cosmology - usp tea session 18 march 2011
TRANSCRIPT
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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!