Download Nucleosynthesis in the Early Universe.

Last Week
Mass-Luminosity relationship
Hubbles Law v = H0d
Expanding Universe
Cosmological principle
Olber’s Paradox
Meaning of expansion λ / λ0 = (1 + Z)
Think in terms of spacetime – we say something 400Mly away has a
Lookback time of 400 My
Cosmological redshift
Cosmological Horizon
Big Bang Model vs. Steady State Model
Cosmic Microwave background
Models of the Universe
Must explain
- Hubble’s Law - v = H0d
- Olber’s paradox – Why is the Sky dark at night?
- Why the Universe does not collapse under its own gravity.
- diversity of objects seen in our telescopes.
It must satisfy
-Cosmological Principle
and be
-Homogeneous and isotropic on largest scale.
Cosmological Models
• Various models can satisfy these criteria.
- Big Bang Model
- Steady State Model
 Is there a way of deciding which is better?
Blackbody Spectrum and Cosmic
Microwave background
 What is the spectrum of EM radiation emitted by
an object of arbitrary temperature T in thermal equilibrum
•Max Planck showed that the spectrum is given by
u d  =
8hc -5.d
[exp(hc/kT) - 1]
Wien’s Displacement Law and Stefan-Boltzmann Law
• Doubling T increases P by 16 since
PA = .T4
where σ = 5.7 x 10-8 Wm-2K-4
• Note that maximum wavelength max
shifts with .This can be quantified in
Wien’s Displacement Law.
• This quantifies the observation
max.T = const.
that an object changes colour
with Temperature e.g.At room
= 2.9 x 10-3 mK
temp. spectrum peaks in infra-red.
• Very important since it allows us to obtain a measure of the SURFACE
TEMPERATURE of a star from max.For the Sun max is in blue with bu
a lot of radiation in red so it looks yellow.For stars with T = 3000k
max is in infrared but significant amount in red.Red Giants are at this T.
Cosmic Microwave Background
• Essentially only three pieces of evidence underpin the Big Bang
Model and the CMB is one of them.
• It was discovered by Penzias and Wilson in 1965.
They are shown here with the
horn antenna they had built
for telecommunications via
satellites.
They found a signal from all
directions at  = 7.35 cm.The
only explanation was that it
is real.Work quickly began to
measure the background at
other wavelengths.
Cosmic Microwave Background
With the addition of more and more points it became clear that it was
a thermal curve at a temp.
of 2.7K.
Later more precise
measurements tell us that it
fits a black-body spectrum
at 2.726 +/- 0.005K
perfectly.
Summary-CMB Measurements
1.CMB is seen in all directions as a perfect BB at T = 2.726+/-0.06K
2.At sensitivity levels of 1 in 103 there is a large scale anisotropy in the
CMB due to the motion of the Earth through
the frame of reference in which the
CMB is uniform.
Earth is moving at about 350 km s-1 w.r.t
this frame.We are moving towards LEO and
away from Aquarius.[Galaxy is moving in
same direction at 600 km s-1 ]
This motion has to be subtracted from the measured spectrum
in order to see the real spectrum.
Cosmic Microwave Backround
For a long time we could
see no fluctuations in the
Cosmic Microwave bgd.
CMB is the spectrum of a
body at 2.726 degrees
seen whichever direction
one looks.
It marks the point where
the Universe became
transparent.
Results from COBE
Evolution of the Universe in Big Bang Model
1 Assume adiabatic process = No heat into or out of the system[Universe]
2.Assume Universe is an idealised,smooth fluid.A good assumption in
the early stages.
3.Constituents are all in thermal eqbm.
E = kT
4.First Law of Thermodynamics dU = dQ + dW
In an adiabatic system dU = dW = PdV.
For a non-viscous fluid P = 1/3  where  = energy density.
5.As Universe expands V and  must change.
We introduce a scale factor R(t) with dimensions of length.
So V = 4/3.. R(t)3
6.Now take a very small volume with only one photon in it.
R = h/V = hc/V  1/V  1/ R(t)3  1/R(t)4
where  depends on redshift and must scale with R(t).
7.Now E = R.V  R(t)3 . 1/R(t)4  1/R(t)
Thus as Space expands [R(t) increases], T decreases.
8.Hence since E = kT we have T  1/R(t)
Big Bang Model
Universe has expanded from a singularity
-infinitely dense, high T, high pressure “point”
The whole Universe expands in line with Hubble’s Law.
As it does so T  1/R(t)
In other words as it expands it cools.
Can we now explain the CMB?
Explanation of the CMB
When Universe was younger it was
not only denser but hotter.If CMB
was emitted at a given T then as
Universe expanded the wavelength
would stretch and effective T goes
down.CMB would appear to have
lower T.
In early Universe it consisted of
75% H:25% He and it was full of
radiation.As a result all the H was
ionised[a) on left].If an atom formed
it soon disintegrated in collision
with a photon.Universe was opaque.
There was a strong coupling
between Matter and Radiation.
At some point( 3 x 105 years) T dropped to 4000K.Now the no.of photons
with sufficient energy is too small to stop atoms forming.
Origin of the CMB
Now H atoms form,photons no
longer interact strongly with Matter
and the Universe becomes
transparent. The photons can now
spread freely throughout the Universe
with a BB spectrum initially at 4000K
but with time it has been shifted
to 2.726K.
Since radiation was continuously
scattered up to this point it is known as
the Last Scattering Surface.
We cannot see anything prior to this
time because the Universe was opaque.
Tiny ripples represent non-uniformity at
that time.Universe was 103 times smaller.
Uniformity was remarkable but present non-uniformity comes from it.
This clinched the Big Bang Model since no other could explain it.
The Expanding Universe and the Friedmann equation
We have a scale factor R(t) which grows in size with the Universe.In
terms of forces we know the Strong and Weak forces are short range and
Electromagnetic effects are
neutral over large volumes
of space.So after about 1 s
the expansion has been
governed by GRAVITY.
Newton wondered why the
Universe did not collapse.
Hubble solved this by
showing that it is expanding
and that the kinetic energy
of expansion overcomes
the gravitational pull.
Expansion of the Universe
As the Universe expands the volume increases proportionally to
the cube of the scale factor.
Scale factor - R(t)
The Expanding Universe and the Friedmann equation
Imagine an arbitrary spherical volume
and let us add a thin shell around it.
The sphere contains mass m and has a
radius d. The matter in the shell is
moving away from the centre with a
velocity v, given by Hubble’s Law.
K.E. = 1/2 msv2
and
P.E. = - Gmms
d
Total energy = K.E. + P.E. ----(A)
Now m = V = 4/3d3 and so eqn. (A) becomes
H(t)2.d2 _ 4Gd2
= total energy ------(B)
ms
2
3
where we have used v = H(t).d
[
]
The Expanding Universe and the Friedmann equation
1.This eqn. contains the density () of the Universe which is proportional
to the inverse cube of the scale factor R(t).
2.If we replace the total energy by an energy constant k,
k = 2ER(t)2
mSd2
3. Eqn. (B) becomes
H(t)2 - 8G
3
=
k
R(t)2
4.This is the Friedmann Eqn. It describes the expansion of the Universe
in terms of measurable quantities.
5.It involves H(t) = H0,  = 0, and we can set R(t) = 1 since it is an
arbitrary measure of the Universe’s size.
If we can determine Hubble’s const. and the density of the Universe we
can solve this eqn for k.
Not so easy! But in principle-----
Friedmann Equation
From consideration of the interaction of a shell of matter with a core
We derived the Friedmann Eqn.
H(t)2- 8G
3
k
=
R(t)2
where k = 2ER(t)2
mSd2
In this form the equation is consistent with Newtonian mechanics.
It has to be modified to take account of General Relativity but it
ends up in a very similar form.
Later we will use it to consider the question of whether the Universe
is “closed or open”. In other words will it expand for ever or will it
stop and then collapse.
Nucleosynthesis in the Early Universe.
1.In the Early Universe the temperature(energy) was so high that all
particles are free. In effect we have a “soup” of particles and photons
all continuously interacting with each other.
2.As time passes the temperature and density fall and gradually when
particles and anti-particles combine they are no longer separated and
they disappear as “free” particles.
3.For example quarks and anti-quarks are initially free.In effect we have
a “Quark-Gluon Plasma”. Once quarks are no longer free they come
together to form nucleons.
[Nucleon is the generic name for protons and neutrons]
Proton = 2 Up Quarks + 1 Down Quark( 2u,1d)
Neutron = 1 Up Quark + 2 Down Quarks( 1u,2d)
4.From this point quarks are no longer free and are forever confined
inside nucleons.
Big Bang Model
So far we have two pieces of evidence for the Standard Big
Bang Model
-- Hubble’s Law
-- Cosmic Microwave Background.
The third piece of evidence relates to Nucleosynthesis
The Boltzmann Distribution Law
 In quantum mechanical systems only certain discrete energy levels can be occupied
 The Boltzmann Distribution gives the probability of finding the system in a particular
energy state. [It applies to classical and quantum systems]
 In a simple system like the nucleon where there are only two states – the neutron
and proton – the energy level diagram is
E1
mNc2 = 939.573 MeV
E2
mPc2 = 938.280 MeV
The ratio of neutrons to protons is
NN/NP = [mN/mP]3/2 exp( - (mN-mP)c2/kT), where k = Boltzmann constant
 At T = 109 K this ratio is 1/7
Nucleosynthesis in the Early Universe.
1.Ratio of n/p declines rapidly with t, T and 
3/2
2
NN
(
m
m
)c
N
P
mN
Exp.
=
mP
kT
NP
2.At T = 109K the ratio is about 1/7 and the Universe is cool enough
for a sequence of two body reactions in which bound states of protons
and neutrons can be made.
Now
n+p
d+
where d represents the deuteron,a nucleus made up of 1 proton and
1 neutron.This is an isotope of Hydrogen.
[ ]
(-
)
3.The deuteron is fragile.It is bound by only 2.223 MeV. There are still
lots of photons around with this energy so that
d+
n+p
4.When T drops to a point where there are too few 2.223 MeV
gammas the creation process wins. Now we can begin to make He.
Nucleosynthesis in the Early Universe.
[n p + e- + e]
1.Mass of neutron = 939.573 MeV
Mass of proton = 938.280 MeV
Difference in rest mass = 1.26 MeV
[Remember E = mc2]
This means that the numbers of neutrons and protons are not equal.
2.Nucleosynthesis begins when T = 109K and t  90 secs.
The Maxwell Boltzmann distribution gives the ratio
NN
NP
=
mN
mP
3/2
[ ]
(-
Exp.
mN - mP
kT
)
---------(A)
3. Point 1 means that free neutrons are unstable and decay with a
mean-life of about 14.8 mins. Point 2 means that there are 7 protons
for each neutron at the time when nucleosynthesis begins.
[ Note:-If the neutron is bound in a nucleus it is no longer unstable.]
Nucleosynthesis in the Early Universe
 So we start with n/p = 1/7
n+p
d+
We can now create deuterons from the protons and neutrons
but
there are so many photons (with energy greater than 2.233 MeV)
that the deuterons break up almost immediately.
This is known as the Deuteron Bottleneck- it causes a delay before
the light nuclei can be formed.
Eventually as T falls the number of photons with E = 2.233 MeV
becomes smaller than needed to destroy the deuterons that are formed.
Now nucleosynthesis can begin.
Big Bang Model
Universe has expanded from a singularity
-infinitely dense, high T, high pressure “point”
The whole Universe expands consistent with Hubble’s Law.[1]
As it does so T  1/R(t)
In other words as it expands it cools.
This allows us to explain the Cosmic Microwave Background.[2]
It also allows us to predict the ratio of H:He in the Early Universe.[3]
The rates of Nuclear reactions in stars
Exp[-E/kT]
• The probabilities of
nuclear reactions in stars
are very small because the
energies of the particles
are very small but there
is a very large number of
particles.
• The number of reactions is just the product of the number of particles
of a given energy multiplied by the probability of the reaction in a
collision at that energy.
RED = Number of particles as a function of energy
Green = Probability of a reaction occurring in a collision
Blue = Number of reactions as a function of energy
 GAMOW PEAK
Nucleosynthesis in the Early Universe.
Now we get a series of fusion reactions
d + d 3He++ + n
3He++ + 
p+d
and the triton (3H = t) is produced in the reactions
n+d
t+
d+d
t+p
n + 3He t + p
Now we might expect d + d 4He +  but the following is preferred
n + 3He++ 4He++ + 
d + 3He++ 4He++ + p
4He++ + 
p+t
4He++ + n
d+t
The delay before these reactions start is called the deuterium bottleneck
In contrast:The p-p chain;the reactions which power the Sun
Overall - 4p  4He + 2e- +2 + 26.7 MeV
Nucleosynthesis
Sequence in the Early Universe
- First neutrons and protons form.
- Initially n + p
d+γ
but photodisintegration occurs at same rate as fusion.
- When T falls further fusion occurs faster than photodisintegration
then deuterons form.
- This leads to formation of 4He
- Process stops at this stage because there is no stable or long-lived
isotope of elements Z = 5 or 8.
 Heavier elements are made in stars!
Creating Helium in the Early Universe.
1. 14p + 2n
4
He + 12p i.e. 75%:25% for H:He in terms of mass
[Remember n/p = 1/7 at 109K – the point when nucleosynthesis starts]
2. On the way a lot of deuterium is created but it is very delicate and is
easily broken up by interaction with the very high flux of photons.
This process is called Photodisintegration. [ n+p d +γ]
[ Deuterium bottleneck ]
3. Once we have made Helium we might expect that we could make
heavier elements by the interaction of He + p or He + He.
However there are no stable nuclei of mass A = 5 or 8.
4.For example 4He + 4He 8Be but it “immediately “ breaks up into
two alpha particles[helium nuclei]
5.Nucleosynthesis in the Early Universe comes to an end. The second
reason being that the Universe is now not dense enough!!
The rates of Nuclear reactions in stars
Exp[-E/kT]
• The probabilities of
nuclear reactions in stars
are very small because the
energies of the particles
are very small but there
is a very large number of
particles.
• The number of reactions is just the product of the number of particles
of a given energy multiplied by the probability of the reaction in a
collision at that energy.
RED = Number of particles as a function of energy
Green = Probability of a reaction occurring in a collision
Blue = Number of reactions as a function of energy
 GAMOW PEAK
Solar System Abundances
Present day abundances!
Here we see the abundances
of the chemical elements in
Solar System.
They are plotted on a log
scale relative to the
abundance of Hydrogen(H)
=1
The abundances of everything
except He are smaller
by at least a factor of 1000.
Cosmic Microwave background
7p
1n
75% H & 25%He
98% of known matter
Where does the rest
come from?
The table summarises the similarities and differences between
Decoupling and Nucleosynthesis. Note the differences in energy
scales appropriate to nuclear and atomic processes.
(CMB)
Predicted Abundances of the light elements from Big Bang
One of the three pieces of evidence
for the Big Bang Model is the
abundances of the light elements.It
depends on the number of types of
neutrino which exist and the
density of baryons(strongly
interacting particles)
Here we see the predictions as a
function of baryon density[at top]
and of the density B.
Band shows observations
Line shows critical density for
H0 = 65 km/sMpc
[Note:-H = 1 in diagram]
The Big Bang Model
What we have seen is that there are three key pieces of evidence
supporting the Big Bang Model.
1. Hubble’s Law and the expansion of the Universe.
2.The isotropy and thermal spectrum of the Cosmic Microwave
Backround.
3. The abundances of the light elements.
These three pieces of evidence are independent and all find a natural
explanation in the standard Hot Big Bang Model of the Universe.
Problems with the Standard Big Bang Model
Friedmann equation
H(t)2
8G
3
=
k
R(t)2
where k = 2ER(t)2
mSd2
This is the Friedmann equation which describes the expansion of the
Universe with k determining the rate of expansion.
•When derived from General Relativity the energy constant k has the
interpretation of the overall curvature of the spacetime continuum.
 Later we will use it to consider the question of whether the Universe
is “closed or open”.
•Overall there are three possibilities which we can see as being similar to
the question of “Escape velocity” for an object leaving a planet etc.
In other words it is a question of the total mass in the Universe.
Curvature or Shape of the Universe.
The matter and energy scattered across all of space give the Universe an
overall curvature.How curved depends on average mass density.This
includes all forms of energy [Remember E = mc2]
1.In a flat Universe two parallel beams of light would stay parallel
forever.No curvature. The Universe will expand forever but more and
more slowly until it just reaches infinity. Here k = 0.
2.If the two light beams converge Universe has positive curvature then
Universe is closed with k +ve. Here there is sufficient matter to slow
down the expansion so that eventually the expansion stops and is
reversed.Then it will start to shrink and eventually return to the
“Big Crunch”.
Note:-This is rather like lines of longitude on the Earth’s surface.They
are parallel at the equator but meet at the poles.However the Universe
would still have no edge or centre.
3.If the two light beams diverge.Here the surface is like a saddle
shape.Here k is -ve. Now the expansion goes on forever because there
is not enough matter to slow it down.
Curvature or Shape of the Universe.
Defined in
next slide
Three possibilities:Geometry
Curvature
of space
Spherical
Flat
Hyperbolic
positive
zero
negative
Type of Universe
closed
flat
open
< Ώ0 >
Ώ0 > ΏC
Ώ0 = ΏC
Ώ0 < ΏC
Hint from CMB
If CMB were truly isotropic then we could not tell which case prevailed.
However there are hotspots. Their apparent size depends on curvature.
If closed, spots appear larger. If open, they seem smaller. If flat then they
appear to be their true size. Calculations suggest they should be about
1 degree in angle, close to what is observed.
Critical Density
Friedmann equation
8G
2
H(t) 3
k
=
R(t)2
Flat Universe:- If k = 0 then the R.H.S. is zero. Then
C = 3 H02
8G
where C is the critical density of the Universe.
We can also write it in terms of  =  ..
This is called the density
parameter.
C
[Here we have the ratio of the combined average mass density(sum of
 for matter,radn & any other form of matter) and critical density 0 ]
If CMB were truly isotropic then we would have absolute uniformity
from all directions.There are localised hotspots however due to small
density variations in the Early Universe.Apparent size will depend on
curvature.Calculations suggest 0 is close to 1-Flat Universe.WHY?
Critical Density
Best estimates from all the matter we can see in galaxies[visible matter]
is that  = 0.02.
From the way galaxies rotate we also have evidence that there is a
large amount of matter we cannot see--Dark Matter.
This raises the value of  to 0.2 or so.This value has a large uncertainty
but it is remarkable that it is so close to a Flat Universe.
Problem:-There is nothing in the model to suggest any particular value
for k but it seems that out of all possible values it is within 1-2
orders-of- magnitude of the critical value.
The problem is made worse by the fact that if the value of the density
parameter departed from 1 even by a little in the Early Universe we
can show that by now it would be different by an enormous factor.
The original expansion velocity would have to have been fine-tuned
to exactly the right velocity so that the critical density is 1 now.
Predicted Abundances of the light elements from Big Bang
One of the three pieces of evidence
for the Big Bang Model is the
abundances of the light elements.It
depends on the number of types of
neutrino which exist and the
density of baryons(strongly
interacting particles)
Here we see the predictions as a
function of baryon density[at top]
and of the density B.
Band shows observations
Line shows critical density for
H0 = 65 km/sMpc
Horizon Problem
Cosmic Particle Horizon:- the Earth is at the centre of an enormous
sphere with radius ~ 15 billion light years. The surface of this sphere
is called the Cosmic particle Horizon.
We can see nothing outside this sphere because there has not been time
for the light to reach us.
This is part of the reason why the Sky is dark at night. The other
reason is that everything is receding from us.
Horizon Problem
Perhaps the biggest problem for
the Big Bang Model is the
Horizon Problem.
It involves communication of
information between different
parts of the Universe.Since the
Universe has a finite age in this
model even light can only have
Cosmic Particle horizon travelled a finite distance in this
time.
This distance defines the OBSERVABLE UNIVERSE.This is what we
can see and is finite whatever the size of the Universe.
As we see in the picture radiation from the Big Bang has just reached A
and B. Radiation from A and B cannot have reached each other.In
particular this means that the two sides of the sky cannot have interacted
to create thermal eqbm and a common T. Very Strange!!
Cosmic Particle horizon
Horizon Problem
CMP
Problem is even worse.The radn.
has been travelling uninterrupted
since decoupling so thermalisation
would have had to occur before
then when the Universe would
have been much smaller. So
places that look quite close in the
CMP sky would not have been able to
interact to establish eqbm.
So how does it happen that the CMB is essentially isotropic without this
communication between the different parts of the Universe?
Worse still how can we create the very small fluctuations, the seeds from
which galaxies etc grow?
An Inflationary Universe
The most widely adopted soluton to the Horizon and flatness problems
is to introduce a period of very rapid expansion in the Early Universe.
This idea was introduced by Alan Guth in 1981.
In essence the inflation is defined as a very short period in which the
scale factor grows exponentially.It is accelerating with
d2R > 0
dt2
From Friedmann’s eqn we can show that
1. d2R = -4G  + 3p
R dt2
3
c2
 + 3p
2
<
0
i.e
p
<
-c
c2
Cosmological Constant
3
Eventually analysis leads to R(t) = exp [(/3)1/2.t]
Thus we have a very dramatic expansion dominated by this constant
[
]
An Inflationary Universe
In simple terms the figure
shows Guth’s idea of an
inflationary Universe.
At the top we see normal
expansion.
Below we see a very rapid
expansion over a very short
time near t = 10-35s.
Now a small part of the
Universe, small enough to
achieve thermalisation
before inflation can expand
to be much bigger than our
presently observable
Universe.
An Inflationary Universe
1.Flatness
Inflation neatly solves the
flatness problem.Before inflation
the Universe was very curved.
Afterwards it would have
expanded so much that our little
bit,the observable Universe
would appear flat
Note:-It is very like looking at
a part of the surface of a balloon
before and after you inflate it.
An Inflationary Universe
2.Horizon Problem.
In the Inflationary Model of the Big Bang the observable Universe is
said to have evolved from a volume some 1050 times smaller than
in the Standard Big Bang Model.
Accordingly, before expansion,the Universe was much smaller than
its horizon distance so all of it could reach the same temperature.Then
inflation made it larger and preserved the uniform temperature that
we see today in the CMB.
3.Why did inflation occur?
One possibility is that it represents a phase transition and in such
transitions there is often a large release of energy.
A new model encompassing this is needed-Supergravity?
10-43secs.--gravity froze out from other forces.
10-35secs--strong Force froze out from Electroweak force-Inflation
10-32secs--Standard Big Bang.
Expansion of the Universe
As the Universe expands the volume increases proportionally to
the cube of the scale factor.
Galaxies
1.We already saw that Hubble settled the debate on the nature of
nebulae with his study of Cepheid variables in Andromeda.M31
is 2.2 Mly away.
2.He went on to study many other galaxies and from the measurements
of redshift and distance he produced Hubble’s Law.
3.He also classified the galaxies he saw by their shapes
ellipticals
spirals
barred spirals
irregulars
then he further subdivided them
M74 Gemini
M31-Andromeda Galaxy-2.2Mly from Earth, Part of our Local
cluster of galaxies.
Photo-mosaic picture of the Sombrero Galaxy taken with the
Hubble Space Telescope over several orbits.Glowing central
bulge of stars surrounded by pancake shaped disc.
Classification of Galaxies
Here we see the main types of galaxy
both in plan view and in side view.
All three types can vary greatly
in detailed shape,size etc.
Hubble arranged them in his so-called
Tuning fork diagram and they are
then sub-classified.For example
Ellipticals are subdivided from
E0 to E7 according to how elliptical
they appear.The E0 are closest to
circular.
Hubble’s Tuning Fork Diagram
Formation of galaxies
1.Formed from contraction of huge clouds of gas under gravity.The rate
of star formation then decides elliptical or spiral.If it is low then gas
has plenty of time to settle into a flattened disc.Star formation
continues in the disc because it has lots of H.It becomes a spiral.
If it is high then all the gas is used up in star formation before disc
forms and we get an elliptical.
2.Alternatively galaxies form by merger of several gas clouds rather than
from a single gigantic cloud of gas.
3.Many small gas clouds form and then merge.
Which idea is correct is not clear!!!
What is clear is that they form under the action of gravity
If the dust cloud starts with some small rotational
velocity then as the dust cloud shrinks this velocity
will increase in order to conserve angular
momentum.
There are two forces on a mass at the surface of the
dust cloud – the gravitational force towards the
centre and the centrifugal force maintaining its
rotation around the axis. Resolving the forces we
see that one component tends to push the mass
towards the “equator”.
We will end up with a disc. The exact form is going
to depend on the timescale.
Coma Cluster - 20Mly across containing thousands of galaxies(300 seen
here). It is about 270 Mly away.Two supergiant galaxies seen in centre.
Hubble Deep Field-A very narrow sample of the sky looking as far
back as 10 10 years in some cases.Data taken over 10 consecutive days.
Galaxies
All Spirals
Ellipticals
Irregular
Mass(solar masses)
109 - 4x1011 105 - 1013
108 - 3x1010
Luminosity(solar)
108 -2x1010 3x105 - 1011
107 - 109
Diameter(kpc)
Types of star
% of observed
galaxies
5-250
Disc-Young
Centre-Pop2
and old pop 1
1-200
Pop 2 and
Old Pop 1
77%
Note:-Pop 1=significant heavy elements
Pop 2 =few heavy elements-Old
20%
1-10
mostly Pop 1
3%
Galaxies
Ellipticals have little dust and interstellar gas-hence few new stars.
As a result they are made mostly of old, red, population 2 stars.
Note:-Pop 1=significant heavy elements
Pop 2 =few heavy elements-Old
Within ellipticals star motion is at random.
Irregulars- they do not fit into any scheme.
Irr 1-look like underdeveloped spirals
Irr 2-odd shapes probably due to collisions or violent activity in centre.
Examples:- Large and Small Magellanic Clouds. Both have substantial
amounts of interstellar gas. Hence active star formation.
Clusters of Galaxies
1.Galaxies are not found at random but are observed in clusters with
the members of the cluster in constant motion under gravity.
2.They are classified as Poor or Rich dependng on number of galaxies
they contain.
3.Milky Way is part of a poor cluster-some 30 galaxies,some of which
were only observed recently. They are mostly dwarf
ellipticals. It is called the Local Group.
4.They are also classified as regular or irregular depending on overall
shape. The Local group is irregular.The Coma Cluster is regular.
5.Shape is related to dominant type.Rich,regular clusters contain mostly
ellipticals and lenticular galaxies.Irregulars have a more even mixture.
6.Clusters are grouped together in superclusters.A typical supercluster
contains dozens of individual clusters spread over a region up to
30Mpc( 100 Mly ) across.
7.Overall there are huge voids in space-they may contain gas or very
dim galaxies.
Voids on the largest Scale
The Evolution of Stars
Ideally we would follow a star’s “life” from its genesis in a cloud
of gas and dust to its “death”.
However the timescale is way beyond our life span.
The alternative approach is to realise that the numbers of stars we
can see is very large. We assume that a) the lifetimes of stars are
shorter than the age of the Universe and b) we can observe stars at
all stages of development.
We have seen now how to measure stellar distances, masses, surface
temperatures, luminosities etc. We can now ask whether these
quantities are correlated in any way.
One way to look at this is the Hertzsprung-Russel diagram.
Hertzsprung-Russell Diagram
Key tool in our understanding of star formation and of star “birth”
and “death”
 Proposed independently by Hertzsprung and Russell
It links stellar luminosity and surface temperature
Note:- You will find it plotted in slightly different ways and for
selected groups of stars.
Hertzsprung-Russell Diagram
1.The H-R diagram plots Luminosity against Surface Temperature.
Note:-Log Luminosity is used because of the large range and it is
plotted against decreasing temperature.
2.Each star is represented by a point on the diagram.
3.The results depend to some extent on the sample of stars.They could
be from stars within a limited volume round the Solar system,
members of a cluster,stars of apparent brightness above a certain
limit,etc.
4.Any H-R diagram shows that only a limited combination of values of
T and L are allowed.
5.Most stars lie on a thin strip running diagonally across the diagram
This is the Main Sequence.
6.Top right is also populated with brighter stars with lower T.Red Giants
7.Lower left is also rich in stars.They are bluish-white and small.The size
is comparable to that of the Earth but with approx. the same mass as
the Sun. They are White Dwarfs.
Hertzsprung-Russell Diagram
1.
Temperature
By restricting the range of stars plotted
one can test ideas of stellar evolution.
Here we see stars from a particular
globular cluster.
These groups of stars are very old and
different from open clusters. The ages
are such that only stars of 1 solar mass
or less are left.They are close to the age
of the Universe. Most other stars not on
the main Sequence here are White
dwarfs or brown/black dwarfs.In
general they are Population 2 stars with
less than 1% of heavy elements
compared with Population 1 stars where
it is 2% or so.
[Contrast with stars in the disc.]
Stellar Birth
1.Seeing the early stages is difficult. It starts with a collapsing cloud of
gas and dust and it is not hot enough to shine so we don’t see it.
As it collapses half of the potential energy is turned into kinetic energy
[Heat]. [Virial Theorem] Triggering of such collapses is not fully
understood.
2.If the temperature of the gas cloud reaches high enough temperature
the particles[protons]will have enough energy to interact and nuclear
reactions will begin at about 8 million Kelvin .As we will see this
releases energy which heats the gas and raises its pressure.
3.If heated enough, the gas pressure will countermand the gravitational
contraction and the star will stabilise under these two opposing forces.
4.At this stage the star will be moving to the left on the H-R diagram
and will end up on the Main Sequence.
GAS
Gravitation
Heat
The rates of Nuclear reactions in stars
• The probabilities of
nuclear reactions in stars
is very small because the
energies of the particles
are very small but there
is a very large number of
particles.
• The number of reactions is just the product of the number of particles
of a given energy multiplied by the probability of the reaction in a
collision at that energy.
RED = Number of particles as a function of energy
Green = Probability of a reaction occurring in a collision
Blue = Number of reactions as a function of energy
 GAMOW PEAK
Hydrogen burning
Gravitación

4p
+ + +
+ 2+ 2e-+26MeV
Hydrogen
Helium or 
Our friend the Sun (6000ºK, yellow)
The p-p chain;the reactions which power the Sun
Overall - 4p  4He + 2e- +2 + 26.7 MeV
The CNO-Cycle:
In stars where we already have
C,N and O we can get hydrogen
burning
4p
 + 2e- + 2 +26.4 MeV
The C,N and O nuclei act as
catalysts for the burning process
Hans Bethe-1938
Reactions and Beta decays compete.
• The probabilities of
nuclear reactions in stars
is very small because the
energies of the particles
are very small but there
is a very large number of
particles.
At each step in the CNO-cycle there is a competition between beta decay
and another proton capture. Which “wins” depends on the average time
between captures or decays.
Since the no. of reactions depends critically on the temperature so does
the competition. [T(Sun) = 1.55 x 107 K]
● Cross-over (p-p to CNO) is for stars slightly more massive than Sun
The CNO-Cycle:
In stars where we already have
C,N and O we can get hydrogen
burning
4p
 + 2e- + 2 +26.4 MeV
The C,N and O nuclei act as
catalysts for the burning process
Hans Bethe-1938
Life Cycle of Stars and Nucleosynthesis
1. Formation from large clouds of gas and dust.
2. Centre of cloud is heated as it collapses under gravity
3. When it reaches high enough temperature then nuclear reactions
can start.
4p 4He + 2e + 2ν + 26.7 MeV
4. This raises temperature further and star eventually reaches
equilibrium under heating internally and gravitational collapse.
5. The process of making heavier nuclei occurs in the next stage.
After the Main Sequence
1.Once a star’s hydrogen is used up its future life is dictated by its mass.
2.During the H-Burning phase the star has been creating He in the core
by turning 4 protons into a He nucleus plus electrons and neutrinos.
Once the H burning stops in the centre the star contracts and some
of the potential energy is turned into heat. If the core temperature
rises far enough then He-burning can begin. Coulomb(electrostatic)
barrier is 4 times higher for two He nuclei compared with protons.
3.Now we face again the problem of there being no stable A = 5 or 8
nuclei.
4.It turns out that we can bypass these bottlenecks but it depends
critically on the properties of the properties of individual levels in
Be and C nuclei.
The Creation of 12C and 16O
• H and 4He were made in the Big Bang.Heavier nuclei were
not produced because there are no stable A = 5 or 8 nuclei.
There are no chains of light nuclei to hurdle the gaps.
• How then can we make 12C and 16O?
• Firstly 8Be from the fusion of
two alphas lives for 2.6 x 10-16 s
cf. scattering time 3 x 10-21 s.
They stick together for a
significant time.
• At equilibrium we get a concentration
of 1 in 109 for 8Be atoms in 4He.
• Salpeter pointed out that this meant that C must be produced
in a two step process.
• Hoyle showed that the second step
must be resonant.He predicted that
since Be and C both have 0+
s-wave fusion must lead to a
0+ state in 12C close to the Gamow
peak at  3 x 108K.
• Experiment shows such a state at
7654 keV with  = 5 x 10-17s
The 7654 keV state
has /  1000
A rare set of
circumstances indeed!
1010
years
Red Giant
(3000ºK
Red)
H burning
The Earth
will be
engulfed!!
++ 12C + 16O
Path of Solar Mass Star on Hertzsprung Russell Diagram
White Dwarf
H, N, O
¡¡only!!
(Hubble)
Fluorescence
Helix Planetary Nebula in the constellation of Aquarius
Binding energies in Nuclei
• E = mc2
• The curve below shows the Binding Energy per nucleon as a
function of the
mass of the nucleus.
A = 56

B.E. per nucleon
in MeV
Mass of the nucleus (A) 
The End of Fusion Reactions in Stars
A = 56
Binding Energy per nucleon as a
function of Nuclear Mass(A)
•When two nuclei fuse together energy is released up to mass A = 56
Beyond A = 56 energy is required to make two nuclei fuse.
•As a result we get the burning of successively more massive nuclei
in stars.First H, then He, then C,N,O etc.
•In massive stars we eventually end up with different materials burning
in layers with the heaviest nuclei burning in the centre where the
temperature is highest.
•When the heaviest(A = 56) fuel runs out the star explodes-Supernova
If theEtoile
star is eight
times more
massive than the Sun
massive
supergéante
H He
C
O
Ne Na Mg
Al Si P S
SUPERNOVA
Gravitación
Fe
C. THIBAULT (CSNSM)
Death of a Red Giant:
SUPERNOVA
October 1987
1056 Joules of energy
This happened 170000 years ago in the nearest galaxy
The Destiny of the Stars…
White
Dwarf
Main
Sequence
AÑOS
Density/
109
109
Red
Giant
Brown
Dwarf
Massive Stars
Supernova
Algún
109
segundo
100 kg
C. THIBAULT (CSNSM)
The probability of Reactions in Stars
The particles in the stellar gas have an energy distribution given by
the Maxwell-Boltzmann distribution(seen on left).
The probability of
penetration of the
Coulomb Barrier is given
by the expression on the
right.
The product of the two
gives the probability of
the two nuclei fusing.
The resulting peak is
called the Gamow
window.
Spectrum of Cassiopeia
We see here the remnants of a
supernova in Cassiopeia.This
radio telescope picture is taken
with theVery Large Array in
New Mexico.
From the measured rate of
expansion it is thought to have
occurred about 320 years ago.
It is 10,000 ly away.
With optical telescopes almost
nothing is seen.
The inset at the bottom shows a small part
of the gamma ray spectrum with a clear
peak at 1157 keV,the energy of a gamma
ray in the decay of 44Ti.
Principe de
nucléosynthèse
Principle
of laNucleosynthesis
protons
63
65
28 Ni
58 59 60 61 62
64
27 Co
26 Fe
59
29 Cu
54 55 56 57 58
35
30
40
neutrons
Il y a compétition
Competition
between twoentre
processes
••Capture
Captureof
d’un
neutron
a neutron
•• Radioactivité
Radioactivity–
n  p + e-+ 
C. THIBAULT (CSNSM)
Part of the Slow Neutron Capture Pathway
In Red Giant Stars neutrons are produced in the 13C( 4He,n) 16O
reactions.
The flux is relatively low.As a result there is time for beta decay before
a second neutron is captured.
The boxes here indicate a stable nuclear species with a particular Z & N.
Successive neutron captures increases N. This stops when the nucleus
created is unstable and beta decays before capture.
The pathways for the s- and r-processes
S-process:Neutron flux is low so beta decay occurs before a second
neutron is captured.We slowly zigzag up in mass.
R-process:Neutron flux is enormous and many neutrons are captured
before we get beta decays back to stability.
The Abundances of the
Elements for A = 70 - 210
Note the double peaks at
N = 46/50, 76/82, 116/126
They are due to production
by the two separate
processes
Abundance Predictions
The Reaction Pathways in Stellar Nucleosynthesis
Remember Elements above
Iron(Fe) are made in s- and
r-processes.
• The reaction pathways in the r- and rp-processes of nucleosynthesis
lie a long way away from the line of stability.
Red Giant:Betelgeuse
Orion Nebula
e.g., Diehl et al., Astron. Astrophys 97, 181 (1993);
Publications of the Astr. Society of the Pacific 110:637 (1999)
Full-sky Comptel
map of 1.8 MeV
gammas in 26Mg
following 26Al GS
-decay.
(a) Spin traps, eg. 26Al, (N=Z=13) 0+ state -decaying spin-trap.
0+, T=1
5+, T=0
(decays direct to 26Mg GS
228.3 keV, T1/2=6.3 secs via superallowed Fermi
+…forking in rp-process
+
26
0 keV, T1/2=7.4x105 yrs (decays to 2 states in Mg
via forbidden, Dl=3 decays).
Cosmic Microwave Background
Cosmic Microwave Background Explorer( COBE), a satellite launched
by NASA in 1989 was the first to show that there are very small
fluctuations in the CMB at the level of one part in 105.
Summary of CMB Measurements
Summary of CMB Measurements
Cosmic Microwave Background
Penzias and Wilson tried hard to make their signals go away.
Unknown to them a group at Princeton had been working on the
question of what sort of radiation would have been left over from
the Big Bang.
Once the two groups got together it was clear that they had observed
just this radiation.
Summary – Last Week.
Big Bang Model:- Three pieces of evidence
- Hubble’s Law
- Cosmic Microwave Background
- Abundance of the light elements in the Early Universe
Problems with the model
- Flatness Problem
- Horizon Problem
Standard Big Bang cannot explain
either.
”Solution” – Inflationary Big Bang
- This “solves” the two problems but no satisfactory
explanation.
Hubble’s classification of galaxies.
Superforce reigns
GUTs
Electroweak era
QGP/Hadron phase
transition
Universe becomes
transparent
Last Week
Big Bang Model – Three major pieces of evidence
- Problems – Horizon and Flatness problems
hence
Inflationary Big Bang – introduced by Guth (1981)
- solves these problems
History of Universe in terms of the Big Bang.
Finally – Formation of stars and galaxies.
Nuclear Radii
Stable Nuclei
R = R0.A1/3