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The difference between a small star and a brown dwarf is fairly clear. If hydrogen fusion is taking place then the object is a dwarf star. If not, the object is a brown dwarf.

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The difference between a small star and a brown dwarf is fairly clear. If hydrogen fusion is taking place then the object is a dwarf star. If not, the object is a brown dwarf.

However the line between a small brown dwarf and a large planet is far more vague. There is no exact cut-off between the two, and there is much debate between astronomers over what qualifies as a brown dwarf instead of a planet.

Many astronomers have adopted 13 Jupiter masses as the separation between planets and brown dwarfs. As this is the minimum mass required for deuterium fusion to take place.

classification cont
Classification (cont.)
  • When observing possible brown dwarf candidates, astronomers can usually distinguish between large mass brown dwarfs from small mass stars by the lithium test. Stars deplete their lithium supply rapidly when a lithium-7 atom and a proton collide to form 2 helium atoms. In brown dwarfs the temperature is not high enough for this process to take place. So lithium lines in an unknown objects observed spectrum is a strong indicator that it is indeed a brown dwarf
  • Brown Dwarfs form in the same process that stars form.
  • Molecular clouds with density greater than the Jeans Density will begin to collapse under their own gravity in the same way we learned how stars are formed in class. As the cloud contracts, its gravitational energy is converted to thermal energy, and thus the cloud begins to heat up.
formation cont
Formation (cont.)
  • The molecular cloud continues to collapse until a counter force can halt it. For normal stars this force is the radiation pressure resultant from nuclear fusion.
  • Brown Dwarfs, however, never get hot enough for stable hydrogen fusion.
  • For brown dwarfs with considerably low mass (Mass<10 Jupiter Masses) the gravitational collapse with be halted by the coulomb force between atoms, the same force governing planets and regular matter. As the atoms get closer together, the electrons begin to repel one another due to their like charges.
  • Where q is the charge of an electron and r is the distance between atoms
formation cont1
Formation (cont.)
  • For brown dwarfs larger than 10 Jupiter masses the coulomb force between atoms is not enough to stop the gravitational collapse. The brown dwarf continues to collapse until its matter begins to partially go degenerate. When this happens the collapse will stop due to the electron degenerate pressure caused by the Pauli exclusion principle.
  • The Pauli exclusion principle states that no two electrons can occupy the same quantum state simultaneously.
  • As the electrons get closer and closer, they must occupy higher and higher energy states as to not violate this principle. As a result, a resisting pressure is produced to halt any further collapse. This is the same pressure that holds up white dwarf stars.
life cycle
Life Cycle
  • After the formation of a brown dwarf, its life will go one of two similar ways.
  • If it is of lower mass (M<13 Jupiter Masses), the brown dwarf will never undergo fusion. It will relatively quickly radiate its thermal energy away over the course of tens of millions of years. Eventually the brown dwarf will cool below an effective temp of 2500k and clouds of silicate crystals will begin to form.
  • As it cools further, below 600k, ice clouds of water and ammonia

form. The brown dwarf becomes very similar

to Jupiter in both appearance and luminosity.

By this point, brown dwarfs are so faint they

become nearly undetectable by visual means,

depending on their distance from earth.

life cycle cont
Life Cycle (cont.)
  • For a brown dwarf of mass greater than 13 Jupiter masses, its life with start out very differently. This brown dwarf will begin deuterium burning.
  • Deuterium is a stable isotope of hydrogen, consisting of one proton and one neutron. It exists naturally, occurring around 6 deuterium atoms for every 10,000 normal hydrogen atoms.
  • The required core temperature for deuterium fusion to take place is about 2 x 10^6 k. Where as the core temp for hydrogen fusion is about 10^7 k.
  • So while the brown dwarf can fuse deuterium, it cannot fuse hydrogen.
life cycle cont1
Life Cycle (cont.)
  • A brown dwarf that is large enough to burn deuterium in its core will do so for about 10 million years.
  • During this period the brown dwarf will have an effective temperature of around 3600 k and a luminosity of ~ 10^31 erg/s.
  • While burning deuterium, they are bright enough that they may be mistaken for a low mass star.
  • After the high mass brown dwarf depletes its deuterium fuel, it will undergo the same fate as its lower mass sibling, quickly cooling down and becoming extremely faint.
  • The mass of brown dwarfs range between 0.07 solar masses (~75 Juipter masses) down to 13 Jupiter masses or even lower. While the lower mass limit is up for debate, the upper mass limit is fairly well established.
  • By relating the thermal energy with gravitational energy, and knowing the onset of degeneracy pressure we get:

Knowing that the temperature required for hydrogen fusion is 10^7k we can solve for M where (Z/A)= 1 for hydrogen. Which results in a value of about 0.08 solar masses. This is the minimum mass required for a normal star to form.

properties cont
Properties (cont.)
  • One interesting aspect about brown dwarfs is that they all have almost the same radius regardless of mass.
  • All observed brown dwarfs have a radius that of Jupiter’s radius to within 10%-15%.
  • Conditions in the core of a brown dwarf are dependent on its mass.
  • Core temperatures can range from 10^4k to 6x10^6k.
  • Densities in the core vary from 10g/cubic cm to 10^3g/cubic cm.
  • Pressures in core can reach up to 10^16Pascal.
properties cont1
Properties (cont.)
  • Typical observed atmospheric temperatures for brown dwarfs not undergoing deuterium fusion range from 2500k to 600k.
  • The luminosity of brown dwarfs at these temperatures can be determined by:
  • Values of the luminosity for a brown dwarf with a radius of Jupiter range from ~10^30 erg/s to ~10^27erg/s. That’s approximately 1/10,000 to 1/1,000,000 of the sun’s luminosity respectively.
dark matter
Dark Matter?
  • Scientists have discovered that the visible matter in the galaxy is only a fraction of the galaxy’s total matter. This missing mass is known as dark matter.
  • One current hypothesis suggests that a large portion of this missing matter could be in the form of brown dwarfs.
  • Recent studies have found numerous brown dwarfs. However, assuming brown dwarfs occur at the same rate throughout the galaxy, they do not occur in large enough numbers to account for the bulk of the galaxy’s missing mass.
  • Maoz, Dan. Astrophysics in a Nutshell. PrincetonUniversity Press, 2007