10.NUCLEAR PROCESSES IN THE LATE STAGES OF THE EVOLUTION OF MASSIVE STARS

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10. NUCLEAR PROCESSES IN THE LATE STAGES OF THE
EVOLUTION OF MASSIVE STARS
10.1 THE EFFECT OF MASS
As massive stars evolve they build up ash from
the previous burning stage, and this material
becomes the fuel for the next phase - that is if
the star is massive enough to be able to create a
suitably high temperature to overcome the
progressively higher Coulomb barrier. We also
know that supernovae explosions take place and
that they are associated with individual stars.
The energy release in these events is typically
1045 Joules which is equivalent to about 10-2
M0c2, i.e. a significant fraction of the
available stellar mass energy. This is clearly a
truly catastrophic event for the star. In the
next sections we try to understand how this comes
about.
10.2 CARBON BURNING
We have seen how lower mass stars M lt 4 M0 can
build up a carbon core and create white dwarfs.
We also know that more massive stars will have a
hotter core since
Clearly if the temperature (i.e the mass) of the
star is high enough then carbon burning may take
place
DE (MeV) Na23 p 2.3 Ne20 a
4.6 Mg23 n -2.6 O16 2 a 0.114
Since there are substantial fluxes of energetic
particles within the plasma near to the centre of
the star, the following reactions occur with high
probability
These reactions require the temperature to be
typically 7 108 K
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10.3 OXYGEN BURNING
At temperatures of typically 1.5 109 K oxygen
burning can take place

Si31 n P31 p Si28 a Si30
2p Mg24 2a
(16.5 MeV)
At higher temperatures (kT 300 keV) there will
be enough g-ray thermal photons around to cause
photodisintegration of significant numbers of
nuclei
The result will be to produce copious alphas
10.4 SILICON BURNING
Si28 is in fact a much more tightly bound nucleus
than S32, and when the temperature is around 2.5
109 K then S32 rapidly photodisintegrates to form
Si28
In fact the core becomes predominantly Si28 since
the a particles at the end of the O burning also
tend to build up the Si28 via
At this stage Si28 Si28 --gt X56 does not happen
since at temperatures around 3 109 K the
photodisintegration means that there will be a
more complex statistical balance between the
photodisintegration and the build-up by as (Note
the a build-up is an easier way to effect
thermonuclear fusion due to the comparatively
lower alpha/nucleus Coulomb barrier).
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The statistical equilibrium may be expressed as
follows
Decay
Build-up
During the silicon burning there will be a
general build up of the iron group i.e. Ni, Fe,
Cr etc The binding energy per nucleus reaches
a maximum for Fe56, so that energy must be
absorbed from the gas whenever particles are
added to a nucleus with Agt56. Hence elements
above the iron group are not formed during this
quasiequilibrium silicon burning. If the
temperature (stellar mass) is high enough then
there will be an iron group nuclei core to the
star, but if the burning terminates before the
Si28 is depleted then the core will contain a
mixture of intermediate mass elements. (30 lt A lt
50)
At the point of forming an iron group core the
star is heading for a catastrophe. It has
exhausted it supply of nuclear fuel. Contraction
is the only other source of heat energy to fight
against gravity.
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10.5 THE ROLE OF NEUTRINOS
Unlike photons which couple to matter through the
electromagnetic forces with a cross-section of
typically 10-20 to 10-28 m2, neutrino processes
involve cross-sections the order of 10-48 (En
/mec2)2 m2 per particle. (En is the energy of the
neutrino). This means that matter under most
conditions is essentially transparent to
neutrinos. The mean free path for neutrinos in
matter with a baryon number density n is
The mean free path in the core of the Sun will be
typically 10 pc, so that the neutrinos escape and
take their energy with them. In the PP and CNO
hydrogen burning phases the neutrinos carry away
between 2 and 5 of the energy generated, making
the lifetime of stars on the main sequence 2 - 5
shorter.

• For massive stars at the end of their lifetime
  the situation is much more dramatic
• They have no replenishment of energy from
  nuclear sources
• With a central temperature of T 109 K i.e.
  (kT mec2) many other processes generate immense
  fluxes of neutrinos
• The result is catastrophic

THE PRODUCTION OF NEUTRINOS IN STELLAR EVOLUTION
BY WEAK INTERACTIONS
Neutrino Pair Production
Since kT mec2 (T 109 K) in massive stars,
much of the thermal spectrum will be in the form
of g-rays with energies Eg gt 2 mec2. We
therefore expect large numbers of
electron-positron pairs to be produced and
subsequently annihilate.
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Most of the time this is what happens, however
direct electron-neutrino coupling is also
possible allowing the electron-positron pair to
decay into neutrinos
Although the probability of this happening is
about 10-22 that of the electromagnetic process,
the vast number of reactions which take place at
the centre of stars results in a considerable
rate of energy loss.
Photoneutrino Process
This process depends on the fact that an electron
can absorb a photon and re-emit a
neutrino-antineutrino pair
This is the (weak) equivalent of the Compton
effect.
Plasma Process
Electromagnetic radiation is strongly affected by
the dielectric properties of the electron gas
when the stellar core density is high. The
collective interaction of a photon with the
plasma is called a plasmon. The plasmons can
decay directly into neutrinos
It is the plasma that enables both energy and
momentum to be conserved.
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URCA PROCESS
During the course of the nuclear processing which
takes place at the core of massive stars a great
many b-decay processes will take place. Some of
these are effectively cyclic such that the same
nuclei are involved in the process many times and
liberate vast amounts of energy in the form of
neutrinos
The material cycles and recycles itself with a
constant drain of energy from the star.
DEPENDENCE ON DENSITY AND TEMPERATURE
Processes involving neutrinos are very dependent
upon the density and temperature. This is
illustrated in the figure, where the dominance of
the various mechanisms are illustrated. The rate
of energy loss by neutrino will have an important
effect on the evolution of the star. For example
for some (mass dependent) stars the neutrino
losses can be comparable to or exceed the nuclear
energy release during silicon burning.
The general effect will be to shorten
considerably the lifetime of a given burning
stage. A typical carbon burning phase would last
about 106 years in the absence of neutrino
losses. With neutrino losses this stage can be
shortened to typically 103 years.
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10.6 THE FINAL STAGES OF A MASSIVE STAR
The neutrino losses greatly speed up the final
stages of thermonuclear evolution for massive
(M0 ³ 8 M0) stars. Below we see the computer
description of the end of a 25 M0 star. The final
stages of other massive stars will be similar,
although many details will be different. This
particular one leaves a 1 M0 neutron star
behind. Under slightly different conditions the
star might blow itself apart leaving no central
object, alternatively a very massive burnout
might undergo gravitational collapse to form a
black hole. We will follow the central objects
later in the course.
During the latter stages the star will have to
contract rapidly. The length of the various
stages depends upon the temperature (and hence
the mass) of the stars interior. In any case the
timescales are effectively determined by neutrino
losses. for example silicon the burning timescale
can typically vary between 10 seconds to 10 days.
Clearly the star is heading for a catastrophe
since as it builds up an iron core it has no
nuclear fuel at the core. The high core density
ensures that neutrinos are generated and the
energy for support has to come from contraction
which further increases the density and the
temperature, leading to increased neutrino
production.
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10.7 EXPLOSION OF THE STAR
7 1011 m
Hydrogen burning shell Helium burning
shell Carbon burning shell Neon burning
shell Oxygen burning shell Silicon burning
shell Iron core
Near the end of its life the star becomes a red
supergiant and the energy comes from concentric
nuclear burning shells at the centre.
The rising temperature of the contracting iron
core also means that the average photon energy of
the thermal bath increases. These g-ray photons
are energetic enough th cause PHOTODISINTEGRATION
of the iron nuclei.
and also
These processes are ENDOTHERMIC with
BANG
and
This loss of support energy results in a
catastrophic collapse of the core (really a
free-fall in seconds). The outer layers of the
star will be blown off into the interstellar
medium. (more ashes and dust for re-cycling) and
the central region will collapse. We will follow
the core region later in the course, next we will
study the exploding material.
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11. SUPERNOVAE
11.1 GENERAL BACKGROUND INFORMATION
Observational Data A supernova represents a
very rapid brightening of a star. The luminosity
increases to typically 1010 L0, such that it can
be as bright as the rest of the galaxy in which
it is situated. It clearly represents a
catastrophic redistribution of the stellar
material. The total energy output is typically of
the order 1044-45 J i.e 0.01 M0c2. Looking at
the distribution of known supernovae remnants
close to the Sun and the measured rate of
occurrence in other galaxies it is possible to
estimate a rate of 1 per 30 years per galaxy. In
this context it should be remembered that,
because of dust etc in the planes of galaxies
many supernovae events are missed. This shows up
in two ways
Discovery Rate.
The rate of discovery over the period 1954 - 1985
is shown in the figure. As the distance increases
we can see that proportionally less supernovae
are discovered than one would expect from a
uniform space density distribution. Clearly many
are missed.
Galactic Supernovae.
The table below gives the date of occurrence,
distance from the Sun, type and height above the
Galactic plane of all known galactic supernovae.
Since only six have been observed in the last
1000 years, many have been missed. At a rate of 1
per 30 years we would expect to have had 30
supernovae events reported over this time period.
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11.2 LIGHT CURVES
The light curves may be used to divide the
supernovae into two main classifications with the
typically inspired and imaginative names, type
I and type II. There are however a number of
subdivisions.
Type II
Type Ia
The light curves show a rapid rise to the maximum
luminosity which is followed by a steep drop
over a period of about 30 days. The subsequent
light curve is very regular showing a straight
exponential (remember magnitude is a logarithmic
scale) decay with a time constant t of about 100
days.
which is thought to correspond to the light curve
being driven by the energy release from
radioactive decay process
for which the decay constant t 110 d (t1/2
70 d)
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Type II (and Ib)
Type II supernovae are about 1 - 2 magnitudes
more luminous than type Is which suggests more
massive progenitor stars. Instead of the regular
L L0 e -t/t seen in type I events type II SN
vary from one event to another, although the
exponential decay often eventually appears. This
variation indicates a more varied scenario.
11.3 OCCURRENCE
Type Ia occur in both spiral and elliptical
galaxies. Since elliptical galaxies do not
contain interstellar dust and thus have no
on-going star formation we can conclude that type
Ia SN are related to older (and less massive)
stars. Type II (and Ib) occur only in the
galaxies with on-going star formation and thus
probably relate to younger (and more massive)
stars
11.4 SPECTRA
During the early stages the spectra exhibit near
black-body spectra with emission and absorption
features which are broadened and blue-shifted by
Dl/l corresponding to velocities of typically
104 km/s. However the main reason for the type
I/II classification is the absence of hydrogen
lines in type Is as opposed to their presence in
type IIs. The Ia/Ib classification comes about
because the both have a lack of hydrogen line
emission, but type Ib events are clearly derived
from different parent stellar types and have many
features which relate them to the type II
events. In the initial phases an intense uv
continuum appears before maximum and fades away.
After the maximum the broadened emission and
absorption lines appear. Forbidden line appear
later as the system expands, and since their
onset is density dependent it is possible to
estimate the mass of gas ejected using the
expansion velocity. Masses in excess of 1M0 are
normal, with type II events characteristically
ejecting considerably more than 1 M0. The
original classifications have been made on the
basis of the historical optical observations.
Supernovae also emit across the electromagnetic
spectrum, embracing radio, ir, uv, X-rays and
g-rays, and as these wavebands accumulate more
diagnostic information on an improved statistical
basis our understanding of the phenomenon will
improve.
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11.5 THE PHYSICS OF SUPERNOVA EXPLOSIONS
TYPE Ia The low ( 1M0) mass , lack of hydrogen
(i.e. no stellar envelope) and the fact that they
are related to very old stars has led to an
association of Type Ia events with white dwarfs.
Furthermore the extreme consistency of the
explosion characteristics is a natural
consequence of a uniform starting condition.
Mechanisms for Type Ia Explosions
The most likely scenario for a type Ia explosion
is that an accreting white dwarf in a binary
system is provoked into thermonuclear instability
by the accumulation of a critical mass. Ignition
then takes place under degenerate conditions such
that a substantial fraction of the mass undergoes
nuclear burning. This is readily understood from
our previous discussion relating to white dwarfs.
The degeneracy pressure
ð K r 5/3 (non relativistic case)
ð K1 r 4/3 (relativistic case)
pF
Whatever
Thus if nuclear burning commences within a white
dwarf the pressure changes negligibly but the
temperature will increase dramatically because of
the excellent conductivity. The thermonuclear
reaction rates rise even faster since
The resultant nuclear burning will be very rapid
(either sub-sonic deflagration or super-sonic
detonation) and because of the homogeneity of the
system will burn through to the logical
conclusion of products in the iron group. In fact
we may expect a 1.4 M0 white dwarf to produce
about 0.5 to 1.0 M0 of the radioactive isotope
56Ni.
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The Production of Radioactive Isotopes and an
Explanation of the Light Curve
A model 1.4 M0 white dwarf produces typically
0.86 M0 of the iron group, 0.58 M0 of which is
the radioactive isotope 56Ni. The decay scheme of
this isotope is as follows
t 9 d
t 110 d key Eg are 0.847, 1.238,
and 2.599 MeV
Such a large mass in the form of a radioactive
isotope has a considerable amount of stored
energy which is liberated exponentially in time
later through the g-rays and positrons. (Some
MeV per disintegration). This has to be the
mechanism which causes the exponential light
curve seen in type Ia SN. It probably operates as
follows The radioactive decay of the 56Ni
isotopes liberates energy at the centre of the
explosion in the form of energetic g-rays over an
e-folding timescale of 110 days. The
surrounding material is opaque to the g-rays and
they cannot escape the expanding envelope. They
degrade their energies into lower energy photons
by interactions with the material of the
expanding shell which eventually emerge to be
radiated away. A large fraction of the g-ray
energy also pushes the expansion along. Note
neutron star production is unlikely in type Ia SN
Optical/ir/uv emission
g-rays
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TYPE II. The association with massive gt 10M0
stars implies that type II SN are the result of
the collapse of the iron core associated with
stars which have evolved through the various
burning stages to the onion model shown earlier.
Let us look at this a little more closely.
Mechanisms for Type II Supernovae
Hydrogen burning shell Helium burning
shell Carbon burning shell Neon burning
shell Oxygen burning shell Silicon burning
shell Iron core
The core of a massive star
When the iron core is formed the only means it
has to support its increasing mass is to contract
adiabatically, raise the temperature and hence
the pressure. This has the unfortunate effect of
causing endothermic photodisintegration
The result is frantic collapse and
ensures a free fall of the core.
Gravitational Potential Energy of the Core.
The gravitational potential energy liberated by
the collapsing core is
i.e just about right
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NEUTRONIZATION AND THE FORMATION OF A COMPACT
OBJECT
This process will generate a pulse (few seconds)
of about 1057 neutrinos which should be emitted
from the star. The falling neutrons will feel the
effects of degeneracy pressure at about 1017 kg
m-3, the sudden stiffening can cause the
so-called core bounce phenomenon. A shock wave
will propagate outwards and transfer energy to
the outer layers of the star. If the neutron
degeneracy is capable of stopping the infall then
a neutron star will be formed. i.e neutron
degeneracy has found a means to compete with
gravity to form a stable object - the neutron
star. If the neutron degeneracy is incapable of
stopping the infall, no known physical forces
left to halt the attraction of gravity and,
presumably, a black hole is created. The
onion-like distribution of the nuclear species
above the central core is subjected to intense
neutron fluxes and rapid heating. Under these
conditions it is easy to understand the variety
of different light curves which are seen from
type II SN. It is thought that Wolf-Rayet stars
(massive stars which have shed their hydrogen
mantles in a similar way to red giants, but
retain the evolving onion core) are the
progenitors of type Ib SN.
As for the case of planetary nebulae supernovae
both eject material into the interstellar medium
for recycling and leave cinders behind.