Power and element generation in
stars
Astronomy 115
Energy transfer
• As the names of the layers
imply, it is not the composition
of the sun that is interesting,
but the manner in which
energy is transmitted from
layer to layer.
• This difference in manner of
energy transfer will be a direct
result of the lessening density
of the Sun outwards; in fact,
the outer edge of the
convective zone (the
photosphere) is far less dense
than the Earth’s atmosphere!
The Sun’s energy is generated by thermonuclear
reactions in its core
• Thermonuclear fusion occurs at very high temperatures
• Hydrogen fusion occurs only at temperatures in excess of
about 107 K
• In the Sun, hydrogen fusion occurs in the dense, hot core
Proton-Proton Chain Reaction
•The Sun’s energy is produced by hydrogen fusion, a
sequence of thermonuclear reactions in which four
hydrogen nuclei combine to produce a single helium
nucleus; called proton-proton chain reaction
Proton-Proton Chain Reaction: Step 1
Proton-Proton Chain Reaction: Step 2
Proton-Proton Chain Reaction: Step 3
Proton-Proton Chain Reaction
4 H  He + energy + neutrinos
Mass of 4 H > Mass of 1 He
•In every second, 600 million tons of hydrogen
converts into helium to power the Sun
•At this rate, the Sun can continue hydrogen
fusion for more than 6 billion years.
Solar neutrinos
How do we know about the interior of the sun
and how it produces power?
One answer is neutrinos.
We, on Earth, can measure neutrinos produced
within the solar core. This is because
neutrinos almost never interact with matter.
Neutrino detection
Neutrinos DO interact with matter, but their crosssection is small, meaning they don’t hit other
matter very much.
• ~7 × 107 neutrinos pass through your thumbnail
(which is an area about 1 cm2) each second. But
your body interacts with a neutrino only about once
in 70 years. This length is jokingly referred to as
the……....
Neutrino Theory of Death! (human
lifespan and all, heh, heh)
Neutrino detection
The first actual detection of a neutrino was made by Frederic
Reines and Clyde Cowan.
They didn’t actually measure a
neutrino, just the by product of
its reaction with a proton (1 in
1018 chance of occurring).
ne + p  n + e+
e+ + e-  2g
In 1956 they measured these gamma rays from a nuclear reactor
at Hanford in E. Washington and (conclusively) Savannah River in
South Carolina.
Why do we care about neutrinos?
Reason 1: Neutrinos are produced in the core of the Sun in
HUGE amounts (about 1038 neutrinos/s).
Reason 2: Most neutrinos escape the Sun without interacting
with the Sun’s matter, so they reach the Earth in 8 minutes !
They travel at very close to the speed of light.
Reason 3: Neutrinos are produced by several reactions in the
proton-proton chain and depend on solar core composition,
pressure, and temperature.
Reason 4: They provide another boundary condition for the
standard model (i.e., the way we describe subatomic particles).
Complete fusion process in the solar core
(colored boxes show neutrino production)
The solar neutrino spectrum
neutrino reactions in the
Sun:
p+ p  D+ e+ + n
p + e- + p  D + n
7Be
7Be
8B
7Be
+ e-  7Li + n
[ 3He + 4He 
8B
7Be]
 7Be + e+ + n
[ 7Be + P 
8B]
(1MeV = 1.6 x 10-13 J)
The relative contributions of the different neutrino reactions
depend on conditions in the solar core.
First detection of solar neutrinos
Homestake Mine experiment led by
Ray Davis in South Dakota 1.5 km
underground 1965-1987:
378,000 liters of cleaning fluid (ultrapure carbon tetrachloride).
When neutrino interacts argon is
produced.
37Cl
+n 
37Ar
+ e-
(17p+ + 20n)
(18p+ +19n)
[En = 0.8 MeV]
Measures ~ one neutrino every 2 days.
The solar neutrino problem
• Standard Model of the Sun says that
Homestake should detect ~1.5 –2
neutrinos per day, but it only detects 0.5
per day. Factor of 3 to 4 difference.
• Either we don’t understand the sun like
we thought we did, or something else is
going on. Hopefully not the first thing,
because then the Standard Model would
be hopelessly wrong.
The solar neutrino problem
Adding up all the neutrinos does not get the amount predicted in
the Standard Model, regardless of the detection method used.
Solution to solar neutrino problem:
neutrino oscillations
There are three flavors of neutrinos: electron
neutrino (ne), muon neutrino (n), and the tau
neutrino(n)
MSW Effect: neutrinos oscillate between
flavors as they travel through space. This is
effect is strongly enhanced when neutrinos
pass through matter (Mikheyev, Smirnov, and
Wolfenstein, 1986)
Homestake Mine could only detect electron
neutrinos
Neutrino oscillations require that the neutrino
has mass (changes the Standard Model of
particle physics)
How do we know if neutrinos oscillate?
Using very large omni-directional sensors of water and heavy water
(D2O). Measure a lack of ne and overabundance of other flavors
Water Based: SuperKamiokande in
Japan, 50,000 tons of ultra-pure water
Able to detect ne above 7.5 MeV
ne scatter with e- in water, producing ethat travel faster than c in water (called
Cherenkov radiation) which produces
radiation detected by thousands of
photomultiplier tubes (PMT)
Measured lack of ne (like Homestake)
Confirmed that neutrinos can oscillate,
but were unable to detect all the solar
neutrinos
The solar neutrino observatories
Neutrinos are hard to measure, so the detectors are large and omnidirectional.
Neutrino observatories are defined mainly by the energy range
and flavors they can sample.
Heavy Water: Sudbury Observatory
(SNO) in Canada 1000 tons of D2O
(UW Physics main US participator):
Can detect all flavors of neutrinos
(ne, n μ ,and n τ) above ~5 MeV
Measured lack of νe and abundance
of n μ and/or n τ
Best evidence for neutrino
oscillations and thus massive
neutrinos
Solar neutrino problem: solved!
• In June of 2001, the SNO team reports that the neutrino deficit
is solved
• Our model of the solar core is correct
• Neutrino mass needed to be added to the Standard Model
Neutrino astrophysics
SN 1987A (supernova): Three hours before observing light,
neutrinos were detected in a 13 second burst.
Kamiokande II:
11 antineutrinos
IMB:
8 antineutrinos
Baksan:
5 antineutrinos
Dark Matter: One candidate for DM is the sterile (truly noninteracting) neutrino.
Cosmic Neutrino Background: Big Bang Nucleosynthesis,
constraints on matter distribution
Nucleosynthesis – Triple Alpha reaction
How are elements heavier than helium produced?
4
4
8
0
He+
He

Be+
2
2
4
0g
8
4
12 * 0
Be+
He

4
2
6 C + 0g
The triple alpha reaction
(3 He’s are involved)
Carbon is formed in an excited state, originally predicted before it was known
that this could happen.
Requires temperatures on the order of
Astronomy 100
.
8
10 K
23
Results of nucleosynthesis: the cosmic abundances of
the elements (not all due to stellar processes)
Abundance relative to hydrogen
Figure: Shu, The Physical Universe
Mass number (number of baryons in nucleus)
Astronomy 100
24
Hotter fusion and heavier elements
• Could stars in principle live forever simply by contracting
gravitationally and increasing their temperature to ignite the
next heavier source of nuclear fuel whenever they run out?
– No. The strong interaction’s range is smaller than the
diameters of all but the smaller nuclei, but the range of the
Coulomb interaction still covers the whole nucleus.
– If nuclei get large enough the increase in electrostatic
repulsion of protons becomes greater than the increase in
binding energy from the strong interaction.
– Thus there is a peak in the binding-energy-per-baryon vs.
atomic mass number relationship, that turns out to lie at
iron (Fe).
Astronomy 100
25
Hotter fusion and heavier elements (continued)
Binding energy per baryon
Implication:
Once a star’s core is
composed completely of
iron, it can no longer
replenish its energy losses
(from luminosity) by fusion.
Stars therefore must die,
eventually.
In other words, you get
energy by fusion all the way
up to production of iron but
not beyond.
Figure: Shu, The Physical Universe
Atomic mass number
Astronomy 100
26
The high mass track
HIGH MASS TRACK
1) Proto Star
2) Main sequence
• While on the main sequence what do
high mass stars burn in their cores?
– Hydrogen
• What fusion process?
– CNO
The CNO cycle
• Low-mass stars rely on the protonproton cycle for their internal
energy
• Higher mass stars have much higher
internal temperatures (20 million
K!), so another fusion process
dominates
– An interaction involving Carbon,
Nitrogen and Oxygen absorbs protons
and releases helium nuclei
– Roughly the same energy released per
interaction as in the proton-proton
cycle.
– The C-N-O cycle!
High mass stars – the end
• Onion structure of the core
.
Beyond helium: nucleosynthesis
• As you saw, the triple alpha reaction makes carbon nucleus.
• Two carbon nuclei can fuse to make an oxygen nucleus.
12
12
16
4
4
0
C+
C
®
O +
He
+
He
+
g
6
6
8
2
2
0
• Two carbon nuclei can fuse to make a magnesium nucleus.
12
12
24
0
6 C+ 6 C ® 12 Mg + 0 g
• To fuse heavier elements generally require higher
temperatures (5 × 108 K and higher)
• Energy is released all the way up to the formation of iron,
usually as gamma rays.
Astronomy 100
33
Higher temps, more massive nuclei
• Nuclei are fused at higher and higher
temperatures in the core of a massive star
until an iron core forms.
• If the star doesn’t reach high enough
temperatures in its core then it can stop at
triple alpha process (lower mass stars).
• Eventually stars cannot burn anything more.
So how are very heavy elements made in the
universe?
Nucelosynthesis summary
• For the majority of stars (~95%, corresponding to stars with
initial masses of less than 8 M-Sun), direct nuclear fusion
does not proceed beyond helium, and carbon is never fused.
• Most of the nucleosynthesis occurs through slow neutron
capture during the asymptotic giant branch (AGB), a brief
phase (~106yr) of stellar evolution where hydrogen and
helium fuse alternately in a shell.
• These newly synthesized elements are raised to the surface
through periodic "dredge-up" episodes, and the observation
of short-lived isotopes in stellar atmospheres provides direct
evidence that nucleosynthesis is occurring in AGB stars.
Supernovae
• A Type I supernova is a massive explosion of a
star that occurs under two possible scenarios.
The first is that a white dwarf star undergoes a
nuclear based explosion after it reaches its
Chandrasekhar limit (1.44 solar masses) from
absorbing mass from a neighboring star
(usually a red giant).
• A Type II supernova (more common) occurs
when a massive star, usually a red giant,
reaches iron in its nuclear fusion (or burning)
processes.
Supernovae
• All nuclear fusion reactions beyond iron are
endothermic (require energy) and so the star doies
not produce energy from these reactions.
• The star's gravity then pulls its outer layers rapidly
inward. The star collapses very quickly; the in-rushing
matter compresses at the center of the star such that
the degenerate matter (electrons and protons,
principally) combine into neutrons.
• Neutrons are not compressible, so the rest of the infalling matter rebounds, which is the supernova
explosion.
Composite image of Kepler's supernova from pictures by the Spitzer Space
Telescope, Hubble Space Telescope, and Chandra X-ray Observatory.
After the supernova
• Supernova remnant includes the remains of the star plus the
nebula of material thrown outwards by the explosion
• The material remains very hot (and glowing) for millions of
years (even if it becomes too dim for us to see)
• The neutron star is very small, very hot, and distorts space
(and time) around it due to its extremely high density
• A black hole is a neutron star whose escape velocity exceeds
the speed of light
art
reality
Black hole structure
The event horizon is
the distance at which
the escape velocity is
greater than the
speed of light. Note
that the singularity
is where the actual
star is.
Black holes aren’t forever
• Hawking radiation can be emitted by a black hole, which
reduces its mass. Once enough mass is lost, the star becomes
an “ordinary” neutron star.
Gamma rays can spontaneously generate
a positron-electron pair (the reverse of
what occurs during hydrogen fusion).
Usually, the electron and positron
annihilate within 10–35 seconds, but if the
“pair production” occurs near the event
horizon, one particle may be trapped
within the event horizon so the
recombination cannot occur; the other
particle is emitted as Hawking radiation
and reduces the mass of the black hole.