ClassificationClassification• The difference between a The difference between a

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

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

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

Classification (cont.)Classification (cont.)

• When observing possible brown dwarf candidates, When observing possible brown dwarf candidates, astronomers can usually distinguish between large mass astronomers can usually distinguish between large mass brown dwarfs from small mass stars by the lithium test. brown dwarfs from small mass stars by the lithium test. Stars deplete their lithium supply rapidly when a lithium-7 Stars deplete their lithium supply rapidly when a lithium-7 atom and a proton collide to form 2 helium atoms. In brown atom and a proton collide to form 2 helium atoms. In brown dwarfs the temperature is not high enough for this process to dwarfs the temperature is not high enough for this process to take place. So lithium lines in an unknown objects observed take place. So lithium lines in an unknown objects observed spectrum is a strong indicator that it is indeed a brown dwarfspectrum is a strong indicator that it is indeed a brown dwarf

FormationFormation

• Brown Dwarfs form in the same process that Brown Dwarfs form in the same process that stars form. stars form.

• Molecular clouds with density greater than the Molecular clouds with density greater than the Jeans Density will begin to collapse under Jeans Density will begin to collapse under their own gravity in the same way we learned their own gravity in the same way we learned how stars are formed in class. As the cloud how stars are formed in class. As the cloud contracts, its gravitational energy is contracts, its gravitational energy is converted to thermal energy, and thus the converted to thermal energy, and thus the cloud begins to heat up.cloud begins to heat up.

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Formation (cont.)Formation (cont.)• The molecular cloud continues to collapse until a counter force The molecular cloud continues to collapse until a counter force

can halt it. For normal stars this force is the radiation pressure can halt it. For normal stars this force is the radiation pressure resultant from nuclear fusion. resultant from nuclear fusion.

• Brown Dwarfs, however, never get hot enough for stable Brown Dwarfs, however, never get hot enough for stable hydrogen fusion. hydrogen fusion.

• For brown dwarfs with considerably low mass (Mass<10 Jupiter For brown dwarfs with considerably low mass (Mass<10 Jupiter Masses) the gravitational collapse with be halted by the coulomb Masses) the gravitational collapse with be halted by the coulomb force between atoms, the same force governing planets and force between atoms, the same force governing planets and regular matter. As the atoms get closer together, the electrons regular matter. As the atoms get closer together, the electrons begin to repel one another due to their like charges. begin to repel one another due to their like charges.

• Where q is the charge of an electron and r is the distance Where q is the charge of an electron and r is the distance between atomsbetween atoms

)4/()/( 022 rqF e

Formation (cont.)Formation (cont.)

• For brown dwarfs larger than 10 Jupiter masses the For brown dwarfs larger than 10 Jupiter masses the coulomb force between atoms is not enough to stop coulomb force between atoms is not enough to stop the gravitational collapse. The brown dwarf the gravitational collapse. The brown dwarf continues to collapse until its matter begins to continues to collapse until its matter begins to partially go degenerate. When this happens the partially go degenerate. When this happens the collapse will stop due to the electron degenerate collapse will stop due to the electron degenerate pressure caused by the Pauli exclusion principle. pressure caused by the Pauli exclusion principle.

• The Pauli exclusion principle states that no two The Pauli exclusion principle states that no two electrons can occupy the same quantum state electrons can occupy the same quantum state simultaneously.simultaneously.

• As the electrons get closer and closer, they must As the electrons get closer and closer, they must occupy higher and higher energy states as to not occupy higher and higher energy states as to not violate this principle. As a result, a resisting pressure violate this principle. As a result, a resisting pressure is produced to halt any further collapse. This is the is produced to halt any further collapse. This is the same pressure that holds up white dwarf stars.same pressure that holds up white dwarf stars.

Life CycleLife Cycle

• After the formation of a brown dwarf, its life will go one of After the formation of a brown dwarf, its life will go one of two similar ways. two similar ways.

• If it is of lower mass (M<13 Jupiter Masses), the brown If it is of lower mass (M<13 Jupiter Masses), the brown dwarf will never undergo fusion. It will relatively quickly dwarf will never undergo fusion. It will relatively quickly radiate its thermal energy away over the course of tens of radiate its thermal energy away over the course of tens of millions of years. Eventually the brown dwarf will cool millions of years. Eventually the brown dwarf will cool below an effective temp of 2500k and clouds of silicate below an effective temp of 2500k and clouds of silicate crystals will begin to form. crystals will begin to form.

• As it cools further, below 600k, ice clouds of water and As it cools further, below 600k, ice clouds of water and ammoniaammonia

form. The brown dwarf becomes very similar form. The brown dwarf becomes very similar to Jupiter in both appearance and luminosity. to Jupiter in both appearance and luminosity. By this point, brown dwarfs are so faint they By this point, brown dwarfs are so faint they

become nearly undetectable by visual means, become nearly undetectable by visual means, depending on their distance from earth.depending on their distance from earth.

Life Cycle (cont.)Life Cycle (cont.)• For a brown dwarf of mass greater than 13 Jupiter For a brown dwarf of mass greater than 13 Jupiter

masses, its life with start out very differently. masses, its life with start out very differently. This brown dwarf will begin deuterium burning. This brown dwarf will begin deuterium burning.

• Deuterium is a stable isotope of hydrogen, Deuterium is a stable isotope of hydrogen, consisting of one proton and one neutron. It consisting of one proton and one neutron. It exists naturally, occurring around 6 deuterium exists naturally, occurring around 6 deuterium atoms for every 10,000 normal hydrogen atoms. atoms for every 10,000 normal hydrogen atoms.

• The required core temperature for deuterium The required core temperature for deuterium fusion to take place is about 2 x 10^6 k. Where fusion to take place is about 2 x 10^6 k. Where as the core temp for hydrogen fusion is about as the core temp for hydrogen fusion is about 10^7 k.10^7 k.

• So while the brown dwarf can fuse deuterium, it So while the brown dwarf can fuse deuterium, it cannot fuse hydrogen.cannot fuse hydrogen.

Life Cycle (cont.)Life Cycle (cont.)

• A brown dwarf that is large enough to burn A brown dwarf that is large enough to burn deuterium in its core will do so for about 10 deuterium in its core will do so for about 10 million years.million years.

• During this period the brown dwarf will have an During this period the brown dwarf will have an effective temperature of around 3600 k and a effective temperature of around 3600 k and a luminosity of ~ 10^31 erg/s.luminosity of ~ 10^31 erg/s.

• While burning deuterium, they are bright enough While burning deuterium, they are bright enough that they may be mistaken for a low mass star.that they may be mistaken for a low mass star.

• After the high mass brown dwarf depletes its After the high mass brown dwarf depletes its deuterium fuel, it will undergo the same fate as deuterium fuel, it will undergo the same fate as its lower mass sibling, quickly cooling down and its lower mass sibling, quickly cooling down and becoming extremely faint.becoming extremely faint.

PropertiesProperties

• The mass of brown dwarfs range between 0.07 solar The mass of brown dwarfs range between 0.07 solar masses (~75 Juipter masses) down to 13 Jupiter masses or masses (~75 Juipter masses) down to 13 Jupiter masses or even lower. While the lower mass limit is up for debate, the even lower. While the lower mass limit is up for debate, the upper mass limit is fairly well established. upper mass limit is fairly well established.

• By relating the thermal energy with gravitational energy, By relating the thermal energy with gravitational energy, and knowing the onset of degeneracy pressure we get: and knowing the onset of degeneracy pressure we get:

Knowing that the temperature required for hydrogen fusion Knowing that the temperature required for hydrogen fusion

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

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Properties (cont.)Properties (cont.)

• One interesting aspect about brown dwarfs is that One interesting aspect about brown dwarfs is that they all have almost the same radius regardless of they all have almost the same radius regardless of mass.mass.

• All observed brown dwarfs have a radius that of All observed brown dwarfs have a radius that of Jupiter’s radius to within 10%-15%. Jupiter’s radius to within 10%-15%.

• Conditions in the core of a brown dwarf are Conditions in the core of a brown dwarf are dependent on its mass.dependent on its mass.

• Core temperatures can range from 10^4k to Core temperatures can range from 10^4k to 6x10^6k.6x10^6k.

• Densities in the core vary from 10g/cubic cm to Densities in the core vary from 10g/cubic cm to 10^3g/cubic cm.10^3g/cubic cm.

• Pressures in core can reach up to 10^16Pascal.Pressures in core can reach up to 10^16Pascal.

Properties (cont.)Properties (cont.)

• Typical observed atmospheric temperatures for Typical observed atmospheric temperatures for brown dwarfs not undergoing deuterium fusion brown dwarfs not undergoing deuterium fusion range from 2500k to 600k. range from 2500k to 600k.

• The luminosity of brown dwarfs at these The luminosity of brown dwarfs at these temperatures can be determined by:temperatures can be determined by:

• Values of the luminosity for a brown dwarf with a Values of the luminosity for a brown dwarf with a radius of Jupiter range from ~10^30 erg/s to radius of Jupiter range from ~10^30 erg/s to ~10^27erg/s. That’s approximately 1/10,000 to ~10^27erg/s. That’s approximately 1/10,000 to 1/1,000,000 of the sun’s luminosity respectively.1/1,000,000 of the sun’s luminosity respectively.

424 TrL

Dark Matter?Dark Matter?

• Scientists have discovered that the visible matter Scientists have discovered that the visible matter in the galaxy is only a fraction of the galaxy’s in the galaxy is only a fraction of the galaxy’s total matter. This missing mass is known as dark total matter. This missing mass is known as dark matter.matter.

• One current hypothesis suggests that a large One current hypothesis suggests that a large portion of this missing matter could be in the portion of this missing matter could be in the form of brown dwarfs. form of brown dwarfs.

• Recent studies have found numerous brown Recent studies have found numerous brown dwarfs. However, assuming brown dwarfs occur dwarfs. However, assuming brown dwarfs occur at the same rate throughout the galaxy, they do at the same rate throughout the galaxy, they do not occur in large enough numbers to account for not occur in large enough numbers to account for the bulk of the galaxy’s missing mass. the bulk of the galaxy’s missing mass.

ResourcesResources

• http://casswww.ucsd.edu/public/tutorial/Dhttp://casswww.ucsd.edu/public/tutorial/DM.htmlM.html

• http://www.daviddarling.info/encyclopedia/http://www.daviddarling.info/encyclopedia/B/browndwarf.htmlB/browndwarf.html

• http://www.scholarpedia.org/article/Brownhttp://www.scholarpedia.org/article/Brown_Dwarfs_Dwarfs

• http://en.wikipedia.org/wiki/Brown_dwarfhttp://en.wikipedia.org/wiki/Brown_dwarf• http://astro.berkeley.edu/~stars/bdwarfs/http://astro.berkeley.edu/~stars/bdwarfs/• Maoz, Dan. Maoz, Dan. Astrophysics in a Nutshell. Astrophysics in a Nutshell.

PrincetonPrinceton University Press, 2007University Press, 2007