Two major fusion processes:
p-p chain (proton-proton reaction)
CNO (carbon, nitrogen, oxygen) cycle
Source of energy at the interior: fusion of hydrogen into
helium due to the high pressures and temperatures.
helium
nucleus
4 protons
fusion
In the process, 4 H nuclei (protons) are forced together
to create 1 He nucleus (2 protons, 2 neutrons)
Proton proton chain
Carbon Nitrogen Oxygen (CNO) cycle
12C
+ 1H ➞ 13N + γ
13N
➞ 13C + e+ + ν
13C
+ 1H ➞ 14N + γ
14N
+ 1H ➞ 15O + γ
15O
15N
➞ 15N + e+ + ν
+ 1H ➞ 4He + 12C
Carbon is a catalyst
It facilitates the reaction
but leaves unchanged
we basically add protons
one at a time to carbon
and finally a helium
nucleus breaks off
The CNO cycle has a very steep temperature
dependence: T17 !!
It requires very high temperatures;
it is important in more massive stars,
M > 1.1 M⊙
It also means that the cores of the more massive
stars are smaller
There is a small mass difference between the starting protons
and resultant helium nucleus
proton mass
mass of 4 protons
mp = 1.673 ×10-27 kg
4 mp = 6.692 ×10-27 kg
mass of helium nucleus mhel = 6.645 ×10-27 kg
mass loss = (6.692 - 6.645) ×10-27 kg = 4.7 ×10-29 kg
This mass is converted into energy.
Mass and energy can be converted into one another,
according to the relation E = m c2 where c is 3 × 108m/sec
so every fusion above results in
(4.7 ×10-29 kg) x (3 x 108 m/sec)2 = 4.2 × 10-12 J
around 4 × 1038 protons are converted into helium in the Sun
every second, producing about 1038 helium nuclei per second.
at 4.2 × 10-12 J released per nucleus thats about 4 × 1026 J/sec
(4 × 1038 protons) (1.673 × 10-27 kg/proton)
= 6.7 × 1011 kg are converted every second.
at this rate, the Sun can last (2 × 1030 kg) / (6.7 × 1011 kg sec)
= 3 × 1018 sec
= (3 × 1018 sec) / (3 × 107 sec/yr)
= 1011 years!
Burn hydrogen - produce helium
Not all hydrogen will be consumed. Detailed computer
calculations give us a Solar life expectancy
T⊙ ~ 1010 years
T* ~
T⊙
M2.5
(Main Sequence Lifetime)
O, B & A stars have much shorter lifetimes
Opposing forces
gravity squeezes the protostar
internal pressure builds up and
resists collapse
as pressure increases,
gas temperature increases
protostar can emit radiation and
mass outflows at this stage;
energy is provided by
gravitational collapse
collapse continues until the forces balance:
equilibrium is reached
Helium builds up, sinks to the center
Hydrogen fusion continues in a shell
eventually this shell expands as
more He accumulates
less mass remains to hold
down the internal pressure
out of equilibrium, forces
unbalanced
outer part of the star expands
until pressure drops
If M < 0.4 M⊙ no helium fusion
If 0.4 M⊙ < M < 3 M⊙ helium flash
Star will exhaust its hydrogen, and the fusion will stop,
temperature will decrease, star will start collapsing,
which will be unstopped until the helium begins fusing!
More massive stars can
build up high internal pressures and
temperatures which can lead to
sustained helium fusion into carbon
Even more massive stars can
sustain fusion of carbon and
heavier elements into
even heavier elements, and
do this in progressively
deep shells in the interior
Text
IK Pegasi A
Class A V
Sun
GV
IK Pegasi B
White Dwarf
far IR image of
Betelgeuse
ESA/Herschel
Artists conception of
Betelgeuse
http://www.eso.org/public/images/eso0927d/
Planetary Nebula