last week mass-luminosity relationship hubbles law v = h 0 d expanding universe cosmological...

Last Week

Mass-Luminosity relationshipHubbles Law v = H0dExpanding UniverseCosmological principleOlber’s ParadoxMeaning of expansion λ / λ0 = (1 + Z)Think in terms of spacetime – we say something 400Mly away has a Lookback time of 400 MyCosmological redshiftCosmological Horizon Big Bang Model vs. Steady State ModelCosmic 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?

•Max Planck showed that the spectrum is given by

ud = 8hc -5.d[exp(hc/kT) - 1]

Blackbody Spectrum and Cosmic Microwave background

What is the spectrum of EM radiation emitted by an object of arbitrary temperature T in thermal equilibrum

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.

max.T = const.

= 2.9 x 10-3 mK

• This quantifies the observation that an object changes colour with Temperature e.g.At room 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 but 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 thehorn antenna they had builtfor telecommunications viasatellites.They found a signal from alldirections at = 7.35 cm.Theonly explanation was that itis real.Work quickly began tomeasure the background at other wavelengths.


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 itfits a black-body spectrumat 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.tthis frame.We are moving towards LEO andaway from Aquarius.[Galaxy is moving insame direction at 600 km s-1 ]This motion has to be subtracted from the measured spectrumin 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 abody at 2.726 degrees seen whichever direction one looks.

It marks the point where the Universe becametransparent.

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 = kT4.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)

8.Hence since E = kT we have T 1/R(t)

Thus as Space expands [R(t) increases], T decreases.

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 CMBWhen Universe was younger it wasnot only denser but hotter.If CMBwas emitted at a given T then as Universe expanded the wavelengthwould 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 wasionised[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 photonswith 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 nowspread freely throughout the Universewith a BB spectrum initially at 4000Kbut with time it has been shifted to 2.726K.

Since radiation was continuouslyscattered up to this point it is known asthe Last Scattering Surface.We cannot see anything prior to thistime 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 equationWe 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 areneutral over large volumesof space.So after about 1 sthe expansion has been governed by GRAVITY.

Newton wondered why theUniverse did not collapse.Hubble solved this byshowing that it is expandingand that the kinetic energyof expansion overcomes the gravitational pull.

Expansion of the Universe

As the Universe expands the volume increases proportionally tothe cube of the scale factor.

Scale factor - R(t)

The Expanding Universe and the Friedmann equation

Imagine an arbitrary spherical volumeand 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

Total energy = K.E. + P.E. ----(A)

Now m = V = 4/3d3 and so eqn. (A) becomes

ms[ H(t)2.d2

2_ 4Gd2

3] = total energy ------(B)

d

P.E. = - Gmms

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 - 8G

3=

kR(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-----

8G3

=k

R(t)2

Friedmann Equation

From consideration of the interaction of a shell of matter with a coreWe derived the Friedmann Eqn.

H(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 Universeis “closed or open”. In other words will it expand for ever or will itstop 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

E2

mNc2 = 939.573 MeV

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


1.Ratio of n/p declines rapidly with t, T and

NP

= [ mN

mP] Exp.(- mN - mP)c2

kT )

3/2NN (

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.


1.Mass of neutron = 939.573 MeV Mass of proton = 938.280 MeV Difference in rest mass = 1.26 MeV

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

3/2

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.]

---------(A)NP

= [ mN

mP] Exp.(- mN - mP

kT)

[n p + e- + e]

[Remember E = mc2]

So we start with n/p = 1/7

n + p d +

We can now create deuterons from the protons and neutrons butthere 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.

Nucleosynthesis in the Early Universe

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

• 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

Exp[-E/kT]


Now we get a series of fusion reactions d + d 3He++ + n p + d 3He++ +

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 p + t 4He++ + d + t 4He++ + n

The delay before these reactions start is called the deuterium bottleneck

The p-p chain;the reactions which power the Sun

Overall - 4p 4He + 2e- +2 + 26.7 MeV

In contrast:-

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

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]

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!!

[ Deuterium bottleneck ]

[Remember n/p = 1/7 at 109K – the point when nucleosynthesis starts]


• 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.


Exp[-E/kT]

Solar System Abundances

Here we see the abundancesof the chemical elements in Solar System.They are plotted on a log scale relative to the abundance of Hydrogen(H) = 1The abundances of everythingexcept He are smaller by at least a factor of 1000.

Present day abundances!

7p 1n 75% H & 25%He 98% of known matter

Cosmic Microwave background

Where does the restcome from?

The table summarises the similarities and differences betweenDecoupling and Nucleosynthesis. Note the differences in energyscales appropriate to nuclear and atomic processes.

(CMB)

Predicted Abundances of the light elements from Big Bang

One of the three pieces of evidencefor the Big Bang Model is the abundances of the light elements.Itdepends on the number of types ofneutrino which exist and the density of baryons(strongly interacting particles)

Here we see the predictions as afunction 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 ModelWhat we have seen is that there are three key pieces of evidencesupporting 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 naturalexplanation in the standard Hot Big Bang Model of the Universe.

Problems with the Standard Big Bang Model

8G3

=k

R(t)2H(t)2 -

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.

where k = 2ER(t)2 mSd2

Friedmann equation

Curvature or Shape of the Universe.The matter and energy scattered across all of space give the Universe anoverall 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.

Three possibilities:-

Geometry Curvature Type of Universe < Ώ0 > of space

Spherical positive closed Ώ0 > ΏC Flat zero flat Ώ0 = ΏC Hyperbolic negative open Ώ0 < ΏC

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 about1 degree in angle, close to what is observed.

Hint from CMB

Defined in next slide

8G3

=k

R(t)2H(t)2 -

Critical Density

Flat Universe:- If k = 0 then the R.H.S. is zero. Then

C = 3 H02

8Gwhere C is the critical density of the Universe.

We can also write it in terms of = ..

C

This is called the density parameter.

[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 smalldensity variations in the Early Universe.Apparent size will depend oncurvature.Calculations suggest 0 is close to 1-Flat Universe.WHY?

Friedmann equation

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 uncertaintybut 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 1-2orders-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-tunedto 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 evidencefor the Big Bang Model is the abundances of the light elements.Itdepends on the number of types ofneutrino which exist and the density of baryons(strongly interacting particles)

Here we see the predictions as afunction 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 forthe Big Bang Model is theHorizon Problem.It involves communication of information between differentparts of the Universe.Since the Universe has a finite age in thismodel even light can only havetravelled a finite distance in thistime.

This distance defines the OBSERVABLE UNIVERSE.This is what wecan see and is finite whatever the size of the Universe.As we see in the picture radiation from the Big Bang has just reached Aand B. Radiation from A and B cannot have reached each other.Inparticular this means that the two sides of the sky cannot have interactedto create thermal eqbm and a common T. Very Strange!!

Cosmic Particle horizon

Cosmic Particle horizon

Horizon Problem

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. Soplaces that look quite close in the sky would not have been able to interact to establish eqbm.

So how does it happen that the CMB is essentially isotropic without thiscommunication between the different parts of the Universe?Worse still how can we create the very small fluctuations, the seeds fromwhich galaxies etc grow?

CMP CMP

An Inflationary Universe

The most widely adopted soluton to the Horizon and flatness problemsis 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

dt2> 0

From Friedmann’s eqn we can show that 1. d2R R dt2

= -4G

3 + 3p

c2[ ]

+ 3p

c2< 0 i.e p < -c2

3Eventually analysis leads to R(t) = exp [(/3)1/2.t]Thus we have a very dramatic expansion dominated by this constant

Cosmological Constant


In simple terms the figureshows Guth’s idea of aninflationary Universe.At the top we see normalexpansion. Below we see a very rapid expansion over a very shorttime near t = 10-35s.Now a small part of the Universe, small enough to achieve thermalisation before inflation can expandto be much bigger than our presently observable Universe.


1.Flatness

Inflation neatly solves the flatness problem.Before inflationthe Universe was very curved.Afterwards it would have expanded so much that our littlebit,the observable Universewould appear flatNote:-It is very like looking at a part of the surface of a balloon before and after you inflate it.


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 tothe 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 Localcluster of galaxies.

Photo-mosaic picture of the Sombrero Galaxy taken with theHubble 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 greatlyin detailed shape,size etc.

Hubble arranged them in his so-calledTuning fork diagram and they arethen sub-classified.For exampleEllipticals are subdivided fromE0 to E7 according to how ellipticalthey 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 thedust cloud – the gravitational force towards the centre and the centrifugal force maintaining its rotation around the axis. Resolving the forces wesee 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

Mass(solar masses) 109 - 4x1011 105 - 1013 108 - 3x1010

All Spirals Ellipticals Irregular

Luminosity(solar) 108 -2x1010 3x105 - 1011 107 - 109

Diameter(kpc) 5-250 1-200 1-10

Types of star Disc-Young Pop 2 and mostly Pop 1 Centre-Pop2 Old Pop 1 and old pop 1

% of observed 77% 20% 3% galaxies

Note:-Pop 1=significant heavy elements Pop 2 =few heavy elements-Old

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.

Within ellipticals star motion is at random.

Irregulars- they do not fit into any scheme.Irr 1-look like underdeveloped spiralsIrr 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.

Note:-Pop 1=significant heavy elements Pop 2 =few heavy elements-Old

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 atall stages of development.

We have seen now how to measure stellar distances, masses, surfacetemperatures, 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.


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 Giants7.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.


1. By restricting the range of stars plottedone can test ideas of stellar evolution.Here we see stars from a particular globular cluster.These groups of stars are very old anddifferent from open clusters. The ages are such that only stars of 1 solar massor less are left.They are close to the ageof the Universe. Most other stars not on the main Sequence here are Whitedwarfs or brown/black dwarfs.Ingeneral they are Population 2 stars withless than 1% of heavy elements compared with Population 1 stars where it is 2% or so.

Temperature [Contrast with stars in the disc.]

Stellar Birth1.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.

GASGravitation

Heat


• 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.


Gravitación

Hydrogen burning

+ + + + 2+ 2e-+26MeV

Our friend the Sun (6000ºK, yellow)

HydrogenHelium or

4p

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 haveC,N and O we can get hydrogenburning 4p + 2e- + 2 +26.4 MeV

The C,N and O nuclei act ascatalysts for the burning process

Hans Bethe-1938

• 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.

Reactions and Beta decays compete.

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 haveC,N and O we can get hydrogenburning 4p + 2e- + 2 +26.4 MeV

The C,N and O nuclei act ascatalysts 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 statehas / 1000

A rare set of circumstances indeed!

1010 years

The Earthwill be

engulfed!!

++ 12C + 16O

Red Giant(3000ºK

Red)

H burning

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.

Mass of the nucleus (A)

B.E. per nucleonin MeV

A = 56

Binding Energy per nucleon as a function of Nuclear Mass(A)

The End of Fusion Reactions in Stars

A = 56

•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

Gravitación

Etoile massive supergéante

C. THIBAULT (CSNSM)

H He

C O

Ne Na Mg

Al Si P S

Fe

If the star is eight times more massive than the Sun

Strong Force

SUPERNOVA

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…

C. THIBAULT (CSNSM)

MainSequence

Red Giant

White Dwarf

Massive StarsSupernova

Density/

AÑOSAlgún

segundo

BrownDwarf

109

109

109

100 kg

The probability of Reactions in Stars

The particles in the stellar gas have an energy distribution given bythe Maxwell-Boltzmann distribution(seen on left).

The probability ofpenetration of the Coulomb Barrier is givenby the expression on the right.

The product of the twogives the probability of the two nuclei fusing.

The resulting peak is called the Gamow window.

Spectrum of Cassiopeia

We see here the remnants of asupernova in Cassiopeia.Thisradio telescope picture is takenwith theVery Large Array in New Mexico.From the measured rate of expansion it is thought to haveoccurred 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 partof the gamma ray spectrum with a clear peak at 1157 keV,the energy of a gamma ray in the decay of 44Ti.

Principe de la nucléosynthèse

C. THIBAULT (CSNSM)

616058

59

59

5756 5855

protons

26 Fe 54

27 Co

28 Ni

29 Cu

62

63 65

•• Capture d’un neutron •• Radioactivité –

epn

neutrons30 4035

64

Il y a compétition entre

Principle of Nucleosynthesis

Capture of a neutron

Competition between two processes

Radioactivity

Part of the Slow Neutron Capture Pathway

In Red Giant Stars neutrons are produced in the 13C( 4He,n) 16Oreactions.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 atN = 46/50, 76/82, 116/126

They are due to productionby the two separate processes

Abundance Predictions

The Reaction Pathways in Stellar Nucleosynthesis

• The reaction pathways in the r- and rp-processes of nucleosynthesis lie a long way away from the line of stability.

Remember Elements aboveIron(Fe) are made in s- andr-processes.

Orion Nebula

Red Giant:Betelgeuse

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.

5+, T=0 0 keV, T1/2=7.4x105 yrs

0+, T=1 228.3 keV, T1/2=6.3 secs(decays direct to 26Mg GS via superallowed Fermi+…forking in rp-process

(decays to 2+ states in 26Mgvia forbidden, l=3 decays).

e.g., Diehl et al., Astron. Astrophys 97, 181 (1993); Publications of the Astr. Society of the Pacific 110:637 (1999)


Cosmic Microwave Background Explorer( COBE), a satellite launched by NASA in 1989 was the first to show that there are very smallfluctuations in the CMB at the level of one part in 105.

Summary of CMB Measurements

Cosmic Microwave BackgroundPenzias 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

”Solution” – Inflationary Big Bang - This “solves” the two problems but no satisfactory explanation.

Hubble’s classification of galaxies.

Standard Big Bang cannot explain either.

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

last week mass-luminosity relationship hubbles law v = h 0 d expanding universe cosmological...

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