cosmology - usp tea session 18 march 2011

8/7/2019 Cosmology - USP Tea Session 18 March 2011

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USP Tea/Seminar Sessions

Dark Matter and Dark Energy

Prof. Frederick H. Willeboordse18 Mar 2011

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Dark Sky

Dark Matter Dark Energy

Dark Universe

The universe appears to be even darker than expected from the night sky. Indeed,

observations strongly suggest that the universe not only contains a significantamount of invisible (and hence dark) matter but that is also contains a significant

amount of unknown (and therefore dark ) energy. In this lecture, we will discuss the

astronomical evidence for dark matter and dark energy and elaborate in somewhat

more detail on a key observational tool based on Einsteins general theory of

relativity, gravitational lensing.


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The Mysteries of Darkness

Sometimes, what you dont see can teach you a great many things! Indeed, in

cosmology, there are probably three main issues of darkness that have major

implications for how we understand the world.

1) Dark sky at night

2) Dark Matter

3) Dark Energy

Not understood!

Well understood!

et us look at these 3 items now.

Night sky.

Bullet cluster reveals dark matter.


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Mystery 1: Olbers Paradox

Once upon a time (about 200 years ago), the prevailing notion

was that the universe is infinite, eternal, static and has a

uniform distribution of stars over large distances.

As can easily be seen from this argument, this idea

conflicts an observational fact we all know: the night sky

is dark! Olbers (1758 1840)

Group the stars into successive shells.

Shells further out have more stars but each star is

dimmer due to the greater distance. The net effect isthat the total amount of light arriving on earth from

each shell is the same.

If the universe is infinite, there are an infinite number

of shells and hence it should be bright at night.

The number of

stars per unit

volume is the

same in each shell.

et us see what the observations tell us.


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Structure of the Universe

Planet

Solar System

Galaxy

Galaxy Clusters

Filament

(simulation)


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Milky Way

Our home!

We live in the Milky Way, an

average size spiral galaxy with

a diameter of about 100,000 lyand a thickness of about 1000

ly.

Panoramic view of the sky at the

Paranal observatory in Chile. Note

the milky white band across the

sky. It is formed by other stars in

our galaxy.

Thats why its called the Milky Way!

The Milky Way contains

about 200 billion stars.


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Some numbers

Planets

Quantity (Approx) Size (Approx)

Stars

Galaxies

Clusters

Super Clusters

109 ~ 108 ly

1012 ~ 104 ly

Example Size

Earth: 109 ly

Sun: 107 ly1022

?

104 ~ 106 ly Andromeda: 105 ly1011

107 ly Local: 107 ly?

108 ~ 109 ly Local (Virgo): 108 ly?

Stars per Galaxy NA Andromeda: 10121011

Galaxies per Clusters NA Local: 30+50 1000

Filaments 108 ~ 109 ly Sloan Great Wall: 109 ly2


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Looking back in Time

When we look at far away objects, we look back in time.

Moon

1.3 s in the past

Andromeda Galaxy

2.5 My in the past

Bullet Cluster

3.4 Gy in the past

13.2 Gy in the past!

Sun

8.3 m in the past

The farthest and one of the very earliest galaxiesever seen in the universe appears as a faint red

blob in this ultra deepfield exposure taken with

NASA's Hubble Space Telescope. This is the

deepest infrared image taken of the universe.

Based on the object's color, astronomers believe it

is 13.2 billion light years away. (Credit: NASA,

ESA, G. Illingworth (University of California,

Santa Cruz), R. Bouwens (University of California,Santa Cruz, and Leiden University), and the


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Hubbles Law

Hydrogen is the most common element in the universe. Light emitted by hydrogen atomsdisplays characteristic emission lines (see topic quantum mechanics). When the light

source is in motion relative to us, the emission lines will shift due to the Doppler effect.

Emission lines from receding stars are red shifted (longerwavelength)Emission lines from approaching stars are blue shifted (shorterwavelength)

Hydrogen spectra Receding Star


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Hubbles Law

Hubble found that all distant stars are receding! And furthermore that the

recession speed is linearly related to the distance as:

v = H0 d Hubbles law

The most logical conclusion is that the universe is expanding and if so it

must have started somewhere the Big Bang!

Hubbles law is one of the

cornerstones of modern cosmology.


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Hubbles Law

Redshift:

= original wavelength

= red shifted wavelength


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Cosmic Microwave Background

With an optical telescope, it appears to be dark between the stars and galaxies.

But is it really completely dark? To find out one needs to measure at all

frequencies. Doing so, it turns out that there is a fairly uniform background

radiation that comes from all sides. This radiation called the cosmic microwave

background is in the microwave band and corresponds to a black body at a

temperature of 2.725 K.

The colors indicate temperature fluctuations of

200 K

(Theoretical) black body

spectrum AND the observed

CMB spectrum. They match soclosely that they cannot be

distinguished!

All sky CMB

e cosmic microwave background shows light from 13.7 billion years ago.


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History of the Universe


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Observable Universe

So how big is the universe? If the furthest we can see is 13.7 billion light years,

then would the diameter of the universe be 27.4 billion light years?

No!

We need to be careful! The size of the universe is almost certainly not equal to the

size of the observable universe.

The size (diameter) of the observable

universe is about 93 billion light years.

The observable universe is the part of

the universe from which light can reach

us, and its size is where the matter that

emitted the light 13.7 billion light yearsago is now. This size is determined from

the expansion rate of the universe we

observe.

he size of the entire universe in unknown.


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Solutions to Olbers Paradox

Light is absorbed on its way to earth

The universe is finite

The universe is expanding

Stars have a finite lifetime

The universe is not isotropic Contradicted by observations

Contradicted by laws of physics. If

the light is absorbed, its energy will

heat up the absorbing material and

subsequently be re radiated.

Big bangtheory


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Cosmological Redshift

From Hubbles law, we know that the wavelengths of light from distant galaxies

are redshifted. This redshift corresponds to a certain velocity but we have to be

careful!

The redshift of the light from distant galaxies is mostly due to the expansion of

space. Hence the Doppler shift component is relatively small and that is why this

redshift is oftne called the cosmological redshift.

tant galaxies recede from us due to 2 separate reasons:

1) Relative motion independent of the expansion of space. This

is called the peculiar velocity.

2) Relative motion due to the expansion of space. This is called

the Hubble flow.

space expanding in the x direction


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Mystery 2: Dark Matter

By considering Olbers paradox much was learned about the universe. However,

careful observation shows that something is amiss!

2) Clusters can be sumo

1) Stars in galaxies can move at speeds different from expected

3) Gravitational Lensing

t us now look at each of those points seperately.


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Evidence 1: Galaxy Rotation Curve

The galaxy rotation curve plots the orbital velocity of the stars in a galaxy versus

their distance from the center of the galaxy.

Stars away from the centersuch as this one move way

too fast!

A: Galaxy rotation curve as calculated with Kepplers laws.

B: Galaxy rotation curve as observed.


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Evidence 2: Cluster sumo

The only way to reliably determine the mass of astronomical objects is through

their motion and the laws of gravity.

In 1933, the Swiss astronomer Fritz Zwicky tried to calculate the

mass of the Coma cluster by measuring the speed of the galaxies

at the edge of the cluster. When doing so, he found that this mass

is much greater than what one can infer from the visible matter in

the cluster. He thought it was about 50 times greater but now it isonly estimated to be about 10 times greater. This was the first

indication of the existence of dark matter.Fritz Zwicky1898 1974

With the help of the so called virial theorem which

applied here means that the total kinetic energy

should be half the total gravitational potentialenergy, Zwicky found the Coma cluster to be a sumo

wrestler in disguise.

Coma cluster. Distance about 321 Mly.

More than 1000 galaxies.


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Evidence 3: Gravitational Lensing

According to Einsteins General Theory of Relativity, gravity will bend light. A

large mass can function as a lens.

Now if, as is sometimes

the case, the size and

distance of both the

distant and foreground

galaxies are known, then

the strength of the lens

can be calculated.

For gravitational

lensing, this strength

depends on the mass.Once the strength is

known the mass follows

immediately.One finds that in many cases the mass calculated with the help of lensing is much

greater than the mass of the visible matter.


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Evidence 3: Gravitational Lensing


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Dark Matter : Lensing

Images of very distant galaxies

not part of the cluster.


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Lensing

nsing can lead to some spectacular phenomena:

Note, that lensing as such does not require the existence of dark matter. Dark

matter is inferred when the lens is stronger than expected from the visible matter.

Einstein Cross. Four images of a

quasar (distance 8 Gly) located

directly behind a foreground galaxy(distance 400 Mly).

Einstein Rings. A ring shaped image of a

distant object lensed by a massive

foreground object.


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Dark Matter

A powerful collision of galaxy clusters has been

captured by NASA's Hubble Space Telescope and

Chandra X ray Observatory. This clash of clusters

provides striking evidence for dark matter andinsight into its properties.

The observations of the cluster known as MACSJ0025.4 1222 indicate that a titanic collision has

separated the dark from ordinary matter and provide

an independent confirmation of a similar effectdetected previously in a target dubbed the Bullet

Cluster. These new results show that the Bullet

Cluster is not an anomalous case.

MACS J0025 formed after an enormously energetic

collision between two large clusters. Using visible

light images from Hubble, the team was able to inferthe distribution of the total mass dark and

ordinary matter. Hubble was used to map the dark

matter (colored in blue) using a technique known as

gravitational lensing. The Chandra data enabled the

astronomers to accurately map the position of theordinary matter, mostly in the form of hot gas, which

glows brightly in X rays (pink).

As the two clusters that formed MACS J0025 (each

almost a quadrillion times the mass of our sun)

merged at speeds of millions of miles per hour, the

hot gas in the two clusters collided and slowed down,

but the dark matter passed right through the

smashup. The separation between the material

shown in pink and blue therefore provides

Pink: Ordinary Matter

lue: Dark Matter inferred by lensing

Source: NASA.ttp://www.nasa.gov/multimedia/imagegallery/image_feature_1163.html


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Or?

Many (most?) globular clusters show little evidence of dark

matter, while some clusters have relatively small amounts of

dark matter. For example NGC4636 (to the right) has been

shown to contain less than 50% of dark matter but likely

around 25%.n isotropy in CMB different than expected.

Some elliptical galaxies such as

Messier 105 (NGC3379) show no

evidence of dark matter.

Nobody has seen any dark matter yet so it is possible that there is a different

explanation for the observations. Of particular interest are some observations

that are odd to say the least:

And neither does the spiral galaxy M94.


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Dark Matter: What is it?

It is matter that does not interact electromagnetically. In other words, it does not

reflect, absorb or emit light and other electromagnetic radiation. Hence it is dark.

hat kind of matter could that be?

Nobody knows!

Do we at least have an idea of how muchthere is? Yes, that can be estimated

and its a lot!

About 80% of all matter is dark!

Cold dark matter:

Warm dark matter:

Hot dark matter:

Slow particles, structure of universe grows

hierarchically from small to large.

Between above two. Speculated particles:

Sterile neutrinos, gravitinos.

Very fast (ultra relativistic) particles. Structure

forms top down by fragmentation. Particle: neutrino.

Candidates:


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Dark Matter

old dark matter problems: Cuspy halo problem: centers of galaxies should

have more dark matter not observed.

Missing satellites: there should be many smallgalaxies but this is not observed.

No clear prediction of what dark matter actually is

Speculated particles:WIMPS: Weakly interacting massive particles

MACHOS: Massive compact halo objects (such as black

holes, neutron stars, white dwarfs ..)

AXIONS: Hypothetical particle to solve a problem in QCD.

Neutralino

The leading theory is called the Cold Dark Matter (CDM) theory. In this theory,

dark matter consists of non relativistic (i.e. relatively slow moving at speeds

below 0.1 c) particles of a yet unknown nature. The 3 main candidates for those

particles are listed on the next slide.


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Dark Matter: What is it?

WIMPS

MACHOs

Axions

WIMPS are Weakly Interacting Massive Particles. This is an

unknown (and thus far undetected) new kind of particle that

interacts via the weak nuclear force and gravity. As the name

indicates, they are thought to have a relatively large masses (10s

1000s proton masses).

MACHOs are Massive Compact Halo

Objects. MACHOs consist of normal

matter that cannot be seen and may bemade of black holes, neutron stars, white

dwarfs and other hard to see matter.

Some observations based on micro lensing

make it rather unlikely that MACHOs can

explain the dark matter mystery even

though they may be (a small) part of it.Axions are a hypothetical particles first

proposed to solve a nagging problem in

theoretical particle physics. Axions are

thought to have very little mass and only

very little interaction with matter. No axion

has ever been found.

Visible Galaxy

Dark Matter Halo

Regardless of what it is

made of, the dark matter

halo extends far beyond

the visible galaxy. In the

case of the Milky Way, the

diameter is thought to

exceed 500,000 ly.


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Mystery 3: Dark Energy

Further careful observation shows that even more is amiss.

ut there is more evidence.

It turns out that the

expansion of the

universe is

accelerating.


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Evidence I: Type Ia Supernovae

In astronomy, a standard candle is an

object with a known luminosity. The

distance can then simply be calculated

from the apparent brightness.

There are several types of supernovae.One of these, called a type Ia

supernova occurs when a white dwarf

exceeds a critical mass.

A supernova is the extremely

luminous explosion of a star.

Remnant from the type Ia Tycho supernova

When running out of fuel, stars with masses smaller

than about 10 times that of the sun end their life aswhite dwarfs. Sometimes, for example when being

part of a binary system, white dwarfs can gain

substantial amounts of mass by attracting it from the

outer layers of the other star.


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Type Ia Supernovae

When the mass of the white dwarf exceeds 1.4 solar masses, it will explode in a

type 1a supernova. Since this explosion always happens at approximately the

same time (namely when exceeding 1.4 solar masses), one can expect all the

explosions to be very similar and hence also have very similar brightnesses.

If one can determine the distance of one of these

supernovae, for example with the help of red shift,

then the distance of the rest can be determined fromtheir apparent brightness with the help of the inverse

square law which means that the amount of light per

unit area decreases as 1/r2.

Type 1a supernovae have a

characteristic light curve which makes

it easy to compare the apparentluminosity from one supernova to the

next. Thus the distance can be

determined rather accurately.

The (peak) brightness of a type Ia

supernova is about 5 billion times that of

the sun!


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Type Ia Supernovae

Gravity is always attractive and pulls things together. Hence it is a force opposing

the expansion of the universe and one would therefore expect this expansion to slow

down over time.

Hubbles law states that the distance of a star is

linearly related to its red shift. This is means that the

universe is expanding at a constant rate. So if the

universes expansion is in fact slowing down, then in

the Hubble plot, we would expect the following: Forthe same red shift, the galaxies will be closer than if

they in a constantly accelerating universe and hence in

the plot they will be below the line.

Perlmutter

etal

1998When studying type Ia supernovae (whose

distance can be determined from their

brightness), the exact opposite was found! Their

distance was larger than expected from the red

shift and the supernovae are above the line in the

Hubble plot.

is indicates that the universes expansion is accelerating!


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Evidence 2: CMB

Dark energy affects the universe over

large distances and time scales. The

furthest object we can see is the

Cosmic Microwave Background.

Gravity bends and shifts light.

Therefore photons of the CMB will be

affected by matter encountered on

their way to earth.

t us see what happens when a CMB photon travels through a large cluster when space expands

Photon enters thegravitational

potential well

Photon gains energy

descending into the well.

Note how the well is less

deep now due to the

expansion of space.

Photon exits the well. The well

is even shallower now.Consequently the photon will

not have to give up all the

energy it gained!

oton traveling through a cluster when space expands gains some energy. This can be measured.


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Evidence 2: CMB

The circles indicate superclusters (huge

groups of clusters of galaxies) and

supervoids (huge swaths of space almost

entirely void of matter). It is found that

superclusters correlate with slightly

higher temperatures and supervoids with

slightly lower temperatures exactly as is

expected for a universe whose expansion

is accelerating.

Top: supercluser; Bottom: supervoid


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Dark Energy: What is it?

It is energy that causes an acceleration in the expansion of the universe. This

energy has thus far not directly been observed. Hence it is dark.

hat kind of energy could that be?

Nobody knows!

Do we at least have an idea of how much

there is? Yes, that can be estimated

and its a lot!

About 73% of all energy is dark!

Candidates:

Cosmological constant: This is a constant that can be added to Einsteins

field equation. Einstein originally added it to make

the universe static. However it can also be used to

account for expansion.Quintessence: This is a field (or fluid like substance) that fills all of

space and opposes gravity hence leading to the

expansion of the universe.


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A truly Dark Universe!

0.4%!!!

ext time if you find something dark you might just have made a great discovery!

cosmology - usp tea session 18 march 2011

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