Download Nuclear fusion in stars

Nuclear fusion in stars
Collapse of primordial density fluctuations
into galaxies and stars, nucleosynthesis in stars
The origin of structure in the Universe
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Until the time of formation of
protogalaxies, the Universe
contained only the cooling H
and He and degraded radiation
The only high-density objects
present at that time could be
black holes (and strings) left
over from the original fireball
The presence of structure in
the 3K background radiation
suggests that slight density
fluctuations in the expanding H
and He gas could develop into
galaxies and first stars
There would be no further
evolution of matter without this
environment
!
Basics of cloud collapse
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Gas cloud collapse occurs, when its gravitational potential energy is
greater than the internal thermal energy. Jeans criterion:
GmM 3mkT
=
rc
2
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4 3
M = "rc #
3
rc > c(T / ")1/ 2
A molecule in a cloud larger than rc would have vthermal < vesc. A cloud
capable of loosing energy by radiation can
! collapse
Collapse remains
!isothermal until the density and opacity become very
high
As collapse continues, more and more energy is stored in vibrational
(3000K) and rotational (300K) states of H. Rotationally excited H will
reradiate its energy in far IR as long as opacity is not too high
A cloud has to become very dense to start retaining its collapse energy
Cloud fragmentation
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If a collapsing cloud has mass M=const and radius R, then for a
smaller cloud of mass m and radius r, m/M=(r/R)3, and:
2Gm 2GM # r &
r"
=
% (
3kT
3kT $ R '
!
3
# 3kT &1/ 2 3 / 2
r "%
( R
$ 2GM '
• If R increases by a factor of 4, r does the same by factor of 8. This means
that a collapsing cloud can fragment
! into smaller collapsing clouds.
• This process ends with star formation or when rotational speed becomes
too high (conservation of angular momentum)
• Hierarchical collapse can produce many levels of structure from clusters
through galaxies down to stellar clusters and stars
• First generation stars are believed to have formed out of small, high ρ,
low angular momentum clouds
The scales of collapse
size
~ 1 Gpc
~ 10-30
g cm-3
~ 1 Mpc
~ 1 mpc
~ 1 µpc
~ 1 kpc
~ 1 pc
density
~1 npc
~1 g cm-3
Nucleosynthesis in stars
Elements production in stars
The star formation process - I
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This process may
take some six
million years!
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In an interstellar cloud,
gravity acts to collapse it,
while thermal motions due to
heat try to take it apart
Large molecular clouds are
generally stable, but they
can be broken into smaller,
denser, and unstable
fragments. Instability is
triggered by shock waves
Such waves may be caused
by supernova explosions,
birth events of very hot stars,
and density waves due to
the spiral structure of our
Galaxy
Stellar birth and the H-R diagram
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As part of a cloud begins to collapse
under its own gravity, it becomes
denser and hotter
The cloud heats up, because its
contraction converts gravitational
energy into heat
Fragments of the original cloud
produce an association of 10-1000
stars that drifts apart over a few
million years
As a star’s luminosity and
temperature change, the star moves
in the H-R diagram along an
evolutionary track
More massive protostars collapse
and become stars faster than the
less massive ones
When collapse is halted by the
onset of nuclear reactions in the
core, a newborn star reaches the
main sequence
Energy production in protostars
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Newly formed stars appear systematically too red for their luminosity
Intrinsic reasons for their over-luminosity: (i) large radii (still shrinking), (ii) extra
energy source form gravitational potential energy-to-heat conversion, and (iii)
deuterium burning:
2
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H+1H" 3He + #
Deuterium burning is the energy source for brown dwarfs (0.013-0.08 Msun
objects)
A cloud collapsing from infinity to radius R radiates the amount of its
gravitational energy:
!
M "
E=
##
0
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0
GM
GM 2
dRdM = $
R2
R
For the Sun, this gives 4 x 1048 ergs, compared to 4 x 1033 ergs on MS
This difference would double the Sun’s L for 3 x 107 years, which is enough to
observe many!such stars in clusters
For a supergiant (say, 100 Msun), the period of over-brightening would only be
~150 years - too brief to be observed at any given time
T Tauri stars and Herbig-Haro objects
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T Tauri stars appear to be protostars in
the process of clearing away the
surrounding cocoon of gas and dust
Observations show strong outflows of
gas in the form of expanding shells and
jets (10-7 Msun in 106 years)
Infrared observations reveal the
presence of the remaining dust,
sometimes in the form of a disk
surrounding the protostar
Herbig-Haro objects are often found
near T Tauri stars
They are small nebulae formed at
points, where jets emanating from
protostars collide with interstellar clouds,
shock-heat them, and make them glow
Often, young stars generate two jets
emerging in the opposite directions.
They are called bipolar flows and appear
to be associated with rotating disks of
circumstellar matter around these stars
The p-p cycle
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Stars found in elliptical galaxies
and globular cluster (Population II
stars) are metal-poor compared to
Sun-like stars in disks of spiral
galaxies (Population I)
Pop II stars are very old, originally
made of the primordial material (H,
He), not enriched in metals
(heavier than He)
The basic nuclear fusion reaction
(proton-proton cycle):
4 p" 4 He + 2e + + 2# e
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p-p cycle energy rate production:
" = 0.28 #X H 2 (T6 /13) 4.1
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Central T~107K is needed to
maintain ε ~ 1 erg g-1 s-1
Hydrogen fusion - II
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Another way to fuse helium
from hydrogen is to use
carbon in series of reactions
called the CNO cycle
Since the Coulomb barrier
for carbon is six times that of
hydrogen, much higher
temperatures are needed for
this reaction to work.
The CNO cycle is important
in stars with masses larger
than 1.1 M (core
temperatures higher than 16
million K)
At even higher temperatures,
carbon fusion leads to
synthesis of numerous
heavy atoms
Post-main sequence evolution of a solarmass star
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Accumulation of a pure He core
takes ~1010 years for a solar-mass
star (its L increases 10-20% over
that period)
When T~108K and the star’s mass >
0.8 Msun, He ignition occurs. The star
becomes a giant or supergiant and
He synthesizes C in the “triplealpha” reaction:
4
He+ 4He" 8Be
8
Be+ 4 He"12C + #
Stars with masses 0.8-8 Msun never
go beyond the He burning and
eventually become white dwarfs
after shedding much of their mass
Pop II stars in clusters are 10-14
billion years old
Nuclear fusion in massive stars
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Massive star do not end their lives
as white dwarfs. They evolve much
faster than sun-like stars and
destroy themselves in supernova
explosions
Massive stars fuse hydrogen, then
helium and develop carbon-oxygen
cores. At ~1 billion K, they are able
to ignite carbon, then oxygen, neon
and magnesium fuse to make
silicon, which finally fuses to make
iron
Because more and more protons
are used up to make heavier and
heavier atoms and progressively
less energy is released, fusion
proceeds and a higher and higher
rate
A 25M star needs 7 million years
to fuse its hydrogen and just one
day to fuse silicon
Carbon burning in the core
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Core temperatures of stars with initial masses > 8Msun exceed
109K, at which point carbon begins to fuse:
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C+12C"20 Ne+ 4He
12
C+12C"23 Na + p
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C+12C"23 Mg + n
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O+16O"28 Si+ 4He
Hydrogen fuses immediately through reactions like:
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He+12C"16 O + #
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C + p"13 N + #
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N"13 C + e + + $
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C+ 4He"16 O + n
Succesive reactions leading up to 56Fe produce energy
(exothermic). Beyond iron they require energy input to occur
(endothermic).
! Exothermic reactions produce feedback
conditions, in which higher T caused by them leads to even
higher T and increases reaction rate
Supernova explosions
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When a stellar core gets converted to
iron, there are no more fusion
reactions that could synthesize heavier
elements and release energy
Electrons of the degenerate core and
gamma-ray photons are captured by
iron atoms. This causes cooling and
rapid collapse of the core in less than
0.1 seconds
When this collapse is halted by
pressure of free neutrons, energy
carried away by neutrinos and huge
convection currents make the outer
layers of a star explode and get
ejected into space
What is left of a star is either a neutron
star or a black hole, depending on the
mass of the core
Conditions in the core
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The iron core has T~ 4 x 109K and density > 1010kg m-3.
Pressure in a 1 Msun core of density 5 x 1010kg m-3 would be:
GM 2
P= 4
R
In such conditions, photon-photon interactions produce e--e+
pairs and neutrinos, which carry away core energy cooling it in a
runaway process leading up to core collapse
! by the core bounce cause detonation of
Heat pulse caused
successive shells of the star and a catastrophic
nucleosynthesis, such as explosive silicon burning:
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Si+ 4He"32 S+ 4He"36 Ar+ 4He"40 Ca
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Ca+ 4He"44 Ti+ 4 He"47 V + p
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Ca+ 4He"45 Ti + n
Explosive burning in successive shells produces all the
remaining elements above 56Fe
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Post – main sequence stellar
evolution
Element recycling scheme
H, He
Interstellar medium
H, He, CNO
“soot”
H, He, CNO,
Si,Mg,S,…Fe…
exp
l
e je o s io n
c ta
B
A
N
G
<10K
exp
l
e je o s io n
c ta
100K
exp
l
e je o s io n
c ta
B
I
G
Stellar
generations
Planets, brown dwarfs, white dwarfs, neutron stars, black holes
Pop. II stars
H+He planets
Pop. I, 2nd generation
stars, H+He+CNO-->
“soot & ice” planets
Pop. I, 3rd generation
stars, H+He+CNO+rock
--> terrestrial planets