planets.

Brown dwarfs were long expected by theorists, but they remained unseen until the late 1980s, when one was found orbiting a degenerate dwarf companion.  Through the 1990s, many more brown dwarfs were discovered, and by the end of the 1990s, with the inauguration of experiments to survey the sky in the infrared, particularly of the 2 Micron All Sky Survey (2MASS), brown dwarfs were found by the hundreds, so that by 2005, nearly 500 brown dwarfs were known.

The brown dwarfs distinguish themselves by their spectra.  These spectra are predominately infrared spectra that have numerous strong absorption bands that are caused by the absorption of light by molecules.  The molecules that cause the lines in brown dwarf spectra are different from those causing the lines in the spectra of M dwarf stars.  In particular, the molecules present in the atmospheres of brown dwarfs require a cooler environment than is provided by an M dwarf star.  Lines from titanium oxide (TiO) and vanadium oxide (VO), which are hallmarks of M dwarf spectra, are generally absent or very weak in the brown dwarf spectra.  On the other hand, the lines of neutral sodium and potassium are very strong in brown dwarfs, while they are absent in the M dwarf stars.  In many brown dwarfs, the sodium and potassium lines are so strong and broad that the spectra deviate dramatically way from a thermal black-body spectrum.  Most brown dwarfs show the absorption lines of water.  To describe these spectral patterns, astronomers added two new spectral types—L and T—that continue the categorization of spectra beyond M.[1]  In this scheme, the progression continues from the stellar types as M, L, and T.  As with spectral types of stars, the progression follow a decline in effective temperature (the black body temperature that would produce the radiation flux leaving the brown dwarf's photosphere).

The photospheric temperatures of the observed brown dwarfs range from 2,500°K down to 700°K.  At the low-end of this range, below 2,000°K, chemicals precipitate out of the atmosphere as flakes of dust to form clouds.  These clouds alter the cooling of brown dwarfs by trapping radiation and altering the convective transport of energy.  They also alter a brown dwarf's spectrum, because many of the elements responsible for lines in a brown dwarf's spectrum at high temperatures precipitate out of the atmosphere below 2,000°K, so that their lines disappear from the spectra below 2,000°K.

Much like clouds of snowflakes in the Earth's atmosphere, the clouds of the brown dwarfs are made up of flakes in equilibrium with their surroundings.  The clouds exist because the rate at which flakes form and grown is in equilibrium with the rate at which they evaporate away.  As with snow flakes in Earth's atmosphere, the flakes in the brown dwarf clouds can rain out, falling deeper into the atmosphere, where they are vaporize and carried by convective currents back to higher altitudes.  But the flakes that make up the clouds in the atmospheres of brown dwarfs are made up of chemicals that have a high condensation temperature: zirconium oxide, corundum (aluminum oxide), iron, vanadium oxide, and enstatite (a translucent crystalline mineral).  These are familiar minerals found within the Earth.  One of these minerals, corundum, can be found in jewelry stores as large crystals contaminated by traces of other elements; they are called sapphires and rubies.  So, when it rains in a brown dwarf, it rains precious gems.

[1]Kirkpatrick, J. Davey.  “New Spectral Types L and T.”  In Annual Reviews of Astronomy and Astrophysics, edited by R. Blandford, G. Burbidge, J. Kormendy, and E. Van Dishoeck, vol. 43.   Palo Alto, California: Annual Reviews, 2005: 195–245.

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