Transcript Brown_Dwarfs

Classification
• The difference between a small
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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.)
• 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
Formation
• Brown Dwarfs form in the same process that
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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.
 j  M /( 4 / 3rj )  3 /( 4M 2 )(3kT / G m)3
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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.
F  (qe / r 2 ) /( 40 )
2
• Where q is the charge of an electron and r is the
distance between atoms
Formation (cont.)
• For brown dwarfs larger than 10 Jupiter masses the
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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
• 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.)
• For a brown dwarf of mass greater than 13
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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 (cont.)
• A brown dwarf that is large enough to burn deuterium in
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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.
Properties
• 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:
kT ~
10Gme m p
3h 2
8/3
(  / A) 5 / 3 M 4 / 3
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.)
• One interesting aspect about brown dwarfs is that they
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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 (cont.)
• Typical observed atmospheric temperatures for brown
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dwarfs not undergoing deuterium fusion range from
2500k to 600k.
The luminosity of brown dwarfs at these temperatures
can be determined by:
L  4r T
2
4
• 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?
• Scientists have discovered that the visible matter in the
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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.
Resources
• http://casswww.ucsd.edu/public/tutorial/DM.htm
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http://www.daviddarling.info/encyclopedia/B/bro
wndwarf.html
http://www.scholarpedia.org/article/Brown_Dwa
rfs
http://en.wikipedia.org/wiki/Brown_dwarf
http://astro.berkeley.edu/~stars/bdwarfs/
Maoz, Dan. Astrophysics in a Nutshell. Princeton
University Press, 2007